Related papers: Simple Maps with Fractal Diffusion Coefficients
We presented a general approach for obtaining the generalized transport equations with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and Zubarev's nonequilibrium…
For an integer $m \geq 2$, let $\mathcal{P}_m$ be the partition of the unit interval $I$ into $m$ equal subintervals, and let $\mathcal{F}_m$ be the class of piecewise linear maps on $I$ with constant slope $\pm m$ on each element of…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
We investigate the spread complexity of a generic two-level subsystem of a larger system to analyze the influence of energy level statistics, comparing chaotic and integrable systems. Initially focusing on the nearest-neighbor level…
We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission…
We investigate three different methods for systematically approximating the diffusion coefficient of a deterministic random walk on the line which contains dynamical correlations that change irregularly under parameter variation. Capturing…
The motion of contaminant particles through complex environments such as fractured rocks or porous sediments is often characterized by anomalous diffusion: the spread of the transported quantity is found to grow sublinearly in time due to…
We expand on a recent study of a lattice model of interacting particles [Phys. Rev. Lett. 111, 110601 (2013)]. The adsorption isotherm and equilibrium fluctuations in particle number are discussed as a function of the interaction. Their…
The scaling invariance for chaotic orbits near a transition from unlimited to limited diffusion in a dissipative standard mapping is explained via the analytical solution of the diffusion equation. It gives the probability of observing a…
A nearly-integrable dynamical system has a natural formulation in terms of actions, $y$ (nearly constant), and angles, $x$ (nearly rigidly rotating with frequency $\Omega(y)$). We study angle-action maps that are close to symplectic and…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding solutions for the probability distribution function are obtained in the form of the Fox…
We study numerically the correlations and the distribution of intervals between successive zeros in the fluctuating geometry of stochastic interfaces, described by the Edwards-Wilkinson equation. For equilibrium states we find that the…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
Stationary probability distributions of one-dimensional random walks on lattices with aperiodic disorder are investigated. The pattern of the distribution is closely related to the diffusional behavior, which depends on the wandering…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients…
Map makers have long searched for a way to construct cartograms -- maps in which the sizes of geographic regions such as countries or provinces appear in proportion to their population or some other analogous property. Such maps are…
We study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
We study the crossover behavior of statistical properties of eigenvalues in a chaotic microcavity with different refractive indices. The level spacing distributions change from Wigner to Poisson distributions as the refractive index of a…