SIAM Journal on Applied Mathematics
Journal Prestige (SJR): 1.108 Citation Impact (citeScore): 2 Number of Followers: 11 Hybrid journal * Containing 1 Open Access article(s) in this issue * ISSN (Print) 00361399  ISSN (Online) 1095712X Published by Society for Industrial and Applied Mathematics [17 journals] 
 Inverse Source Problems for the Stochastic Wave Equations: FarField
Patterns
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Authors: Jianliang Li, Peijun Li, Xu Wang
Pages: 1113  1134
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 11131134, August 2022.
This paper addresses the direct and inverse source problems for the stochastic acoustic, biharmonic, electromagnetic, and elastic wave equations in a unified framework. The driven source is assumed to be a centered generalized microlocally isotropic Gaussian random field, whose covariance and relation operators are classical pseudodifferential operators. Given the random source, the direct problems are shown to be wellposed in the sense of distributions and the regularity of the solutions are given. For the inverse problems, we demonstrate by ergodicity that the principal symbols of the covariance and relation operators can be uniquely determined by a single realization of the farfield pattern averaged over the frequency band with probability one.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220711T07:00:00Z
DOI: 10.1137/21M1467663
Issue No: Vol. 82, No. 4 (2022)

 Reconstructing Stieltjes Functions from Their Approximate Values: A Search
for a Needle in a Haystack
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Authors: Yury Grabovsky
Pages: 1135  1166
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 11351166, August 2022.
Material response of real, passive, linear, timeinvariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functionsa special class of analytic functions mapping a complex upper halfplane into itself. Reconstructing such functions from their experimentally measured values at specific frequencies is one of the central problems that we address in this paper. A definitive reconstruction algorithm that produces a certificate of optimality as well as a graphical representation of the uncertainty of reconstruction is proposed. Its effectiveness is demonstrated in the context of the electrochemical impedance spectroscopy.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220714T07:00:00Z
DOI: 10.1137/21M1392279
Issue No: Vol. 82, No. 4 (2022)

 A Multiscale Poromechanics Model Integrating Myocardial Perfusion and the
Epicardial Coronary Vessels
Open Access Article
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Authors: Nicolás Alejandro Barnafi Wittwer, Simone Di Gregorio, Luca Dede', Paolo Zunino, Christian Vergara, Alfio Quarteroni
Pages: 1167  1193
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 11671193, August 2022.
The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these components. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasiincompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic circulation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220721T07:00:00Z
DOI: 10.1137/21M1424482
Issue No: Vol. 82, No. 4 (2022)

 Oscillations in a BeckerDöring Model with Injection and Depletion

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Authors: B. Niethammer, R. L. Pego, A. Schlichting, J. J. L. Velázquez
Pages: 1194  1219
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 11941219, August 2022.
We study the BeckerDöring bubblelator, a variant of the BeckerDöring coagulationfragmentation system that models the growth of clusters by gain or loss of monomers. Motivated by models of gas evolution oscillators from physical chemistry, we incorporate the injection of monomers and depletion of large clusters. For a wide range of physical rates, the BeckerDöring system itself exhibits a dynamic phase transition as mass density increases past a critical value. We connect the BeckerDöring bubblelator to a transport equation coupled with an integrodifferential equation for the excess monomer density by formal asymptotics in the nearcritical regime. For suitable injection/depletion rates, we argue that timeperiodic solutions appear via a Hopf bifurcation. Numerics confirm that the generation and removal of large clusters can become desynchronized, leading to temporal oscillations associated with bursts of largecluster nucleation.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220721T07:00:00Z
DOI: 10.1137/20M1398664
Issue No: Vol. 82, No. 4 (2022)

 Existence, Uniqueness, and Numerical Modeling of Wine Fermentation Based
on IntegroDifferential Equations
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Authors: Christina Schenk, Volker H. Schulz
Pages: 1220  1245
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 12201245, August 2022.
Predictive modeling is key for saving time and resources in manufacturing processes such as fermentation arising in food and chemical manufacturing. To make reliable predictions, realistic models representing the most important process features are required. Several models describing the white wine fermentation process already exist. However, all of these models lack a combination of features, such as the importance of oxygen at the beginning of the process, the consumption of sugar due to yeast activity, and the toxicity of alcohol on the yeast cells combined with the singlecell yeast dynamics. This work introduces a new population balance model representing all these features in one model. It is based on a system of highly nonlinear weakly hyperbolic partial/ordinary integrodifferential equations which poses a number of theoretical and numerical challenges. This paper increases the understanding of the latter and of the process itself by combining theoretical with numerical investigations. Existence and uniqueness of solutions to a simplified problem are studied based on semigroup theory. For the numerical solution of the problem, a numerical methodology based on a finite volume scheme combined with a time implicit scheme is derived. The impact of the initial cell distribution on the dynamics is studied. The detailed model is compared to a simpler model based on ordinary differential equations. The observed differences for different initial cell distributions and distinct models turn out to be smaller than expected. The outcomes of this paper are specifically relevant for applied mathematicians, winemakers, and process engineers.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220721T07:00:00Z
DOI: 10.1137/20M1362309
Issue No: Vol. 82, No. 4 (2022)

