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Variational construction of tubular and toroidal streamsurfaces for flow visualization Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Mingwu Li, Bálint Kaszás, George Haller
Approximate streamsurfaces of a three-dimensional velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces enable effective and efficient visualization of vortical regions in three-dimensional flows. Here we propose a variational construction of these approximate streamsurfaces to remove the limitation of Fourier
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Inertia-gravity waves in geophysical vortices Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Jérémie Vidal, Yves Colin de Verdière
Pancake-like vortices are often generated by turbulence in geophysical flows. Here, we study the inertia-gravity oscillations that can exist within such geophysical vortices, due to the combined action of rotation and gravity. We consider a fluid enclosed within a triaxial ellipsoid, which is stratified in density with a constant Brunt–Väisälä frequency (using the Boussinesq approximation) and uniformly
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Harmonic wave scattered by an inclusion in an elastic plane: The complete Gurtin-Murdoch model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Ming Dai, Peter Schiavone
We consider the propagation of a harmonic elastic wave in a composite inclusion–matrix structure subjected to plane deformation. The interface between the inclusion and matrix is described by the complete Gurtin-Murdoch model with non-vanishing interface tension and interface stretching rigidity. We consider an inclusion of general shape and formulate the corresponding boundary value problem for the
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Super band gaps and periodic approximants of generalised Fibonacci tilings Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Bryn Davies, Lorenzo Morini
We present mathematical theory for self-similarity induced spectral gaps in the spectra of systems generated by generalised Fibonacci tilings. Our results characterise super band gaps, which are spectral gaps that exist for all sufficiently large periodic systems in a Fibonacci-generated sequence. We characterise super band gaps in terms of a growth condition on the traces of the associated transfer
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Quasi steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, I: modelling Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Yanxing Wang, Hui Wan, Rusitan Refuaiti, Tie Wei, Fangjun Shu
A quasi steady-state model (QSM) for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems with a broad range of distributions of particle size and aspect ratio has been developed. A rigorous, mathematics-based QSM of the dissolution of single spheroidal particles has been incorporated into the well-established
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Response of flexible structures to air-blast: nonlinear compressibility effects in fluid–structure interaction Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Aninda Pal, Ritwik Ghoshal
This paper presents a coupled model that considers the nonlinear compressibility effect in fluid–structure interaction (FSI) during air-blast loading on flexible structures. In this coupled model, structural behaviour is idealized as a linear single-degree-of-freedom mass-spring-damper system whereas nonlinear fluid compressibility is considered by applying Rankine–Hugoniot jump conditions across a
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Zig-zag dynamics in a Stern–Gerlach spin measurement Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-13 Simon Krekels, Christian Maes, Kasper Meerts, Ward Struyve
The century-old Stern–Gerlach setup is paradigmatic for a quantum measurement. We visualize the electron trajectories following the Bohmian zig-zag dynamics. This dynamics was developed in order to deal with the fundamentally massless nature of particles (with mass emerging from the Brout–Englert–Higgs mechanism). The corresponding trajectories exhibit a stochastic zig-zagging, as the result of the
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Asymptotic numerical method for hyperelasticity and elastoplasticity: a review Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Michel Potier-Ferry
The literature about the asymptotic numerical method (ANM) is reviewed in this paper as well as its application to hyperelasticity and elastoplasticity. ANM is a generic continuation method based on the computation of Taylor series for solving nonlinear partial differential equations. Modern techniques of high-order differentiation provide simple tools for computing these power series, the corresponding
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Complex systems in ecology: a guided tour with large Lotka–Volterra models and random matrices Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Imane Akjouj, Matthieu Barbier, Maxime Clenet, Walid Hachem, Mylène Maïda, François Massol, Jamal Najim, Viet Chi Tran
Ecosystems represent archetypal complex dynamical systems, often modelled by coupled differential equations of the form dxidt=xiϕi(x1,…,xN),where N represents the number of species and xi, the abundance of species i. Among these families of coupled differential equations, Lotka–Volterra (LV) equations, corresponding to ϕi(x1,…,xN)=ri−xi+(Γx)i,play a privileged role, as the LV model represents an acceptable
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Generating new gravitational solutions by matrix multiplication Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 M. Cristina Câmara, Gabriel Lopes Cardoso
Explicit solutions to the nonlinear field equations of some gravitational theories can be obtained, by means of a Riemann–Hilbert approach, from a canonical Wiener–Hopf factorization of certain matrix functions called monodromy matrices. In this paper, we describe other types of factorization from which solutions can be constructed in a similar way. Our approach is based on an invariance problem, which
