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Trust your source: quantifying source condition elements for variational regularisation methods IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-03-11 Martin Benning, Tatiana A Bubba, Luca Ratti, Danilo Riccio
Source conditions are a key tool in regularisation theory that are needed to derive error estimates and convergence rates for ill-posed inverse problems. In this paper, we provide a recipe to practically compute source condition elements as the solution of convex minimisation problems that can be solved with first-order algorithms. We demonstrate the validity of our approach by testing it on two inverse
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Global existence and boundedness in a two-species chemotaxis-fluid system with indirect pursuit-evasion interaction IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-03-03 Chao Liu, Bin Liu
This paper investigates a two-species chemotaxis-fluid system with indirect pursuit-evasion interaction in a bounded domain with smooth boundary. Under suitably regular initial data and no-flux/no-flux/no-flux/no-flux/Dirichlet boundary conditions, we prove that the system possesses a global bounded classical solution in the two-dimensional and three-dimensional cases. Our results extend the result
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The comparison between effects of heterogeneous and homogeneous half-spaces underlying homogeneous layer on solitary Love waves IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-02-21 Ekin Deliktas-Ozdemir
A comparative analysis is performed on the effects of heterogeneity in both linear and nonlinear material characteristics of half-space on the propagation of bright and dark solitary Love waves in a nonlinear layered half-space. The layer is assumed to be homogeneous, nonlinear, elastic while the half-space is vertically heterogeneous. The problem is formulated for two types of elastic materials, incompressible
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Tangential Tensor Fields on Deformable Surfaces – How to Derive Consistent L2-Gradient Flows IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-02-19 Ingo Nitschke, Souhayl Sadik, Axel Voigt
We consider gradient flows of surface energies which depend on the surface by a parameterization and on a tangential tensor field. The flow allows for dissipation by evolving the parameterization and the tensor field simultaneously. This requires the choice of a notation for independence. We introduce different gauges of surface independence and show their consequences for the evolution. In order to
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Learning a microlocal prior for limited-angle tomography IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-02-07 Siiri Rautio, Rashmi Murthy, Tatiana A Bubba, Matti Lassas, Samuli Siltanen
Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. In this paper, a new method is introduced
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The slow viscous flow around a general rectangular doubly-periodic arrays of infinite slender cylinders IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-02-01 Lyndon Koens, Rohan Vernekar, Timm Krüger, Maciej Lisicki, David W Inglis
The slow viscous flow through a doubly-periodic array of cylinders does not have an analytical solution. However, as a reduced model for the flow within fibrous porous media and microfluidic arrays, this solution is important for many real-world systems. We asymptotically determine the flow around a general rectangular doubly-periodic array of infinite slender cylinders, extending the existing asymptotic
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A Bubble Model for the Gating of Kv Channels IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-01-25 Zilong Song, Robert Eisenberg, Shixin Xu, Huaxiong Huang
Voltage-gated K$_{\mathrm{v}}$ channels play fundamental roles in many biological processes, such as the generation of the action potential. The gating mechanism of K$_{\mathrm{v}}$ channels is characterized experimentally by single-channel recordings and ensemble properties of the channel currents. In this work, we propose a bubble model coupled with a Poisson-Nernst-Planck (PNP) system to capture
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Reaction dynamics and early-time behaviour of chemical decontamination IMA J. Appl. Math. (IF 1.2) Pub Date : 2024-01-25 S Murphy, M Vynnycky, S L Mitchell, D O’Kiely
When a hazardous chemical soaks into a porous material such as a concrete floor, it can be difficult to remove. One approach is chemical decontamination, where a cleanser is added to react with and neutralise the contaminating agent. The goal of this paper is to investigate the reaction dynamics and the factors that affect the efficacy of the decontamination procedure. We consider a one-dimensional
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Interfacial growth morphologies in dense eutectic crystal mushes IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-12-01 A C Fowler, Marian B Holness
We consider the interfacial growth morphologies of crystals growing in contact in crystal mushes, with a specific application to those formed by the solidification of basaltic magma. We focus on the particular case of an augite (pyroxene) crystal growing between two plagioclase crystals. The augite is treated as an equant unfaceted crystal, whereas the plagioclase is faceted, and our treatment applies
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Analyzing inexact hypergradients for bilevel learning IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-12-01 Matthias J Ehrhardt, Lindon Roberts
Estimating hyperparameters has been a long-standing problem in machine learning. We consider the case where the task at hand is modeled as the solution to an optimization problem. Here the exact gradient with respect to the hyperparameters cannot be feasibly computed and approximate strategies are required. We introduce a unified framework for computing hypergradients that generalizes existing methods
