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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- recent issues1471-2946Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[A construction of a large family of commuting pairs of integrable symplectic birational four-dimensional maps]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160535?rss=1
We give a construction of completely integrable four-dimensional Hamiltonian systems with cubic Hamilton functions. Applying to the corresponding pairs of commuting quadratic Hamiltonian vector fields the so called Kahan–Hirota–Kimura discretization scheme, we arrive at pairs of birational four-dimensional maps. We show that these maps are symplectic with respect to a symplectic structure that is a perturbation of the standard symplectic structure on R4, and possess two independent integrals of motion, which are perturbations of the original Hamilton functions and which are in involution with respect to the perturbed symplectic structure. Thus, these maps are completely integrable in the Liouville–Arnold sense. Moreover, under a suitable normalization of the original pairs of vector fields, the pairs of maps commute and share the invariant symplectic structure and the two integrals of motion.
]]>2017-02-15T00:05:25-08:00info:doi/10.1098/rspa.2016.0535hwp:master-id:royprsa;rspa.2016.05352017-02-15Research articles47321982016053520160535<![CDATA[A wave theory of heat transport with applications to Kapitsa resistance and thermal rectification]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160584?rss=1
We develop a theory of thermal transport in nanoscale-layered structures based on wave processes. The theory incorporates two fundamental principles, first, that the spectra of thermally excited waves are determined by the temperature differential and the heat flux, and second, that the wave fields in the heat exchanging domains are coupled. The developed method includes classical theories as special cases that are valid in larger scales, and it naturally explains such phenomena as interface thermal resistance (Kapitsa resistance) and thermal rectification (asymmetry of thermal transport). Numerical examples demonstrate the feasibility of the approach, and they show good agreement with measurements of Kapitsa resistance reported in the literature.
]]>2017-02-15T00:05:25-08:00info:doi/10.1098/rspa.2016.0584hwp:master-id:royprsa;rspa.2016.05842017-02-15Research articles47321982016058420160584<![CDATA[An experimental study of ultrasonic vibration and the penetration of granular material]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160673?rss=1
This work investigates the potential use of direct ultrasonic vibration as an aid to penetration of granular material. Compared with non-ultrasonic penetration, required forces have been observed to reduce by an order of magnitude. Similarly, total consumed power can be reduced by up to 27%, depending on the substrate and ultrasonic amplitude used. Tests were also carried out in high-gravity conditions, displaying a trend that suggests these benefits could be leveraged in lower gravity regimes.
]]>2017-02-15T00:05:25-08:00info:doi/10.1098/rspa.2016.0673hwp:master-id:royprsa;rspa.2016.06732017-02-15Research articles47321982016067320160673<![CDATA[Stability of vertical magnetic chains]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160703?rss=1
A linear stability analysis is performed for a pair of coaxial vertical chains made from permanently magnetized balls under the influence of gravity. While one chain rises from the ground, the other hangs from above, with the remaining ends separated by a gap of prescribed length. Various boundary conditions are considered, as are situations in which the magnetic dipole moments in the two chains are parallel or antiparallel. The case of a single chain attached to the ground is also discussed. The stability of the system is examined with respect to three quantities: the number of balls in each chain, the length of the gap between the chains, and a single dimensionless parameter which embodies the competition between magnetic and gravitational forces. Asymptotic scaling laws involving these parameters are provided. The Hessian matrix is computed in exact form, allowing the critical parameter values at which the system loses stability and the respective eigenmodes to be determined up to machine precision. A comparison with simple experiments for a single chain attached to the ground shows good agreement.
]]>2017-02-08T00:05:14-08:00info:doi/10.1098/rspa.2016.0703hwp:master-id:royprsa;rspa.2016.07032017-02-08Research articles47321982016070320160703<![CDATA[On the role of micro-inertia in enriched continuum mechanics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160722?rss=1
In this paper, the role of gradient micro-inertia terms {macron}|| u,t||2 and free micro-inertia terms ||P,t||2 is investigated to unveil their respective effects on the dynamic behaviour of band-gap metamaterials. We show that the term {macron}|| u,t||2 alone is only able to disclose relatively simplified dispersive behaviour. On the other hand, the term ||P,t||2 alone describes the full complex behaviour of band-gap metamaterials. A suitable mixing of the two micro-inertia terms allows us to describe a new feature of the relaxed-micromorphic model, i.e. the description of a second band-gap occurring for higher frequencies. We also show that a split of the gradient micro-inertia {macron}|| u,t||2, in the sense of Cartan–Lie decomposition of matrices, allows us to flatten separately the longitudinal and transverse optic branches, thus giving us the possibility of a second band-gap. Finally, we investigate the effect of the gradient inertia {macron}|| u,t||2 on more classical enriched models such as the Mindlin–Eringen and the internal variable ones. We find that the addition of such a gradient micro-inertia allows for the onset of one band-gap in the Mindlin–Eringen model and three band-gaps in the internal variable model. In this last case, however, non-local effects cannot be accounted for, which is a too drastic simplification for most metamaterials. We conclude that, even when adding gradient micro-inertia terms, the relaxed micromorphic model remains the best performing one, among the considered enriched models, for the description of non-local band-gap metamaterials.
]]>2017-02-01T01:05:46-08:00info:doi/10.1098/rspa.2016.0722hwp:master-id:royprsa;rspa.2016.07222017-02-01Research articles47321982016072220160722<![CDATA[Bioinspired turbine blades offer new perspectives for wind energy]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160726?rss=1
Wind energy is becoming a significant alternative solution for future energy production. Modern turbines now benefit from engineering expertise, and a large variety of different models exists, depending on the context and needs. However, classical wind turbines are designed to operate within a narrow zone centred around their optimal working point. This limitation prevents the use of sites with variable wind to harvest energy, involving significant energetic and economic losses. Here, we present a new type of bioinspired wind turbine using elastic blades, which passively deform through the air loading and centrifugal effects. This work is inspired from recent studies on insect flight and plant reconfiguration, which show the ability of elastic wings or leaves to adapt to the wind conditions and thereby to optimize performance. We show that in the context of energy production, the reconfiguration of the elastic blades significantly extends the range of operating regimes using only passive, non-consuming mechanisms. The versatility of the new turbine model leads to a large increase of the converted energy rate, up to 35%. The fluid/elasticity mechanisms involved for the reconfiguration capability of the new blades are analysed in detail, using experimental observations and modelling.
]]>2017-02-15T00:05:25-08:00info:doi/10.1098/rspa.2016.0726hwp:master-id:royprsa;rspa.2016.07262017-02-15Research articles47321982016072620160726<![CDATA[Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160751?rss=1
Multi-fidelity modelling enables accurate inference of quantities of interest by synergistically combining realizations of low-cost/low-fidelity models with a small set of high-fidelity observations. This is particularly effective when the low- and high-fidelity models exhibit strong correlations, and can lead to significant computational gains over approaches that solely rely on high-fidelity models. However, in many cases of practical interest, low-fidelity models can only be well correlated to their high-fidelity counterparts for a specific range of input parameters, and potentially return wrong trends and erroneous predictions if probed outside of their validity regime. Here we put forth a probabilistic framework based on Gaussian process regression and nonlinear autoregressive schemes that is capable of learning complex nonlinear and space-dependent cross-correlations between models of variable fidelity, and can effectively safeguard against low-fidelity models that provide wrong trends. This introduces a new class of multi-fidelity information fusion algorithms that provide a fundamental extension to the existing linear autoregressive methodologies, while still maintaining the same algorithmic complexity and overall computational cost. The performance of the proposed methods is tested in several benchmark problems involving both synthetic and real multi-fidelity datasets from computational fluid dynamics simulations.
]]>2017-02-08T00:05:14-08:00info:doi/10.1098/rspa.2016.0751hwp:master-id:royprsa;rspa.2016.07512017-02-08Research articles47321982016075120160751<![CDATA[Efficient least angle regression for identification of linear-in-the-parameters models]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160775?rss=1
Least angle regression, as a promising model selection method, differentiates itself from conventional stepwise and stagewise methods, in that it is neither too greedy nor too slow. It is closely related to L_{1} norm optimization, which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability. In this paper, we propose an efficient least angle regression algorithm for model selection for a large class of linear-in-the-parameters models with the purpose of accelerating the model selection process. The entire algorithm works completely in a recursive manner, where the correlations between model terms and residuals, the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step. The model coefficients are only computed when the algorithm finishes. The direct involvement of matrix inversions is thereby relieved. A detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency, compared with the original approach where the well-known efficient Cholesky decomposition is involved in solving least angle regression. Three artificial and real-world examples are employed to demonstrate the effectiveness, efficiency and numerical stability of the proposed algorithm.
]]>2017-02-01T01:05:46-08:00info:doi/10.1098/rspa.2016.0775hwp:master-id:royprsa;rspa.2016.07752017-02-01Research articles47321982016077520160775<![CDATA[Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160808?rss=1
Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified.
]]>2017-02-15T01:16:11-08:00info:doi/10.1098/rspa.2016.0808hwp:master-id:royprsa;rspa.2016.08082017-02-15Research articles47321982016080820160808<![CDATA[Methodical fitting for mathematical models of rubber-like materials]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160811?rss=1
A great variety of models can describe the nonlinear response of rubber to uniaxial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the so-called Mooney plot transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strain-hardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the ‘upturn’ of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak nonlinear elasticity theory and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of nonlinear elasticity is much more robust that seemed at first sight.
]]>2017-02-08T00:05:14-08:00info:doi/10.1098/rspa.2016.0811hwp:master-id:royprsa;rspa.2016.08112017-02-08Research articles47321982016081120160811<![CDATA[Challenges to deployment of twenty-first century nuclear reactor systems]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160815?rss=1
The science and engineering of materials have always been fundamental to the success of nuclear power to date. They are also the key to the successful deployment and operation of a new generation of nuclear reactor systems and their associated fuel cycles. This article reflects on some of the historical issues, the challenges still prevalent today and the requirement for significant ongoing materials R&D and discusses the potential role of small modular reactors.
