Related papers: Interacting vacuum at infinity
We provide an extension of the method of asymptotic decompositions of vector fields with finite-time singularities by applying the central extension technique of Poincar\'e to the dominant part of the vector field on approach to the…
We study the asymptotic dynamics of dark energy as a mixture of pressureless matter and an interacting vacuum component. We find that the only dynamics compatible with current observational data favors an asymptotically vanishing…
The aim of this paper is to explore the possibilities of Conley index techniques in the study of heteroclinic connections between finite and infinite invariant sets. For this, we remind the reader of the Poincar\'e compactification: this…
Twistor phase spaces are used to provide a general description of the dynamics of a finite number of directly interacting massless spinning particles forming a closed relativistic massive and spinning system with an internal structure. A…
We study a free interface problem related to combustion of condensed matter and some non-equilibrium exothermal phase transitions. In spite of a variety of non-trivial dynamical scenarios exhibited by the model the solutions are uniformly…
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally…
We study three interacting dark energy models within the framework of four-dimensional General Relativity and a spatially flat Universe. In particular, we first consider two vacuum models where dark energy interacts with dark matter, while…
Dynamical system techniques are extremely useful to study cosmology. It turns out that in most of the cases, we deal with finite isolated fixed points corresponding to a given cosmological epoch. However, it is equally important to analyse…
We study the structure and dynamics of the infinite sequence of extensions of the Poincar{\'e} algebra whose method of construction was described in a previous paper [1]. We give explicitly the Maurer-Cartan (MC) 1-forms of the extended Lie…
We consider an original variational approach for building new models of quintessence interacting with dark or baryonic matter. The coupling is introduced at the Lagrangian level using a variational formulation for relativistic fluids, where…
We study the general form of the Casimir interaction between two flat finite-width, parallel, infinite mirrors, described by their respective vacuum polarization tensors, under the assumption of translation invariance along the directions…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We perform a detailed investigation of interacting phantom cosmology, by applying the powerful method of dynamical system analysis. We consider two well-studied interaction forms, namely one global and one local one, while the novel…
We consider a diffuse interface model for incompressible isothermal mixtures of two immiscible fluids with matched constant densities. This model consists of the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard equation…
We consider a diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids. This model consists of the Navier-Stokes equations coupled with a convective nonlocal Cahn-Hilliard equation.…
We solve a class of attractor neural network models with a mixture of 1D nearest-neighbour and infinite-range interactions, which are of a Hebbian-type form. Our solution is based on a combination of mean-field methods, transfer matrices…
We examine an interacting dark matter--variable vacuum energy model for a spatially flat Friedmann-Roberston-Walker spacetime, focusing on the appearance of cosmological singularities such as \emph{big rip, big brake, big freeze}, and…
We study a nonlinear system coupling the Darcy-Forchheimer-Brinkman equations with a convection-diffusion-reaction equation, arising in reactive transport through porous media. The model features a nonlinear viscosity coupling, Forchheimer…
We use qualitative arguments combined with numerical simulations to argue that, in the approach to the singularity in a vacuum solution of Einstein's equations with $T^2$ isometry, the evolution at a generic point in space is an endless…