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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- current issue1471-2946March, 2017Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[A laboratory study of nonlinear changes in the directionality of extreme seas]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160290?rss=1
This paper concerns the description of surface water waves, specifically nonlinear changes in the directionality. Supporting calculations are provided to establish the best method of directional wave generation, the preferred method of directional analysis and the inputs on which such a method should be based. These calculations show that a random directional method, in which the phasing, amplitude and direction of propagation of individual wave components are chosen randomly, has benefits in achieving the required ergodicity. In terms of analysis procedures, the extended maximum entropy principle, with inputs based upon vector quantities, produces the best description of directionality. With laboratory data describing the water surface elevation and the two horizontal velocity components at a single point, several steep sea states are considered. The results confirm that, as the steepness of a sea state increases, the overall directionality of the sea state reduces. More importantly, it is also shown that the largest waves become less spread or more unidirectional than the sea state as a whole. This provides an important link to earlier descriptions of deterministic wave groups produced by frequency focusing, helps to explain recent field observations and has important practical implications for the design of marine structures and vessels.
]]>2017-03-08T01:00:53-08:00info:doi/10.1098/rspa.2016.0290hwp:master-id:royprsa;rspa.2016.02902017-03-08Research articles47321992016029020160290<![CDATA[Fluid dynamics of acoustic and hydrodynamic cavitation in hydraulic power systems]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160345?rss=1
Cavitation is the transition from a liquid to a vapour phase, due to a drop in pressure to the level of the vapour tension of the fluid. Two kinds of cavitation have been reviewed here: acoustic cavitation and hydrodynamic cavitation. As acoustic cavitation in engineering systems is related to the propagation of waves through a region subjected to liquid vaporization, the available expressions of the sound speed are discussed. One of the main effects of hydrodynamic cavitation in the nozzles and orifices of hydraulic power systems is a reduction in flow permeability. Different discharge coefficient formulae are analysed in this paper: the Reynolds number and the cavitation number result to be the key fluid dynamical parameters for liquid and cavitating flows, respectively. The latest advances in the characterization of different cavitation regimes in a nozzle, as the cavitation number reduces, are presented. The physical cause of choked flows is explained, and an analogy between cavitation and supersonic aerodynamic flows is proposed. The main approaches to cavitation modelling in hydraulic power systems are also reviewed: these are divided into homogeneous-mixture and two-phase models. The homogeneous-mixture models are further subdivided into barotropic and baroclinic models. The advantages and disadvantages of an implementation of the complete Rayleigh–Plesset equation are examined.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0345hwp:master-id:royprsa;rspa.2016.03452017-03-15Review articles47321992016034520160345<![CDATA[Equilibrium shapes of a heterogeneous bubble in an electric field: a variational formulation and numerical verifications]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160494?rss=1
The equilibrium shape of a bubble/droplet in an electric field is important for electrowetting over dielectrics (EWOD), electrohydrodynamic (EHD) enhancement for heat transfer and electro-deformation of a single biological cell among others. In this work, we develop a general variational formulation in account of electro-mechanical couplings. In the context of EHD, we identify the free energy functional and the associated energy minimization problem that determines the equilibrium shape of a bubble in an electric field. Based on this variational formulation, we implement a fixed mesh level-set gradient method for computing the equilibrium shapes. This numerical scheme is efficient and validated by comparing with analytical solutions at the absence of electric field and experimental results at the presence of electric field. We also present simulation results for zero gravity which will be useful for space applications. The variational formulation and numerical scheme are anticipated to have broad applications in areas of EWOD, EHD and electro-deformation in biomechanics.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0494hwp:master-id:royprsa;rspa.2016.04942017-03-15Research articles47321992016049420160494<![CDATA[Reciprocal absorbing boundary condition for the time-domain numerical analysis of wave motion in unbounded layered media]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160528?rss=1
A global absorbing boundary condition is introduced for the time-domain numerical analysis of wave motion in unbounded layered media. This condition is obtained by applying the reciprocity theorem for linearly viscoelastic media. Example problems are solved towards evaluation of the accuracy and effectiveness of the approach developed in this work.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0528hwp:master-id:royprsa;rspa.2016.05282017-03-22Research articles47321992016052820160528<![CDATA[Landslides and tsunamis predicted by incompressible smoothed particle hydrodynamics (SPH) with application to the 1958 Lituya Bay event and idealized experiment]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160674?rss=1
