Related papers: Necessary and sufficient condition for hydrostatic…
In this work we study the stability of the equilibria reached by ecosystems formed by a large number of species. The model we focus on are Lotka-Volterra equations with symmetric random interactions. Our theoretical analysis, confirmed by…
The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness, and bearing in mind possible applications of our results to neutron stars, it is assumed that…
In this paper, we consider the 3-D compressible isentropic radiation hydrodynamics (RHD) equations. The local existence of strong solutions with vacuum is firstly established when the initial data is arbitrarily large, contains vacuum and…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
Within the context of Rastall gravity, we investigate the hydrostatic equilibrium and dynamical stability against radial pulsations of compact stars, where a free parameter $\beta$ measures the deviations from General Relativity (GR). We…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
The ideal magnetohydrodynamic equations are, roughly speaking, a quasi-linear symmetric hyperbolic system of PDEs, but not all the unknowns play the same role in this system. Indeed, in the regime of small magnetic fields, the equations are…
We summarize recent progress on one- and multi-dimensional stability of viscous shock wave solutions of compressible Navier--Stokes equations and related symmetrizable hyperbolic--parabolic systems, with an emphasis on the large-amplitude…
The dynamical stability of massive thin shells with a given equation of state (EOS) is here compared (both for the barotropic and non-barotropic case) with the results coming from thermodynamical stability. Our results show that the…
The present paper deals with sufficient conditions for orbital stability of periodic waves of a general class of evolution equations supporting nonlinear dispersive waves. Our method can be seen as an extension to spatially periodic waves…
Measurement incompatibility is the most basic resource that distinguishes quantum from classical physics. Contextuality is the critical resource behind the power of some models of quantum computation and is also a necessary ingredient for…
We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically…
Recently we proposed a novel approach to the formulation of relativistic dissipative hydrodynamics by extending the so-called matching conditions in the Eckart frame [Phys. Rev. {\bf C 85}, (2012) 14906]. We extend this formalism further to…
The condition for pressure isotropy is reduced to a recurrence equation with variable, rational coefficients of order three. We prove that this difference equation can be solved in general. Consequently we can find an exact solution to the…
Living systems are forced away from thermodynamic equilibrium by exchange of mass and energy with their environment. In order to model a biochemical reaction network in a non-equilibrium state one requires a mathematical formulation to…
In this paper, we establish a new criterion for the orbital stability of periodic waves related to a general class of regularized dispersive equations. More specifically, we present sufficient conditions for the stability without knowing…
We study the existence and properties of the non-equilibrium steady state which arises by putting two copies of systems at different temperatures into a thermal contact. We solve the problem for the relativistic systems that are described…
Let $f_\theta$ be the joint density of a random sample $X$. A frequently used criterion asserts that a statistic $T(X)$ is minimal sufficient if, for any sample points $x$ and $y$, $T(x) = T(y)$ exactly when there exists a finite constant…
The hydrostatic equilibrium and the stability against radial perturbation of charged strange quark stars composed of a charged perfect fluid are studied. For this purpose, it is considered that the perfect fluid follows the MIT bag model…
Under the hydrodynamic equilibrium Buchdahl's conditions on the behavior of the density and the pressure, for regular fluid static circularly symmetric star in (2 + 1) dimensions in the presence of a cosmological constant, is established…