 Doubly Stochastic Pairwise Interactions for Agreement and Alignment

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Authors: Thomas Dagès, Alfred M. Bruckstein
Pages: 1246  1266
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 12461266, August 2022.
Random pairwise encounters often occur in large populations or groups of mobile agents, and various types of local interactions that happen at encounters account for emergent global phenomena. In particular, in the fields of swarm robotics, sociobiology, and social dynamics, several types of local pairwise interactions were proposed and analyzed leading to spatial gathering, clustering, agreement, or coordinated motion in teams of robotic agents, in animal herds, or in human societies. We here propose a very simple stochastic interaction at encounters that leads to agreement or geometric alignment in swarms of simple agents and analyze the process of converging to consensus. Consider a group of agents whose “states" evolve in time by pairwise interactions: the state of an agent is either a real value (a randomly initialized position within an interval) or a vector that is either unconstrained (e.g., the location of the agent in the plane) or constrained to have unit length (e.g., the direction of the agent's motion). The interactions are doubly stochastic in the sense that, at discrete time steps, pairs of agents are randomly selected and their new states are independently and uniformly set at random in (local) domains or intervals defined by the states of the interacting pair. We show that such processes lead, in finite expected time (measured by the number of interactions that occurred) to agreement in case of unconstrained states and alignment when the states are unit vectors.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220721T07:00:00Z
DOI: 10.1137/21M1394680
Issue No: Vol. 82, No. 4 (2022)

 Tilt Grain Boundaries of Hexagonal Structures: A Spectral Viewpoint

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Authors: Kai Jiang, Wei Si, Jie Xu
Pages: 1267  1286
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 12671286, August 2022.
We propose a spectral viewpoint for grain boundaries that are generally quasiperiodic. To accurately capture the spectra computationally, it is crucial to adopt the projection method for quasiperiodic functions. Armed with the LifshitzPetrich free energy, we take the spectral viewpoint to examine tilt grain boundaries of the hexagonal phase. Several ingredients of grain boundaries are extracted, which are not easy to obtain from realspace profiles. We find that only a few spectra substantially contribute to the formation of grain boundaries. Their linear relation to the intrinsic spectra of the bulk hexagonal phase is independent of the tilt angle. By examining the feature of the spectral intensities, we propose a definition of the interface width. The widths calculated from this definition are consistent with visual estimation.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220721T07:00:00Z
DOI: 10.1137/21M1463288
Issue No: Vol. 82, No. 4 (2022)

 On the HalfSpace Matching Method for Real Wavenumber

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Authors: AnneSophie BonnetBen Dhia, Simon N. ChandlerWilde, Sonia Fliss
Pages: 1287  1311
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 12871311, August 2022.
The HalfSpace Matching (HSM) method has recently been developed as a new method for the solution of twodimensional scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary conditions. Based on halfplane representations for the solution, the scattering problem is rewritten as a system coupling (1) a standard finite element discretization localized around the scatterer and (2) integral equations whose unknowns are traces of the solution on the boundaries of a finite number of overlapping halfplanes contained in the domain. While satisfactory numerical results have been obtained for real wavenumbers, wellposedness and equivalence of this HSM formulation to the original scattering problem have been established for complex wavenumbers only. In the present paper we show, in the case of a homogeneous background, that the HSM formulation is equivalent to the original scattering problem also for real wavenumbers, and so is wellposed, provided the traces satisfy radiation conditions at infinity analogous to the standard Sommerfeld radiation condition. As a key component of our argument we show that if the trace on the boundary of a halfplane satisfies our new radiation condition, then the corresponding solution to the halfplane Dirichlet problem satisfies the Sommerfeld radiation condition in a slightly smaller halfplane. We expect that this last result will be of independent interest, in particular in studies of rough surface scattering.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220726T07:00:00Z
DOI: 10.1137/21M1459216
Issue No: Vol. 82, No. 4 (2022)

