相关论文: Critical transitions in piecewise uniformly contin…
Many-variable differential equations with random coefficients provide powerful models for the dynamics of many interacting species in ecology. These models are known to exhibit a dynamical phase transition from a phase where population…
The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view. We consider the transitions from a steady state of an abstract nonlinear dissipative system. To shed light…
Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…
In a new type of percolation phase transition, which was observed in a set of non-equilibrium models, each new connection between vertices is chosen from a number of possibilities by an Achlioptas-like algorithm. This causes preferential…
A binary liquid near its consolute point exhibits critical fluctuations of the local composition; the diverging correlation length has always challenged simulations. The method of choice for the calculation of critical points in the phase…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We experimentally study the critical properties of the non-equilibrium solid-liquid-like transition that takes place in vibrated granular matter. The critical dynamics is characterized by the coupling of the density field with the…
Non-thermal dynamical critical behavior can arise in isolated quantum systems brought out of equilibirum by a change in time of their parameters. While this phenomenon has been studied in a variety of systems in the case of a sudden quench,…
We show that optomechanical quantum systems can undergo dissipative phase transitions within the limit of small nonlinear interaction and strong external drive. In such a defined thermodynamical limit, the nonlinear interaction stabilizes…
The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In…
We study decoherence induced by a dynamic environment undergoing a quantum phase transition. Environment's susceptibility to perturbations - and, consequently, efficiency of decoherence - is amplified near a critical point. Over and above…
This article is aimed at studying the effects of the dimensional crossover (DC) on physical properties of condensed systems near phase transition and critical points. Here we consider the following problems: (1) the theoretical provisions…
We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
The dynamics at the critical-point of a general first-order quantum phase transition in a finite system is examined, from an algebraic perspective. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states…
This paper studies the oscillatory behavior of solutions to linear nonautonomous impulsive differential equations with piecewise constant arguments, including both advanced and delayed cases \[ x'(t) = a(t)x(t) + b(t)x([t-k]), \quad k \in…
We give a general introduction to quantum phase transitions in strongly-correlated electron systems. These transitions which occur at zero temperature when a non-thermal parameter $g$ like pressure, chemical composition or magnetic field is…
Symmetry breaking surface fields give rise to nontrivial and long-ranged order parameter profiles for critical systems such as fluids, alloys or magnets confined to wedges. We discuss the properties of the corresponding universal scaling…