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On integral theorems and their statistical properties Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-24 Nhat Ho, Stephen G. Walker
We introduce a class of integral theorems based on cyclic functions and Riemann sums approximating integrals. The Fourier integral theorem, derived as a combination of a transform and inverse transform, arises as a special case. The integral theorems provide natural estimators of density functions via Monte Carlo methods. Assessment of the quality of the density estimators can be used to obtain optimal
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Two-dimensional nonlocal Eshelby’s inclusion theory: eigenstress-driven formulation and applications Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-24 Wei Ding, Fabio Semperlotti
The classical Eshelby’s theory, developed based on local linear elasticity, cannot be applied to inclusion problems that involve nonlocal (long range) elastic effects often observed in micromechanical systems. In this study, we introduce the extension of Eshelby’s inclusion theory to nonlocal elasticity. Starting from Eringen’s integral formulation of nonlocal elasticity, an eigenstress-driven nonlocal
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The eco-evolutionary dynamics of strategic species Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-24 Sourav Roy, Subrata Ghosh, Arindam Saha, Prakash Chandra Mali, Matjaž Perc, Dibakar Ghosh
Much research has in recent years been devoted to better our understanding of the intricate relationships between ecology and the evolutionary success of species. These explorations have often focused on understanding the complex interplay among ecological factors and evolutionary rhythms of the species in various environments. Central to these studies is the concept of the survival of the fittest
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Allowing Wigner’s friend to sequentially measure incompatible observables Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-17 Aníbal Utreras-Alarcón, Eric G. Cavalcanti, Howard M. Wiseman
The Wigner’s friend thought experiment has gained a resurgence of interest in recent years thanks to no-go theorems that extend it to Bell-like scenarios. One of these, by us and co-workers, showcased the contradiction that arises between quantum theory and a set of assumptions, weaker than those in Bell’s theorem, which we named ‘Local Friendliness’. Using these assumptions, it is possible to arrive
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Axisymmetric blockfold origami: a non-flat-foldable Miura variant with self-locking mechanisms and enhanced stiffness Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-17 Xiangxin Dang, Glaucio H. Paulino
Origami foldcores, especially the blockfold cores, have emerged as promising components of high-performance sandwich composites. Inspired by the blockfold origami, we propose the axisymmetric blockfold origami (ABO), which is composed of both rectangular and trapezoidal panels. The ABO inherits the non-flat-foldability of the blockfold origami, and furthermore, displays self-locking mechanisms and
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The linear viscoelastic fracture theory applies to soft solids better when they are…viscoelastic Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-17 Etienne Barthel
Over the last half-century, linear viscoelastic models for crack growth in soft solids have flourished but their predictions have rarely been compared to experiments. In fact, most available models are either very approximate or cast in forms which are not quite suitable for the analysis of actual data. Here, we propose a linear viscoelastic approach which consistently exploits the dynamic mechanical
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A rigorous mathematical theory for topological phases and edge modes in spring-mass mechanical systems Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-10 Ridvan Ozdemir, Junshan Lin
In this work, we examine the topological phases of the spring-mass lattices when the spatial inversion symmetry of the system is broken and prove the existence of edge modes when two lattices with different topological phases are glued together. In particular, for the one-dimensional lattice consisting of an infinite array of masses connected by springs, we show that the Zak phase of the lattice is
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Free propagation of resonant waves in nonlinear dissipative metamaterials Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-10 Alessandro Fortunati, Andrea Arena, Marco Lepidi, Andrea Bacigalupo, Walter Lacarbonara
This paper deals with the free propagation problem of resonant and close-to-resonance waves in one-dimensional lattice metamaterials endowed with nonlinearly viscoelastic resonators. The resonators' constitutive and geometric nonlinearities imply a cubic coupling with the lattice. The analytical treatment of the nonlinear wave propagation equations is carried out via a perturbation approach. In particular
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Stability of penetrative convective currents in local thermal non-equilibrium Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-10 Giuseppe Arnone, Florinda Capone, Jacopo Alfonso Gianfrani