]]>2017-02-01T01:05:46-08:00info:doi/10.1098/rspa.2016.0815hwp:master-id:royprsa;rspa.2016.08152017-02-01Perspective47321982016081520160815<![CDATA[Field patterns: a new mathematical object]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2198/20160819?rss=1
Field patterns occur in space–time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is the field pattern. In one spatial direction plus time, the field patterns occur when the slope of the characteristics is, in a sense, commensurate with the space–time microstructure. Field patterns with different spatial shifts do not generally interact, but rather evolve as if they live in separate dimensions, as many dimensions as the number of field patterns. Alternatively one can view a collection as a multi-component potential, with as many components as the number of field patterns. Presumably, if one added a tiny nonlinear term to the wave equation one would then see interactions between these field patterns in the multi-dimensional space that one can consider them to live, or between the different field components of the multi-component potential if one views them that way. As a result of PT-symmetry many of the complex eigenvalues of an appropriately defined transfer matrix have unit norm and hence the corresponding eigenvectors correspond to propagating modes. There are also modes that blow up exponentially with time.
]]>2017-02-15T01:16:11-08:00info:doi/10.1098/rspa.2016.0819hwp:master-id:royprsa;rspa.2016.08192017-02-15Research articles47321982016081920160819<![CDATA[Why do students quit school? Implications from a dynamical modelling study]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160204?rss=1
In 2012, more than three million students dropped out from high school. At this pace, we will have more than 30 million Americans without a high school degree by 2022 and relatively high dropout rates among Hispanic and African American students. We have developed and analysed a data-driven mathematical model that includes multiple interacting mechanisms and estimates of parameters using data from a specifically designed survey applied to a certain group of students of a high school in Chicago to understand the dynamics of dropouts. Our analysis suggests students' academic achievement is directly related to the level of parental involvement more than any other factors in our study. However, if the negative peer influence (leading to lower academic grades) increases beyond a critical value, the effect of parental involvement on the dynamics of dropouts becomes negligible.
]]>2017-01-18T00:05:26-08:00info:doi/10.1098/rspa.2016.0204hwp:master-id:royprsa;rspa.2016.02042017-01-18Research articles47321972016020420160204<![CDATA[Learning partial differential equations via data discovery and sparse optimization]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160446?rss=1
We investigate the problem of learning an evolution equation directly from some given data. This work develops a learning algorithm to identify the terms in the underlying partial differential equations and to approximate the coefficients of the terms only using data. The algorithm uses sparse optimization in order to perform feature selection and parameter estimation. The features are data driven in the sense that they are constructed using nonlinear algebraic equations on the spatial derivatives of the data. Several numerical experiments show the proposed method's robustness to data noise and size, its ability to capture the true features of the data, and its capability of performing additional analytics. Examples include shock equations, pattern formation, fluid flow and turbulence, and oscillatory convection.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0446hwp:master-id:royprsa;rspa.2016.04462017-01-18Research articles47321972016044620160446<![CDATA[Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160461?rss=1
We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0461hwp:master-id:royprsa;rspa.2016.04612017-01-11Research articles47321972016046120160461<![CDATA[On compression and damage evolution in two thermoplastics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160495?rss=1
The well-known Taylor cylinder impact test, which follows the impact of a flat-ended cylindrical rod onto a rigid stationary anvil, is conducted over a range of impact speeds for two polymers, polytetrafluoroethylene (PTFE) and polyetheretherketone (PEEK). In previous work, experiments and a model were developed to capture the deformation behaviour of the cylinder after impact. These works showed a region in which spatial and temporal variation of both longitudinal and radial deformation provided evidence of changes in phase within the material. In this further series of experiments, this region is imaged in a range of impacted targets at the Diamond synchrotron. Further techniques were fielded to resolve compressed regions within the recovered polymer cylinders that showed a fracture zone in the impact region. The combination of macroscopic high-speed photography and three-dimensional X-ray imaging has identified the development of failure with these polymers and shown that there is no abrupt transition in behaviours but rather a continuous range of responses to competing operating mechanisms. The behaviours noted in PEEK in these polymers show critical gaps in understanding of polymer high strain-rate response.
]]>2017-01-18T00:05:27-08:00info:doi/10.1098/rspa.2016.0495hwp:master-id:royprsa;rspa.2016.04952017-01-18Research articles47321972016049520160495<![CDATA[Identification of internal properties of fibres and micro-swimmers]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160517?rss=1
In this paper, we address the identifiability of constitutive parameters of passive or active micro-swimmers. We first present a general framework for describing fibres or micro-swimmers using a bead-model description. Using a kinematic constraint formulation to describe fibres, flagellum or cilia, we find explicit linear relationship between elastic constitutive parameters and generalized velocities from computing contact forces. This linear formulation then permits one to address explicitly identifiability conditions and solve for parameter identification. We show that both active forcing and passive parameters are both identifiable independently but not simultaneously. We also provide unbiased estimators for generalized elastic parameters in the presence of Langevin-like forcing with Gaussian noise using a Bayesian approach. These theoretical results are illustrated in various configurations showing the efficiency of the proposed approach for direct parameter identification. The convergence of the proposed estimators is successfully tested numerically.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0517hwp:master-id:royprsa;rspa.2016.05172017-01-18Research articles47321972016051720160517<![CDATA[Beyond linear fields: the Lie-Taylor expansion]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160525?rss=1
The work extends the linear fields’ solution of compressible nonlinear magnetohydrodynamics (MHD) to the case where the magnetic field depends on superlinear powers of position vector, usually, but not always, expressed in Cartesian components. Implications of the resulting Lie–Taylor series expansion for physical applicability of the Dolzhansky–Kirchhoff (D–K) equations are found to be positive. It is demonstrated how resistivity may be included in the D–K model. Arguments are put forward that the D–K equations may be regarded as illustrating properties of nonlinear MHD in the same sense that the Lorenz equations inform about the onset of convective turbulence. It is suggested that the Lie–Taylor series approach may lead to valuable insights into other fluid models.
]]>2017-01-04T00:05:20-08:00info:doi/10.1098/rspa.2016.0525hwp:master-id:royprsa;rspa.2016.05252017-01-04Research articles47321972016052520160525<![CDATA[The problem of missing terms in term by term integration involving divergent integrals]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160567?rss=1
Term by term integration may lead to divergent integrals, and naive evaluation of them by means of, say, analytic continuation or by regularization or by the finite part integral may lead to missing terms. Here, under certain analyticity conditions, the problem of missing terms for the incomplete Stieltjes transform, 0af(x)(+x)–1 dx, and the Stieltjes transform itself, 0f(x)(+x)–1 dx, is resolved by lifting the integration in the complex plane. It is shown that the missing terms arise from the singularities of the complex-valued function f(z)(+z)^{–1}, with the divergent integrals arising from term by term integration interpreted as finite part integrals.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0567hwp:master-id:royprsa;rspa.2016.05672017-01-18Research articles47321972016056720160567<![CDATA[The onset of thermalization in finite-dimensional equations of hydrodynamics: insights from the Burgers equation]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160585?rss=1
Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber KG), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite dimensional partial differential equations or their viscous counterparts. Surprisingly, the solutions to such Galerkin-truncated equations develop sharp localized structures, called tygers (Ray et al. 2011 Phys. Rev. E84, 016301 (doi:10.1103/PhysRevE.84.016301)), which eventually lead to completely thermalized states associated with an equipartition energy spectrum. We now obtain, by using the analytically tractable Burgers equation, precise estimates, theoretically and via direct numerical simulations, of the time c at which thermalization is triggered and show that c~KG, with =–49. Our results have several implications, including for the analyticity strip method, to numerically obtain evidence for or against blow-ups of the three-dimensional incompressible Euler equations.
]]>2017-01-18T00:05:27-08:00info:doi/10.1098/rspa.2016.0585hwp:master-id:royprsa;rspa.2016.05852017-01-18Research articles47321972016058520160585<![CDATA[An investigation into inflection-point instability in the entrance region of a pulsating pipe flow]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160590?rss=1
This paper investigates the inflection-point instability that governs the flow disturbance initiated in the entrance region of a pulsating pipe flow. Under such a flow condition, the flow instability grows within a certain phase region in a pulsating cycle, during which the inflection point in the unsteady mean flow lifts away from the viscous effect-dominated region known as the Stokes layer. The characteristic frequency of the instability is found to be in agreement with that predicted by the mixing-layer model. In comparison with those cases not falling in this category, it is further verified that the flow phenomenon will take place only if the inflection point lifts away sufficiently from the Stokes layer.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0590hwp:master-id:royprsa;rspa.2016.05902017-01-11Research articles47321972016059020160590<![CDATA[A study on the temperature field of a bronze-bonded diamond wheel dressed using a laser/ultrasonic vibration combined method]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160597?rss=1
To solve problems in dressings for metal-bonded super-hard abrasive wheels, such as low efficiency and rapid wear, this article introduces a laser-assisted ultrasonic vibration dressing technique. Firstly, finite-element simulations were conducted on the dressing process of a bronze-bonded diamond wheel, and the wheel's temperature field distributions under different laser parameters were simulated. By analysing the simulation results of temperature fields and the melting point of the bronze bond, the laser parameters for laser-assisted ultrasonic vibration dressing tests were optimized, and then actual tests were carried out on the bronze-bonded diamond wheel. Results showed that, with appropriate technology parameters, the laser-assisted ultrasonic vibration dressing technique achieved desirable dressing results; specifically, the dressing force was low, the abrasive particles had high protrusions and the wheel had a large chip space and favourable surface topography.
