Related papers: Shape Coherence and Finite-Time Curvature Evolutio…
A dynamical mechanism for symmetry breaking is investigated under the circumstances with the finite curvature, finite size and non-trivial topology. A four- and eight-fermion interaction model is considered as a prototype model which…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
In this paper, we present new results on finite- and fixed-time convergence for dynamical systems using LaSalle-like invariance principles. In particular, we provide first and second-order non-smooth Lyapunov-like results for finite- and…
The mean curvature flow is an evolution process under which a submanifold deforms in the direction of its mean curvature vector. The hypersurface case has been much studied since the eighties. Recently, several theorems on regularity,…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
In this letter, by regarding finite-time stability as an inverse problem, we reveal the essence of finite-time stability and fixed-time stability. Some necessary and sufficient conditions are given. As application, we give a new approach…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
Evolution equations for the moments of a photonic quantum state propagating through atmospheric turbulence are derived. These evolution equations are obtain from an evolution equation for the characteristic functional of the state,…
We define a new finite type invariant for stably homeomorphic class of curves on compact oriented surfaces without boundaries and extend to a regular homotopy invariant for spherical curves.
Evolution of a universe with homogeneous extra dimensions is studied with the benefit of a well-chosen parameter space that provides a systematic, useful, and convenient way for analysis. In this model we find a natural evolution pattern…
We formalize the intuitive idea of a labelled discrete surface which evolves in time, subject to two natural constraints: the evolution does not propagate information too fast; and it acts everywhere the same.
In this paper, the projective geometry is used to describe the features of spherical manifold and discreteness in quantum evolution. As a system evolves in time the state vector changes and it traces out a curve in Hilbert space.…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
The present paper provides a sufficient condition to ensure output finite-time and fixed-time stability. Comparing with analogous researches the proposed result is less restrictive and obtained for a wider class of systems. The presented…
Evolutionary forms, as well as exterior forms, are skew-symmetric differential forms. But in contrast to the exterior forms, the basis of evolutionary forms is deforming manifolds (with unclosed metric forms). Such forms possess a…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
We prove a short time existence result for a system consisting of a geometric evolution equation for a hypersurface and a parabolic equation on this evolving hypersurface. More precisely, we discuss a mean curvature flow scaled with a term…
The dynamics of an infinite continuum system of randomly jumping and coalescing point particles is studied. The states of the system are probability measures on the corresponding configuration space $\Gamma$ the evolution of which is…
Phenotypically structured equations arise in population biology to describe the interaction of species with their environment that brings the nutrients. This interaction usually leads to selection of the fittest individuals. Models used in…