Tsunamis caused by landslides may result in significant destruction of the surroundings with both societal and industrial impact. The 1958 Lituya Bay landslide and tsunami is a recent and well-documented terrestrial landslide generating a tsunami with a run-up of 524 m. Although recent computational techniques have shown good performance in the estimation of the run-up height, they fail to capture all the physical processes, in particular, the landslide-entry profile and interaction with the water. Smoothed particle hydrodynamics (SPH) is a versatile numerical technique for describing free-surface and multi-phase flows, particularly those that exhibit highly nonlinear deformation in landslide-generated tsunamis. In the current work, the novel multi-phase incompressible SPH method with shifting is applied to the Lituya Bay tsunami and landslide and is the first methodology able to reproduce realistically both the run-up and landslide-entry as documented in a benchmark experiment. The method is the first paper to develop a realistic implementation of the physics that in addition to the non-Newtonian rheology of the landslide includes turbulence in the water phase and soil saturation. Sensitivity to the experimental initial conditions is also considered. This work demonstrates the ability of the proposed method in modelling challenging environmental multi-phase, non-Newtonian and turbulent flows.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0674hwp:master-id:royprsa;rspa.2016.06742017-03-22Research articles47321992016067420160674<![CDATA[Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160681?rss=1
We study the higher-order generalized nonlinear Schrödinger (NLS) equation describing the propagation of ultrashort optical pulse in optical fibres. By using Darboux transformation, we derive the superregular breather solution that develops from a small localized perturbation. This type of solution can be used to characterize the nonlinear stage of the modulation instability (MI) of the condensate. In particular, we show some novel characteristics of the nonlinear stage of MI arising from higher-order effects: (i) coexistence of a quasi-Akhmediev breather and a multipeak soliton; (ii) two multipeak solitons propagation in opposite directions; (iii) a beating pattern followed by two multipeak solitons in the same direction. It is found that these patterns generated from a small localized perturbation do not have the analogues in the standard NLS equation. Our results enrich Zakharov’s theory of superregular breathers and could provide helpful insight on the nonlinear stage of MI in presence of the higher-order effects.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0681hwp:master-id:royprsa;rspa.2016.06812017-03-08Research articles47321992016068120160681<![CDATA[A restatement of the natural science evidence concerning catchment-based 'natural flood management in the UK]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160706?rss=1
Flooding is a very costly natural hazard in the UK and is expected to increase further under future climate change scenarios. Flood defences are commonly deployed to protect communities and property from flooding, but in recent years flood management policy has looked towards solutions that seek to mitigate flood risk at flood-prone sites through targeted interventions throughout the catchment, sometimes using techniques which involve working with natural processes. This paper describes a project to provide a succinct summary of the natural science evidence base concerning the effectiveness of catchment-based ‘natural’ flood management in the UK. The evidence summary is designed to be read by an informed but not technically specialist audience. Each evidence statement is placed into one of four categories describing the nature of the underlying information. The evidence summary forms the appendix to this paper and an annotated bibliography is provided in the electronic supplementary material.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0706hwp:master-id:royprsa;rspa.2016.07062017-03-15Review article47321992016070620160706<![CDATA[Device-independent tests of quantum channels]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160721?rss=1
We develop a device-independent framework for testing quantum channels. That is, we falsify a hypothesis about a quantum channel based only on an observed set of input–output correlations. Formally, the problem consists of characterizing the set of input–output correlations compatible with any arbitrary given quantum channel. For binary (i.e. two input symbols, two output symbols) correlations, we show that extremal correlations are always achieved by orthogonal encodings and measurements, irrespective of whether or not the channel preserves commutativity. We further provide a full, closed-form characterization of the sets of binary correlations in the case of: (i) any dihedrally covariant qubit channel (such as any Pauli and amplitude-damping channels) and (ii) any universally-covariant commutativity-preserving channel in an arbitrary dimension (such as any erasure, depolarizing, universal cloning and universal transposition channels).