]]>2017-01-18T00:05:26-08:00info:doi/10.1098/rspa.2016.0597hwp:master-id:royprsa;rspa.2016.05972017-01-18Research articles47321972016059720160597<![CDATA[Entropy in sound and vibration: towards a new paradigm]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160602?rss=1
This paper describes a discussion on the method and the status of a statistical theory of sound and vibration, called statistical energy analysis (SEA). SEA is a simple theory of sound and vibration in elastic structures that applies when the vibrational energy is diffusely distributed. We show that SEA is a thermodynamical theory of sound and vibration, based on a law of exchange of energy analogous to the Clausius principle. We further investigate the notion of entropy in this context and discuss its meaning. We show that entropy is a measure of information lost in the passage from the classical theory of sound and vibration and SEA, its thermodynamical counterpart.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0602hwp:master-id:royprsa;rspa.2016.06022017-01-11Research articles47321972016060220160602<![CDATA[Reconfiguration of a smart surface using heteroclinic connections]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160614?rss=1
A reconfigurable smart surface with multiple equilibria is presented, modelled using discrete point masses and linear springs with geometric nonlinearity. An energy-efficient reconfiguration scheme is then investigated to connect equal-energy unstable (but actively controlled) equilibria. In principle, zero net energy input is required to transition the surface between these unstable states, compared to transitions between stable equilibria across a potential barrier. These transitions between equal-energy unstable states, therefore, form heteroclinic connections in the phase space of the problem. Moreover, the smart surface model developed can be considered as a unit module for a range of applications, including modules which can aggregate together to form larger distributed smart surface systems.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0614hwp:master-id:royprsa;rspa.2016.06142017-01-11Research articles47321972016061420160614<![CDATA[Domain structure of ultrathin ferromagnetic elements in the presence of Dzyaloshinskii-Moriya interaction]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160666?rss=1
Recent advances in nanofabrication make it possible to produce multilayer nanostructures composed of ultrathin film materials with thickness down to a few monolayers of atoms and lateral extent of several tens of nanometers. At these scales, ferromagnetic materials begin to exhibit unusual properties, such as perpendicular magnetocrystalline anisotropy and antisymmetric exchange, also referred to as Dzyaloshinskii–Moriya interaction (DMI), because of the increased importance of interfacial effects. The presence of surface DMI has been demonstrated to fundamentally alter the structure of domain walls. Here we use the micromagnetic modelling framework to analyse the existence and structure of chiral domain walls, viewed as minimizers of a suitable micromagnetic energy functional. We explicitly construct the minimizers in the one-dimensional setting, both for the interior and edge walls, for a broad range of parameters. We then use the methods of -convergence to analyse the asymptotics of the two-dimensional magnetization patterns in samples of large spatial extent in the presence of weak applied magnetic fields.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0666hwp:master-id:royprsa;rspa.2016.06662017-01-11Research articles47321972016066620160666<![CDATA[The theory on 'gravity-driven horizontal locomotion is flawed; a commentary on 'Gravity-driven horizontal locomotion: theory and experiment by Kanstad & Kononoff (2015)]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160683?rss=1
In a recent paper, Kanstad & Kononoff (Proc. R. Soc. A471, 20150287. (doi:10.1098/rspa.2015.0287)) presented a theoretical analysis of the mechanical energetics of a particular style of human walking and running. According to their analysis, the force of gravity provides energy when this style of horizontal walking/running is adopted. Furthermore, Kanstad & Kononoff suggested that uphill walking at zero energy cost is possible when the suggested style of walking is adopted. In this commentary, we argue that these claims violate the basic laws of thermodynamics, and are based on erroneous application of the basic laws of classical mechanics.
]]>2017-01-18T00:05:27-08:00info:doi/10.1098/rspa.2016.0683hwp:master-id:royprsa;rspa.2016.06832017-01-18Comments and invited replies47321972016068320160683<![CDATA['Full fusion is not ineluctable during vesicular exocytosis of neurotransmitters by endocrine cells]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160684?rss=1
Vesicular exocytosis is an essential and ubiquitous process in neurons and endocrine cells by which neurotransmitters are released in synaptic clefts or extracellular fluids. It involves the fusion of a vesicle loaded with chemical messengers with the cell membrane through a nanometric fusion pore. In endocrine cells, unless it closes after some flickering (‘Kiss-and-Run’ events), this initial pore is supposed to expand exponentially, leading to a full integration of the vesicle membrane into the cell membrane—a stage called ‘full fusion’. We report here a compact analytical formulation that allows precise measurements of the fusion pore expansion extent and rate to be extracted from individual amperometric spike time courses. These data definitively establish that, during release of catecholamines, fusion pores enlarge at most to approximately one-fifth of the radius of their parent vesicle, hence ruling out the ineluctability of ‘full fusion’.
]]>2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0684hwp:master-id:royprsa;rspa.2016.06842017-01-11Special feature47321972016068420160684<![CDATA[Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160705?rss=1
Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.
]]>2017-01-25T00:05:42-08:00info:doi/10.1098/rspa.2016.0705hwp:master-id:royprsa;rspa.2016.07052017-01-25Research articles47321972016070520160705<![CDATA[Whitham modulation theory for the Ostrovsky equation]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160709?rss=1
This paper derives the Whitham modulation equations for the Ostrovsky equation. The equations are then used to analyse localized cnoidal wavepacket solutions of the Ostrovsky equation in the weak rotation limit. The analysis is split into two main parameter regimes: the Ostrovsky equation with normal dispersion relevant to typical oceanic parameters and the Ostrovsky equation with anomalous dispersion relevant to strongly sheared oceanic flows and other physical systems. For anomalous dispersion a new steady, symmetric cnoidal wavepacket solution is presented. The new wavepacket can be represented as a solution of the modulation equations and an analytical solution for the outer solution of the wavepacket is given. For normal dispersion the modulation equations are used to describe the unsteady finite-amplitude wavepacket solutions produced from the rotation-induced decay of a Korteweg–de Vries solitary wave. Again, an analytical solution for the outer solution can be given. The centre of the wavepacket closely approximates a train of solitary waves with the results suggesting that the unsteady wavepacket is a localized, modulated cnoidal wavetrain. The formation of wavepackets from solitary wave initial conditions is considered, contrasting the rapid formation of the packets in anomalous dispersion with the slower formation of unsteady packets under normal dispersion.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0709hwp:master-id:royprsa;rspa.2016.07092017-01-18Research articles47321972016070920160709<![CDATA[Reflections on the value of electron microscopy in the study of heterogeneous catalysts]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160714?rss=1
Electron microscopy (EM) is arguably the single most powerful method of characterizing heterogeneous catalysts. Irrespective of whether they are bulk and multiphasic, or monophasic and monocrystalline, or nanocluster and even single-atom and on a support, their structures in atomic detail can be visualized in two or three dimensions, thanks to high-resolution instruments, with sub-Ångstrom spatial resolutions. Their topography, tomography, phase-purity, composition, as well as the bonding, and valence-states of their constituent atoms and ions and, in favourable circumstances, the short-range and long-range atomic order and dynamics of the catalytically active sites, can all be retrieved by the panoply of variants of modern EM. The latter embrace electron crystallography, rotation and precession electron diffraction, X-ray emission and high-resolution electron energy-loss spectra (EELS). Aberration-corrected (AC) transmission (TEM) and scanning transmission electron microscopy (STEM) have led to a revolution in structure determination. Environmental EM is already playing an increasing role in catalyst characterization, and new advances, involving special cells for the study of solid catalysts in contact with liquid reactants, have recently been deployed.
]]>2017-01-25T01:06:58-08:00info:doi/10.1098/rspa.2016.0714hwp:master-id:royprsa;rspa.2016.07142017-01-25Perspective47321972016071420160714<![CDATA[Observation-based correction of dynamical models using thermostats]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160730?rss=1
Models used in simulation may give accurate short-term trajectories but distort long-term (statistical) properties. In this work, we augment a given approximate model with a control law (a ‘thermostat’) that gently perturbs the dynamical system to target a thermodynamic state consistent with a set of prescribed (possibly evolving) observations. As proof of concept, we provide an example involving a point vortex fluid model on the sphere, for which we show convergence of equilibrium quantities (in the stationary case) and the ability of the thermostat to dynamically track a transient state.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0730hwp:master-id:royprsa;rspa.2016.07302017-01-18Research articles47321972016073020160730<![CDATA[Finite-element modelling of elastic wave propagation and scattering within heterogeneous media]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160738?rss=1
The scattering treated here arises when elastic waves propagate within a heterogeneous medium defined by random spatial fluctuation of its elastic properties. Whereas classical analytical studies are based on lower-order scattering assumptions, numerical methods conversely present no such limitations by inherently incorporating multiple scattering. Until now, studies have typically been limited to two or one dimension, however, owing to computational constraints. This article seizes recent advances to realize a finite-element formulation that solves the three-dimensional elastodynamic scattering problem. The developed methodology enables the fundamental behaviour of scattering in terms of attenuation and dispersion to be studied. In particular, the example of elastic waves propagating within polycrystalline materials is adopted, using Voronoi tessellations to randomly generate representative models. The numerically observed scattering is compared against entirely independent but well-established analytical scattering theory. The quantitative agreement is found to be excellent across previously unvisited scattering regimes; it is believed that this is the first quantitative validation of its kind which provides significant support towards the existence of the transitional scattering regime and facilitates future deployment of numerical methods for these problems.
]]>2017-01-04T00:05:20-08:00info:doi/10.1098/rspa.2016.0738hwp:master-id:royprsa;rspa.2016.07382017-01-04Research articles47321972016073820160738<![CDATA[Topological origin and not purely antisymmetric wave functions of many-body states in the lowest Landau level]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160758?rss=1
In this paper, we recall the topological approach to quantum Hall effects. We note that, in the presence of a magnetic field, trajectories representing elements of the system’s braid group are of cyclotron orbit type. In two-dimensional spaces, this leads to the restriction of the full braid group, _{1}()—loopless generators (exchanges of M^{N} coordinates or classical particles) are unenforceable. As a result, the identification of a possible Hall-like state comes down to the identification of a possible subgroup of _{1}(). The latter follows from the connection between the one-dimensional unitary representation of the system’s braid group and particle statistics (unavoidable for any correlated state). In this work, we implement the topological approach to derive the lowest Landau-level pyramid of fillings. We point out that it contains all mysterious odd-denominator filling factors—like 411, 413 or 617—not trivial to explain within the standard picture. We also introduce, explicitly, cyclotron subgroup generators for all derived fractions. Preliminary results on wave functions, supported by several Monte Carlo calculations, are presented. It is worth emphasizing that not all proposed many-body functions are purely antisymmetric—they, however, transform in agreement with the scalar representations of the system’s braid group. The latter is enforced by standard quantization methods.
