Related papers: A simple transcendental travelling wave solution a…
We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value.…
This paper deals with a nonhomogeneous scalar parabolic equation with possibly degenerate diffusion term; the process has only one stationary state. The equation can be interpreted as modeling collective movements (crowd dynamics, for…
We study the propagation of plasmons on graphene. The problem is considered in two dimensions with a transverse magnetic (TM) electromagnetic field. The graphene material is assumed to be flat and is modeled as a conductive sheet. This…
The paper addresses an important issue of cloaking transformations for fourth-order partial differential equations representing flexural waves in thin elastic plates. It is shown that, in contrast with the Helmholtz equation, the general…
Efficient and stable solution of partial differential equations (PDEs) is central to scientific and engineering applications, yet existing numerical solvers rely heavily on matrix based discretizations, while learning based methods require…
Mapping the thermal transport properties of materials at the nanoscale is of critical importance for optimizing heat conduction in nanoscale devices. Several methods to determine the thermal conductivity of materials have been developed,…
Graphene, in addition to its unique electronic and optical properties, revealed unusually high thermal conductivity. The fact that thermal conductivity of large enough graphene sheets should be higher than that of basal planes of bulk…
This article is concerned with the existence of traveling wave solutions, including standing waves, to some models based on configurational forces, describing respectively the diffusionless phase transformations of solid materials, e.g.,…
A thermal transport mechanism leading to the enhanced thermal conductivity of Graphene nanofluids has been proposed. The Graphene sheet size is postulated to be the key to the underlying mechanism. Based on a critical sheet size derived…
The unusual electronic properties of single-layer graphene make it a promising material system for fundamental advances in physics, and an attractive platform for new device technologies. Graphene's spin transport properties are expected to…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
In this work, the propagation of an ultrasonic pulse in a thin plate is computed solving the differential equations modeling this problem. To solve these equations finite differences are used to discretize the temporal variable, while…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
We propose a 2D graphene structure containing atomic ensemble as a platform for implementing nanoscale enhanced coherent interactions of plasmonic fields with resonant atomic systems. We determine the graphene surface plasmon modes, and the…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
The recent results attained from a thermodynamically conceived numerical scheme applied on wave propagation in viscoelastic/rheological solids are generalized here, both in the sense that the scheme is extended to four spacetime dimensions…
In this paper, we present the solutions of the Dirac-Weyl equation for graphene under a constant magnetic field. The resulting spectrum is used to determine the partition function, a key quantity in the study of thermodynamic properties.…
Thermal management is an important challenge in modern electronics, avionics, automotive, and energy storage systems. While passive thermal solutions (like heat sinks or heat spreaders) are often used, actively modulating heat flow (e.g.…
How well do multisymplectic discretisations preserve travelling wave solutions? To answer this question, the 5-point central difference scheme is applied to the semi-linear wave equation. A travelling wave ansatz leads to an ordinary…