Related papers: Stability of Cosmological Detonation Fronts
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
We consider a simple model for multidimensional cone-wise linear dynamics around cusp-like equilibria. We assume that the local linear evolution is either $\mathbf{v}^\prime=\mathbb{A}\mathbf{v}$ or $\mathbb{B}\mathbf{v}$ (with…
We consider front propagation in a reactive Boussinesq system in an infinite vertical strip. We establish nonlinear stability of planar fronts for narrow domains when the Rayleigh number is not too large. Planar fronts are shown to be…
There are now evidences that the cosmological constant $\Lambda$ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the…
We consider the transition from a spatially uniform state to a steady, spatially-periodic pattern in a partial differential equation describing long-wavelength convection. This both extends existing work on the study of rolls, squares and…
There is a close connection between stability and oscillation of delay differential equations. For the first-order equation $$ x^{\prime}(t)+c(t)x(\tau(t))=0,~~t\geq 0, $$ where $c$ is locally integrable of any sign, $\tau(t)\leq t$ is…
In [1], the authors have studied stability of certain causal properties of space-times in general relativity. As a continuation of this work, in the present paper, we review and discuss, some more aspects of stability which occur in various…
We present a new application of Lagrangian Perturbation Theory (LPT): the stability analysis of fluid flows. As a test case that demonstrates the framework we focus on the plane Couette flow. The incompressible Navier-Stokes equation is…
We consider linear cosmological perturbations on the background of a D-brane gas in which the compact dimensions and the dilaton are stabilized. We focus on long wavelength fluctuations and find that there are no instabilities. In…
We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter $\lambda(t) =…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend…
We investigate hydrodynamic instability of accelerating ionization fronts using two dimensional hydrodynamic simulations that include detailed energy deposition and release due to the absorption of UV radiation, recombination of hydrogen,…
We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting…
This paper is a first step toward understanding the effect of toroidal geometry on the rigorous stability theory of plasmas. We consider a collisionless plasma inside a torus, modeled by the relativistic Vlasov-Maxwell system. The surface…
We consider positive travelling fronts of the time-delayed reaction-diffusion equation with the monostable birth function. Our main result says that for every fixed and sufficiently large velocity c, the positive travelling front is unique…
The mechanism of detonation instability and deflagration-to-detonation transition is studied by one-dimensional numerical simulation with overall one-step chemical reaction kinetics in this paper. The detonation is ignited at the left…
We consider conditions for existence and stability of a static cosmological solution in quadratic gravity. It appears that such a solution for a Universe filled by only one type of perfect fluid is possible in a wide range of the equation…
We construct high-precision models of the Universe that contain radiation, a cosmological constant, and periodically distributed inhomogeneous matter. The density contrasts in these models are allowed to be highly non-linear, and the…
We study the linear properties, nonlinear saturation and a steady, strongly nonlinear state of the Parker instability in galaxies. We consider magnetic buoyancy and its consequences with and without cosmic rays. Cosmic rays are described…