]]>2017-01-18T03:28:12-08:00info:doi/10.1098/rspa.2016.0758hwp:master-id:royprsa;rspa.2016.07582017-01-18Research articles47321972016075820160758<![CDATA[Recycling of waste gasket rubber granules by bulk CuCl2 and nano CuCl2: removal of Hg(II) ions by recycled rubber granules]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160771?rss=1
Environmental problems arise due to the millions of tons of waste rubber that are thrown away in the natural environment. Management of this waste rubber is a big environmental challenge. So, a new, simple and cost-effective recycling method for obtaining recycled waste rubber should be developed. In this study, we found that waste gasket rubber can be desulfurized by means of bulk and nano-sized transition metal halides in the presence of solvents. The recycled product of desulfurized waste gasket rubber granules that is obtained can be used as the cheapest adsorbent in the removal of mercury(II) ions from aqueous solution. Comparative batch studies have been conducted to elucidate the adsorption efficiency of desulfurized rubber using bulk copper chloride and also using nano-sized copper chloride under optimum conditions with commercial activated carbon.
]]>2017-01-18T00:05:26-08:00info:doi/10.1098/rspa.2016.0771hwp:master-id:royprsa;rspa.2016.07712017-01-18Research articles47321972016077120160771<![CDATA[Origin of the scaling laws of sediment transport]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160785?rss=1
In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 + )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 + )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 + )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘–Z’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 – )’, ‘–4/(3 – )’ and ‘–(1 + )/(3 – )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.
]]>2017-01-25T00:05:42-08:00info:doi/10.1098/rspa.2016.0785hwp:master-id:royprsa;rspa.2016.07852017-01-25Research articles47321972016078520160785<![CDATA[Real wave propagation in the isotropic-relaxed micromorphic model]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160790?rss=1
For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity.
]]>2017-01-11T00:28:48-08:00info:doi/10.1098/rspa.2016.0790hwp:master-id:royprsa;rspa.2016.07902017-01-11Research articles47321972016079020160790<![CDATA[Numerical and analytical results for the two discs capacitor problem]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160792?rss=1
In this paper, we study the two discs capacitor, for equal and different radii. The new results obtained allow a complete characterization of capacity coefficients and forces at short distances. An extensive numerical calculation confirms the theoretical results. The study shows the existence of a hierarchy in the divergent behaviour of the capacitance coefficients and this implies some unusual behaviour of the forces, strictly related to the dimensionality of the near-contact zone between electrodes.
]]>2017-01-25T00:05:42-08:00info:doi/10.1098/rspa.2016.0792hwp:master-id:royprsa;rspa.2016.07922017-01-25Research articles47321972016079220160792<![CDATA[Correction to 'On the energy partition in oscillations and waves]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160839?rss=1
2017-01-04T00:05:20-08:00info:doi/10.1098/rspa.2016.0839hwp:master-id:royprsa;rspa.2016.08392017-01-04Erratum47321972016083920160839<![CDATA[Editorial January 2017]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2197/20160897?rss=1
2017-01-11T00:05:17-08:00info:doi/10.1098/rspa.2016.0897hwp:master-id:royprsa;rspa.2016.08972017-01-11Editorial47321972016089720160897<![CDATA[Effect of wall-mediated hydrodynamic fluctuations on the kinetics of a Brownian nanoparticle]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160397?rss=1
The reactive flux formalism (Chandler 1978 J. Chem. Phys.68, 2959–2970. (doi:10.1063/1.436049)) and the subsequent development of methods such as transition path sampling have laid the foundation for explicitly quantifying the rate process in terms of microscopic simulations. However, explicit methods to account for how the hydrodynamic correlations impact the transient reaction rate are missing in the colloidal literature. We show that the composite generalized Langevin equation (Yu et al. 2015 Phys. Rev. E91, 052303. (doi:10.1103/PhysRevE.91.052303)) makes a significant step towards solving the coupled processes of molecular reactions and hydrodynamic relaxation by examining how the wall-mediated hydrodynamic memory impacts the two-stage temporal relaxation of the reaction rate for a nanoparticle transition between two bound states in the bulk, near-wall and lubrication regimes.
]]>2016-12-21T00:05:17-08:00info:doi/10.1098/rspa.2016.0397hwp:master-id:royprsa;rspa.2016.03972016-12-21Research articles47221962016039720160397<![CDATA[Measurement of the Earth's rotation: 720 BC to AD 2015]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160404?rss=1
New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century. Besides this linear change in the lod, there are fluctuations about this trend on time scales of decades to centuries. A power spectral density analysis of fluctuations in the range 2–30 years follows a power law with exponent –1.3, and there is evidence of increased power at a period of 6 years. There is some indication of an oscillation in the lod with a period of roughly 1500 years. Our measurements of the Earth’s rotation for the period 720 BC to AD 2015 set firm boundaries for future work on post-glacial rebound and core–mantle coupling which are invoked to explain the departures from tidal friction.
]]>2016-12-07T02:15:14-08:00info:doi/10.1098/rspa.2016.0404hwp:master-id:royprsa;rspa.2016.04042016-12-07Research articles47221962016040420160404<![CDATA[Multiphase wavetrains, singular wave interactions and the emergence of the Korteweg-de Vries equation]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160456?rss=1
Multiphase wavetrains are multiperiodic travelling waves with a set of distinct wavenumbers and distinct frequencies. In conservative systems, such families are associated with the conservation of wave action or other conservation law. At generic points (where the Jacobian of the wave action flux is non-degenerate), modulation of the wavetrain leads to the dispersionless multiphase conservation of wave action. The main result of this paper is that modulation of the multiphase wavetrain, when the Jacobian of the wave action flux vector is singular, morphs the vector-valued conservation law into the scalar Korteweg–de Vries (KdV) equation. The coefficients in the emergent KdV equation have a geometrical interpretation in terms of projection of the vector components of the conservation law. The theory herein is restricted to two phases to simplify presentation, with extensions to any finite dimension discussed in the concluding remarks. Two applications of the theory are presented: a coupled nonlinear Schrödinger equation and two-layer shallow-water hydrodynamics with a free surface. Both have two-phase solutions where criticality and the properties of the emergent KdV equation can be determined analytically.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0456hwp:master-id:royprsa;rspa.2016.04562016-12-07Research articles47221962016045620160456<![CDATA[Perspectives on magnetic reconnection]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160479?rss=1
Magnetic reconnection is a topological rearrangement of magnetic field that occurs on time scales much faster than the global magnetic diffusion time. Since the field lines break on microscopic scales but energy is stored and the field is driven on macroscopic scales, reconnection is an inherently multi-scale process that often involves both magnetohydrodynamic (MHD) and kinetic phenomena. In this article, we begin with the MHD point of view and then describe the dynamics and energetics of reconnection using a two-fluid formulation. We also focus on the respective roles of global and local processes and how they are coupled. We conclude that the triggers for reconnection are mostly global, that the key energy conversion and dissipation processes are either local or global, and that the presence of a continuum of scales coupled from microscopic to macroscopic may be the most likely path to fast reconnection.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0479hwp:master-id:royprsa;rspa.2016.04792016-12-07Special feature47221962016047920160479<![CDATA[Generalized statistical mechanics approaches to earthquakes and tectonics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160497?rss=1
Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0497hwp:master-id:royprsa;rspa.2016.04972016-12-07Review articles47221962016049720160497<![CDATA[Modulations of viscous fluid conduit periodic waves]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160533?rss=1
Modulated periodic interfacial waves along a conduit of viscous liquid are explored using nonlinear wave modulation theory and numerical methods. Large-amplitude periodic-wave modulation (Whitham) theory does not require integrability of the underlying model equation, yet often either integrable equations are studied or the full extent of Whitham theory is not developed. Periodic wave solutions of the nonlinear, dispersive, non-integrable conduit equation are characterized by their wavenumber and amplitude. In the weakly nonlinear regime, both the defocusing and focusing variants of the nonlinear Schrödinger (NLS) equation are derived, depending on the carrier wavenumber. Dark and bright envelope solitons are found to persist in long-time numerical solutions of the conduit equation, providing numerical evidence for the existence of strongly nonlinear, large-amplitude envelope solitons. Due to non-convex dispersion, modulational instability for periodic waves above a critical wavenumber is predicted and observed. In the large-amplitude regime, structural properties of the Whitham modulation equations are computed, including strict hyperbolicity, genuine nonlinearity and linear degeneracy. Bifurcating from the NLS critical wavenumber at zero amplitude is an amplitude-dependent elliptic region for the Whitham equations within which a maximally unstable periodic wave is identified. The viscous fluid conduit system is a mathematically tractable, experimentally viable model system for wide-ranging nonlinear, dispersive wave dynamics.
]]>2016-12-14T00:47:45-08:00info:doi/10.1098/rspa.2016.0533hwp:master-id:royprsa;rspa.2016.05332016-12-14Research articles47221962016053320160533<![CDATA[A new self-propelled magnetic bearing with helical windings]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160579?rss=1
In this work, a design is proposed for an active, permanent magnet based, self-propelled magnetic bearing, i.e. levitating motor having the following features: (i) simple winding structure, (ii) high load supporting capacity, (iii) no eccentricity sensors, (iv) stable confinement in all translational dimensions, (v) stable confinement in all rotational dimensions, and (vi) high efficiency. This design uses an architecture consisting of a helically wound three-phase stator, and a rotor with the magnets also arranged in a helical manner. Active control is used to excite the rotor at a torque angle lying in the second quadrant. This torque angle is independent of the rotor's position inside the stator cavity; hence the control algorithm is similar to that of a conventional permanent magnet synchronous motor. It is motivated through a physical argument that the bearing rotor develops a lift force proportional to the output torque and that it remains stably confined in space. These assertions are then proved rigorously through a calculation of the magnetic fields, forces and torques. The stiffness matrix of the system is presented and a discussion of stable and unstable operating regions is given.
