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Materials with complex inner structure can be challenging to characterize in an effective way. First, it is difficult to determine the representative volume for such a heterogeneous material. Second, the effective material parameters…
We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/permeability which models a metal at optical frequency or an ideal negative metamaterial. We…
A parameter dependent perturbation of the spectrum of the scalar Laplacian is studied for a class of nonlocal and non-self-adjoint rank one perturbations. A detailed description of the perturbed spectrum is obtained both for Dirichlet…
We present a general mechanistic model of mass diffusion for a composite sphere placed in a large ambient medium. The multi-layer problem is described by a system of diffusion equations coupled via interlayer boundary conditions such as…
The paper presents a versatile framework for solids which undergo nonisothermal processes with irreversibly changing microstructure at large strains. It outlines rate-type and incremental variational principles for the full thermomechanical…
We show that a two-atoms Bose-Hubbard model exhibits three different phases in the behavior of thermal entanglement in its parameter space. These phases are demonstrated to be traceable back to the existence of quantum phase transitions in…
The subject matter of this paper concerns anisotropic diffusion equations: we consider heat equations whose diffusion matrix have disparate eigenvalues. We determine first and second order approximations, we study the well-posedness of them…
We describe a novel fluctuating-surface current formulation of radiative heat transfer between bodies of arbitrary shape that exploits efficient and sophisticated techniques from the surface-integral-equation formulation of classical…
An exactly solvable model in heat conduction is considered. The $C$-integrable (i.e., change-of-variables-integrable) equation for second sound (i.e., heat wave) propagation in a thin, rigid dielectric heat conductor uniformly heated on its…
This article discusses the modeling of perturbed potential temperature in an atmospheric boundary layer. We adopt a convection-diffusion model with specified initial and boundary conditions that resulted from simplifying the linearized…
A fundamental challenge in multiparameter persistent homology is the absence of a complete and discrete invariant. To address this issue, we propose an enhanced framework that realizes a holistic understanding of a fully commutative…
Hidden defects affecting the interface in a composite slab are evaluated from thermal data collected on the upper side of the specimen. First we restrict the problem to the upper component of the object. Then we investigate heat transfer…
Let M be a compact Riemannian manifold without boundary and let H be a self-adjoint generalized Laplace operator acting on sections in a bundle over M. We give a path integral formula for the solution to the corresponding heat equation.…
We develop a linear method for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. Our method, based on perturbation theory, is compared with heuristic linearizations of…
Radiative thermal diodes based on two-element structures rectify heat flows thanks to a temperature dependence of material optical properties. The heat transport asymmetry through these systems, however, remains weak without a significant…
In order to account for non-Fourier heat transport, occurring on short time and length scales, the often-praised Dual-Phase-Lag (DPL) model was conceived, introducing a causality relation between the onset of heat flux and the temperature…
We discuss analytically and numerically the propagation and energy transmission of electromagnetic waves caused by the coupling of surface plasmon polaritons (SPPs) between two spatially separated layers of 2D materials, such as graphene,…
Rosseland equation is one of the most popular models of the conduction-radiation coupled heat transfer in the thermal protection system. The well-posedness, the corresponding mathematical theory and the Multi-scale analysis method for the…
We present a fast adaptive method for the evaluation of heat potentials, which plays a key role in the integral equation approach for the solution of the heat equation, especially in a non-stationary domain. The algorithm utilizes a…
Among the three heat conduction modes, the ballistic propagation is the most difficult to model. In the present paper, we discuss its physical interpretations and showing different alternatives to its modeling. We highlight two of them: a…