Related papers: Deterministic Equations of Motion and Dynamic Crit…
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional Heisenberg model with long-range correlated disorder at criticality, in the case corresponding to linear defects. The static and dynamic critical…
We analyse collective motion that occurs during rare (large deviation) events in systems of active particles, both numerically and analytically. We discuss the associated dynamical phase transition to collective motion, which occurs when…
Recently, a morphological transition in the velocity distribution of a relativistic gas has been pointed out which shows hallmarks of a critical phenomenon. Here, we provide a general framework which allows for a thermodynamic approach to…
We study the scalar one-component two-dimensional (2D) $\phi^4$ model by computer simulations, with local Metropolis moves. The equilibrium exponents of this model are well-established, e.g. for the 2D $\phi^4$ model $\gamma= 1.75$ and…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
Discontinuous time derivatives are used to model threshold-dependent switching in such diverse applications as dry friction, electronic control, and biological growth. In a continuous flow, a discon- tinuous derivative can generate multiple…
Monte Carlo simulations of the short-time dynamic behavior are reported for three-dimensional weakly site-diluted Ising model with spin concentrations $p=0.95$ and 0.8 at criticality. In contrast to studies of the critical behavior of the…
Results for transport properties, in conjunction with phase behavior and thermodynamics, are presented at the criticality of a binary Lennard-Jones fluid from Monte Carlo and molecular dynamics simulations. Evidence for much stronger…
The dynamics of the second order rational difference equation in the title with complex parameters and arbitrary complex initial conditions is investigated. Two associated difference equations are also studied. The solutions in the complex…
We introduce the concept of a deterministic walk. Confining our attention to the finite state case, we establish hypotheses that ensure that the deterministic walk is transitive, and show that this property is in some sense robust. We also…
We deform conformal field theories with classical gravity duals by marginally relevant random disorder. We show that the disorder generates a flow to IR fixed points with a finite amount of disorder. The randomly disordered fixed points are…
An elementary system leading to the notions of fractional integrals and derivatives is considered. Various physical situations whose description is associated with fractional differential equations of motion are discussed.
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
We investigate two distinct universality classes for probe particles that move stochastically in a one-dimensional driven system. If the random force that drives the probe particles is fully generated by the current fluctuations of the…
Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…
Dynamics with choice is a generalization of discrete-time dynamics where instead of the same evolution operator at every time step there is a choice of operators to transform the current state of the system. This notion is new and…
We address the decision problem for a fragment of real analysis involving differentiable functions with continuous first derivatives. The proposed theory, besides the operators of Tarski's theory of reals, includes predicates for…
We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are…
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a…
A version of the second order phase transition theory, in which the Nernst theorem holds automatically, is proposed. The theory is constructed in terms of the order parameter and the (configurational) entropy. It faithfully reproduces the…