]]>2016-12-21T00:05:18-08:00info:doi/10.1098/rspa.2016.0579hwp:master-id:royprsa;rspa.2016.05792016-12-21Research articles47221962016057920160579<![CDATA[Quaternionic-like manifolds and homogeneous twistor spaces]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160598?rss=1
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the ‘quaternionic-like manifolds’. These contain, as particular subclasses, the CR quaternionic and the -quaternionic manifolds. Moreover, the notion of ‘heaven space’ finds its adequate level of generality in this setting: (essentially) any real analytic quaternionic-like manifold admits a (germ) unique heaven space, which is a -quaternionic manifold. We, also, give a natural construction of homogeneous complex manifolds endowed with embedded spheres, thus, emphasizing the abundance of the quaternionic-like manifolds.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0598hwp:master-id:royprsa;rspa.2016.05982016-12-07Research articles47221962016059820160598<![CDATA[Using wire shaping techniques and holographic optics to optimize deposition characteristics in wire-based laser cladding]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160603?rss=1
In laser cladding, the potential benefits of wire feeding are considerable. Typical problems with the use of powder, such as gas entrapment, sub-100% material density and low deposition rate are all avoided with the use of wire. However, the use of a powder-based source material is the industry standard, with wire-based deposition generally regarded as an academic curiosity. This is because, although wire-based methods have been shown to be capable of superior quality results, the wire-based process is more difficult to control. In this work, the potential for wire shaping techniques, combined with existing holographic optical element knowledge, is investigated in order to further improve the processing characteristics. Experiments with pre-placed wire showed the ability of shaped wire to provide uniformity of wire melting compared with standard round wire, giving reduced power density requirements and superior control of clad track dilution. When feeding with flat wire, the resulting clad tracks showed a greater level of quality consistency and became less sensitive to alterations in processing conditions. In addition, a 22% increase in deposition rate was achieved. Stacking of multiple layers demonstrated the ability to create fully dense, three-dimensional structures, with directional metallurgical grain growth and uniform chemical structure.
]]>2016-12-21T00:05:18-08:00info:doi/10.1098/rspa.2016.0603hwp:master-id:royprsa;rspa.2016.06032016-12-21Research articles47221962016060320160603<![CDATA[The effect of a longitudinal density gradient on electron plasma wake field acceleration]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160630?rss=1
Three-dimensional, particle-in-cell, fully electromagnetic simulations of electron plasma wake field acceleration in the blow-out regime are presented. Earlier results are extended by (i) studying the effect of a longitudinal density gradient, (ii) avoiding the use of a co-moving simulation box, (iii) inclusion of ion motion, and (iv) studying fully electromagnetic plasma wake fields. It is established that injecting driving and trailing electron bunches into a positive density gradient of 10-fold increasing density over 10 cm long lithium vapour plasma results in spatially more compact and three times larger, compared with the uniform density case, electric fields (–6.4x10^{10} V m^{–1}), leading to acceleration of the trailing bunch up to 24.4 GeV (starting from an initial 20.4 GeV), with energy transfer efficiencies from the leading to trailing bunch of 75%. In the uniform density case, a –2.5x10^{10} V m^{–1} wake is created leading to acceleration of the trailing bunch up to 22.4 GeV, with energy transfer efficiencies of 65%. It is also established that injecting the electron bunches into a negative density gradient of 10-fold decreasing density over 10 cm long plasma results in spatially more spread and two and a half smaller electric fields (–1.0x10^{10} V m^{–1}), leading to a weaker acceleration of the trailing bunch up to 21.4 GeV, with energy transfer efficiencies of 45%. Taking ion motions into consideration shows that in the plasma wake ion number density can increase over a few times the background value. It is also shown that transverse electromagnetic fields in a plasma wake are of the same order as the longitudinal (electrostatic) ones.
]]>2016-12-14T00:05:25-08:00info:doi/10.1098/rspa.2016.0630hwp:master-id:royprsa;rspa.2016.06302016-12-14Research articles47221962016063020160630<![CDATA[Lamb's problem on random mass density fields with fractal and Hurst effects]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160638?rss=1
This paper reports on a generalization of Lamb's problem to a linear elastic, infinite half-space with random fields (RFs) of mass density, subject to a normal line load. Both, uncorrelated and correlated (with fractal and Hurst characteristics) RFs without any weak noise restrictions, are proposed. Cellular automata (CA) is used to simulate the wave propagation. CA is a local computational method which, for rectangular discretization of spatial domain, is equivalent to applying the finite difference method to the governing equations of classical elasticity. We first evaluate the response of CA to an uncorrelated mass density field, more commonly known as white-noise, of varying coarseness as compared to CA's node density. We then evaluate the response of CA to multiscale mass density RFs of Cauchy and Dagum type; these fields are unique in that they are able to model and decouple the field's fractal dimension and Hurst parameter. We focus on stochastic imperfection sensitivity; we determine to what extent the fractal or the Hurst parameter is a significant factor in altering the solution to the planar stochastic Lamb's problem by evaluating the coefficient of variation of the response when compared with the coefficient of variation of the RF.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0638hwp:master-id:royprsa;rspa.2016.06382016-12-07Research articles47221962016063820160638<![CDATA[A computational framework for ptychographic reconstructions]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160640?rss=1
Ptychography is now a well-established X-ray microscopy tool for synchrotron end-stations equipped with a scanning stage and a pixelated detector. Ptychographic phasing algorithms use information from coherent diffraction to deliver quantitative images of the specimen at a resolution higher than the scanning resolution. These algorithms have traditionally been implemented in software on a per-instrument basis in various degrees of user-friendliness and sophistication. Here, we present Ptypy, a ptychography software written with the intention to serve as a framework across the diverse sets of available instruments and usage cases. A distinctive feature of the software is its formalism, which provides a convenient abstraction of the physical model, thus allowing for concise algorithmic implementations and portability across set-up geometries. We give an overview of the supported usage cases, explain the abstraction layer and design principles, and provide a step-by-step guide describing how an algorithm may be realized in a concise and readable manner. The software capabilities are illustrated with reconstructions from visible light and X-ray data.
]]>2016-12-21T00:05:18-08:00info:doi/10.1098/rspa.2016.0640hwp:master-id:royprsa;rspa.2016.06402016-12-21Research articles47221962016064020160640<![CDATA[Closed-form rocking overturning conditions for a family of pulse ground motions]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160662?rss=1
This paper characterizes the stability of a rigid rocking block subjected to a family of multi-lobe pulse ground motions. It unveils a counter to intuition plurality of overturning (OT) modes despite the short duration and bounded energy of the examined ground motions. Accordingly, it describes with original closed-form expressions the critical conditions of all OT modes involving a finite number of impacts. It also proposes pertinent semi-analytical, exact analytical and approximate analytical solutions with respect to the determination of the (unknown) times of impact, as appropriate. The analysis reveals that the first, or lower bound, critical OT mode is in most cases toppling during free rocking after one impact specifically before the end of the pulse. For this case, it elucidates the physical mechanism behind the timing of impact that produces minimum amplitude and maximum amplitude critical OT, respectively, and proposes pertinent closed-form approximations. Finally, the study derives, in ‘universal’ terms, global ‘safety walls’ against rocking OT considering a large number of different pulse shapes.
]]>2016-12-21T00:05:18-08:00info:doi/10.1098/rspa.2016.0662hwp:master-id:royprsa;rspa.2016.06622016-12-21Research articles47221962016066220160662<![CDATA[The anelastic Ericksen problem: universal eigenstrains and deformations in compressible isotropic elastic solids]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160690?rss=1
The elastic Ericksen problem consists of finding deformations in isotropic hyperelastic solids that can be maintained for arbitrary strain-energy density functions. In the compressible case, Ericksen showed that only homogeneous deformations are possible. Here, we solve the anelastic version of the same problem, that is, we determine both the deformations and the eigenstrains such that a solution to the anelastic problem exists for arbitrary strain-energy density functions. Anelasticity is described by finite eigenstrains. In a nonlinear solid, these eigenstrains can be modelled by a Riemannian material manifold whose metric depends on their distribution. In this framework, we show that the natural generalization of the concept of homogeneous deformations is the notion of covariantly homogeneous deformations—deformations with covariantly constant deformation gradients. We prove that these deformations are the only universal deformations and that they put severe restrictions on possible universal eigenstrains. We show that, in a simply-connected body, for any distribution of universal eigenstrains the material manifold is a symmetric Riemannian manifold and that in dimensions 2 and 3 the universal eigenstrains are zero-stress.
]]>2016-12-14T00:05:25-08:00info:doi/10.1098/rspa.2016.0690hwp:master-id:royprsa;rspa.2016.06902016-12-14Research articles47221962016069020160690<![CDATA[Lax pairs of discrete Painleve equations: (A2+A1)(1) case]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160696?rss=1
In this paper, we provide a comprehensive method for constructing Lax pairs of discrete Painlevé equations by using a reduced hypercube structure. In particular, we consider the A5(1)-surface q-Painlevé system, which has the affine Weyl group symmetry of type (A_{2}+A_{1})^{(1)}. Two new Lax pairs are found.
]]>2016-12-14T00:47:45-08:00info:doi/10.1098/rspa.2016.0696hwp:master-id:royprsa;rspa.2016.06962016-12-14Research articles47221962016069620160696<![CDATA[Initiation and directional control of period-1 rotation for a parametric pendulum]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2196/20160719?rss=1
We study a time-delayed feedback control for initiating period-1 rotations of a vertically excited parametric pendulum from arbitrary initial conditions. The possibility of controlling the direction of rotation has also been explored. We start with a simple linear time-delayed control for which the control gain corresponding to the most stable period-1 rotation has been obtained using the Floquet theory. This control increases the basins of attraction of rotations, but they do not encompass the full initial condition space. We modify our control law by using a switched control gain that destabilizes all the oscillatory solutions, and the entire initial condition space becomes the basin of attraction of either the clockwise or the anticlockwise rotation. By a suitable modification of the switching condition, we can choose a preferential stable direction of rotation. Hence, we can initiate either clockwise or anticlockwise rotation for a parametric pendulum from arbitrary initial conditions. Performance of our controller in achieving this objective has been demonstrated for different sets of parameters to establish its effectiveness.
]]>2016-12-07T01:14:17-08:00info:doi/10.1098/rspa.2016.0719hwp:master-id:royprsa;rspa.2016.07192016-12-07Research articles47221962016071920160719<![CDATA[An optimal tuning strategy for tidal turbines]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160047?rss=1
Tuning wind and tidal turbines is critical to maximizing their power output. Adopting a wind turbine tuning strategy of maximizing the output at any given time is shown to be an extremely poor strategy for large arrays of tidal turbines in channels. This ‘impatient-tuning strategy’ results in far lower power output, much higher structural loads and greater environmental impacts due to flow reduction than an existing ‘patient-tuning strategy’ which maximizes the power output averaged over the tidal cycle. This paper presents a ‘smart patient tuning strategy’, which can increase array output by up to 35% over the existing strategy. This smart strategy forgoes some power generation early in the half tidal cycle in order to allow stronger flows to develop later in the cycle. It extracts enough power from these stronger flows to produce more power from the cycle as a whole than the existing strategy. Surprisingly, the smart strategy can often extract more power without increasing maximum structural loads on the turbines, while also maintaining stronger flows along the channel. This paper also shows that, counterintuitively, for some tuning strategies imposing a cap on turbine power output to limit loads can increase a turbine’s average power output.
]]>2016-11-16T00:05:25-08:00info:doi/10.1098/rspa.2016.0047hwp:master-id:royprsa;rspa.2016.00472016-11-16Research articles47221952016004720160047<![CDATA[Formal groups and Z-entropies]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160143?rss=1
We shall prove that the celebrated Rényi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the Z-entropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Rényi. A crucial aspect is that every Z-entropy is composable (Tempesta 2016 Ann. Phys.365, 180–197. (doi:10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth Shannon–Khinchin axiom (postulating additivity), is a highly non-trivial requirement. Indeed, in the trace-form class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the non-trace form class, the Z-entropies arise as new entropic functions possessing the mathematical properties necessary for information-theoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying group-theoretical structure determines crucially the statistical properties of the corresponding entropies.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0143hwp:master-id:royprsa;rspa.2016.01432016-11-23Research articles47221952016014320160143<![CDATA[Indications for influence of artificial (man-made) activity on radon signals, in simulation experiments]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160311?rss=1
Radon (Rn-222; a radioactive noble gas) is characterized by large temporal variations that differ significantly from variations of (i) other trace elements in geogas (noble gases); (ii) variation patterns of other dynamic geophysical systems (atmospheric, tidal). Consensus exists that there is no simple and straightforward understanding of the phenomena and its behaviour. This lacuna in the understanding of the underlying principles hampers the development of applications—such as radon as a proxy of processes in the seismogenic context. Using results from field investigations and simulation experiments the GSI suggested that an unidentified extraterrestrial component, probably in solar radiation, drives periodic radon signals in the diurnal and annual frequency bands. Recent findings from experimental investigations shed additional perspectives allowing a new evaluation of the issue. Particular transient signals, measured with alpha and gamma detectors, are interpreted to reflect the influence of artificial activity. Criteria are (i) signals lasting several hours that occur around midday on workdays (Sunday–Thursday); (ii) signals composed of a train of around 10 strong pulses, each lasting less than 15 min, occurring within several hours once a week, from Wednesday afternoon/evening to Thursday morning. A first interpretation is that an unidentified artificial activity of some sort (industrial?) generates and emits an unidentified agent that reaches enhanced confined mode experiments at the GSI laboratory, which respond to the incoming agent in the form of radon signals. Developing the capability of identification of such an earth-bound source generating an influencing agent is a key step towards understanding of external influence on radioactivity of radon.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0311hwp:master-id:royprsa;rspa.2016.03112016-11-23Research articles47221952016031120160311<![CDATA[Length filtration of the separable states]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160350?rss=1
We investigate the separable states of an arbitrary multi-partite quantum system with Hilbert space H of dimension d. The length L() of is defined as the smallest number of pure product states having as their mixture. The length filtration of the set of separable states, S, is the increasing chain S1'S2'···, where Si'={S:L()≤i}. We define the maximum length, Lmax=maxSL(), critical length, L_{crit}, and yet another special length, L_{c}, which was defined by a simple formula in one of our previous papers. The critical length indicates the first term in the length filtration whose dimension is equal to Dim S. We show that in general d≤L_{c}≤L_{crit}≤L_{max}≤d^{2}. We conjecture that the equality L_{crit}=L_{c} holds for all finite-dimensional multi-partite quantum systems. Our main result is that L_{crit}=L_{c} for the bipartite systems having a single qubit as one of the parties. This is accomplished by computing the rank of the Jacobian matrix of a suitable map having S as its range.
]]>2016-11-02T00:05:18-07:00info:doi/10.1098/rspa.2016.0350hwp:master-id:royprsa;rspa.2016.03502016-11-02Research articles47221952016035020160350<![CDATA[Gravity-capillary waves in finite depth on flows of constant vorticity]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160363?rss=1
This paper considers two-dimensional periodic gravity–capillary waves propagating steadily in finite depth on a linear shear current (constant vorticity). A perturbation series solution for steady periodic waves, accurate up to the third order, is derived using a classical Stokes expansion procedure, which allows us to include surface tension effects in the analysis of wave–current interactions in the presence of constant vorticity. The analytical results are then compared with numerical computations with the full equations. The main results are (i) the phase velocity is strongly dependent on the value of the vorticity; (ii) the singularities (Wilton singularities) in the Stokes expansion in powers of wave amplitude that correspond to a Bond number of 1/2 and 1/3, which are the consequences of the non-uniformity in the ordering of the Fourier coefficients, are found to be influenced by vorticity; (iii) different surface profiles of capillary–gravity waves are computed and the effect of vorticity on those profiles is shown to be important, in particular that the solutions exhibit type-2-like wave features, characterized by a secondary maximum on the surface profile with a trough between the two maxima.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0363hwp:master-id:royprsa;rspa.2016.03632016-11-23Research articles47221952016036320160363<![CDATA[Globalization and pollution: tele-connecting local primary PM2.5 emissions to global consumption]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160380?rss=1
Globalization pushes production and consumption to geographically diverse locations and generates a variety of sizeable opportunities and challenges. The distribution and associated effects of short-lived primary fine particulate matter (PM_{2.5}), a representative of local pollution, are significantly affected by the consumption through global supply chain. Tele-connection is used here to represent the link between production and consumption activity at large distances. In this study, we develop a global consumption-based primary PM_{2.5} emission inventory to track primary PM_{2.5} emissions embodied in the supply chain and evaluate the extent to which local PM_{2.5} emissions are triggered by international trade. We further adopt consumption-based accounting and identify the global original source that produced the emissions. We find that anthropogenic PM_{2.5} emissions from industrial sectors accounted for 24 Tg globally in 2007; approximately 30% (7.2 Tg) of these emissions were embodied in export of products principally from Brazil, South Africa, India and China (3.8 Tg) to developed countries. Large differences (up to 10 times) in the embodied emissions intensity between net importers and exporters greatly increased total global PM_{2.5} emissions. Tele-connecting production and consumption activity provides valuable insights with respect to mitigating long-range transboundary air pollution and prompts concerted efforts aiming at more environmentally conscious globalization.
]]>2016-11-16T03:18:34-08:00info:doi/10.1098/rspa.2016.0380hwp:master-id:royprsa;rspa.2016.03802016-11-16Research articles47221952016038020160380<![CDATA[Pointwise gradient bounds for degenerate semigroups (of UFG type)]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160442?rss=1
In this paper, we consider diffusion semigroups generated by second-order differential operators of degenerate type. The operators that we consider do not, in general, satisfy the Hörmander condition and are not hypoelliptic. In particular, instead of working under the Hörmander paradigm, we consider the so-called UFG (uniformly finitely generated) condition, introduced by Kusuoka and Strook in the 1980s. The UFG condition is weaker than the uniform Hörmander condition, the smoothing effect taking place only in certain directions (rather than in every direction, as it is the case when the Hörmander condition is assumed). Under the UFG condition, Kusuoka and Strook deduced sharp small time asymptotic bounds for the derivatives of the semigroup in the directions where smoothing occurs. In this paper, we study the large time asymptotics for the gradients of the diffusion semigroup in the same set of directions and under the same UFG condition. In particular, we identify conditions under which the derivatives of the diffusion semigroup in the smoothing directions decay exponentially in time. This paper constitutes, therefore, a stepping stone in the analysis of the long-time behaviour of diffusions which do not satisfy the Hörmander condition.
]]>2016-11-16T00:48:33-08:00info:doi/10.1098/rspa.2016.0442hwp:master-id:royprsa;rspa.2016.04422016-11-16Research articles47221952016044220160442<![CDATA[Self-assembling iron oxyhydroxide/oxide tubular structures: laboratory-grown and field examples from Rio Tinto]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160466?rss=1
Rio Tinto in southern Spain has become of increasing astrobiological significance, in particular for its similarity to environments on early Mars. We present evidence of tubular structures from sampled terraces in the stream bed at the source of the river, as well as ancient, now dry, terraces. This is the first reported finding of tubular structures in this particular environment. We propose that some of these structures could be formed through self-assembly via an abiotic mechanism involving templated precipitation around a fluid jet, a similar mechanism to that commonly found in so-called chemical gardens. Laboratory experiments simulating the formation of self-assembling iron oxyhydroxide tubes via chemical garden/chemobrionic processes form similar structures. Fluid-mechanical scaling analysis demonstrates that the proposed mechanism is plausible. Although the formation of tube structures is not itself a biosignature, the iron mineral oxidation gradients across the tube walls in laboratory and field examples may yield information about energy gradients and potentially habitable environments.
