Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences current issue
http://rspa.royalsocietypublishing.org
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences RSS feed -- current issue1471-2946October, 2018Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences1364-5021<![CDATA[Topological data analysis for true step detection in periodic piecewise constant signals]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180027?rss=1
This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0027hwp:master-id:royprsa;rspa.2018.00272018-10-03Research articles47422182018002720180027<![CDATA[Proton tunnelling in hydrogen bonds and its implications in an induced-fit model of enzyme catalysis]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180037?rss=1
The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0037hwp:master-id:royprsa;rspa.2018.00372018-10-03Research articles47422182018003720180037<![CDATA[Allosteric interactions in a birod model of DNA]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180136?rss=1
Allosteric interactions between molecules bound to DNA at distant locations have been known for a long time. The phenomenon has been studied via experiments and numerical simulations, but a comprehensive understanding grounded in a theory of DNA elasticity remains a challenge. Here, we quantify allosteric interactions between two entities bound to DNA by using the theory of birods. We recognize that molecules bound to DNA cause local deformations that can be captured in a birod model which consists of two elastic strands interacting via an elastic web representing the basepairs. We show that the displacement field caused by bound entities decays exponentially with distance from the binding site. We compute the interaction energy between two proteins on DNA as a function of distance between them and find that it decays exponentially while oscillating with the periodicity of the double helix, in excellent agreement with experiments. The decay length of the interaction energy can be determined in terms of the mechanical properties of the strands and the webbing in our birod model, and it varies with the GC content of the DNA. Our model provides a framework for viewing allosteric interactions in DNA within the ambit of configurational forces of continuum elasticity.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0136hwp:master-id:royprsa;rspa.2018.01362018-10-03Research articles47422182018013620180136<![CDATA[A Hamiltonian mean field system for the Navier-Stokes equation]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180178?rss=1
We use a Hamiltonian interacting particle system to derive a stochastic mean field system whose McKean–Vlasov equation yields the incompressible Navier–Stokes equation. Since the system is Hamiltonian, the particle relabeling symmetry implies a Kelvin Circulation Theorem along stochastic Lagrangian paths. Moreover, issues of energy dissipation are discussed and the model is connected to other approaches in the literature.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0178hwp:master-id:royprsa;rspa.2018.01782018-10-03Research articles47422182018017820180178<![CDATA[On the computation of hybrid modes in planar layered waveguides with multiple anisotropic conductive sheets]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180288?rss=1
A reliable method is presented for the computation of the propagation constants and the corresponding hybrid modal fields in multilayered planar dielectric stacks comprising multiple anisotropic conducting sheets. The appropriate dispersion functions (DFs) are formulated and evaluated using a numerically stable scattering matrix methodology. The roots of the DFs are computed by the Cauchy integration method with automatic differentiation of the DF.
]]>2018-10-17T00:05:20-07:00info:doi/10.1098/rspa.2018.0288hwp:master-id:royprsa;rspa.2018.02882018-10-17Research articles47422182018028820180288<![CDATA[Uniformity of stresses inside a non-elliptical inhomogeneity interacting with a mode III crack]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180304?rss=1
Using conformal mapping techniques and the theory of Cauchy singular integral equations, we prove that it is possible to maintain a uniform internal stress field inside a non-elliptical elastic inhomogeneity embedded in an infinite matrix subjected to uniform remote stress despite the fact that the inhomogeneity interacts with a finite mode III crack. The crack can be modelled either as a Griffith crack or as a Zener–Stroh crack. Our analysis further indicates that the existence of the crack plays a key role in influencing the shape of the corresponding inhomogeneity but not the internal uniform stress field inside the inhomogeneity. Numerical examples are presented to demonstrate the solution.
]]>2018-10-17T00:05:20-07:00info:doi/10.1098/rspa.2018.0304hwp:master-id:royprsa;rspa.2018.03042018-10-17Research articles47422182018030420180304<![CDATA[Coupled constitutive relations: a second law based higher-order closure for hydrodynamics]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180323?rss=1
In the classical framework, the Navier–Stokes–Fourier equations are obtained through the linear uncoupled thermodynamic force-flux relations which guarantee the non-negativity of the entropy production. However, the conventional thermodynamic descrip- tion is only valid when the Knudsen number is sufficiently small. Here, it is shown that the range of validity of the Navier–Stokes–Fourier equations can be extended by incorporating the nonlinear coupling among the thermodynamic forces and fluxes. The resulting system of conservation laws closed with the coupled constitutive relations is able to describe many interesting rarefaction effects, such as Knudsen paradox, transpiration flows, thermal stress, heat flux without temperature gradients, etc., which cannot be predicted by the classical Navier–Stokes–Fourier equations. For this system of equations, a set of phenomenological boundary conditions, which respect the second law of thermodynamics, is also derived. Some of the benchmark problems in fluid mechanics are studied to show the applicability of the derived equations and boundary conditions.
]]>2018-10-17T00:05:20-07:00info:doi/10.1098/rspa.2018.0323hwp:master-id:royprsa;rspa.2018.03232018-10-17Research articles47422182018032320180323<![CDATA[A diffuse interface model for the analysis of propagating bulges in cylindrical balloons]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180333?rss=1
With the aim to characterize the formation and propagation of bulges in cylindrical rubber balloons, we carry out an expansion of the nonlinear axisymmetric membrane model assuming slow axial variations. We obtain a diffuse interface model similar to that introduced by van der Waals in the context of liquid–vapour phase transitions. This provides a quantitative basis to the well-known analogy between propagating bulges and phase transitions. The diffuse interface model is amenable to numerical as well as analytical solutions, including linear and nonlinear bifurcation analyses. Comparisons to the original membrane model reveal that the diffuse interface model captures the bulging phenomenon very accurately, even for well-localized phase boundaries.