The aim of this paper is to investigate the onset of penetrative convection in a Darcy–Brinkman porous medium under the hypothesis of local thermal non-equilibrium. For the problem at stake, the strong form of the principle of exchange of stabilities has been proved, i.e. convective motions can occur only through secondary stationary motions. We perform linear and nonlinear stability analyses of the
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Describing financial crisis propagation through epidemic modelling on multiplex networks Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-10 Malvina Bozhidarova, Frank Ball, Yves van Gennip, Reuben D. O’Dea, Gilles Stupfler
This paper proposes a novel framework for modelling the spread of financial crises in complex networks, combining financial data, Extreme Value Theory and an epidemiological transmission model. We accommodate two key aspects of contagion modelling: fundamentals-based contagion, where the transmission is due to direct financial linkages, and pure contagion, where a crisis might trigger additional crises
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A dynamic trap well model of hydrothermal shape-memory effect in amorphous polymers undergoing tailorable shape recovery behaviour Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-10 Jiabin Shi, Galina Gorbacheva, Haibao Lu, Denvid Lau
A dynamic trap well model is developed to describe the complex relaxations of functional segments, and explore the working principles behind the hydrothermal coupling effect in shape memory polymers (SMPs). A constitutive relationship among shape fixity strain, shape recovery strain and relaxation time has been formulated to characterize the hydrothermal coupling effect using geometrical parameters
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Steklov eigenvalues of nearly hyperspherical domains Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-03 Chee Han Tan, Robert Viator
We consider Steklov eigenvalues of nearly hyperspherical domains in Rd+1 with d≥3. In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion and show that the first-order perturbations are eigenvalues of a Hermitian matrix
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Elastic response of a cylinder loaded by a Hertzian contact pressure and maintained in equilibrium by its inertia Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-03 Pierric Mora, Fabien Treyssède, Laurent Laguerre
We derive the compliance of an elastic cylinder submitted to a line Hertzian contact. The cylinder is maintained in static equilibrium by bulk forces that are proportional to rigid body motions. Displacements are measured by setting integral gauges that amount to prescribing zero net linear and angular momentum, if the problem were to depend upon time. Various cases are covered, representing either
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Droplet evaporation on curved surfaces: transients of internal and external transport phenomena Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-04-03 Arnov Paul, Subhadeep Mondal, Purbarun Dhar
We explore the transient evolution of thermo-fluid-dynamics of evaporating sessile droplets over curved substrates in the liquid and gaseous domains. A computational model using the Arbitrary Lagrangian-Eulerian framework is adopted. The governing equations in both liquid and gaseous domains are solved in a fully coupled manner, considering coupled effects of evaporative cooling and heat advection
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Periodic finite-band solutions to the focusing nonlinear Schrödinger equation by the Fokas method: inverse and direct problems Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Dmitry Shepelsky, Iryna Karpenko, Stepan Bogdanov, Jaroslaw E. Prilepsky
We consider the Riemann–Hilbert (RH) approach to the construction of periodic finite-band solutions to the focusing nonlinear Schrödinger (NLS) equation. An RH problem for the solution of the finite-band problem has been recently derived via the Fokas method (Deconinck et al. 2021 Lett. Math. Phys. 111, 1–18. (doi:10.1007/s11005-021-01356-7); Fokas & Lenells. 2021 Proc. R. Soc. A 477, 20200605. (doi:10
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The Robin boundary condition for modelling heat transfer Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Eduard Marušić-Paloka, Igor Pažanin
The heat exchange between a rigid body and a fluid is usually modelled by the Robin boundary condition saying that the heat flux through the interface is proportional to the difference between their temperatures. Such interface law describes only the unilateral heat exchange. The goal of this paper is to compare the Robin boundary condition starting with the transmission condition (the temperature
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Structural identifiability analysis of linear reaction–advection–diffusion processes in mathematical biology Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Alexander P. Browning, Maria Taşcă, Carles Falcó, Ruth E. Baker