 High Spots for the IceFishing Problem with Surface Tension

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Authors: Nathan Willis, Chee Han Tan, Christel Hohenegger, Braxton Osting
Pages: 1312  1335
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 13121335, August 2022.
In the icefishing problem, a halfspace of fluid lies below an infinite rigid plate (``the ice'') with a hole. We investigate the icefishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the effect of surface tension is called the Bond number. For holes that are infinite parallel strips or circular holes, we transform the problem to an equivalent eigenvalue integrodifferential equation on an interval and expand in the appropriate basis (Legendre and radial polynomials, respectively). We use computational methods to demonstrate that the high spot, i.e., the maximal elevation of the fundamental sloshing profile, for the icefishing problem is in the interior of the free surface for large Bond numbers, but for a sufficiently small Bond number the high spot is on the boundary of the free surface. While several papers have proven high spot results in the absence of surface tension as it depends on the shape of the container, to the best of our knowledge, this is the first study investigating the effects of surface tension on the location of the high spot.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220726T07:00:00Z
DOI: 10.1137/21M1458879
Issue No: Vol. 82, No. 4 (2022)

 Time and Energy Costs for Synchronization of KuramotoOscillator Networks
With or Without Noise Perturbation
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Authors: Nan Liang, Maoxing Liu, Yongzheng Sun, Rui Xiao, Lingzhi Zhao
Pages: 1336  1355
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 13361355, August 2022.
In this paper, time and energy costs for achieving synchronization of the Kuramotooscillator network with or without noise perturbation are investigated. In order to achieve synchronization and optimize time and energy consumption, a novel switching controller is designed, which combines the advantages of both the proportional feedback control method and the finitetime control technology. Sufficient conditions for achieving synchronization are established, and the estimates of time and energy costs are obtained mathematically as well. Particularly, the theoretical analysis and simulating calculation show that there exists a tradeoff between time and energy costs. That is to say, the energy consumption can be reduced by adjusting the control parameters, but the time cost will increase inevitably, and vice versa. Further, we find that for fixed weights of time and energy costs of the performance index, the optimal values of parameters can be chosen to minimize the total cost.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220726T07:00:00Z
DOI: 10.1137/21M1457928
Issue No: Vol. 82, No. 4 (2022)

 NearExact Radiating Fins via Boundary Tracing

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Authors: Conway Li, Neville Fowkes, Brendan Florio, Miccal Matthews
Pages: 1356  1368
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 13561368, August 2022.
In contexts such as space travel, thermal radiation is the primary mode of heat transfer. The StefanBoltzmann law gives rise to a boundary flux which is quartic in temperature, and this nonlinearity renders even the simplest of conductionradiation problems analytically insurmountable in more than one dimension. An unconventional approach known as boundary tracing allows for analytical inroads into flux boundary value problems that would otherwise require numerical study. In this paper, the method of boundary tracing is used to generate nearexact results for an infinite family of conductionradiation domains representing radiating fins; realistic lengths and temperatures can be realized.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220726T07:00:00Z
DOI: 10.1137/22M1476228
Issue No: Vol. 82, No. 4 (2022)

 Analysis of Obstacles Immersed in Viscous Fluids Using Brinkman's Law for
Steady Stokes and NavierStokes Equations
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Authors: Jorge Aguayo, Hugo Carrillo Lincopi
Pages: 1369  1386
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 13691386, August 2022.
From the steady Stokes and NavierStokes models, a penalization method has been considered by several authors for approximating those fluid equations around obstacles. In this work, we present a justification for using fictitious domains to study obstacles immersed in incompressible viscous fluids through a simplified version of Brinkman's law for porous media. If the scalar function $\psi$ is considered as the inverse of permeability, it is possible to study the singularities of $\psi$ as approximations of obstacles (when $\psi$ tends to $\infty$) or of the domain corresponding to the fluid (when $\psi = 0$ or is very close to 0). The strong convergence of the solution of the perturbed problem to the solution of the strong problem is studied, also considering error estimates that depend on the penalty parameter, for fluids modeled with both the Stokes and NavierStokes equations with inhomogeneous boundary conditions. A numerical experiment is presented that validates this result and allows us to study the application of this perturbed problem simulation of flows and the identification of obstacles.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220728T07:00:00Z
DOI: 10.1137/20M138569X
Issue No: Vol. 82, No. 4 (2022)