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A unified and constructive framework for the universality of neural networks IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-11-12 Tan Bui-Thanh
One of the reasons why many neural networks are capable of replicating complicated tasks or functions is their universal approximation property. Though the past few decades have seen tremendous advances in theories of neural networks, a single constructive and elementary framework for neural network universality remains unavailable. This paper is an effort to provide a unified and constructive framework
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A Reduced Landau-de Gennes Study for Nematic Equilibria in Three-Dimensional Prisms IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-11-10 Yucen Han, Baoming Shi, Lei Zhang, Apala Majumdar
We model nematic liquid crystal configurations inside three-dimensional prisms, with a polygonal cross-section and Dirichlet boundary conditions on all prism surfaces. We work in a reduced Landau-de Gennes framework, and the Dirichlet conditions on the top and bottom surfaces are special in the sense, that they are critical points of the reduced Landau-de Gennes energy on the polygonal cross-section
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Application of the topological sensitivity method to the detection of Breast cancer IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-10-23 Sabeur Mansouri, Mohamed BenSalah
This paper is concerned with an approach based on the topological sensitivity notion to solve a geometric inverse problem for a linear wave equation. The considered inverse problem is motivated by elastography. More precisely, the modeling of our application system has been aimed toward the detection of a breast tumor, in particular, and to enable the calculation of the tumor size, location, and type
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Oscillatory and regularized shock waves for a dissipative Peregrine-Boussinesq system IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-10-19 Larkspur Brudvik-Lindner, Dimitrios Mitsotakis, Athanasios E Tzavaras
We consider a dissipative, dispersive system of the Boussinesq type, which describes wave phenomena in scenarios where dissipation plays a significant role. Examples include undular bores in rivers or oceans, where turbulence-induced dissipation significantly influences their behavior. In this study, we demonstrate that the proposed system admits traveling wave solutions known as diffusive-dispersive
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The feasibility and inevitability of stealth attacks IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-10-19 Ivan Y Tyukin, Desmond J Higham, Alexander Bastounis, Eliyas Woldegeorgis, Alexander N Gorban
We develop and study new adversarial perturbations that enable an attacker to gain control over decisions in generic Artificial Intelligence (AI) systems including deep learning neural networks. In contrast to adversarial data modification, the attack mechanism we consider here involves alterations to the AI system itself. Such a stealth attack could be conducted by a mischievous, corrupt or disgruntled
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Initial-boundary value problem for a fractional heat equation on an interval IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-10-12 Y Peña Pérez, J Sánchez Ortíz, F J Ariza Hernández, M P Árciga Alejandre
In this paper, we study a Dirichlet problem for a fractional heat equation, with spacial fractional derivative in the sense of Riemann-Liouville on a finite interval. The main ideas of Fokas method is employed, where the Lax pairs are used to obtain an integral representation of solutions.
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Uniqueness of refractive indices and transmission coefficients by an inhomogeneous medium in acoustic scattering IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-09-02 Jianli Xiang, Guozheng Yan
We are concerned with the inverse scattering problem of recovering the refractive indices and transmission coefficients by the corresponding acoustic far-field measurement encoded into the scattering amplitude. Our first uniqueness result is to determine a constant refractive index by the fixed incident direction scattering amplitude, the proof of which is mainly based on the discreteness of the corresponding
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Solving forward and inverse problems involving a nonlinear three-dimensional partial differential equation via asymptotic expansions IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-08-28 Dmitrii Chaikovskii, Ye Zhang
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction–diffusion–advection equation. By using an asymptotic expansion with the local coordinates in the transition-layer region, we prove the existence and uniqueness of a smooth solution with a sharp transition layer for a three-dimensional
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Analysis of point-contact models of the bounce of a hard spinning ball on a compliant frictional surface. IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-08-02 Stanisław W Biber, Alan R Champneys, Robert Szalai
Inspired by the turf-ball interaction in golf, this paper seeks to understand the bounce of a ball that can be modelled as a rigid sphere and the surface as supplying a viscoelastic contact force in addition to Coulomb friction. A general formulation is proposed that models the finite time interval of bounce from touch-down to lift-off. Key to the analysis is understanding transitions between slip
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Adversarial Ink: Componentwise Backward Error Attacks on Deep Learning IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-06-27 Lucas Beerens, Desmond J Higham