]]>2016-11-09T00:05:21-08:00info:doi/10.1098/rspa.2016.0466hwp:master-id:royprsa;rspa.2016.04662016-11-09Research articles47221952016046620160466<![CDATA[Thirty per cent contrast in secondary-electron imaging by scanning field-emission microscopy]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160475?rss=1
We perform scanning tunnelling microscopy (STM) in a regime where primary electrons are field-emitted from the tip and excite secondary electrons out of the target—the scanning field-emission microscopy regime (SFM). In the SFM mode, a secondary-electron contrast as high as 30% is observed when imaging a monoatomic step between a clean W(110)- and an Fe-covered W(110)-terrace. This is a figure of contrast comparable to STM. The apparent width of the monoatomic step attains the 1 nm mark, i.e. it is only marginally worse than the corresponding width observed in STM. The origin of the unexpected strong contrast in SFM is the material dependence of the secondary-electron yield and not the dependence of the transported current on the tip–target distance, typical of STM: accordingly, we expect that a technology combining STM and SFM will highlight complementary aspects of a surface while simultaneously making electrons, selected with nanometre spatial precision, available to a macroscopic environment for further processing.
]]>2016-11-02T00:05:18-07:00info:doi/10.1098/rspa.2016.0475hwp:master-id:royprsa;rspa.2016.04752016-11-02Research articles47221952016047520160475<![CDATA[Anomalous diffusion and transport in heterogeneous systems separated by a membrane]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160502?rss=1
Diffusion of particles in a heterogeneous system separated by a semipermeable membrane is investigated. The particle dynamics is governed by fractional diffusion equations in the bulk and by kinetic equations on the membrane, which characterizes an interface between two different media. The kinetic equations are solved by incorporating memory effects to account for anomalous diffusion and, consequently, non-Debye relaxations. A rich variety of behaviours for the particle distribution at the interface and in the bulk may be found, depending on the choice of characteristic times in the boundary conditions and on the fractional index of the modelling equations.
]]>2016-11-09T00:05:16-08:00info:doi/10.1098/rspa.2016.0502hwp:master-id:royprsa;rspa.2016.05022016-11-09Research articles47221952016050220160502<![CDATA[Closed-form evaluation of two-dimensional static lattice sums]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160510?rss=1
Closed-form formulae for the conditionally convergent two-dimensional (2D) static lattice sums S_{2} (for conductivity) and T_{2} (for elasticity) are deduced in terms of the complete elliptic integrals of the first and second kind. The obtained formulae yield asymptotic analytical formulae for the effective tensors of 2D composites with circular inclusions up to the third order in concentration. Exact relations between S_{2} and T_{2} for different lattices are established. In particular, the value S_{2}= for the square and hexagonal arrays is discussed and T_{2}=/2 for the hexagonal is deduced.
]]>2016-11-02T00:05:19-07:00info:doi/10.1098/rspa.2016.0510hwp:master-id:royprsa;rspa.2016.05102016-11-02Research articles47221952016051020160510<![CDATA[Steady streaming around a cylinder pair]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160522?rss=1
The steady streaming motion that appears around a pair of circular cylinders placed in a small-amplitude oscillatory flow is considered. Attention is focused on the case where the Stokes layer thickness at the surface of the cylinders is much smaller than the cylinder radius, and the streaming Reynolds number is of order unity or larger. In that case, the steady streaming velocity that persists at the edge of the Stokes layer can be imposed as a boundary condition to numerically solve the outer streaming motion that it drives in the bulk of the fluid. It is investigated how the gap width between the cylinders and the streaming Reynolds number affect the flow topology. The results are compared against experimental observations.
]]>2016-11-09T00:05:16-08:00info:doi/10.1098/rspa.2016.0522hwp:master-id:royprsa;rspa.2016.05222016-11-09Research articles47221952016052220160522<![CDATA[Tight focusing of light beams: a set of exact solutions]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160538?rss=1
Exact solutions of Maxwell's equations representing light beams are explored. The solutions satisfy all of the physical requirements of causal propagation and of energy, momentum and angular momentum conservation. A set of solutions can be found from a proto-beam by an imaginary translation along the beam direction. The proto-beam is given analytically in terms of the Bessel functions J_{0}, J_{1} and the Lommel functions U_{0}, U_{1}, or equivalently in terms of products of the spherical Bessel functions and Legendre polynomials. The complex wavefunction has rings of zeros in the focal plane. Localization of the focal region is to within about one half of the vacuum wavelength.
]]>2016-11-30T02:32:41-08:00info:doi/10.1098/rspa.2016.0538hwp:master-id:royprsa;rspa.2016.05382016-11-30Research articles47221952016053820160538<![CDATA[Contact probing of stretched membranes and adhesive interactions: graphene and other two-dimensional materials]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160550?rss=1
Contact probing is the preferable method for studying mechanical properties of thin two-dimensional (2D) materials. These studies are based on analysis of experimental force–displacement curves obtained by loading of a stretched membrane by a probe of an atomic force microscope or a nanoindenter. Both non-adhesive and adhesive contact interactions between such a probe and a 2D membrane are studied. As an example of the 2D materials, we consider a graphene crystal monolayer whose discrete structure is modelled as a 2D isotropic elastic membrane. Initially, for contact between a punch and the stretched circular membrane, we formulate and solve problems that are analogies to the Hertz-type and Boussinesq frictionless contact problems. A general statement for the slope of the force–displacement curve is formulated and proved. Then analogies to the JKR (Johnson, Kendall and Roberts) and the Boussinesq–Kendall contact problems in the presence of adhesive interactions are formulated. General nonlinear relations among the actual force, displacements and contact radius between a sticky membrane and an arbitrary axisymmetric indenter are derived. The dimensionless form of the equations for power-law shaped indenters has been analysed, and the explicit expressions are derived for the values of the pull-off force and corresponding critical contact radius.
]]>2016-11-16T00:05:25-08:00info:doi/10.1098/rspa.2016.0550hwp:master-id:royprsa;rspa.2016.05502016-11-16Research articles47221952016055020160550<![CDATA[Buckling of spherical shells revisited]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160577?rss=1
A study is presented of the post-buckling behaviour and imperfection sensitivity of complete spherical shells subject to uniform external pressure. The study builds on and extends the major contribution to spherical shell buckling by Koiter in the 1960s. Numerical results are presented for the axisymmetric large deflection behaviour of perfect spheres followed by an extensive analysis of the role axisymmetric imperfections play in reducing the buckling pressure. Several types of middle surface imperfections are considered including dimple-shaped undulations and sinusoidal-shaped equatorial undulations. Buckling occurs either as the attainment of a maximum pressure in the axisymmetric state or as a non-axisymmetric bifurcation from the axisymmetric state. Several new findings emerge: the abrupt mode localization that occurs immediately after the onset of buckling, the existence of an apparent lower limit to the buckling pressure for realistically large imperfections, and comparable reductions of the buckling pressure for dimple and sinusoidal equatorial imperfections.
]]>2016-11-16T00:05:25-08:00info:doi/10.1098/rspa.2016.0577hwp:master-id:royprsa;rspa.2016.05772016-11-16Research articles47221952016057720160577<![CDATA[Optimal energy harvesting from vortex-induced vibrations of cables]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160583?rss=1
Vortex-induced vibrations (VIV) of flexible cables are an example of flow-induced vibrations that can act as energy harvesting systems by converting energy associated with the spontaneous cable motion into electricity. This work investigates the optimal positioning of the harvesting devices along the cable, using numerical simulations with a wake oscillator model to describe the unsteady flow forcing. Using classical gradient-based optimization, the optimal harvesting strategy is determined for the generic configuration of a flexible cable fixed at both ends, including the effect of flow forces and gravity on the cable’s geometry. The optimal strategy is found to consist systematically in a concentration of the harvesting devices at one of the cable’s ends, relying on deformation waves along the cable to carry the energy towards this harvesting site. Furthermore, we show that the performance of systems based on VIV of flexible cables is significantly more robust to flow velocity variations, in comparison with a rigid cylinder device. This results from two passive control mechanisms inherent to the cable geometry: (i) the adaptability to the flow velocity of the fundamental frequencies of cables through the flow-induced tension and (ii) the selection of successive vibration modes by the flow velocity for cables with gravity-induced tension.
]]>2016-11-02T00:05:19-07:00info:doi/10.1098/rspa.2016.0583hwp:master-id:royprsa;rspa.2016.05832016-11-02Research articles47221952016058320160583<![CDATA[The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160588?rss=1
In this paper, we implement the Fokas method to study initial-boundary value problems of the mixed coupled nonlinear Schrödinger equation formulated on the half-line with Lax pairs involving 3x3 matrices. The solution can be written in terms of the solution to a 3x3 Riemann–Hilbert problem. The relevant jump matrices are explicitly expressed in terms of the matrix-value spectral functions s(k) and S(k), which are determined by the initial values and boundary values at x=0, respectively. Some of these boundary values are unknown; however, using the fact that these specific functions satisfy a certain global relation, the unknown boundary values can be expressed in terms of the given initial and boundary data.
]]>2016-11-30T02:32:41-08:00info:doi/10.1098/rspa.2016.0588hwp:master-id:royprsa;rspa.2016.05882016-11-30Research articles47221952016058820160588<![CDATA[Analytic materials]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160613?rss=1
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an integer p. If p takes its maximum value, then we have a complete analytic material. Otherwise, it is incomplete analytic material of rank p. For two-dimensional materials, further progress can be made in the identification of analytic materials by using the well-known fact that a 90^{°} rotation applied to a divergence-free field in a simply connected domain yields a curl-free field, and this can then be expressed as the gradient of a potential. Other exact results for the fields in inhomogeneous media are reviewed. Also reviewed is the subject of metamaterials, as these materials provide a way of realizing desirable coefficients in the equations.
