Related papers: Stable static structures in models with higher-ord…
A powerful tool for studying the behavior of classical field theories is Derrick's theorem: one may rule out the existence of localized inhomogeneous stable field configurations (solitons) by inspecting the Hamiltonian and making scaling…
Flexibility and rigidity properties of steady (time-independent) solutions of the Euler, Boussinesq and Magnetohydrostatic equations are investigated. Specifically, certain Liouville-type theorems are established which show that suitable…
This work investigates twinlike scalar field models that support kinks with the same energy density and stability. We find the first order equations compatible with the equations of motion. We use them to calculate the conditions under…
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
We discuss the stability of (charged) static black holes in higher-dimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schroedinger equation type for black hole perturbations…
We continue the study of the existence and stability of static spherical membrane configurations in curved spacetimes. We first consider higher order membranes described by a Lagrangian which, besides the Dirac term, includes a term…
Polarity fields are known to exhibit long distance patterns, in both physical and biological systems. The mechanisms behind such patterns are poorly understood. Here, we describe the dynamics of polarity fields using an original physical…
In this paper we generalize the higher-degree smoothness results in perturbation theory from the case that the stable maps have the fixed domain $S^2$ to the general genus zero case.
We study general linear transport-reaction systems on an arbitrary dimensional hypercube with periodic boundary conditions. Transport-reaction systems are often used to model the finite speed movement and interaction of particles, bacteria…
We study the dynamics of domain walls in Einstein-Born-Infeld-dilaton theory. Dilaton is non-trivially coupled with the Born-Infeld electromagnetic field. We find three different types of solutions consistent with the dynamic domain walls.…
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…
In this paper we study the rigidity problem for sub-static systems with possibly non-empty boundary. First, we get local and global splitting theorems by assuming the existence of suitable compact minimal hypersurfaces, complementing recent…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In this note, we study the integrability of geodesic flow in the background of a very general class of spacetimes with NUT-charge(s) in higher dimensions. This broad set encompasses multiply NUT-charged solutions, electrically and…
We consider localization of gravity in domain wall solutions of Einstein's gravity coupled to a scalar field with a generic potential. We discuss conditions on the scalar potential such that domain wall solutions are non-singular. Such…
We study the role of domain walls and their relics in the very early Universe within the framework of the mode-matching technique. Domain walls formed during the spontaneous breaking of discrete symmetries are modelled as a short lived…
We reconsider a cosmological evolution of domain walls produced by spontaneous breaking of an approxime discrete symmetry. We show, that domain walls may never collapse even if the standard bound on the vacuum energy asymmetry is satisfied.…
A method for obtaining solutions to the classical equations for scalars plus gravity in five dimensions is applied to some recent suggestions for brane-world phenomenology. The method involves only first order differential equations. It is…
The problem of global-in-time regularity for the 3D Navier-Stokes equations, i.e., the question of whether a smooth flow can exhibit spontaneous formation of singularities, is a fundamental open problem in mathematical physics. Due to the…
The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from…