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Multichannel scattering for the Schrödinger equation on a line with different thresholds at both infinities Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Peter O. Kazinski, Petr S. Korolev
The multichannel scattering problem for the stationary Schrödinger equation on a line with different thresholds at both infinities is investigated. The analytical structure of the Jost solutions and of the transition matrix relating the Jost solutions as functions of the spectral parameter is described. Unitarity of the scattering matrix is proved in the general case when some of the scattering channels
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Axisymmetric vibration and stability of dielectric-elastic tubular bilayer system Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Ahmad Almamo, Yipin Su, Weiqiu Chen, Huiming Wang
Modern transducers and actuators may have functional layers with multi-field coupling and some elastic layers. This paper considers a tubular bilayer system consisting of a thin dielectric tube coated with a thick elastic layer. We study the nonlinear electromechanical response and the linear axisymmetric vibration of the system subject to different applied voltages and inner/outer pressures within
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Unstable cores are the source of instability in chemical reaction networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Nicola Vassena, Peter F. Stadler
In biochemical networks, complex dynamical features such as superlinear growth and oscillations are classically considered a consequence of autocatalysis. For the large class of parameter-rich kinetic models, which includes generalized mass action kinetics and Michaelis–Menten kinetics, we show that certain submatrices of the stoichiometric matrix, so-called unstable cores, are sufficient for a reaction
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Connecting continuum poroelasticity with discrete synthetic vascular trees for modelling liver tissue Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-06 Adnan Ebrahem, Etienne Jessen, Marco F. P. ten Eikelder, Tarun Gangwar, Michał Mika, Dominik Schillinger
The modelling of liver tissue across multiple length scales constitutes a significant challenge, primarily due to the multiphysics coupling of mechanical response and perfusion within the complex multiscale vascularization of the organ. In this paper, we present a modelling framework that connects continuum poroelasticity and discrete vascular tree structures to model liver tissue across disparate
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Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-14 Filipe A. dos Santos, Antonino Favata, Andrea Micheletti, Roberto Paroni, Marco Picchi Scardaoni
The control of the shape of complex metasurfaces is a challenging task often addressed in the literature. This work presents a class of tessellated plates able to deform into surfaces of preprogrammed shape upon activation by any flexural load and that can be controlled by a single actuator. Quadric metasurfaces are obtained from infinitesimal origami maps of monohedral hexagonal tessellations of the
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Multi-fidelity reduced-order surrogate modelling Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Paolo Conti, Mengwu Guo, Andrea Manzoni, Attilio Frangi, Steven L. Brunton, J. Nathan Kutz
High-fidelity numerical simulations of partial differential equations (PDEs) given a restricted computational budget can significantly limit the number of parameter configurations considered and/or time window evaluated. Multi-fidelity surrogate modelling aims to leverage less accurate, lower-fidelity models that are computationally inexpensive in order to enhance predictive accuracy when high-fidelity
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Unifying temperature definition in atomistic and field representations of conservation laws Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Youping Chen
In this work, a field representation of the conservation law of linear momentum is derived from the atomistic, using the theory of distributions as the mathematical tool, and expressed in terms of temperature field by defining temperature as a derived quantity as that in molecular kinetic theory and atomistic simulations. The formulation leads to a unified atomistic and continuum description of temperature
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Role of electromagnetic energy and momentum in the Aharonov–Bohm effect Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Alexander L. Kholmetskii, Oleg V. Missevitch, Tolga Yarman
We analyse the physical meaning of the Aharonov–Bohm (AB) phase based on its representation through electromagnetic (EM) potentials as a sum of four components, which, in addition to the known electric and magnetic phase components, contains two more terms recently disclosed by our team in the analysis of quantum phase effects for dipoles and charges, and which we named the complementary electric AB
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Supply chain loss from easing COVID-19 restrictions: an evolutionary economic-epidemiological modelling study Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Yang Ye, Zhidong Cao, Daniel Dajun Zeng, Qingpeng Zhang
Since the start of the COVID-19 pandemic, many firms have been shifting their supply chains away from countries with stringent control measures to mitigate supply-chain disruption. Nowadays, the global economy has reopened from the COVID-19 pandemic at various paces in different countries. Understanding how the global supply network evolves during and after the pandemic is necessary for determining
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Multi-parametric optimization for controlling bifurcation structures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 A. Mélot, E. Denimal, L. Renson
Bifurcations organize the dynamics of many natural and engineered systems. They induce qualitative and quantitative changes to a system’s dynamics, which can have catastrophic consequences if ignored during design. In this paper, we propose a general computational method to control the local bifurcations of dynamical systems by optimizing design parameters. We define an objective functional that enforces