]]>2016-11-16T00:05:25-08:00info:doi/10.1098/rspa.2016.0613hwp:master-id:royprsa;rspa.2016.06132016-11-16Research articles47221952016061320160613<![CDATA[The quantum CP-violating kaon system reproduced in the electronic laboratory]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160615?rss=1
The equivalence between the Schrödinger dynamics of a quantum system with a finite number of basis states and a classical dynamics is realized in terms of electric networks. The isomorphism that connects in a univocal way both dynamical systems was applied to the case of neutral mesons, kaons in particular, and the class of electric networks univocally related to the quantum system was analysed. Moreover, under CPT invariance, the relevant parameter that measures CP violation in the kaon system is reinterpreted in terms of network parameters. All these results were explicitly shown by means of both a numerical simulation of the implied networks and by constructing the corresponding circuits.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0615hwp:master-id:royprsa;rspa.2016.06152016-11-23Research articles47221952016061520160615<![CDATA[Electrodynamics of spoof plasmons in periodically corrugated waveguides]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160616?rss=1
States of the electromagnetic field confined near a periodically corrugated surface of a perfect conductor, spoof surface plasmon polaritons (SSPP), are approached systematically based on the developed adaptation of the mode matching technique to the transfer matrix formalism. Within this approach, in the approximation of narrow grooves, systems with arbitrary transversal structure can be investigated straightforwardly, thus lifting the restrictions of the effective medium description and usual implementations of mode matching. A compact expression for the SSPP coupling parameter accounting for the effect of higher Bloch modes is found. The results of the general analysis are applied for studying the effect of dielectric environment on SSPP spectra. It is shown that the effective SSPP plasma frequency is unaffected by the dielectric constant of the medium outside of the grooves and the main effect of sufficiently wide dielectric slabs covering the corrugated surface is described by simple rescaling of the maximal value of the Bloch wavenumber and the coupling parameter. Additionally, in the case of a thin dielectric layer, it is shown that SSPP are sensitive to variation of the thickness of the layer on the sub-wavelength scale.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0616hwp:master-id:royprsa;rspa.2016.06162016-11-23Research articles47221952016061620160616<![CDATA[On the continuum limit for a semidiscrete Hirota equation]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160628?rss=1
In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as ->0.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0628hwp:master-id:royprsa;rspa.2016.06282016-11-23Research articles47221952016062820160628<![CDATA[Guided wave tomography with an improved scattering model]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160643?rss=1
Producing accurate thickness maps of corrosion damage is of great importance for assessing life in the petrochemical industry. Guided wave tomography provides a solution for this, by sending guided waves through the region of interest, then using tomographic imaging techniques to reconstruct the thickness map, importantly eliminating the need to take measurements at all points across the surface. However, to achieve accurate maps, the imaging algorithm must account for the way in which the guided waves interact with corrosion defects, and the complex scattering which occurs. Traditional approaches have exploited the dispersive nature of guided waves: a velocity map is produced from a dataset, then converted to thickness using the dispersion relationship. However, these relationships are derived for plates of constant thickness, which is not the case in the majority of defects, causing significant inaccuracies to exist in the images. This paper develops a more sophisticated inversion solution which accounts for the full-guided wave scattering, enabling more accurate images with resolution better than a wavelength, compared with two wavelengths previously. This is demonstrated with simulated and experimental data. The speed and stability of the algorithm in the presence of random noise and systematic errors is also demonstrated.
]]>2016-11-02T00:05:19-07:00info:doi/10.1098/rspa.2016.0643hwp:master-id:royprsa;rspa.2016.06432016-11-02Research articles47221952016064320160643<![CDATA[Thermal convection in a magnetized conducting fluid with the Cattaneo-Christov heat-flow model]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160649?rss=1
By substituting the Cattaneo–Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number Rc(c)(Q) which exhibits inhibition of convection by the field according to Rc(c)->2Q as Q->, where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number Rc(o)(Q,P1,P2,C) is given by a more complicated function of the thermal Prandtl number P1, magnetic Prandtl number P2 and Cattaneo number C. To elucidate features of this dependence, we neglect P2 (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour Rc(o)->Q/C, as Q->. One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value C_{T}(Q); indeed, crucially we show that when Q is large, CT1/Q, meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.
]]>2016-11-16T00:05:25-08:00info:doi/10.1098/rspa.2016.0649hwp:master-id:royprsa;rspa.2016.06492016-11-16Research articles47221952016064920160649<![CDATA[Small-on-large geometric anelasticity]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160659?rss=1
In this paper, we are concerned with finding exact solutions for the stress fields of nonlinear solids with non-symmetric distributions of defects (or more generally finite eigenstrains) that are small perturbations of symmetric distributions of defects with known exact solutions. In the language of geometric mechanics, this corresponds to finding a deformation that is a result of a perturbation of the metric of the Riemannian material manifold. We present a general framework that can be used for a systematic analysis of this class of anelasticity problems. This geometric formulation can be thought of as a material analogue of the classical small-on-large theory in nonlinear elasticity. We use the present small-on-large anelasticity theory to find exact solutions for the stress fields of some non-symmetric distributions of screw dislocations in incompressible isotropic solids.
]]>2016-11-09T00:05:16-08:00info:doi/10.1098/rspa.2016.0659hwp:master-id:royprsa;rspa.2016.06592016-11-09Research articles47221952016065920160659<![CDATA[Photophysics of sunscreen molecules in the gas phase: a stepwise approach towards understanding and developing next-generation sunscreens]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160677?rss=1
The relationship between exposure to ultraviolet (UV) radiation and skin cancer urges the need for extra photoprotection, which is presently provided by widespread commercially available sunscreen lotions. Apart from having a large absorption cross section in the UVA and UVB regions of the electromagnetic spectrum, the chemical absorbers in these photoprotective products should also be able to dissipate the excess energy in a safe way, i.e. without releasing photoproducts or inducing any further, harmful, photochemistry. While sunscreens are tested for both their photoprotective capability and dermatological compatibility, phenomena occurring at the molecular level upon absorption of UV radiation are largely overlooked. To date, there is only a limited amount of information regarding the photochemistry and photophysics of these sunscreen molecules. However, a thorough understanding of the intrinsic mechanisms by which popular sunscreen molecular constituents dissipate excess energy has the potential to aid in the design of more efficient, safer sunscreens. In this review, we explore the potential of using gas-phase frequency- and time-resolved spectroscopies in an effort to better understand the photoinduced excited-state dynamics, or photodynamics, of sunscreen molecules. Complementary computational studies are also briefly discussed. Finally, the future outlook of expanding these gas-phase studies into the solution phase is considered.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0677hwp:master-id:royprsa;rspa.2016.06772016-11-23Review articles47221952016067720160677<![CDATA[Self-locking degree-4 vertex origami structures]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160682?rss=1
A generic degree-4 vertex (4-vertex) origami possesses one continuous degree-of-freedom for rigid folding, and this folding process can be stopped when two of its facets bind together. Such facet-binding will induce self-locking so that the overall structure stays at a pre-specified configuration without additional locking elements or actuators. Self-locking offers many promising properties, such as programmable deformation ranges and piecewise stiffness jumps, that could significantly advance many adaptive structural systems. However, despite its excellent potential, the origami self-locking features have not been well studied, understood, and used. To advance the state of the art, this research conducts a comprehensive investigation on the principles of achieving and harnessing self-locking in 4-vertex origami structures. Especially, for the first time, this study expands the 4-vertex structure construction from single-component to dual-component designs and investigates their self-locking behaviours. By exploiting various tessellation designs, this research discovers that the dual-component designs offer the origami structures with extraordinary attributes that the single-component structures do not have, which include the existence of flat-folded locking planes, programmable locking points and deformability. Finally, proof-of-concept experiments investigate how self-locking can effectively induce piecewise stiffness jumps. The results of this research provide new scientific knowledge and a systematic framework for the design, analysis and utilization of self-locking origami structures for many potential engineering applications.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0682hwp:master-id:royprsa;rspa.2016.06822016-11-23Research articles47221952016068220160682<![CDATA[Eliminating incident subtraction in diffraction tomography]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160707?rss=1
Diffraction tomography is a powerful algorithm for producing high-resolution quantitative reconstructions across a wide range of applications. A major drawback of the method is that it operates on the scattered field, which cannot generally be directly measured, but must instead be calculated by subtracting the incident field, i.e. the equivalent field with no scatterer present. Unfortunately, often the incident field is not measurable and hence must be estimated, causing errors. This paper highlights an important, but not widely recognized, result: for particular widely used formulations of the algorithm, the subtraction of the incident field is unnecessary, and the algorithm can actually be applied directly to measured signals. The theory behind this is derived, showing that the incident field will vanish under far-field conditions, and the result is demonstrated in practice. Tests with subsampled arrays show that aliasing artefacts can appear, but can be removed with a filter at the expense of resolution. The incident field also has no effect for a variety of array configurations tested. Finally, the performance in the presence of both correlated and uncorrelated errors is confirmed, in all cases demonstrating that the incident field has a negligible effect on the final reconstruction.
]]>2016-11-30T02:32:41-08:00info:doi/10.1098/rspa.2016.0707hwp:master-id:royprsa;rspa.2016.07072016-11-30Research articles47221952016070720160707<![CDATA[Hydroelectromechanical modelling of a piezoelectric wave energy converter]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160715?rss=1
We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.
]]>2016-11-23T01:26:18-08:00info:doi/10.1098/rspa.2016.0715hwp:master-id:royprsa;rspa.2016.07152016-11-23Research articles47221952016071520160715<![CDATA[Mechanics of advection of suspended particles in turbulent flow]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/472/2195/20160749?rss=1
In this paper, we explore the mechanics and the turbulent structure of two-phase (fluid–solid particle) flow system, for the first time, by considering the dynamic equilibrium coupled with suspended solid particle concentration, fluid flow and energetics of the two-phase flow system. The continuity, momentum and turbulent kinetic energy (TKE) equations of the fluid and the solid phases are treated separately to derive a generalized relationship of the two-phase flow system aided by suitable closure relationships. The results obtained from the numerical solution of resulting equations show that the particle concentration and the TKE diminish with an increase in the Rouse number, while the horizontal velocity component increases. On the other hand, the TKE flux, diffusion and production rates increase with an increase in the Rouse number, while the TKE dissipation rate decreases. In the vicinity of the reference level (that is, the hypothetical level from which the particles come in suspension), the Kolmogorov number increases with an increase in the Rouse number. However, as the vertical distance increases, this behaviour becomes reverse. A close observation of the turbulent length scales reveals that the Prandtl's mixing length decreases with an increase in the Rouse number, but the Taylor microscale and the Kolmogorov length scale increase.
]]>2016-11-30T02:32:41-08:00info:doi/10.1098/rspa.2016.0749hwp:master-id:royprsa;rspa.2016.07492016-11-30Research articles47221952016074920160749