Related papers: The Dielectric Breakdown Model at Small $\eta$: Po…
This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an…
In classical mechanics, solutions can be classified according to their stability. Each of them is part of the possible trajectories of the system. However, the signatures of unstable solutions are hard to observe in an experiment, and most…
We study statistical scale invariance and dynamic scaling in a simple solid-on-solid 2+1 - dimensional limited mobility discrete model of nonequilibrium surface growth, which we believe should describe the low temperature kinetic roughening…
In this work we study the dynamics and stability of charged solitons in trans-polyacetylene (tPA), and revisit the issue of the stability of these non-linear excitations under the effect of an external electric field applied parallel to the…
We give a necessary and sufficient condition, of geometric type, for the uniform decay of energy of solutions of the linear system of magnetoelasticity in a bounded domain with smooth boundary. A Dirichlet-type boundary condition is…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
We study the evolution of eastward propagating dipoles (modons) in a two-layer quasi-geostrophic $\beta$-plane model using high-resolution numerical simulations. Various combinations of background gradients of potential vorticity in the…
By analytically solving some simple models of phase-ordering kinetics, we suggest a mechanism for the onset of non-equilibrium behaviour in colloid-polymer mixtures. These mixtures can function as models of atomic systems; their physics…
Based on a microscopic model of nonequilibrium carrier generation in a leaky dielectric, we analytically derive hysteresis loops for the dielectric response of non-polar, non-ferroelectric materials. We demonstrate how complex dielectric…
We consider a model of an elastic body immersed between two layers of incompressible viscous fluid. The elastic displacement $w$ is governed by the damped wave equation $w_{tt} + \alpha w_t + \Delta w =0$ without any stabilization terms,…
The standard Maxwell formulation of the problem of polarized dielectrics suffers from a number of difficulties, both conceptual and practical. These difficulties are particularly significant in the case of liquid interfaces, where the…
We analyze the instability of a vortex column in a dilute polymer solution at large $\textit{Re}$ and $\textit{De}$ with $\textit{El} = \textit{De}/\textit{Re}$, the elasticity number, being finite. Here, $\textit{Re} = \Omega_0 a^2/\nu_s$…
We investigate the linear tearing instability in weakly collisional plasmas using a non-ideal gyrotropic-MHD framework, uncovering a previously unknown scaling relation for the instability growth rate in high-$\beta$ environments. Even…
The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion.…
Although stable solutions of dynamical systems are typically considered more important than unstable ones, unstable solutions have a critical role in the dynamical integrity of stable solutions. In fact, usually, basins of attraction…
It is shown, that the saturated $\alpha$-effect taken from the nonlinear dynamo equations for the thin disk can still produce exponentially growing magnetic field in the case, when this field does not feed back on the $\alpha$. For negative…
In this work, the static stability of plates with fixed trailing edges in axial airflow is studied using the framework of Possio integral equation. First, we introduce a new derivation of a Possio integral equation that relates the pressure…
Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in…
We consider Diffusion Limited Aggregation (DLA) in a two-dimensional wedge. We prove that if the angle of the wedge is smaller than $\pi/4$, there is some $a>2$ such that almost surely, for all $R$ large enough, after time $R^a$ all new…
The nonlinear dynamics of the free surface of an ideal dielectric liquid in a strong electric field is studied. The equation for the evolution of surface electrohydrodynamic waves is derived in the approximation of small surface-slope…