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0721hwp:master-id:royprsa;rspa.2016.07212017-03-15Research articles47321992016072120160721<![CDATA[The cross-over to magnetostrophic convection in planetary dynamo systems]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160731?rss=1
Global scale magnetostrophic balance, in which Lorentz and Coriolis forces comprise the leading-order force balance, has long been thought to describe the natural state of planetary dynamo systems. This argument arises from consideration of the linear theory of rotating magnetoconvection. Here we test this long-held tenet by directly comparing linear predictions against dynamo modelling results. This comparison shows that dynamo modelling results are not typically in the global magnetostrophic state predicted by linear theory. Then, in order to estimate at what scale (if any) magnetostrophic balance will arise in nonlinear dynamo systems, we carry out a simple scaling analysis of the Elsasser number , yielding an improved estimate of the ratio of Lorentz and Coriolis forces. From this, we deduce that there is a magnetostrophic cross-over length scale, LX(o2/Rmo)D, where _{o} is the linear (or traditional) Elsasser number, Rm_{o} is the system scale magnetic Reynolds number and D is the length scale of the system. On scales well above LX, magnetostrophic convection dynamics should not be possible. Only on scales smaller than LX should it be possible for the convective behaviours to follow the predictions for the magnetostrophic branch of convection. Because LX is significantly smaller than the system scale in most dynamo models, their large-scale flows should be quasi-geostrophic, as is confirmed in many dynamo simulations. Estimating _{o}~=1 and Rm_{o}~=10^{3} in Earth’s core, the cross-over scale is approximately 1/1000 that of the system scale, suggesting that magnetostrophic convection dynamics exists in the core only on small scales below those that can be characterized by geomagnetic observations.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0731hwp:master-id:royprsa;rspa.2016.07312017-03-15Special feature47321992016073120160731<![CDATA[Incompatibility-governed elasto-plasticity for continua with dislocations]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160734?rss=1
In this paper, a novel model for elasto-plastic continua is presented and developed from the ground up. It is based on the interdependence between plasticity, dislocation motion and strain incompatibility. A generalized form of the equilibrium equations is provided, with as additional variables, the strain incompatibility and an internal thermodynamic variable called incompatibility modulus, which drives the plastic behaviour of the continuum. The traditional equations of elasticity are recovered as this modulus tends to infinity, while perfect plasticity corresponds to the vanishing limit. The overall nonlinear scheme is determined by the solution of these equations together with the computation of the topological derivative of the dissipation, in order to comply with the second principle of thermodynamics.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0734hwp:master-id:royprsa;rspa.2016.07342017-03-08Research articles47321992016073420160734<![CDATA[Efficient generation of receiver operating characteristics for the evaluation of damage detection in practical structural health monitoring applications]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160736?rss=1
Permanently installed guided wave monitoring systems are attractive for monitoring large structures. By frequently interrogating the test structure over a long period of time, such systems have the potential to detect defects much earlier than with conventional one-off inspection, and reduce the time and labour cost involved. However, for the systems to be accepted under real operational conditions, their damage detection performance needs to be evaluated in these practical settings. The receiver operating characteristic (ROC) is an established performance metric for one-off inspections, but the generation of the ROC requires many test structures with realistic damage growth at different locations and different environmental conditions, and this is often impractical. In this paper, we propose an evaluation framework using experimental data collected over multiple environmental cycles on an undamaged structure with synthetic damage signatures added by superposition. Recent advances in computation power enable examples covering a wide range of practical scenarios to be generated, and for multiple cases of each scenario to be tested so that the statistics of the performance can be evaluated. The proposed methodology has been demonstrated using data collected from a laboratory pipe specimen over many temperature cycles, superposed with damage signatures predicted for a flat-bottom hole growing at different rates at various locations. Three damage detection schemes, conventional baseline subtraction, singular value decomposition (SVD) and independent component analysis (ICA), have been evaluated. It has been shown that in all cases, the component methods perform significantly better than the residual method, with ICA generally the better of the two. The results have been validated using experimental data monitoring a pipe in which a flat-bottom hole was drilled and enlarged over successive temperature cycles. The methodology can be used to evaluate the performance of an installed monitoring system and to show whether it is capable of detecting particular damage growth at any given location. It will enable monitoring results to be evaluated rigorously and will be valuable in the development of safety cases.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0736hwp:master-id:royprsa;rspa.2016.07362017-03-22Research articles47321992016073620160736<![CDATA[History dependence and the continuum approximation breakdown: the impact of domain growth on Turings instability]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160744?rss=1
A diffusively driven instability has been hypothesized as a mechanism to drive spatial self-organization in biological systems since the seminal work of Turing. Such systems are often considered on a growing domain, but traditional theoretical studies have only treated the domain size as a bifurcation parameter, neglecting the system non-autonomy. More recently, the conditions for a diffusively driven instability on a growing domain have been determined under stringent conditions, including slow growth, a restriction on the temporal interval over which the prospect of an instability can be considered and a neglect of the impact that time evolution has on the stability properties of the homogeneous reference state from which heterogeneity emerges. Here, we firstly relax this latter assumption and observe that the conditions for the Turing instability are much more complex and depend on the history of the system in general. We proceed to relax all the above constraints, making analytical progress by focusing on specific examples. With faster growth, instabilities can grow transiently and decay, making the prediction of a prospective Turing instability much more difficult. In addition, arbitrarily high spatial frequencies can destabilize, in which case the continuum approximation is predicted to break down.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0744hwp:master-id:royprsa;rspa.2016.07442017-03-15Research articles47321992016074420160744<![CDATA[SPARSE--A subgrid particle averaged Reynolds stress equivalent model: testing with a priori closure]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160769?rss=1
A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.
