Related papers: Stability of Cosmological Detonation Fronts
We consider first-order phase transitions of the Universe in the radiation-dominated era. We argue that in general the velocity of interfaces is non-relativistic due to the interaction with the plasma and the release of latent heat. We…
We investigate the evolution of interfaces among phases of the interstellar medium with different temperature. It is found that, for some initial conditions, the dynamical effects related to conductive fronts are very important even if…
Bubble growth as a detonation is studied in the context of cosmological phase transitions. It is proved that the so called Chapman-Jouguet hypothesis, which restricts the types of detonations that can occur in spherically symmetric chemical…
In cosmological first-order phase transitions, the microscopic interaction of the phase transition fronts with non-equilibrium plasma particles manifests itself macroscopically as friction forces. In general, it is a nontrivial problem to…
This paper establishes the spectral stability of monotone, stationary front solutions for reaction-diffusion equations where the reaction function is of Nagumo (or bistable) type and with diffusion coefficients which are density dependent…
We apply phase space analysis to inhomogeneous cosmological model given by Lema\^itre-Tolman model. We describe some general conditions required to interpret the model stable enough and, in the present paper, apply them to two special…
We study the stability of the isotropic vacuum Friedmann universe in gravity theories with higher-order curvature terms of the form $(R_{ab}R^{ab})^{n}$ added to the Einstein-Hilbert Lagrangian of general relativity on approach to an…
We study a one-dimensional reaction-diffusion system which describes an isothermal autocatalytic chemical reaction involving both a quadratic (A + B -> 2B) and a cubic (A + 2B -> 3B) autocatalysis. The parameters of this system are the…
In our previous papers we proposed a continuum model for the dynamics of the systems of self-propelling particles with conservative kinematic constraints on the velocities. We have determined a class of stationary solutions of this…
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…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
A precise modelling of the dynamics of bubbles nucleated during first-order phase transitions in the early Universe is pivotal for a quantitative determination of various cosmic relics, including the stochastic background of gravitational…
In this paper, we consider the phenomenon of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media. Recent results have addressed the existence of pulsating fronts and the linear…
We study the formation, evolution and structure of dissipative fronts produced by overtaking collisions of relativistic streams, with emphasis on strongly magnetized flows. The evolution of the system is followed using analytical approach…
There have been several existence results for the standing waves of FitzHugh-Nagumo equations. Such waves are the connecting orbits of an autonomous second-order Lagrangian system and the corresponding kinetic energy is an indefinite…
Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear…
When a liquid slams into a solid, the intermediate gas is squeezed out at a speed that diverges when approaching the moment of impact. Although there is mounting experimental evidence that instabilities form on the liquid interface during…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
The spatial and temporal persistence, or first-return distributions are measured for slow combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…