相关论文: Multi-Group Discontinuous Asymptotic $P_1$ Approxi…
The anisotropic 3D equation describing the pointlike particles diffusion in slender impermeable tubes of revolution with cross section smoothly depending on the longitudial coordinate is the object of our study. We use singular…
Phonons are the main heat carriers in semiconductor devices. In small devices, heat is not driven by a local temperature gradient, but by local points of heat input and removal. This complicates theoretical modeling. Study of the…
Complex Gaussian basis sets are optimized to accurately represent continuum radial wavefunctions over the whole space. First, attention is put on the technical ability of the optimization method to get more flexible series of Gaussian…
The description of gravity waves propagating on the water surface is considered from a historical point of view, with specific emphasis on the development of a theoretical framework and equations of motion for long waves in shallow water.…
The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First…
This work is devoted to the asymptotic analysis of high frequency wave propagation in random media with long-range dependence. We are interested in two asymptotic regimes, that we investigate simultaneously: the paraxial approximation,…
Metamaterials possess artificial bulk and surface electromagnetic states. Tamed dispersion properties of surface waves allow one to achieve controllable super-Planckian radiative heat transfer (RHT) process between two closely spaced…
A cell method is developed, which takes into account the bubble geometry of polyhedral foams, and provides for the generalized Rayleigh-Plesset equation that contains the non-local in time term corresponding to heat relaxation. The…
We introduce novel approximate systems for dispersive and diffusive-dispersive equations with nonlinear fluxes. For purely dispersive equations, we construct a first-order, strictly hyperbolic approximation. Local well-posedness of smooth…
A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based…
Context. MHD waves are proposed to transport sufficient energy from the photosphere to heat the transition-region (TR) and corona. However, various aspects of these waves such as their nature, propagation characteristics and role in the…
We present a general and convenient first principle method to study near-field radiative heat transfer. We show that the Landauer-like expression of heat flux can be expressed in terms of a frequency and wave-vector dependent macroscopic…
A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…
A modelling of low-frequency sound propagation in slowly varying ducts with smoothly varying lining is proposed leading to an acoustic mild-slope equation analogue to the with mild-slope equation for water waves. This simple 1D Mild Slope…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
The present study examines the possibility of numerical simulation of a strong shock wave propagating over the surface of a dense layer of particles poured onto an impermeable wall using the Baer-Nunizato two-phase flow model. The setting…
Recent numerical and analytic work has highlighted some shortcomings in our understanding of the dynamics of H II region expansion, especially at late times, when the H II region approaches pressure equilibrium with the ambient medium. Here…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
We introduce a (linear) positive and asymptotic preserving method or solving the one-group radiation transport equation. The approximation in space is discretization agnostic: the space approximation can be done with continuous or…
We study a "div-grad type" sub-Laplacian with respect to a smooth measure and its associated heat semigroup on a compact equiregular sub-Riemannian manifold. We prove a short time asymptotic expansion of the heat trace up to any order. Our…