]]>2017-03-22T01:44:10-07:00info:doi/10.1098/rspa.2016.0769hwp:master-id:royprsa;rspa.2016.07692017-03-22Research articles47321992016076920160769<![CDATA[Identifying the significance of nonlinear normal modes]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160789?rss=1
Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.
]]>2017-03-01T00:05:20-08:00info:doi/10.1098/rspa.2016.0789hwp:master-id:royprsa;rspa.2016.07892017-03-01Research articles47321992016078920160789<![CDATA[G-Strands on symmetric spaces]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160795?rss=1
We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S^{1} and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa–Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions.
]]>2017-03-08T01:00:53-08:00info:doi/10.1098/rspa.2016.0795hwp:master-id:royprsa;rspa.2016.07952017-03-08Research articles47321992016079520160795<![CDATA[Analytical results regarding electrostatic resonances of surface phonon/plasmon polaritons: separation of variables with a twist]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160796?rss=1
The boundary integral equation (BIE) method ascertains explicit relations between localized surface phonon and plasmon polariton resonances and the eigenvalues of its associated electrostatic operator. We show that group-theoretical analysis of the Laplace equation can be used to calculate the full set of eigenvalues and eigenfunctions of the electrostatic operator for shapes and shells described by separable coordinate systems. These results not only unify and generalize many existing studies, but also offer us the opportunity to expand the study of phenomena such as cloaking by anomalous localized resonance. Hence, we calculate the eigenvalues and eigenfunctions of elliptic and circular cylinders. We illustrate the benefits of using the BIE method to interpret recent experiments involving localized surface phonon polariton resonances and the size scaling of plasmon resonances in graphene nanodiscs. Finally, symmetry-based operator analysis can be extended from the electrostatic to the full-wave regime. Thus, bound states of light in the continuum can be studied for shapes beyond spherical configurations.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0796hwp:master-id:royprsa;rspa.2016.07962017-03-15Research articles47321992016079620160796<![CDATA[Modelling damped acoustic waves by a dissipation-preserving conformal symplectic method]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160798?rss=1
We propose a novel stable and efficient dissipation-preserving method for acoustic wave propagations in attenuating media with both correct phase and amplitude. Through introducing the conformal multi-symplectic structure, the intrinsic dissipation law and the conformal symplectic conservation law are revealed for the damped acoustic wave equation. The proposed algorithm is exactly designed to preserve a discrete version of the conformal symplectic conservation law. More specifically, two subsystems in conjunction with the original damped wave equation are derived. One is actually the conservative Hamiltonian wave equation and the other is a dissipative linear ordinary differential equation (ODE) system. Standard symplectic method is devoted to the conservative system, whereas the analytical solution is obtained for the ODE system. An explicit conformal symplectic scheme is constructed by concatenating these two parts of solutions by the Strang splitting technique. Stability analysis and convergence tests are given thereafter. A benchmark model in homogeneous media is presented to demonstrate the effectiveness and advantage of our method in suppressing numerical dispersion and preserving the energy dissipation. Further numerical tests show that our proposed method can efficiently capture the dissipation in heterogeneous media.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0798hwp:master-id:royprsa;rspa.2016.07982017-03-08Research articles47321992016079820160798<![CDATA[Rapidly convergent quasi-periodic Green functions for scattering by arrays of cylinders--including Wood anomalies]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160802?rss=1
This paper presents a full-spectrum Green-function methodology (which is valid, in particular, at and around Wood-anomaly frequencies) for evaluation of scattering by periodic arrays of cylinders of arbitrary cross section—with application to wire gratings, particle arrays and reflectarrays and, indeed, general arrays of conducting or dielectric bounded obstacles under both transverse electric and transverse magnetic polarized illumination. The proposed method, which, for definiteness, is demonstrated here for arrays of perfectly conducting particles under transverse electric polarization, is based on the use of the shifted Green-function method introduced in a recent contribution (Bruno & Delourme 2014 J. Computat. Phys.262, 262–290 (doi:10.1016/j.jcp.2013.12.047)). A certain infinite term arises at Wood anomalies for the cylinder-array problems considered here that is not present in the previous rough-surface case. As shown in this paper, these infinite terms can be treated via an application of ideas related to the Woodbury–Sherman–Morrison formulae. The resulting approach, which is applicable to general arrays of obstacles even at and around Wood-anomaly frequencies, exhibits fast convergence and high accuracies. For example, a few hundreds of milliseconds suffice for the proposed approach to evaluate solutions throughout the resonance region (wavelengths comparable to the period and cylinder sizes) with full single-precision accuracy.