 Acoustics of a Partially Partitioned Narrow Slit Connected to a
HalfPlane: Case Study for Exponential QuasiBound States in the Continuum
and their Resonant Excitation
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Authors: Ory Schnitzer, Richard Porter
Pages: 1387  1410
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 13871410, August 2022.
Localized wave oscillations in an open system that do not decay or grow in time, despite their frequency lying within a continuous spectrum of radiation modes carrying energy to or from infinity, are known as bound states in the continuum (BIC). Small perturbations from the typically delicate conditions for BIC almost always result in the waves weakly coupling with the radiation modes, leading to leaky states called quasiBIC that have a large quality factor. We study the asymptotic nature of this weak coupling in the case of acoustic waves interacting with a rigid substrate featuring a partially partitioned slita setup that supports quasiBIC that exponentially approach BIC as the slit is made increasingly narrow. In that limit, we use the method of matched asymptotic expansions in conjunction with reciprocal relations to study those quasiBIC and their resonant excitation. In particular, we derive a leading approximation for the exponentially small imaginary part of each wavenumber eigenvalue (inversely proportional to quality factor), which is beyond all orders of the expansion for the wavenumber eigenvalue itself. Furthermore, we derive a leading approximation for the exponentially large amplitudes of the states in the case where they are resonantly excited by a plane wave at oblique incidence. These resonances occur in exponentially narrow wavenumber intervals and are physically manifested in cylindricaldipolar waves emanating from the slit aperture and exponentially large field enhancements inside the slit. The asymptotic approximations are validated against numerical calculations.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220728T07:00:00Z
DOI: 10.1137/22M1470426
Issue No: Vol. 82, No. 4 (2022)

 Boundary Tracing for Laplace's Equation with Conformal Mapping

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Authors: Conway Li, Neville Fowkes, Miccal Matthews
Pages: 1411  1422
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 14111422, August 2022.
The conformal mapping technique has long been used to obtain exact solutions to Laplace's equation in twodimensional domains with awkward geometries. However, a major limitation of the technique is that it is only directly compatible with Dirichlet and zeroflux Neumann boundary conditions. It would be useful to have a means of adapting the technique to handle more general boundary conditions, for example, Robin or nonlinear flux conditions. Boundary tracing is an unconventional method for tackling boundary value problems with generic flux boundary conditions, where one takes a known solution to the field equation and seeks new boundaries satisfying the prescribed boundary condition. In this paper, we adapt boundary tracing for compatibility with conformal mapping to produce a new prescription for studying Laplace's equation coupled with general flux boundary conditions. We illustrate the procedure via two simple examples involving heat transfer. In both cases, we demonstrate how to construct infinite families of nontrivial domains in which the solution to the chosen flux boundary value problem is exactly equal to a selected harmonic function.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220802T07:00:00Z
DOI: 10.1137/22M1476241
Issue No: Vol. 82, No. 4 (2022)

 Soil Searching by an Artificial Root

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Authors: Fabio Ancona, Alberto Bressan, Maria Teresa Chiri
Pages: 1423  1445
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 14231445, August 2022.
We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integropartial differential equations: one for the growth of the body and the other for the elongation of the tip. At any given time, the angular velocity of the root is obtained by solving a minimization problem with state constraints. We prove the existence of solutions to the evolution problem, up to the first time where a “breakdown configuration” is reached. Some numerical simulations are performed to test the effectiveness of our feedback control algorithm.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220808T07:00:00Z
DOI: 10.1137/20M1338678
Issue No: Vol. 82, No. 4 (2022)

 Spurious QuasiResonances in Boundary Integral Equations for the Helmholtz
Transmission Problem
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Authors: Ralf Hiptmair, Andrea Moiola, Euan A. Spence
Pages: 1446  1469
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 14461469, August 2022.
We consider the Helmholtz transmission problem with piecewiseconstant material coefficients and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral operators grow rapidly through an increasing sequence of frequencies, even though this is not the case for the solution operator of the transmission problem; we call this phenomenon that of spurious quasiresonances. We give a rigorous explanation of why and when spurious quasiresonances occur and propose modified boundary integral equations that are not affected by them.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220811T07:00:00Z
DOI: 10.1137/21M1447052
Issue No: Vol. 82, No. 4 (2022)