Deep neural networks are capable of state-of-the-art performance in many classification tasks. However, they are known to be vulnerable to adversarial attacks—small perturbations to the input that lead to a change in classification. We address this issue from the perspective of backward error and condition number, concepts that have proved useful in numerical analysis. To do this, we build on the work
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Mappings, Dimensionality and Reversing Out of Deep Neural Networks IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-06-23 Zhaofang Cui, Peter Grindrod
We consider a large cloud of vectors formed at each layer of a standard neural network, corresponding to a large number of separate inputs which were presented independently to the classifier. Although the embedding dimension (the total possible degrees of freedom) reduces as we pass through successive layers, from input to output, the actual dimensionality of the point clouds that the layers contain
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Nonlinear ill-posed problem in low-dose dental cone-beam computed tomography IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-06-23 Hyoung Suk Park, Chang Min Hyun, Jin Keun Seo
This paper describes the mathematical structure of the ill-posed nonlinear inverse problem of low-dose dental cone-beam computed tomography (CBCT) and explains the advantages of a deep learning-based approach to the reconstruction of computed tomography images over conventional regularization methods. This paper explains the underlying reasons why dental CBCT is more ill-posed than standard computed
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Estimating conformal capacity using asymptotic matching IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-06-23 Hiroyuki Miyoshi, Darren G Crowdy
Conformal capacity is a mathematical quantity relevant to a wide range of physical and mathematical problems and there has been a recent resurgence of interest in devising new methods for its computation. In this paper we show how ideas from matched asymptotics can be used to derive estimates for conformal capacity. The formulas derived here are explicit, and evidence is given that they provide excellent
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Traveling edge states in massive Dirac equations along slowly varying edges IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-21 Pipi Hu, Peng Xie, Yi Zhu
Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling wave solutions to the two-dimensional Dirac equation with a domain wall mass in this work. It is known that the system admits exact and explicit traveling wave solutions, which are termed edge states if the interface is
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Stability of fixed points in an approximate solution of the spring-mass running model IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-13 Zofia Wróblewska, Piotr Kowalczyk, Łukasz Płociniczak
We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we introduce an analytical approximation of a reduced mapping. Although approximate solutions already exist in the literature, our results have some benefits over them. They give us
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Dynamics of an age-structured HIV model with general nonlinear infection rate IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-04 Yuan Yuan, Xianlong Fu
In this paper, the asymptotical behavior of an age-structured HIV infection model with general nonlinear infection function and logistic proliferation term is studied. Based on the existence of the equilibria and theory of operator semigroups, linearized stability/instability of the disease-free and endemic equilibria are investigated through the distribution of eigenvalues of the linear operator.
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Global threshold dynamics of a spatial chemotactic mosquito-borne disease model IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-04 Kai Wang, Hao Wang, Hongyong Zhao
It is natural that mosquitoes move toward high human population density and environmental heterogeneity plays a pivotal role on disease transmission, and thus we formulate and analyze a mosquito-borne disease model with chemotaxis and spatial heterogeneity. The global existence and boundedness of solutions are proven to guarantee the solvability of the model and is challenging due to the model complexity
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On global in time self-similar solutions of Smoluchowski equation with multiplicative kernel IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-04 G Breschi, M A Fontelos
We study the similarity solutions (SS) of Smoluchowski coagulation equation with multiplicative kernel $K(x,y)=(xy)^{s}$ for $s<\frac {1}{2}$. When $s<0$ , the SS consists of three regions with distinct asymptotic behaviours. The appropriate matching yields a global description of the solution consisting of a Gamma distribution tail, an intermediate region described by a lognormal distribution and
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On a hierarchy of effective models for the biomechanics of human compact bone tissue IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-04 Grigor Nika
We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy of four characteristic lengths: The size of the heterogeneities, two intrinsic lengths of the constituents, and the overall characteristic length of the domain. Depending
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Identifying a response parameter in a model of brain tumor evolution under therapy IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-04-04 G Baravdish, B T Johansson, O Svensson, W Ssebunjo
A nonlinear conjugate gradient method is derived for the inverse problem of identifying a treatment parameter in a nonlinear model of reaction-diffusion type corresponding to the evolution of brain tumors under therapy. The treatment parameter is reconstructed from additional information about the tumour taken at a fixed instance of time. Well-posedness of the direct problems used in the iterative
