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SIAM Journal on Applied Mathematics
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SIAM Journal on Applied Mathematics

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0036-1399

SIAM Journal on Applied Mathematics/Journal SIAM Journal on Applied MathematicsSCIEIISTPAHCI
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    DETECTING A PREY IN A SPIDER ORB-WEB FROM IN-PLANE VIBRATION

    Kawano, AlexandreMorassi, AntoninoZaera, Ramon
    26页
    查看更多>>摘要：Spiders perform a task similar to solving an inverse problem when detecting the position of a prey, a mate, or a predator perturbing the orb-web. Recent work has advanced in the study of the orb-web asa sensor when it is subjected to small transverse vibrations, using a continuous membrane model for the orb-web. However, in-plane vibrations have not been investigated yet as data for the prey detection problem. In the present work, we develop the structure of the small in -plane vibratory response of an axially symmetric orb-web supported at the boundary. Additionally, we prove that knowledge of the in-plane dynamic response inside an annulus centered at the origin of the orb-web, where the spider is assumed to stay for a sufficiently large registration time, allows us to determine uniquely the in-plane distributed load simulating the prey's impact. The theoretical outcome is illustrated with a numerical implementation of the reconstruction method.
      原文链接:
    • NSTL
    • Siam Publications

    RANDOM WALKS ON DENSE GRAPHS AND GRAPHONS

    Petit, JulienLambiotte, RenaudCarletti, Timoteo
    23页
    查看更多>>摘要：Graph-limit theory focuses on the convergence of sequences of increasingly large graphs, providing a framework for the study of dynamical systems on massive graphs, where classical methods would become computationally intractable. Through an approximation procedure, the standard ordinary differential equations are replaced by nonlocal evolution equations on the unit interval. In this work, we adopt this methodology to prove the validity of the continuum limit of random walks, a largely studied model for diffusion on graphs. We focus on two classes of processes on dense weighted graphs, in discrete and in continuous time, whose dynamics are encoded in the transition matrix of the associated Markov chain or in the random-walk Laplacian. We further show that previous works on the discrete heat equation, associated to the combinatorial Laplacian, fall within the scope of our approach. Finally, we characterize the relaxation time of the process in the continuum limit.
      原文链接:
    • NSTL
    • Siam Publications

    THE GARDNER EQUATION IN ELASTODYNAMICS

    Coclite, G. M.Maddalena, F.Puglisi, G.Romano, M....
    16页
    查看更多>>摘要：The Gardner equation is an integrable system which includes the Korteweg-de Vries (for quadratic nonlinearitry) and the modified Korteweg-de Vries equation (for cubic nonlinearity) as special cases. It is well known that shear waves in isotropic elasticity are usually attained by introducing cubic nonlinearities in the constitutive assumptions. Here, by considering different perturbative limits, within the classical Mooney-Rivlin energy, we obtain that for weakly dispersive materials in different perturbative limits, the resulting Boussinesq equations lead to the Gardner equation. Specifically this is attained in the three cases of prestrained, anisotropic, and when a substrate interaction is taken into account. This result allows us also to discuss the possible occurrence of flatons as solitary transverse waves.
      原文链接:
    • NSTL
    • Siam Publications

    STOCHASTIC MODELS OF NEURAL SYNAPTIC PLASTICITY: A SCALING APPROACH

    Robert, PhilippeVignoud, Gaetan
    25页
    查看更多>>摘要：In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dy-namics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A spike-timing-dependent plasticity (STDP) rule is a biologically based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. A general mathematical framework has been introduced in [P. Robert and G. Vignoud, SIAM. J. Appl. Math., 81 (2021), pp. 1821-1846]. In this paper, we develop and investigate a scaling approach of these models based on several biological assumptions. Experiments show that long-term synaptic plasticity evolves on a much slower timescale than the cellular mechanisms driving the activity of neuronal cells, like their spiking activity or the concentration of various chemical compo-nents created/suppressed by this spiking activity. For this reason, a scaled version of the stochastic model of Robert and Vignoud [SIAM. J. Appl. Math., 81 (2021), pp. 1821--1846] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [P. Robert and G. Vignoud, J. Stat. Phys. 183 (2021), 47] is entirely devoted to the tightness properties used to prove these convergence results. These averaging principles are used to study two important STDP models: pair-based rules and calcium-based rules. Our results are compared with the approximations of neuroscience STDP models. A class of discrete models of STDP rules is also investigated for the analytical tractability of its limiting dynamical system.
      原文链接:
    • NSTL
    • Siam Publications

    SOURCE RECONSTRUCTION WITH MULTIFREQUENCY SPARSE SCATTERED FIELDS

    Ji, XiaLiu, Xiaodong
    18页
    查看更多>>摘要：We consider the reconstruction of acoustic sources with multifrequency sparse scattered fields. Specifically, we shall use the multifrequency scattered fields at finitely many measurement points to prove some uniqueness results and introduce three numerical schemes. The underlying sources can be an extended source or a sum of monopoles and dipoles. At a fixed measurement point, we show that the spheres centered at the point passing through the point sources can be uniquely determined by the multifrequency scattered fields. For M multipolar point sources, the uniqueness for locating the positions and recovering scattering strengths has been proved using multifrequency scattered fields for at most 6M + 1 measurement points. For an extended source, we show that the smallest annular containing the source centered at the measurement point can be uniquely determined by the multifrequency scattered field. Motivated by the uniqueness proofs, we then introduce three schemes for reconstructing the sources. Some numerical examples in three dimensions are presented to show the validity and robustness of the proposed numerical schemes.
      原文链接:
    • NSTL
    • Siam Publications

    DYNAMICS OF A DIFFUSIVE NUTRIENT-PHYTOPLANKTON-ZOOPLANKTON MODEL WITH SPATIO-TEMPORAL DELAY

    Tao, YiwenPoulin, Francis J.Campbell, Sue Ann
    28页
    查看更多>>摘要：We study a diffusive nutrient-phytoplankton-zooplankton (NPZ) model with spatiotemporal delay. The closed nature of the system allows the formulation of a conservation law of biomass that governs the ecosystem. We advance the understanding of the local stability for equilibrium solutions of the NPZ model by proposing a new local stability theorem for generalized three-dimensional systems. Using a specific delay kernel, we perform a qualitative analysis of the solutions, including existence, uniqueness, and boundedness of the solutions, global stability of the trivial equilibrium, and Hopf bifurcation of the nontrivial equilibrium. Numerical simulations are also performed to verify and supplement our analytical results. We show that diffusion predominantly has a stabilizing effect; however, if sufficient nutrient is present, complex spatio-temp oral dynamics may occur.
      原文链接:
    • NSTL
    • Siam Publications

    IMPEDANCE EIGENVALUES IN LINEAR ELASTICITY

    Levitin, MichaelMonk, PeterSelgas, Virginia
    24页
    查看更多>>摘要：This paper is devoted to studying impedance eigenvalues (that is, eigenvalues of a particular Dirichlet-to-Neumann map) for the time harmonic linear elastic wave problem and their potential use as target signatures for fluid-solid interaction problems. We first consider several possible families of eigenvalues of the elasticity problem, focusing on certain impedance eigenvalues that are an analogue of Steklov eigenvalues. We show that one of these families arises naturally in inverse scattering. We also analyze their approximation from far field measurements of the scattered pressure field in the fluid and illustrate several alternative methods of approximation in the case of an isotropic elastic disk.
      原文链接:
    • NSTL
    • Siam Publications

    REACTION-SUBDIFFUSION EQUATIONS WITH SPECIES-DEPENDENT MOVEMENT

    Alexander, Amanda M.Lawley, Sean D.
    23页
    查看更多>>摘要：Reaction-diffusion equations are one of the most common mathematical models in the natural sciences and are used to model systems that combine reactions with diffusive motion. However, rather than normal diffusion, anomalous subdiffusion is observed in many systems and is especially prevalent in cell biology. What are the reaction-sub diffusion equations describing a system that involves first-order reactions and subdiffusive motion? In this paper, we derive fractional reaction-sub diffusion equations describing an arbitrary number of molecular species that react at first-order rates and move subdiffusively. Importantly, different species may have different diffusivities and drifts, which contrasts previous approaches to this question that assume that each species has the same movement dynamics. We derive the equations by combining results on time dependent fractional Fokker-Planck equations with methods of analyzing stochastically switching evolution equations. Furthermore, we construct the stochastic description of individual molecules whose deterministic concentrations follow these reaction-sub diffusion equations. This stochastic description involves subordinating a diffusion process whose dynamics are controlled by a subordinated jump process. We illustrate our results in several examples and show that solutions of the reactionsubdiffusion equations agree with stochastic simulations of individual molecules.
      原文链接:
    • NSTL
    • Siam Publications

    THE LOTTERY MODEL FOR ECOLOGICAL COMPETITION IN NONSTATIONARY ENVIRONMENTS

    Cheng, JiaqiChesson, PeterHan, Xiaoying
    23页
    查看更多>>摘要：A two-species lottery competition model with nonstationary reproduction and mor-tality rates of both species is studied. First, a diffusion approximation for the fraction of sites occu-pied by each adult species is derived as the continuum limit of a classical discrete-time lottery model. Then a nonautonomous SDE on sites occupied by the species as well as a Fokker-Planck equation on its transitional probability are developed. Existence, uniqueness, and dynamics of solutions for the resulting SDE are investigated, from which sufficient conditions for the existence of a time-dependent limiting process and coexistence of species in the sense of stochastic persistence are established. A unique classical solution to the Fokker-Planck equation is also proved to exist and shown to be a probability density. Numerical simulations are presented to illustrate the theoretical results.
      原文链接:
    • NSTL
    • Siam Publications

    STABILITY FOR AN INVERSE SOURCE PROBLEM OF THE BIHARMONIC OPERATOR

    Li, PeijunYao, XiaohuaZhao, Yue
    23页
    查看更多>>摘要：In this paper, we study for the first time the stability of the inverse source problem for the biharmonic operator with a compactly supported potential in R3. An eigenvalue problem is considered for the bi-Schro"\dinger operator \Delta 2 + V (x) on a ball which contains the support of the potential V. A Weyl-type law is proved for the upper bounds of spherical normal derivatives of both the eigenfunctions \phi and their Laplacian \Delta \phi corresponding to the bi-Schro"\dinger operator. These types of upper bounds was proved by Hassell and Tao [Math. Res. Lett., 9 (2012), pp. 289305] for the Schro"\dinger operator. The meromorphic continuation is investigated for the resolvent of the bi-Schro"\dinger operator, which is shown to have a resonance-free region and an estimate of L2comp - L2lo c type for the resolvent. As an application, we prove a bound of the analytic continuation of the data with respect to the frequency. Finally, the stability estimate is derived for the inverse source problem. The estimate consists of the Lipschitz-type data discrepancy and the high-frequency tail of the source function, where the latter decreases as the upper bound of the frequency increases.
      原文链接:
    • NSTL
    • Siam Publications