]]>2017-03-01T00:05:20-08:00info:doi/10.1098/rspa.2016.0802hwp:master-id:royprsa;rspa.2016.08022017-03-01Research articles47321992016080220160802<![CDATA[Efficient computation of null geodesics with applications to coherent vortex detection]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160807?rss=1
Recent results suggest that boundaries of coherent fluid vortices (elliptic coherent structures) can be identified as closed null geodesics of appropriate Lorentzian metrics defined on the flow domain. Here we derive an automated method for computing such null geodesics based on the geometry of the underlying geodesic flow. Our approach simplifies and improves existing procedures for computing variationally defined Eulerian and Lagrangian vortex boundaries. As an illustration, we compute objective vortex boundaries from satellite-inferred ocean velocity data. A MATLAB implementation of our method is available at https://github.com/MattiaSerra/Closed-Null-Geodesics-2D.
]]>2017-03-01T00:43:08-08:00info:doi/10.1098/rspa.2016.0807hwp:master-id:royprsa;rspa.2016.08072017-03-01Research articles47321992016080720160807<![CDATA[A biochemo-mechano coupled, computational model combining membrane transport and pericellular proteolysis in tissue mechanics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160812?rss=1
We present a computational model for the interaction of surface- and volume-bound scalar transport and reaction processes with a deformable porous medium. The application in mind is pericellular proteolysis, i.e. the dissolution of the solid phase of the extracellular matrix (ECM) as a response to the activation of certain chemical species at the cell membrane and in the vicinity of the cell. A poroelastic medium model represents the extra cellular scaffold and the interstitial fluid flow, while a surface-bound transport model accounts for the diffusion and reaction of membrane-bound chemical species. By further modelling the volume-bound transport, we consider the advection, diffusion and reaction of sequestered chemical species within the extracellular scaffold. The chemo-mechanical coupling is established by introducing a continuum formulation for the interplay of reaction rates and the mechanical state of the ECM. It is based on known experimental insights and theoretical work on the thermodynamics of porous media and degradation kinetics of collagen fibres on the one hand and a damage-like effect of the fibre dissolution on the mechanical integrity of the ECM on the other hand. The resulting system of partial differential equations is solved via the finite-element method. To the best of our knowledge, it is the first computational model including contemporaneously the coupling between (i) advection–diffusion–reaction processes, (ii) interstitial flow and deformation of a porous medium, and (iii) the chemo-mechanical interaction impelled by the dissolution of the ECM. Our numerical examples show good agreement with experimental data. Furthermore, we outline the capability of the methodology to extend existing numerical approaches towards a more comprehensive model for cellular biochemo-mechanics.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0812hwp:master-id:royprsa;rspa.2016.08122017-03-08Research articles47321992016081220160812<![CDATA[Biofriendly nanocomposite containers with inhibition properties for the protection of metallic surfaces]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160827?rss=1
An attempt to combine two ‘green’ compounds in nanocomposite microcontainers in order to increase protection properties of waterborne acryl-styrene copolymer (ASC) coatings has been made. N-lauroylsarcosine (NLS) served as a corrosion inhibitor, and linseed oil (LO) as a carrier-forming component. LO is compatible with this copolymer and can impart to the coating self-healing properties. For the evaluation of the protective performance, three types of coatings were compared. In the first two, NLS was introduced in the coating formulation in the forms of free powder and micro-containers filled with LO, correspondingly. The last one was a standard ASC coating without inhibitor at all. Low-carbon steel substrates were coated by these formulations by spraying and subjected subsequently to the neutral salt spray test according to DIN ISO 9227. Results of these tests as well as the data obtained by electrochemical study suggest that such containers can be used for the improvement of adhesion of ASC-based coatings to the substrate and for the enhancement of their protective performance upon integrity damage, whereas the barrier properties of intact coatings were decreased.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0827hwp:master-id:royprsa;rspa.2016.08272017-03-22Research articles47321992016082720160827<![CDATA[Comment on 'Are some people suffering as a result of increasing mass exposure of the public to ultrasound in air?]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160828?rss=1