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A theory of stochastic fluvial landscape evolution Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 G. G. Roberts, O. Wani
Geometries of eroding landscapes contain important information about geologic, climatic, biotic and geomorphic processes. They are also characterized by variability, which makes disentangling their origins challenging. Observations and physical models of fluvial processes, which set the pace of erosion on most continents, emphasize complexity and variability. By contrast, the spectral content of longitudinal
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Nonlinear acoustics of an aperture under grazing flow Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Alexander K. Stoychev, Tiemo Pedergnana, Nicolas Noiray
This work presents a mathematical model of a dynamically forced, acoustically compact aperture subject to one-sided mean grazing flow in two or three dimensions. By contrast to other simplified theoretical representations of a grazed aperture, the one proposed in this contribution considers some of the nonlinear effects a reduced order model should naturally inherit from the conservation equations
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Critical transitions in spatial systems induced by Ornstein–Uhlenbeck noise: spatial mutual information as a precursor Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Smita Deb, Partha Sharathi Dutta
Complex dynamical systems are subject to perturbations across space and time, which can induce a critical transition or tipping in the state of the system. External perturbations are often correlated in time and can interplay with the underlying nonlinearity of the spatial system, affecting the occurrence of critical transitions. Theoretical analysis of the spatial system perturbed by the Ornstein–Uhlenbeck
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An Eulerian hyperbolic model for heat transfer derived via Hamilton’s principle: analytical and numerical study Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-02-07 Firas Dhaouadi, Sergey Gavrilyuk
In this paper, we present a new model for heat transfer in compressible fluid flows. The model is derived from Hamilton’s principle of stationary action in Eulerian coordinates, in a setting where the entropy conservation is recovered as an Euler–Lagrange equation. A sufficient criterion for the hyperbolicity of the model is formulated. The governing equations are asymptotically consistent with the
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Experimental studies on snaking in 3D-printed cylindrical shells under axial compression using photogrammetry Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 V. Ravulapalli, G. Raju, V. Narayanamurthy
The buckling instability of cylindrical shells under axial compression has been one of the most renowned problems in structural engineering for several decades. Many pioneering works in the twentieth century have provided insights into understanding the shells’ infamous imperfection sensitivity and led to reliability-based designs. However, a recent surge in numerical studies of the snaking phenomenon
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Toward a further understanding of the loop formation and elimination in twisted filament: experiments and validation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 Jiongjiong Hu, Jiahui Teng, Lei Liu, Dabiao Liu
Motivated by observations of loop formation and elimination phenomena in elastic filaments subjected to torsion and axial end displacement, we develop a tension–torsion tester to study the slack–extension responses of filaments with varied initial twists. The experiments are conducted by initially twisting the filament by a specific degree and subsequently adjusting the axial end displacement. By continuously
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Estimation of auto-covariance of log hydraulic conductivity from Generalized Sub-Gaussian porosity and particle size random fields Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 M. Harrison, M. Riva, M. Mousavi Nezhad, A. Guadagnini
We derive analytical formulations relating the spatial covariance ( C Y ) of (log-transformed) hydraulic conductivities to auto- and cross-covariances of porosity ( ϕ ) and representative soil particle sizes within the framework of the classical Terzaghi model. The latter provides an empirical relationship which is widely used to obtain conductivity estimates. We frame the study within recent stochastic
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Direct method to determine singular point of enveloped surface and its application to worm wheel tooth surface Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 Jian Cui, Yaping Zhao, Qingxiang Meng, Gongfa Li
A novel methodology for determining the singular point of an enveloped surface is put forward. Unlike some existing methods, the presented method starts directly from the equation of the enveloped surface instead of that of the generating surface, and it is thus called a direct method. The calculation for the normal vector of the enveloped surface is well simplified with the help of the moving frame
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An equivariant Reeb–Beltrami correspondence and the Kepler–Euler flow Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 Josep Fontana-McNally, Eva Miranda, Daniel Peralta-Salas
We prove that the correspondence between Reeb and Beltrami vector fields presented in Etnyre & Ghrist (Etnyre, Ghrist 2000 Nonlinearity 13 , 441–458 ( doi:10.1088/0951-7715/13/2/306 )) can be made equivariant whenever additional symmetries of the underlying geometric structures are considered. As a corollary of this correspondence, we show that energy levels above the maximum of the potential energy
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Thermal convection with a Cattaneo heat flux model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-31 M. Gentile, B. Straughan