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Inverse problems for a model of biofilm growth IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-03-27 Tommi Brander, Daniel Lesnic, Kai Cao
A bacterial biofilm is an aggregate of micro-organisms growing fixed onto a solid surface, rather than floating freely in a liquid. Biofilms play a major role in various practical situations such as surgical infections and water treatment. We consider a non-linear PDE model of biofilm growth subject to initial and Dirichlet boundary conditions, and the inverse coefficient problem of recovering the
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Scattering resonances in unbounded transmission problems with sign-changing coefficient IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-20 Camille Carvalho, Zoïs Moitier
It is well-known that classical optical cavities can exhibit localized phenomena associated to scattering resonances, leading to numerical instabilities in approximating the solution. This result can be established via the “quasimodes to resonances” argument from the black box scattering framework. Those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery
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The analytic extension of solutions to initial-boundary value problems outside their domain of definition IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-13 Matthew Farkas, Jorge Cisneros, Bernard Deconinck
We examine the analytic extension of solutions of linear, constant-coefficient initial-boundary value problems outside their spatial domain of definition. We use the Unified Transform Method or Method of Fokas, which gives a representation for solutions to half-line and finite-interval initial-boundary value problems as integrals of kernels with explicit spatial and temporal dependence. These solution
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Scattering in a partially open waveguide: the forward problem IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-02 Laurent Bourgeois, Sonia Fliss, Jean-François Fritsch, Christophe Hazard, Arnaud Recoquillay
This paper is dedicated to an acoustic scattering problem in a two-dimensional partially open waveguide, in the sense that the left part of the waveguide is closed, that is with a bounded cross-section, while the right part is bounded in the transverse direction by some Perfectly Matched Layers that mimic the situation of an open waveguide, that is with an unbounded cross-section. We prove well-posedness
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On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-02 Nastaran Naghshineh, W Cade Reinberger, Nathaniel S Barlow, Mohamed A Samaha, Steven J Weinstein
We examine the power series solutions of two classical nonlinear ordinary differential equations of fluid mechanics that are mathematically related by their large-distance asymptotic behaviors in semi-infinite domains. The first problem is that of the “Sakiadis” boundary layer over a moving flat wall, for which no exact analytic solution has been put forward. The second problem is that of a static
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Homogenization results for the generator of multiscale Langevin dynamics in weighted Sobolev spaces IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-02 Andrea Zanoni
We study the homogenization of the Poisson equation with a reaction term and of the eigenvalue problem associated to the generator of multiscale Langevin dynamics. Our analysis extends the theory of two-scale convergence to the case of weighted Sobolev spaces in unbounded domains. We provide convergence results for the solution of the multiscale problems above to their homogenized surrogate. A series
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Computing spectral properties of topological insulators without artificial truncation or supercell approximation IMA J. Appl. Math. (IF 1.2) Pub Date : 2023-02-01 Matthew J Colbrook, Andrew Horning, Kyle Thicke, Alexander B Watson
Topological insulators (TIs) are renowned for their remarkable electronic properties: quantised bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in the presence of material defects and disorder. Computations of these physical properties generally rely on artificial periodicity (the supercell approximation, which struggles in the presence of edges), or unphysical boundary
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On a random entanglement problem IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-11-04 Gage Bonner, Jean-Luc Thiffeault, Benedek Valkó
We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental groupoid of the region. We quantify entanglement of the path with the length of the appropriate element in this groupoid. Our main results are a law of large numbers
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Numerical methods and hypoexponential approximations for gamma distributed delay differential equations IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-11-02 Tyler Cassidy, Peter Gillich, Antony R Humphries, Christiaan H van Dorp
Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic gamma distributed DDEs have not previously been implemented. Modellers have therefore resorted to approximating the gamma distribution with an Erlang distribution and using the linear chain technique to derive an equivalent system of ordinary differential
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Extensions of the d’Alembert formulae to the half line and the finite interval obtained via the unified transform IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-10-29 A S Fokas, K Kalimeris
We derive the solution of the one dimensional wave equation for the Dirichlet and Robin initial-boundary value problems (IBVPs) formulated on the half line and the finite interval, with nonhomogeneous boundary conditions. Although explicit formulas already exist for these problems, the unified transform method provides a convenient framework for deriving different representations of the solutions for