A number of queries regarding the paper ‘Are some people suffering as a result of increasing mass exposure of the public to ultrasound in air?’ (Leighton 2016 Proc. R. Soc. A472, 20150624 (doi:10.1098/rspa.2015.0624)) have been sent in from readers, almost all based around some or all of a small set of questions. These can be grouped into issues of engineering, human factors and timeliness. Those issues (represented by the most typical wording used in queries) and my responses are summarized in this comment.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0828hwp:master-id:royprsa;rspa.2016.08282017-03-15Comment47321992016082820160828<![CDATA[Mechanics of ultrasound elastography]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160841?rss=1
Ultrasound elastography enables in vivo measurement of the mechanical properties of living soft tissues in a non-destructive and non-invasive manner and has attracted considerable interest for clinical use in recent years. Continuum mechanics plays an essential role in understanding and improving ultrasound-based elastography methods and is the main focus of this review. In particular, the mechanics theories involved in both static and dynamic elastography methods are surveyed. They may help understand the challenges in and opportunities for the practical applications of various ultrasound elastography methods to characterize the linear elastic, viscoelastic, anisotropic elastic and hyperelastic properties of both bulk and thin-walled soft materials, especially the in vivo characterization of biological soft tissues.
]]>2017-03-01T00:05:20-08:00info:doi/10.1098/rspa.2016.0841hwp:master-id:royprsa;rspa.2016.08412017-03-01Review articles47321992016084120160841<![CDATA[Emerging surface characterization techniques for carbon steel corrosion: a critical brief review]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160852?rss=1
Carbon steel is a preferred construction material in many industrial and domestic applications, including oil and gas pipelines, where corrosion mitigation using film-forming corrosion inhibitor formulations is a widely accepted method. This review identifies surface analytical techniques that are considered suitable for analysis of thin films at metallic substrates, but are yet to be applied to analysis of carbon steel surfaces in corrosive media or treated with corrosion inhibitors. The reviewed methods include time of flight-secondary ion mass spectrometry, X-ray absorption spectroscopy methods, particle-induced X-ray emission, Rutherford backscatter spectroscopy, Auger electron spectroscopy, electron probe microanalysis, near-edge X-ray absorption fine structure spectroscopy, X-ray photoemission electron microscopy, low-energy electron diffraction, small-angle neutron scattering and neutron reflectometry, and conversion electron Moessbauer spectrometry. Advantages and limitations of the analytical methods in thin-film surface investigations are discussed. Technical parameters of nominated analytical methods are provided to assist in the selection of suitable methods for analysis of metallic substrates deposited with surface films. The challenges associated with the applications of the emerging analytical methods in corrosion science are also addressed.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0852hwp:master-id:royprsa;rspa.2016.08522017-03-08Review articles47321992016085220160852<![CDATA[The Fourier decomposition method for nonlinear and non-stationary time series analysis]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160871?rss=1
for many decades, there has been a general perception in the literature that Fourier methods are not suitable for the analysis of nonlinear and non-stationary data. In this paper, we propose a novel and adaptive Fourier decomposition method (FDM), based on the Fourier theory, and demonstrate its efficacy for the analysis of nonlinear and non-stationary time series. The proposed FDM decomposes any data into a small number of ‘Fourier intrinsic band functions’ (FIBFs). The FDM presents a generalized Fourier expansion with variable amplitudes and variable frequencies of a time series by the Fourier method itself. We propose an idea of zero-phase filter bank-based multivariate FDM (MFDM), for the analysis of multivariate nonlinear and non-stationary time series, using the FDM. We also present an algorithm to obtain cut-off frequencies for MFDM. The proposed MFDM generates a finite number of band-limited multivariate FIBFs (MFIBFs). The MFDM preserves some intrinsic physical properties of the multivariate data, such as scale alignment, trend and instantaneous frequency. The proposed methods provide a time–frequency–energy (TFE) distribution that reveals the intrinsic structure of a data. Numerical computations and simulations have been carried out and comparison is made with the empirical mode decomposition algorithms.
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0871hwp:master-id:royprsa;rspa.2016.08712017-03-15Research articles47321992016087120160871<![CDATA[Microprocessors: the engines of the digital age]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160893?rss=1
The microprocessor—a computer central processing unit integrated onto a single microchip—has come to dominate computing across all of its scales from the tiniest consumer appliance to the largest supercomputer. This dominance has taken decades to achieve, but an irresistible logic made the ultimate outcome inevitable. The objectives of this Perspective paper are to offer a brief history of the development of the microprocessor and to answer questions such as: where did the microprocessor come from, where is it now, and where might it go in the future?
]]>2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2016.0893hwp:master-id:royprsa;rspa.2016.08932017-03-15Perspective47321992016089320160893<![CDATA[Screened Coulomb interactions with non-uniform surface charge]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160906?rss=1
The screened Coulomb interaction between a pair of infinite parallel planes with spatially varying surface charge is considered in the limit of small electrical potentials for arbitrary Debye lengths. A simple expression for the disjoining pressure is derived in terms of a two-dimensional integral in Fourier space. The integral is evaluated for periodic and random charge distributions and the disjoining pressure is expressed as a sum over Fourier–Bloch reciprocal lattice vectors or in terms of an integral involving the autocorrelation function, respectively. The force between planes with a finite area of uniform charge, a model for the DLVO interaction between finite surfaces, is also calculated. It is shown that the overspill of the charge cloud beyond the region immediately between the charged areas results in a reduction of the disjoining pressure, as reported by us recently in the long Debye length limit for planes of finite width.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0906hwp:master-id:royprsa;rspa.2016.09062017-03-22Research articles47321992016090620160906<![CDATA[Resistive-pulse and rectification sensing with glass and carbon nanopipettes]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160931?rss=1
Along with more prevalent solid-state nanopores, glass or quartz nanopipettes have found applications in resistive-pulse and rectification sensing. Their advantages include the ease of fabrication, small physical size and needle-like geometry, rendering them useful for local measurements in small spaces and delivery of nanoparticles/biomolecules. Carbon nanopipettes fabricated by depositing a thin carbon layer on the inner wall of a quartz pipette provide additional means for detecting electroactive species and fine-tuning the current rectification properties. In this paper, we discuss the fundamentals of resistive-pulse sensing with nanopipettes and our recent studies of current rectification in carbon pipettes.
]]>2017-03-08T00:05:22-08:00info:doi/10.1098/rspa.2016.0931hwp:master-id:royprsa;rspa.2016.09312017-03-08Special feature47321992016093120160931<![CDATA[A computational continuum model of poroelastic beds]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20160932?rss=1
Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to describe such configurations by deriving and validating a continuum model for the poroelastic bed and its interface with the above free fluid. We show that, using stress continuity condition and slip velocity condition at the interface, the effective model captures the effects of small changes in the microstructure anisotropy correctly and predicts the overall behaviour in a physically consistent and controllable manner. Moreover, we show that the performance of the effective model is accurate by validating with fully microscopic resolved simulations. The proposed computational tool can be used in investigations in a wide range of fields, including mechanical engineering, bio-engineering and geophysics.
]]>2017-03-22T00:05:49-07:00info:doi/10.1098/rspa.2016.0932hwp:master-id:royprsa;rspa.2016.09322017-03-22Research articles47321992016093220160932<![CDATA[Introduction for perspectives in geophysical and astrophysical fluids]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20170078?rss=1
2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2017.0078hwp:master-id:royprsa;rspa.2017.00782017-03-15Special feature47321992017007820170078<![CDATA[Obituary: Prof. Anjan Kundu]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/473/2199/20170107?rss=1
2017-03-15T00:05:21-07:00info:doi/10.1098/rspa.2017.0107hwp:master-id:royprsa;rspa.2017.01072017-03-15Editorial47321992017010720170107