The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to
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Improved estimates for the number of non-negative integer matrices with given row and column sums Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 Maximilian Jerdee, Alec Kirkley, M. E. J. Newman
The number of non-negative integer matrices with given row and column sums features in a variety of problems in mathematics and statistics but no closed-form expression for it is known, so we rely on approximations. In this paper, we describe a new such approximation, motivated by consideration of the statistics of matrices with non-integer numbers of columns. This estimate can be evaluated in time
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Suppression of soliton collapses, modulational instability and rogue-wave excitation in two-Lévy-index fractional Kerr media Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 Ming Zhong, Yong Chen, Zhenya Yan, Boris A. Malomed
We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, α 1 α 2 ∈ ( 1 , 2 ] , and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison
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Geometric mechanics of hybrid origami assemblies combining developable and non-developable patterns Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 Kevin T. Liu, G. H. Paulino
Origami provides a method to transform a flat surface into complex three-dimensional geometries, which has applications in deployable structures, meta-materials, robotics and beyond. The Miura-ori and the eggbox are two fundamental planar origami patterns. Both patterns have been studied closely, and have become the basis for many engineering applications and derivative origami patterns. Here, we study
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Surface impedance and topologically protected interface modes in one-dimensional phononic crystals Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 A. Coutant, B. Lombard
When semi-infinite phononic crystals (PCs) are in contact, localized modes may exist at their boundary. The central question is generally to predict their existence and to determine their stability. With the rapid expansion of the field of topological insulators, powerful tools have been developed to address these questions. In particular, when applied to one-dimensional systems with mirror symmetry
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Scattering kernel of an array of floating ice floes: application to water wave transport in the marginal ice zone Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 F. Montiel, M. H. Meylan, S. C. Hawkins
A radiative transfer model of water wave scattering in the marginal ice zone is considered. In this context, wave energy redistribution across the directional components of the spectrum as a result of scattering by the constituent ice floes is typically modelled via a scattering kernel describing the far-field directionality of the scattered wave field produced by a single floe in isolation. Recognizing
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Explorations of the holonomy of a rolling sphere Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 Theresa E. Honein, Oliver M. O’Reilly
Consider a rigid body rolling with one point in contact with a fixed surface. Now suppose that the instantaneous point of contact traces out a closed path. As a demonstration of a phenomenon known as holonomy, the body will typically not return to its original orientation. The simplest demonstration of this phenomenon in rigid body dynamics occurs in the motion of a rolling sphere and finds application
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Numerical direct scattering transform for breathers Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-24 I. I. Mullyadzhanov, A. S. Gudko, R. I. Mullyadzhanov, A. A. Gelash
We consider the model of the focusing one-dimensional nonlinear Schrödinger equation (fNLSE) in the presence of an unstable constant background, which exhibits coherent solitary wave structures—breathers. Within the inverse scattering transform (IST) method, we study the problem of the scattering data numerical computation for a broad class of breathers localized in space. Such a direct scattering
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Stability analysis of evolutionary dynamics of 2 × 2 × 2 asymmetric games Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-17 Sha Song, Qiuhui Pan, Xubin Gao, Mingfeng He
In biology, economics, sociology as well as other fields, there is often a 2 × 2 × 2 asymmetric evolutionary game problem in which each party has a set of strategies, and different strategy combinations correspond to the specific pay-offs of each party. Since each participant dynamically adjusts the strategy for maximizing their own interests, the pay-off matrix plays an important role in the evolution
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General efficiency relation for dissipative molecular machines Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-17 Milo M. Lin
Living systems use chemical fuel to process information, assemble structures and maintain fluxes. Many of these processes are dissipative: energy is consumed purely to maintain non-equilibrium steady-state outputs. How efficiently the input energy is transduced toward the output dissipation as opposed to being lost during intermediate steps, and whether the efficiency is constrained by general principles
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Dynamics of elastic lattices with sliding constraints Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-17 L. Cabras, D. Bigoni, A. Piccolroaz
This study investigates the impact of sliders – constraints acting on elastic rods allowing for a transverse displacement jump while maintaining axial and rotational displacement continuity – on the dynamics of a periodic elastic grid, including the effects of axial preload. The grid is linearly elastic and subject to in-plane incremental deformation, involving normal and shear forces and bending moment
