Related papers: Simulation-Based Equations for Propagation Constan…
In the present work, we investigate the potential of fractional derivatives to model atmospheric dispersion of pollutants. We propose simple fractional differential equation models for the steady state spatial distribution of concentration…
Exact expressions for all the steady-state fields (E, H, D, B) in uniaxial linear media composed of an arbitrary number of layers having arbitrary thicknesses subjected to normal incidence are derived. Generic boundary condition relations…
Interconnects are a major discriminator for superconducting digital technology, enabling energy efficient data transfer and high-bandwidth heterogeneous integration. We report a method to simulate propagation of picosecond pulses in…
Continuum solvation models are becoming increasingly relevant in condensed matter simulations, allowing to characterize materials interfaces in the presence of wet electrified environments at a reduced computational cost with respect to all…
This work analyzes the forward and inverse scattering series for scalar waves based on the Helmholtz equation and the diffuse waves from the time-independent diffusion equation, which are important PDEs in various applications. Different…
The propagation of an electromagnetic wave in closed structures led to numerous applications ranging from the characterization of materials in resonating cavities to the measurements using pregnant reverberant EMF. We created models to…
We study the propagation of surface waves across structured surfaces with random, localized inhomogeneities. A discrete analogue of Gurtin-Murdoch model is employed and surface elasticity, in contrast to bulk elasticity, is captured by…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
In non-destructive and biomedical imaging, spatial patterns inside a sample are imaged without destroying it. Therefore, propagating waves, including electromagnetic or ultrasonic signals, or even diffuse heat are generated or modified by…
Radiative transfer effects need to be taken into account when analysing spectral line observations. When the data are not sufficient for detailed modelling, simpler methods are needed. The escape probability formalism (EPF) is one such…
Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…
The propagation of high-power femtosecond laser pulses in air under conditions of superposed spatial phase modulation is considered theoretically. The numerical simulations are carried out on the basis of the reduced form of nonlinear…
Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for…
We introduce the diffusion and superposition distances as two metrics to compare signals supported in the nodes of a network. Both metrics consider the given vectors as initial temperature distributions and diffuse heat trough the edges of…
We set up the theory for a distributed algorithm for computing persistent homology. For this purpose we develop linear algebra of persistence modules. We present bases of persistence modules, and give motivation as for the advantages of…
Meta-atoms, nano-antennas, plasmonic particles and other small scatterers are commonly modeled in terms of their modes. However these modal solutions are seldom determined explicitly, due to the conceptual and numerical difficulties in…
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…
Free-space optical (FSO) transmission enables fast, secure, and efficient next-generation communications with abundant spectrum resources. However, atmospheric turbulence, pointing errors, path loss, and atmospheric loss induce random…
Linear time-domain simulations of acoustic oscillations are unstable in the stellar convection zone. To overcome this problem it is customary to compute the oscillations of a stabilized background stellar model. The stabilization, however,…
Dye experimentation is a widely used method in experimental fluid mechanics for flow analysis or for the study of the transport of particles within a fluid. This technique is particularly useful in biomedical diagnostic applications ranging…