Related papers: Pressure Fronts in 1D Damped Nonlinear Lattices
This paper provides numerical results that demonstrate the validity of the nonclassical diffusion approximation to the nonclassical transport equation in certain 1-D diffusive systems. This result provides a more solid foundation in which…
We investigate the stabilization mechanisms due to viscous forces in the invasion front during drainage displacement in two-dimensional porous media using a network simulator. We find that in horizontal displacement the capillary pressure…
We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a…
In this paper, we investigate the structure of condensation fronts from warm diffuse gas to cold neutral medium (CNM) under the plane parallel geometry. The solutions have two parameters, the pressure of the CNM and the mass flux across the…
This paper is concerned with the interaction between a planar traveling front and a compact obstacle for monotone bistable reaction-diffusion systems in exterior domains. By constructing appropriate sub- and supersolutions, we first…
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one correspondence between the set of global orbits…
We study the conservative and deterministic dynamics of two nonlinearly interacting particles evolving in a one-dimensional spatially periodic washboard potential. A weak tilt of the washboard potential is applied biasing one direction for…
A uniform solidification front undergoes non-trivial deformations when encountering an insoluble dispersed particle in a melt. For solid particles, the overall deformation characteristics are primarily dictated by heat transfer between the…
We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of…
This paper analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODEs with constant coeffcients. The novel part of this research is that the…
An external load on a particle packing is distributed internally through a heterogeneous network of particle contacts. This contact force distribution determines the stability of the particle packing and the resulting structure. Here, we…
We investigate the inside structure of one-dimensional reaction-diffusion traveling fronts. The reaction terms are of the monostable, bistable or ignition types. Assuming that the fronts are made of several components with identical…
Based on a recent work on traveling waves in spatially nonlocal reaction-diffusion equations, we investigate the existence of traveling fronts in reaction-diffusion equations with a memory term. We will explain how such memory terms can…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…
We examine the motions of particles in quadrupole ion traps as a function of damping and trapping forces, including cases where nonlinear damping or nonlinearities in the electric field geometry play significant roles. In the absence of…
We investigate an energy-subcritical defocusing nonlinear Schr\"odinger equation in $\mathbb R^3$ subject to a lower order nonlinear trapping potential and a spatially dependent nonlinear damping: \begin{equation*} i\partial_t u + \Delta u…
In this Letter we describe a novel class of dynamical excitations -- accelerating oscillatory fronts in a new genre of nonlinear sonic vacua with strongly non-local effects. Indeed, it is surprising that such models naturally arise in…
The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts…