Related papers: Stability analysis of multiple nonequilibrium fixe…
In this paper, we present a general methodology for investigating the linear stability of localized solutions in PDEs and nonlocal equations on $\mathbb{R}^m$. More specifically, we control the spectrum of the Jacobian…
We study the equilibrium statics and nonequilibrium driven dynamics of flux line liquids in presence of a random pinning potential. Under the assumption of replica symmetry, we find in the static case using a replica Gaussian variational…
We prove a scattering result near certain steady states for a Hartree equation for a random field. This equation describes the evolution of a system of infinitely many particles. It is an analogous formulation of the usual Hartree equation…
We study the role of the unstable equilibrium points in the transfer of matter in a galaxy using the potential of a rotating triaxial system. In particular, we study the neighbourhood of these points for energy levels and for main model…
Quantum transport is often characterized not just by mean observables like the particle or energy current, but by their fluctuations and higher moments, which can act as detailed probes of the physical mechanisms at play. However,…
We present a stable finite element method for incompressible nonlinear elasticity based on a four-field mixed formulation involving the displacement, displacement gradient, first Piola--Kirchhoff stress and pressure. Unlike existing…
We consider a prototypical dynamical lattice model, namely, the discrete nonlinear Schroedinger equation on nonsquare lattice geometries. We present a systematic classification of the solutions that arise in principal six-lattice-site and…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three…
The electrostatic stability of electron-positron plasmas is investigated in the point-dipole and Z-pinch limits of dipole geometry. The kinetic dispersion relation for sub-bounce-frequency instabilities is derived and solved. For the…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the deterministic system retain their orbital stability if the…
Solution of the Dyson equation for the small-gap systems can be plagued by large non-converging iterations. In addition to the convergence issues, due to a high non-linearity, the Dyson equation may have multiple solutions. We apply the…
We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as…
We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…
We consider a non-interacting one-dimensional gas accelerated by a constant and uniform external field. The energy absorbed from the field is transferred via elastic collisions to a bath of scattering obstacles. At gas-obstacle encounters…
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects…
The Enskog kinetic theory of multicomponent granular suspensions employed previously [G\'omez Gonz\'alez, Khalil, and Garz\'o, Phys. Rev. E \textbf{101}, 012904 (2020)] is considered further to determine the four transport coefficients…
We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…
The equilibrium of magneto-elastic rods, formed of an elastic matrix containing a uniform distribution of paramagnetic particles, that are subject to terminal loads and are immersed in a uniform magnetic field, is studied. The deduced…
We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…