Related papers: Exponent Inequalities in Dynamical Systems
The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on…
The behavior of dynamical system interacting with non-equilibrium medium is investigated. Formally exact kinetic equations are derived for the statistical operator of the dynamical system and the macroscopic parameters of the medium. In the…
Behavior of condensed matter systems deviating from the standard equilibrium conditions is discussed. Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the…
We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a…
For a pinched Hadamard manifold $X$ and a discrete group of isometries $\Gamma$ of $X$, the critical exponent $\delta_\Gamma$ is the exponential growth rate of the orbit of a point in $X$ under the action of $\Gamma$. We show that the…
The effects of spatially correlated noise on a phenomenological equation equivalent to a non-local version of the Kardar-Parisi-Zhang equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
Typically, a stochastic model relates stochastic "inputs" and, perhaps, controls to stochastic "outputs". A general version of the Yamada-Watanabe and Engelbert theorems relating existence and uniqueness of weak and strong solutions of…
By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space Gamma,…
In this paper we discuss mechanical systems with inequality constraints. We demonstrate how such constraints can be taken into account by proper modification of the action which describes the original unconstrained dynamics. To illustrate…
The dynamic critical exponent $z$ is determined from numerical simulations for the three-dimensional (3D) lattice Coulomb gas (LCG) and the 3D XY models with relaxational dynamics. It is suggested that the dynamics is characterized by two…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…
We show that a general, exact cosmological solution, where dynamics of scalar field is assigned by an exponential potential, fulfils all the issues of dark energy approach, both from a theoretical point of view and in comparison with…
Let $\Gamma$ be a subset of $\{0,1,2,...\}$. We show that if $\Gamma$ has `gaps' then the completeness and frame properties of the system $\{t^ke^{2\pi i nt}: n\in\mathbb{Z},k\in\Gamma\}$ differ from those of the classical exponential…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Stoichiometric constraints play a role in the dynamics of natural populations, but are not explicitly considered in most mathematical models. Recent theoretical works suggest that these constraints can have a significant impact and should…