 Slow Migration of Brine Inclusions in FirstYear Sea Ice

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Authors: Noa Kraitzman, Keith Promislow, Brian Wetton
Pages: 1470  1494
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 14701494, August 2022.
We derive a thermodynamically consistent model for liquidsolid phase change in sea ice by incorporating a phase sensitive scalar to a classical framework of liquidsolid phase change. The entropy of the scalar is taken relative to the liquid molar fraction which induces a chemotactic behavior. This provides a transparent mechanism for the rejection of the scalar under formation of the solid phase. We identify slow varying coordinates, including the scalar density relative to liquid molarity weighted by latent heat, and use multiscale analysis to derive a quasiequilibrium Stefantype problem via a sharp interface scaling. The singular limit is underdetermined, and the leading order system is closed by imposing local conservation of the scalar under interface perturbation. The quasisteady system determines interface motion as balance of curvature, temperature gradient, and scalar density. We resolve this numerically for axisymmetric surfaces and show that the thermal gradients typical of arctic sea ice can have a decisive impact on the mode of pinchoff of cylindrical brine inclusions and on the size distribution of the resultant spherical shapes. The density and distribution of these inclusion sizes is a key component of sea ice albedo which factors into global climate models.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220811T07:00:00Z
DOI: 10.1137/21M1440244
Issue No: Vol. 82, No. 4 (2022)

 Diffraction by a RightAngled NoContrast Penetrable Wedge Revisited: A
Double WienerHopf Approach
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Authors: Valentin D. Kunz, Raphael Assier
Pages: 1495  1519
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 14951519, August 2022.
In this paper, we revisit Radlow's innovative approach to diffraction by a penetrable wedge by means of a double WienerHopf technique. We provide a constructive way of obtaining his ansatz and give yet another reason for why his ansatz cannot be the true solution to the diffraction problem at hand. The twocomplexvariable WienerHopf equation is reduced to a system of two equations, one of which contains Radlow's ansatz plus some correction term consisting of an explicitly known integral operator applied to a yet unknown function, whereas the other equation, the compatibility equation, governs the behavior of this unknown function.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220811T07:00:00Z
DOI: 10.1137/21M1461861
Issue No: Vol. 82, No. 4 (2022)

 Classifying Minimum Energy States for Interacting Particles: Spherical
Shells
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Authors: Cameron Davies, Tongseok Lim, Robert J. McCann
Pages: 1520  1536
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 15201536, August 2022.
Particles interacting through longrange attraction and shortrange repulsion given by powerlaws have been widely used to model physical and biological systems and to predict or explain many of the patterns they display. Apart from rare values of the attractive and repulsive exponents $(\alpha,\beta)$, the energy minimizing configurations of particles are not explicitly known, although simulations and local stability considerations have led to conjectures with strong evidence over a much wider region of parameters. For dimension $n\ge 2$ and for a segment $\beta=2
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220815T07:00:00Z
DOI: 10.1137/21M1455309
Issue No: Vol. 82, No. 4 (2022)

 Wobbling of Pedestrian Bridges

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Authors: Guillermo H. Goldsztein
Pages: 1537  1557
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 15371557, August 2022.
On June 10, 2000, the Millennium Bridge in London opened to the public. As people crossed it, it wobbled, leading to its closure three days later. It reopened after modifications to prevent the wobbling were made. To gain understanding on the physics behind this event, we developed and studied a toy model of a pedestrianbridge system. Within this model, when the natural frequency of the bridge is the same as the walking frequency of the pedestrian, the lateral oscillations of the bridge and the pedestrian synchronize in antiphase. The model predicts the amplitude of the bridge oscillations.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220815T07:00:00Z
DOI: 10.1137/21M1463148
Issue No: Vol. 82, No. 4 (2022)

 Efficient and Reliable Overlay Networks for Decentralized Federated
Learning
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Authors: Yifan Hua, Kevin Miller, Andrea L. Bertozzi, Chen Qian, Bao Wang
Pages: 1558  1586
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 15581586, August 2022.
We propose nearoptimal overlay networks based on $d$regular expander graphs to accelerate decentralized federated learning (DFL) and improve its generalization. In DFL a massive number of clients are connected by an overlay network, and they solve machine learning problems collaboratively without sharing raw data. Our overlay network design integrates spectral graph theory and the theoretical convergence and generalization bounds for DFL. As such, our proposed overlay networks accelerate convergence, improve generalization, and enhance robustness to client failures in DFL with theoretical guarantees. Also, we present an efficient algorithm to convert a given graph to a practical overlay network and maintain the network topology after potential client failures. We numerically verify the advantages of DFL with our proposed networks on various benchmark tasks, ranging from image classification to language modeling using hundreds of clients.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220818T07:00:00Z
DOI: 10.1137/21M1465081
Issue No: Vol. 82, No. 4 (2022)

