Related papers: Some Consequences of the Phase Space Choice
Phase transitions between the quantum spin Hall and the insulator phases in three dimensions are studied. We find that in inversion-asymmetric systems there appears a gapless phase between the quantum spin Hall and insulator phases in three…
The aim of this work is to establish the existence of invariant manifolds in complex systems. Considering trajectory curves integral of multiple time scales dynamical systems of dimension two and three (predator-prey models, neuronal…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in…
Topology optimization is concerned with the identification of optimal shapes of deformable bodies with respect to given target functionals. The focus of this paper is on a topology optimization problem for a time-evolving elastoplastic…
Unlike the case of surfaces of topologically finite type, there are several different Teichm\"uller spaces that are associated to a surface of topological infinite type. These Teichm\"uller spaces first depend (set-theoretically) on whether…
We review the current issues of nonequilibrium phase transitions, in particular, in the early universe. Phase transitions cannot maintain thermal equilibrium and become nonequilibrium when the thermal relaxation time scale is greater than…
In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges…
The global topology of the Universe could, in principle, affect quantum systems through boundary condition constraints. We investigate this connection by analyzing how compact, flat, cosmologically inspired topologies, specifically the…
We consider the Euler system set on a bounded convex planar domain, endowed with impermeability boundary conditions. This system is a model for the barotropic mode of the Primitive Equations on a rectangular domain. We show the existence of…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
In this brief, the spontaneous symmetry breaking (SSB) of the $\varphi^4$ theory in phase space, is studied. This phase space results from the appropriate system of Poincare maps, produced in both the Minkowski and the Euclidean time. The…
This article addresses control problems for semilinear impulsive neutral integro-differential equations with memory in a Banach space. It investigates the approximate controllability of linear and semilinear systems and proves the…
The main concern of this paper is to study large-time behavior of the sheath to the full Euler-Poisson system. As is well known, the monotone stationary solution under the Bohm criterion can be referred to as the sheath which is formed by…
We study the global wellposedness of pressure-less Eulerian dynamics in multi-dimensions, with radially symmetric data. Compared with the 1D system, a major difference in multi-dimensional Eulerian dynamics is the presence of the spectral…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
Nonlinear topology has been much less inquired compared to its linear counterpart. Existing advances have focused on nonlinearities of limited magnitudes and fairly homogeneous types. As such, the realizations have rarely been concerned…
We report upon the numerical computation of the Euler characteristic \chi (a topologic invariant) of the equipotential hypersurfaces \Sigma_v of the configuration space of the two-dimensional lattice $\phi^4$ model. The pattern…
While quasi-two-dimensional (layered) materials can be highly anisotropic, their asymptotic long-distance behavior generally reflects the properties of a fully three dimensional phase of matter. However, certain topologically ordered…