Related papers: Microscopic Deterministic Dynamics and Persistence…
We prove that deterministic motion in dissipative systems emerges as a strict geometric attractor of contact flow, not a statistical approximation. Building on the contact geometry of stochastic vector bundles, we develop time-dependent…
This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law…
We study the dynamics of a single inertial run-and-tumble particle on a straight line. The motion of this particle is characterized by two intrinsic time-scales, namely, an inertial and an active time-scale. We show that interplay of these…
The consistency condition, which guarantees a well organized small-coupling asymptotic expansion for the thermodynamics of massless $\phi^4$-theory, is generalized to any desired order of the perturbative treatment. Based on a strong…
We analyze the statistical physics of self-propelled particles from a general theoretical framework that properly describes the most salient characteristic of active motion, $persistence$, in arbitrary spatial dimensions. Such a framework…
The presence of temporal correlations in random movement trajectories is a widespread phenomenon across biological, chemical and physical systems. The ubiquity of persistent and anti-persistent motion in many natural and synthetic systems…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
Taking the two-dimensional Ising model for example, short-time behavior of critical dynamics with a conserved order parameter is investigated by Monte Carlo simulations. Scaling behavior is observed, but the dynamic exponent $z$ is updating…
This article investigates several properties related to densities of solutions X to differential equations driven by a fractional Brownian motion with Hurst parameter H>1/4. We first determine conditions for strict positivity of the density…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter…
Studying systems where many individual bodies in motion interact with one another is a complex and interesting area. Simple mechanisms that may be determined for biological, chemical, or physical reasons can lead to astonishingly complex…
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of corresponding diffusion…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
Zheng [Phys. Rev. E {\bf 61}, 153 (2000), cond-mat/9909324] claims that phase ordering dynamics in the microcanonical $\phi^4$ model displays unusual scaling laws. We show here, performing more careful numerical investigations, that Zheng…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
We study the distributional and asymptotic properties of the supremum of Brownian motion with drift and exponential resetting. We obtain an explicit renewal-type formula for the distribution of the supremum and then derive an approximation…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…