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Acceleration of Gossip Algorithms through the Euler–Poisson–Darboux Equation IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-10-27 Raphaël Berthier, Mufan (Bill) Li
Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach, and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. These limits lead to well-known partial differential equations (PDEs) with insightful properties. On lattices, we prove that the non-accelerated
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Optimal analyticity estimates for non-linear active-dissipative evolution equations IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-10-14 Demetrios T Papageorgiou, Yiorgos-Sokratis Smyrlis, Ruben J Tomlin
Active-dissipative evolution equations emerge in a variety of physical and technological applications including liquid film flows, flame propagation, epitaxial film growth in materials manufacturing, to mention a few. They are characterised by three main ingredients: a term producing growth (active), a term providing damping at short length scales (dissipative), and a nonlinear term that transfers
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Singular fourth-order Sturm–Liouville operators and acoustic black holes IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-10-10 Boris P Belinskiy, Don B Hinton, Roger A Nichols
We derive conditions for a one-term fourth-order Sturm–Liouville operator on a finite interval with one singular endpoint to have essential spectrum equal to $[0,\infty )$ or $\varnothing $. Of particular usefulness are Kummer–Liouville transformations which have been a valuable tool in the study of second-order equations. Applications to a mechanical beam with a thickness tapering to zero at one of
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The Hermitian symmetric space Fokas-Lenells equation: spectral analysis and long-time asymptotics IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-09-07 Xianguo Geng, Kedong Wang, Mingming Chen
Based on the inverse scattering transformation, we carry out spectral analysis of the $4\times 4$ matrix spectral problems related to the Hermitian symmetric space Fokas-Lenells equation, by which the solution of the Cauchy problem of the Hermitian symmetric space Fokas-Lenells equation is transformed into the solution of a Riemann-Hilbert problem. The nonlinear steepest descent method is extended
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Boundary integral equation methods for the solution of scattering and transmission 2D elastodynamic problems IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-08-24 Víctor Domínguez, Catalin Turc
We introduce and analyse various regularized combined field integral equations (CFIER) formulations of time-harmonic Navier equations in media with piece-wise constant material properties. These formulations can be derived systematically starting from suitable coercive approximations of Dirichlet-to-Neumann operators (DtN), and we present a periodic pseudodifferential calculus framework within which
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On an inverse photoacoustic tomography problem of small absorbers with inhomogeneous sound speed IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-08-24 Hanin Al Jebawy, Abdellatif El Badia
This work is devoted to the study of the inverse photoacoustic tomography (PAT) problem. It is an imaging technique similar to TAT studied in El Badia & Ha-Duong (2000); however, in this case, a high-frequency radiation is delivered into the biological tissue to be imaged, such as visible or near infra red light that are characterized by their high frequency compared with that of radio waves that are
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Polarity-driven laminar pattern formation by lateral-inhibition in 2D and 3D bilayer geometries IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-08-12 Joshua W Moore, Trevor C Dale, Thomas E Woolley
Fine-grain patterns produced by juxtacrine signalling have previously been studied using static monolayers as cellular domains. However, analytic results are usually restricted to a few cells due to the algebraic complexity of non-linear dynamical systems. Motivated by concentric patterning of Notch expression observed in the mammary gland, we combine concepts from graph and control theory to represent
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A Generalized mathematical representation of the shape of the Wheatley heart valve and the associated static stress fields upon opening and closing IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-08-01 H L Oliveira, S McKee, G C Buscaglia, J A Cuminato, I W Stewart, D J Wheatley
This note extends previous work of the authors modelling the Wheatley valve by using six intersecting and contiguous ellipses to obtain a generalized mathematical representation of the Wheatley valve: this provides a number of free parameters that could be employed to obtain an optimal design. Since optimality is multi-objective with many of the objectives conflicting we focus on the stresses imposed
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Asymptotic solutions of the SIR and SEIR models well above the epidemic threshold IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-07-26 Gregory Kozyreff
A simple and explicit expression of the solution of the SIR epidemiological model of Kermack and McKendrick is constructed in the asymptotic limit of large basic reproduction numbers ${\mathsf R_0}$. The proposed formula yields good qualitative agreement already when ${\mathsf R_0}\geq 3$ and rapidly becomes quantitatively accurate as larger values of ${\mathsf R_0}$ are assumed. The derivation is
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Modelling alternating current effects in a submerged arc furnace IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-07-14 Ellen K Luckins, James M Oliver, Colin P Please, Benjamin M Sloman, Aasgeir M Valderhaug, Robert A Van Gorder