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Kinematics and dynamics of non-developable origami Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-17 Yu Zou, Fan Feng, Ke Liu, Pengyu Lv, Huiling Duan
Non-developable origami is a unique type of origami structures that cannot be unfolded into a flat sheet without stretching. In this work, we study the kinematics and dynamics of such origami, theoretically, numerically and experimentally, considering rigid panels and stretchable creases. Unlike developable origami, we find that non-developable origami exhibits distinct folding angle relationships
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Localized pattern formation: semi-strong interaction asymptotic analysis for three components model Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-10 Fahad Al Saadi, Chunyi Gai, Mark Nelson
We investigate a three-component system involving the Belousov–Zhabotinsky reaction in water-in-oil microemulsions. Our goal is to investigate the connection between homoclinic snaking and semi-strength interaction in a three-variable reaction–diffusion system. A two-parameter bifurcation diagram of homogeneous, periodic and localized patterns is obtained numerically, and a natural asymptotic scaling
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Organ registration from partial surface data in augmented surgery from an optimal control perspective Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-10 Stéphane Cotin, Guillaume Mestdagh, Yannick Privat
We address the problem of organ registration in augmented surgery, where the deformation of the patient’s organ is reconstructed in real-time from a partial observation of its surface. Physics-based registration methods rely on adding artificial forces to drive the registration, which may result in implausible displacement fields. In this paper, we look at this inverse problem through the lens of optimal
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Pushing coarse-grained models beyond the continuum limit using equation learning Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-10 Daniel J. VandenHeuvel, Pascal R. Buenzli, Matthew J. Simpson
Mathematical modelling of biological population dynamics often involves proposing high-fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an approximate coarse-grained differential equation that captures population-level features only. These coarse-grained models are only accurate in certain asymptotic
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Bifurcations of an elastic disc coated with an elastic inextensible rod Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-03 M. Gaibotti, S. G. Mogilevskaya, A. Piccolroaz, D. Bigoni
An analytical solution is derived for the bifurcations of an elastic disc that is constrained on the boundary with an isoperimetric Cosserat coating. The latter is treated as an elastic circular rod, either perfectly or partially bonded (with a slip interface in the latter case) and is subjected to three different types of uniformly distributed radial loads (including hydrostatic pressure). The proposed
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A constitutive model for transversely isotropic dispersive materials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-01-03 A. Amendola, J. de Castro Motta, G. Saccomandi, L. Vergori
Due to their intrinsic complexity, it is not easy to model the mechanical behaviour of biomaterials. Despite the challenges they faced, some researchers have presented mathematical models to describe some aspects of the mechanical response of soft tissues. Since most of the materials of biological interest are composites made of different constituents reinforced by collagen and/or elastin fibres, material
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Viscoplastic simple shear at finite strains Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-20 F. Califano, J. Ciambella
The equations governing the simple shear deformation of an incompressible inelastic material undergoing finite strain are derived in this paper. The constitutive assumptions are kept in their most general form to allow the incorporation of widely used viscoplastic or viscoelastic models from the literature. It is shown that, while for a hyperelastic material the simple shear problem is completely determined
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Chirality and curvature determine the meandering of spirals in multilayer excitable media Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-20 Dorsa Nezhad Hajian, Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Matjaž Perc, Eva Klemenčič
We study the emergence of meandering spiral waves in a multilayer structure where two spirals, originating independently, evolve in space–time. The FitzHugh-Nagumo model, enhanced with electromagnetic induction effects, defines the nodal dynamics. The layers are chemically coupled, and the drift of spirals is influenced by interlayer flux coupling. An external magnetic flux force is also necessary
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Paraxial Dirac equation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-20 Tomasz Radożycki
In this work, the paraxial approximation of the free Dirac equation is examined. The results are first obtained by constructing superpositions of exact solutions with suitable profiles, which are borrowed from paraxial optics. In this manner, the paraxial Dirac beams are obtained in four cases: as Gaussian, Bessel-Gaussian, modified Bessel-Gaussian and elegant Laguerre-Gaussian beams. In the second
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The theory of fifth-order Stokes waves in a linear shear current Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-20 Haiqi Fang, Philip L.-F. Liu, Lian Tang, Pengzhi Lin
In this study, a new set of fifth-order Stokes wave solutions, incorporating the effects of a linear shear current, is derived by using the perturbation method originally proposed for pure waves that was recently published. The present solutions are checked against the existing experimental data, the third-order stream function solutions, as well as the numerical results. The comparisons demonstrate