Effective application of mathematical models to interpret biological data and make accurate predictions often requires that model parameters are identifiable. Approaches to assess the so-called structural identifiability of models are well established for ordinary differential equation models, yet there are no commonly adopted approaches that can be applied to assess the structural identifiability
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Quasi-steady-state modelling and characterization of diffusion-controlled dissolution from polydisperse spheroidal particles, II: characterization Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Yanxing Wang, Hui Wan, Cody Barka, Tie Wei, Fangjun Shu
A quasi-steady-state model for accurately predicting the detailed diffusion-dominated dissolution process of polydisperse spheroidal (prolate, oblate and spherical) particle systems was presented in Part I of this study. In the present paper, the dissolution characteristics of typical polydisperse spheroidal particle systems have been extensively investigated. The effects of the distributions of particle
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Variational implicit solvation with Legendre-transformed Poisson–Boltzmann electrostatics Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Zunding Huang, Bo Li
The variational implicit-solvent model (VISM) is an efficient approach to biomolecular interactions, where electrostatic interactions are crucial. The total VISM free energy of a dielectric boundary (i.e. solute–solvent interface) consists of the interfacial energy, solute–solvent interaction energy and dielectric electrostatic energy. The last part is the maximum value of the classical and concave
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Data-driven discovery of invariant measures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Jason J. Bramburger, Giovanni Fantuzzi
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gathered from a system. Our method does not require an explicit model for the dynamics and allows one to target specific invariant measures, such as physical and ergodic measures. Moreover, it applies to both deterministic and
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A mathematical model of thermoplastic elastomers for analysing the topology of microstructures and mechanical properties during elongation Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-27 Hiroki Kodama, Hiroshi Morita, Motoko Kotani
In this study, a mathematical model based on graph theory is developed to analyse the deformed structures and mechanical properties of thermoplastic elastomers (TPEs) using ABA-type triblock copolymers. TPEs exhibit a network structure formed by bridge chains; deformation of this network structure causes stress. During the deformation of TPEs, domain breakage and coalescence occur, accompanied by topological
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Scattering of surface waves by inhomogeneities in crystalline structures Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-20 Basant Lal Sharma
In current scientific and technological scenarios, studies of transmittance of surface waves across structured interfaces have gained some wind amidst applications to metasurfaces, electronic edge-waves, crystal grain boundaries, etc. The results presented in the present article shed a light on the influence of material inhomogeneities on propagation of surface waves. Within the framework of classical
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Jamming problems and the effects of compliance in dual peg-hole disassembly Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-20 Farzaneh Goli, Yongquan Zhang, Mo Qu, Yue Zang, Mozafar Saadat, Duc Truong Pham, Yongjing Wang
Disassembly is a crucial step in remanufacturing and is currently mainly performed by humans. Automating disassembly can reduce labour costs and make remanufacturing more economically attractive. This paper focuses on identifying and characterizing a common disassembly task, dual peg-hole disassembly, with the aim of building a robotic disassembly system for this task. We enumerate the possible contact
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Bayesian autoencoders for data-driven discovery of coordinates, governing equations and fundamental constants Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-20 L. Mars Gao, J. Nathan Kutz
Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under ℓ1 constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated video frames. However, it is challenging for ℓ1-based sparse inference to perform correct identification for real data due to the noisy measurements and often limited
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Melting of wall-mounted ice in shear flow Proc. Royal Soc. A: Math. Phys. Eng. Sci. (IF 3.5) Pub Date : 2024-03-20 Ellen M. Jolley, Thuy Duong Dang, Frank T. Smith
The melting of wall-mounted ice deep inside a water layer flow is investigated, the ice being initially in the form of a slender hump or step-up and the oncoming water upstream near the wall being warmer than the ice. The wall is at the same temperature as the oncoming water except beneath the ice where the wall temperature is the same as that of the ice. The unsteady interaction of the flow, heat
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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