 On the Dynamics of a Diffusive FootandMouth Disease Model with Nonlocal
Infections
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Authors: GuiQuan Sun, HongTao Zhang, LiLi Chang, Zhen Jin, Hao Wang, Shigui Ruan
Pages: 1587  1610
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 15871610, August 2022.
Footandmouth disease (FMD) is an acute and highly contagious infectious disease of clovenhoofed animals. In order to reveal the transmission dynamics and explore effective control measures of FMD, we formulate a diffusive FMD model with a fixed latent period and nonlocal infections. The threshold dynamics of the FMD model are determined by using the basic reproduction number $\mathcal{R}_0$: if $\mathcal{R}_01$: at a low infection level, the faster the infectious individuals and virus diffuse, the faster the disease reaches the steady state. However, at a high infection level (i.e., the value of $\mathcal{R}_0$ is relatively large), the influence of diffusion on time from initial values to steady state is more complicated, but at least it is certain that the time will be shortened overall. By carrying out some sensitivity analysis of $\mathcal{R}_0 (>1)$ and the equilibrium value of the infectious individuals $I^\ast$ in terms of $\beta_1$ and $\beta_2,$ it is found that the $(\beta_1, \beta_2)$plane is divided into two regions by the intersection of two parameterrelated surfaces; the sensitivity of $\mathcal{R}_0$ and $I^\ast$ varies when $\beta_1$ and $\beta_2$ belong to different regions. When the values of both $\beta_1$ and $\beta_2$ are very large or very small, $\beta_1$ plays a more significant role in the transmission of FMD. These results indicate that stamping out the infected individuals and blocking the epidemic spots and areas are effective in preventing and controlling the spread of FMD.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220818T07:00:00Z
DOI: 10.1137/21M1412992
Issue No: Vol. 82, No. 4 (2022)

 On the Validity of the TightBinding Method for Describing Systems of
Subwavelength Resonators
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Authors: Habib Ammari, Francesco Fiorani, Erik Orvehed Hiltunen
Pages: 1611  1634
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 16111634, August 2022.
The goal of this paper is to relate the capacitance matrix formalism to the tightbinding approximation. By doing so, we open the way to the use of mathematical techniques and tools from condensed matter theory in the mathematical and numerical analysis of metamaterials, in particular for the understanding of their topological properties. We first study how the capacitance matrix formalism, both when the material parameters are static and modulated, can be posed in a Hamiltonian form. Then, we use this result to compare this formalism to the tightbinding approximation. We prove that the correspondence between the capacitance formulation and the tightbinding approximation holds only in the case of dilute resonators. On the other hand, the tightbinding model is often coupled with a nearestneighbor approximation, whereby longrange interactions are neglected. Even in the dilute case, we show that longrange interactions between subwavelength resonators are relatively strong and nearestneighbor approximations are not generally appropriate.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220822T07:00:00Z
DOI: 10.1137/21M1449804
Issue No: Vol. 82, No. 4 (2022)

 Phase Separation in Systems of Interacting Active Brownian Particles

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Authors: Maria Bruna, Martin Burger, Antonio Esposito, Simon M. Schulz
Pages: 1635  1660
Abstract: SIAM Journal on Applied Mathematics, Volume 82, Issue 4, Page 16351660, August 2022.
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for selfpropelled particles. We present four microscopic models with different types of repulsive interactions between particles and their associated macroscopic models, which are formally obtained using different coarsegraining methods. The macroscopic limits are integrodifferential equations for the density in phase space (positions and orientations) of the particles and may include nonlinearities in both the diffusive and advective components. In contrast to passive particles, systems of active particles can undergo phase separation without any attractive interactions, a mechanism known as motilityinduced phase separation (MIPS). We explore the onset of such a transition for each model in the parameter space of occupied volume fraction and Péclet number via a linear stability analysis and numerical simulations at both the microscopic and macroscopic levels. We establish that one of the models, namely, the meanfield model which assumes longrange repulsive interactions, cannot explain the emergence of MIPS. In contrast, MIPS is observed for the remaining three models that assume shortrange interactions that localize the interaction terms in space.
Citation: SIAM Journal on Applied Mathematics
PubDate: 20220830T07:00:00Z
DOI: 10.1137/21M1452524
Issue No: Vol. 82, No. 4 (2022)