Modelling the production of silicon in a submerged arc furnace (SAF) requires accounting for the wide range of timescales of the different physical and chemical processes: the electric current which is used to heat the furnace varies over a timescale of around $10^{-2}\,$ s, whereas the flow and chemical consumption of the raw materials in the furnace occurs over several hours. Models for the silicon
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Grazing bifurcations and transitions between periodic states of the PP04 model for the glacial cycle IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-07-10 Chris Budd, Kgomotso S Morupisi
We look at the periodic behaviour of the Earth’s glacial cycles and the transitions between different periodic states when either external parameters (such as $\omega $) or internal parameters (such as $d$) are varied. We model this using the PP04 model of climate change. This is a forced discontinuous Filippov (non-smooth) dynamical system. When periodically forced this has coexisting periodic orbits
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The factorization method for inverse scattering by a two-layered cavity with conductive boundary condition IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-04-05 Jianguo Ye, Guozheng Yan
In this paper we consider the inverse scattering problem of determining the shape of a two-layered cavity with conductive boundary condition from sources and measurements placed on a curve inside the cavity. First, we show the well-posedness of the direct scattering problem by using the boundary integral equation method. Then, we prove that the factorization method can be applied to reconstruct the
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Quasisteady models for weld temperatures in fused filament fabrication IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-04-01 D A Edwards
Abstract During fused filament fabrication (FFF), strands of hot extruded polymer are layered onto a cooler substrate. The bond strength between layers is related to the weld temperature at the polymer/substrate interface, and hence understanding temperature evolution is of keen interest. A series of increasingly sophisticated models is presented: a standard heat equation, an unsteady fin equation
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Integrability of local and non-local non-commutative fourth-order quintic non-linear Schrödinger equations IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-03-17 Simon J A Malham
Abstract We prove integrability of a generalized non-commutative fourth-order quintic non-linear Schrödinger equation. The proof is relatively succinct and rooted in the linearization method pioneered by Ch. Pöppe. It is based on solving the corresponding linearized partial differential system to generate an evolutionary Hankel operator for the ‘scattering data’. The time-evolutionary solution to the
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Stability analysis of a standby system with an unreliable server and switching failure IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-03-11 Chao Gao,Xing-Min Chen
Abstract This paper is devoted to analysing stability of a standby system with an unreliable server and switching failure, where both the time-to-repair of units and the time-to-repair of server follow general distributions. By employing $C_0$ semigroup theory, we show that time-dependent solution of the system converges to steady-state solution under a rather mild condition. Further, if component’
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A parallel sampling algorithm for some nonlinear inverse problems IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-01-27 Darko Volkov
We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data are noisy and that the linear part of the problem is ill-posed. The vector of nonlinear parameters ${m} $ is modeled as a random variable. A dilation parameter $\alpha $ is used to scale the regularity
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Corrigendum to: Reconstruction of an impenetrable obstacle in anisotropic inhomogeneous background IMA J. Appl. Math. (IF 1.2) Pub Date : 2021-11-19 Kow P, Wang J.
MOST10.13039/100007225108-2115-M-002-002-MY3109-2115-M-002-001-MY3
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Delayed Hopf Bifurcation and Space–Time Buffer Curves in the Complex Ginzburg–Landau Equation IMA J. Appl. Math. (IF 1.2) Pub Date : 2022-01-13 Ryan Goh, Tasso J Kaper, Theodore Vo
In this article, the recently discovered phenomenon of delayed Hopf bifurcations (DHB) in reaction–diffusion partial differential equations (PDEs) is analysed in the cubic Complex Ginzburg–Landau equation, as an equation in its own right, with a slowly varying parameter. We begin by using the classical asymptotic methods of stationary phase and steepest descents on the linearized PDE to show that solutions
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Long-time solutions of scalar hyperbolic reaction equations incorporating relaxation and the Arrhenius combustion nonlinearity IMA J. Appl. Math. (IF 1.2) Pub Date : 2021-12-20 J A Leach, Andrew P Bassom
We consider an initial-value problem based on a class of scalar nonlinear hyperbolic reaction–diffusion equations of the general form $$\begin{align*} & u_{\tau\tau}+u_{\tau}=u_{{xx}}+\varepsilon (F(u)+F(u)_{\tau} ), \end{align*}$$in which ${x}$ and $\tau $ represent dimensionless distance and time, respectively, and $\varepsilon>0$ is a parameter related to the relaxation time. Furthermore, the reaction
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Dynamical aspects of a restricted three-vortex problem IMA J. Appl. Math. (IF 1.2) Pub Date : 2021-10-18 Sreethin Sreedharan Kallyadan, Priyanka Shukla
Point vortex systems that include vortices with constant coordinate functions are largely unexplored, even though they have reasonable physical interpretations in the geophysical context. Here, we investigate the dynamical aspects of the restricted three-vortex problem when one of the point vortices is assumed to be fixed at a location in the plane. The motion of the passive tracer is explored from