Related papers: Diffusion rate of windtree models and Lyapunov exp…
Consider a piecewise smooth expanding map of the interval possessing several invariant subintervals and the same number of ergodic absolutely continuous invariant probability measures (ACIMs). After this system is perturbed to make the…
We consider generalized linear stochastic dynamical systems with second-order state transition matrices. The entries of the matrix are assumed to be either independent and exponentially distributed or equal to zero. We give an overview of…
An asymptotic solution is derived for the motion of inertial particles exposed to Stokes drag in an unsteady random flow. This solution provides the finite-time Lyapunov exponents as a function of Stokes number and Lagrangian strain- and…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed…
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
We introduce a new universality class of one-dimensional iteration model giving rise to self-similar motion, in which the Feigenbaum constants are generalized as self-similar rates and can be predetermined. The curves of the mean-square…
The mean Poincarr\'e recurrence time as well as the Lyapunov time are measured for the Fermi-Ulam model. We confirm the mean recurrence time is dependent on the size of the window chosen in the phase space to where particles are allowed to…
The recently discovered correspondence between the distribution of rapidity gaps in electron-nucleus diffractive processes and the statistics of the height of genealogical trees in branching random walks is reviewed. In addition, a new…
Many random flows, including 2D unsteady and stagnation-free 3D steady flows, exhibit non-trivial braiding of pathlines as they evolve in time or space. We show that these random flows belong to a pathline braiding \emph{universality class}…
The paper provides a new integral formula for the largest Lyapunov exponent of Gaussian matrices, which is valid in the real, complex and quaternion-valued cases. This formula is applied to derive asymptotic expressions for the largest…
Diffusion rates through a membrane can be asymmetric, if the diffusing particles are spatially extended and the pores in the membrane have asymmetric structure. This phenomenon is demonstrated here via a deterministic simulation of a…
The stochastic approach to the determination of the largest Lyapunov exponent of a many-particle system is tested in the so-called mean-field XY-Hamiltonians. In weakly chaotic regimes, the stochastic approach relates the Lyapunov exponent…
We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…
The periodic wind-tree model is a family T(a,b) of billiards in the plane in which identical rectangular scatterers of size axb are disposed at each integer point. It was proven by P. Hubert, S. Leli\`evre and S. Troubetzkoy…
This is a survey of known results on estimating the principal Lyapunov exponent of a time-dependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of…
We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong coupling limit. We…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…