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The Painlevé paradox in three dimensions: resolution with regularization Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-20 N. D. Cheesman, S. J. Hogan, K. Uldall Kristiansen
The classical Painlevé paradox consists of a slender rigid rod slipping on a rigid rough surface. If the coefficient of friction μ is high enough, the governing equations predict that the rod would be driven into the surface. The paradox is well studied in two dimensions, in which the paradox is resolved via regularization, where the rod tip meets the surface. In this paper, we consider the three-dimensional
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Spectral wear modelling of rubber friction on a hard substrate with large surface roughness Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-13 H. Tanaka, S. Yanagihara, K. Shiomi, T. Kuroda, Y. Oku
Soft-hard matter friction is a long-standing tribology problem that remains unclarified, requiring engineers to empirically predict the wear life. To clarify this issue, this study examines the transient running-in regime of rubber friction on a hard rough substrate and models the temporal wear progression using the spectrum curves of surface roughness for both materials. Performing a series of friction
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Going round the bend: reflection and transmission of long waves by waveguide corners and labyrinths Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-13 P. A. Martin
Long-wave asymptotic approximations are developed for two-dimensional acoustic waves along rigid ducts. The waves are scattered by obstacles, constrictions, bulges and/or bends. Matched asymptotic expansions are used, requiring the calculation of blockage coefficients, which are defined in terms of the solution of related potential-flow problems. The emphasis is on estimating reflection and transmission
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Electrosteric, van der Waals and elastic interaction of polyelectrolyte hydrogels Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-13 Reghan J. Hill
The electrosteric interaction energy for a charged hydrogel and hard plane, and between two charged hydrogels is derived in the Debye–Hückel approximation. This is combined with a van der Waals potential that explicitly addresses the Hamaker constant for the solvent-mediated hydrogel interactions. Then, in the Derjaguin approximation, DLVO-type interaction potentials are provided for hydrogel and hard/rigid
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Matrix factorizations and pentagon maps Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-13 Pavlos Kassotakis
We propose a specific class of matrices that participate in factorization problems that turn out to be equivalent to constant and entwining (non-constant) pentagon, reverse-pentagon or Yang–Baxter maps, expressed in non-commutative variables. In detail, we show that factorizations of order N = 2 matrices of this specific class are equivalent to the homogeneous normalization map . From order N = 3 matrices
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Determinants of successful mitigation in coupled social-climate dynamics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-13 Longmei Shu, Feng Fu
Understanding the impact of human behaviour is crucial for successful mitigation of climate change across the globe. To shed light onto this issue, here we couple the forest dieback model with human behaviours. Using evolutionary game theory, we build a time-delay system where forest growth is impacted by both temperature and human mitigation choices, the latter being informed by temperature forecasts
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Prediction of general high-order lump solutions in the Davey–Stewartson II equation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-12-06 Xue-Wei Yan, Haie Long, Yong Chen
Under investigation in this work is the Davey–Stewartson (DS) II equation. Based on the Kadomtsev–Petviashvili (KP) reduction method and Schur polynomial theory, we construct the general high-order lump solutions. The prediction solutions consisting of fundamental lumps and their positions are derived by extracting leading-order asymptotics of the Schur polynomials of true solutions. When indexes of
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Modulation instability and localized wave excitations for a higher-order modified self-steepening nonlinear Schrödinger equation in nonlinear optics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-11-29 Haotian Wang, Qin Zhou, Hujiang Yang, Xiankui Meng, Ye Tian, Wenjun Liu
This paper investigates a higher-order modified nonlinear Schrödinger equation with higher-order dispersion and self-steepening effects, which can be used to study the dynamics of asymmetric and steepened optical pulse transmission in optical fibres. The modulation instability of the plane-wave solution has been analysed, and the state transition of the rogue waves under the higher-order dispersion
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A model to validate effective waves in random particulate media: spherical symmetry Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-11-29 Artur L. Gower, Stuart C. Hawkins, Gerhard Kristensson
There has not been a satisfying numerical validation of the theory of effective waves in random particulate materials. Validation has been challenging because the theoretical methods for effective waves have been limited to random particulate media in infinite slabs or half-spaces, which require a very large number of particles to perform accurate numerical simulations. This paper offers a solution
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Flutter instability in solids and structures, with a view on biomechanics and metamaterials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2023-11-29 Davide Bigoni, Francesco Dal Corso, Oleg N. Kirillov, Diego Misseroni, Giovanni Noselli, Andrea Piccolroaz
The phenomenon of oscillatory instability called ‘flutter’ was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing