SIAM Journal on Applied Mathematics

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 ...

Material response of real, passive, linear, time-invariant media to external influences is described by complex analytic functions of frequency that can always be written in terms of Stieltjes functions---a special class of analytic functions mapping a ...

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 ...

We study the Becker--Döring bubblelator, a variant of the Becker--Döring coagulation-fragmentation 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 ...

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 ...

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, ...

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 Lifshitz--Petrich free ...

The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of two-dimensional scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary ...

In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. We investigate the ice-fishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the ...

In this paper, time and energy costs for achieving synchronization of the Kuramoto-oscillator network with or without noise perturbation are investigated. In order to achieve synchronization and optimize time and energy consumption, a novel switching ...

In contexts such as space travel, thermal radiation is the primary mode of heat transfer. The Stefan--Boltzmann law gives rise to a boundary flux which is quartic in temperature, and this nonlinearity renders even the simplest of conduction--radiation ...

From the steady Stokes and Navier--Stokes 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 ...

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 ...

The conformal mapping technique has long been used to obtain exact solutions to Laplace's equation in two-dimensional domains with awkward geometries. However, a major limitation of the technique is that it is only directly compatible with Dirichlet and ...

We model an artificial root which grows in the soil for underground prospecting. Its evolution is described by a controlled system of two integro-partial differential equations: one for the growth of the body and the other for the elongation of the tip. At ...

We consider the Helmholtz transmission problem with piecewise-constant material coefficients and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral ...

We derive a thermodynamically consistent model for liquid-solid phase change in sea ice by incorporating a phase sensitive scalar to a classical framework of liquid-solid phase change. The entropy of the scalar is taken relative to the liquid molar ...

Particles interacting through long-range attraction and short-range repulsion given by power-laws 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 ...

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 ...

We propose near-optimal 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 ...

Foot-and-mouth disease (FMD) is an acute and highly contagious infectious disease of cloven-hoofed 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 ...

The goal of this paper is to relate the capacitance matrix formalism to the tight-binding 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 ...