]]>2018-10-10T00:34:51-07:00info:doi/10.1098/rspa.2018.0333hwp:master-id:royprsa;rspa.2018.03332018-10-10Research articles47422182018033320180333<![CDATA[Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180382?rss=1
The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.
]]>2018-10-10T00:34:51-07:00info:doi/10.1098/rspa.2018.0382hwp:master-id:royprsa;rspa.2018.03822018-10-10Research articles47422182018038220180382<![CDATA[Biological imaging with scanning electrochemical microscopy]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180409?rss=1
Scanning electrochemical microscopy (SECM) is a powerful and versatile technique for visualizing the local electrochemical activity of a surface as an ultramicroelectrode tip is moved towards or over a sample of interest using precise positioning systems. In comparison with other scanning probe techniques, SECM not only enables topographical surface mapping but also gathers chemical information with high spatial resolution. Considerable progress has been made in the analysis of biological samples, including living cells and immobilized biomacromolecules such as enzymes, antibodies and DNA fragments. Moreover, combinations of SECM with complementary analytical tools broadened its applicability and facilitated multi-functional analysis with extended life science capabilities. The aim of this review is to present a brief topical overview on recent applications of biological SECM, with particular emphasis on important technical improvements of this surface imaging technique, recommended applications and future trends.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0409hwp:master-id:royprsa;rspa.2018.04092018-10-03Review articles47422182018040920180409<![CDATA[Determination of the instantaneous geostrophic flow within the three-dimensional magnetostrophic regime]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180412?rss=1
In his seminal work, Taylor (1963 Proc. R. Soc. Lond. A274, 274–283. (doi:10.1098/rspa.1963.0130).) argued that the geophysically relevant limit for dynamo action within the outer core is one of negligibly small inertia and viscosity in the magnetohydrodynamic equations. Within this limit, he showed the existence of a necessary condition, now well known as Taylor's constraint, which requires that the cylindrically averaged Lorentz torque must everywhere vanish; magnetic fields that satisfy this condition are termed Taylor states. Taylor further showed that the requirement of this constraint being continuously satisfied through time prescribes the evolution of the geostrophic flow, the cylindrically averaged azimuthal flow. We show that Taylor's original prescription for the geostrophic flow, as satisfying a given second-order ordinary differential equation, is only valid for a small subset of Taylor states. An incomplete treatment of the boundary conditions renders his equation generally incorrect. Here, by taking proper account of the boundaries, we describe a generalization of Taylor's method that enables correct evaluation of the instantaneous geostrophic flow for any three-dimensional Taylor state. We present the first full-sphere examples of geostrophic flows driven by non-axisymmetric Taylor states. Although in axisymmetry the geostrophic flow admits a mild logarithmic singularity on the rotation axis, in the fully three-dimensional case we show that this is absent and indeed the geostrophic flow appears to be everywhere regular.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0412hwp:master-id:royprsa;rspa.2018.04122018-10-03Research articles47422182018041220180412<![CDATA[Strategies for data acquisition using ultrasonic phased arrays]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180451?rss=1
Ultrasonic phased arrays have produced major benefits in a range of fields, from medical imaging to non-destructive evaluation. The maximum information, which can be measured by an array, corresponds to the Full Matrix Capture (FMC) data acquisition technique and contains all possible combinations of transmitter–receiver signals. However, this method is not fast enough for some applications and can result in a very large volume of data. In this paper, the problem of optimal array data acquisition strategy is considered, that is, how to make the minimum number of array measurements without loss of information. The main result is that under the single scattering assumption the FMC dataset has a specific sparse structure, and this property can be used to design an optimal data acquisition method. An analytical relationship between the minimum number of array firings, maximum steering angle and signal-to-noise ratio is derived, and validated experimentally. An important conclusion is that the optimal number of emissions decreases when the angular aperture of the array increases. It is also shown that plane wave imaging data are equivalent to the FMC dataset, but requires up to an order of magnitude fewer array firings.
]]>2018-10-17T00:05:20-07:00info:doi/10.1098/rspa.2018.0451hwp:master-id:royprsa;rspa.2018.04512018-10-17Research articles47422182018045120180451<![CDATA[Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition]]>
http://rspa.royalsocietypublishing.org/cgi/content/short/474/2218/20180535?rss=1
The generation of mechanical metamaterials with tailored effective properties through carefully engineered microstructures requires avenues to predict optimal microstructural architectures. Phase separation in heterogeneous systems naturally produces complex microstructural patterns whose effective response depends on the underlying process of spinodal decomposition. During this process, anisotropy may arise due to advection, diffusive chemical gradients or crystallographic interface energy, leading to anisotropic patterns with strongly directional effective properties. We explore the link between anisotropic surface energies during spinodal decomposition, the resulting microstructures and, ultimately, the anisotropic elastic moduli of the resulting medium. We simulate the formation of anisotropic patterns within representative volume elements, using recently developed stabilized spectral techniques that circumvent further regularization, and present a powerful alternative to current numerical techniques. The interface morphology of representative phase-separated microstructures is shown to strongly depend on surface anisotropy. The effective elastic moduli of the thus-obtained porous media are identified by periodic homogenization, and directionality is demonstrated through elastic surfaces. Our approach not only improves upon numerical tools to simulate phase separation; it also offers an avenue to generate tailored microstructures with tunable resulting elastic anisotropy.
]]>2018-10-03T01:50:17-07:00info:doi/10.1098/rspa.2018.0535hwp:master-id:royprsa;rspa.2018.05352018-10-03Research articles47422182018053520180535