Related papers: Deciphering Non-Gaussianity of Diffusion Based on …
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical…
Probabilistic regression models the entire predictive distribution of a response variable, offering richer insights than classical point estimates and directly allowing for uncertainty quantification. While diffusion-based generative models…
Non-linear gravitational collapse introduces non-Gaussian statistics into the matter fields of the late Universe. As the large-scale structure is the target of current and future observational campaigns, one would ideally like to have the…
We examine the statistics of active scalar fluctuations in high-Rayleigh number fingering convection with high-resolution three-dimensional numerical experiments. The one-point distribution of buoyancy fluctuations is found to present…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
We develop a class of non-Gaussian translation processes that extend classical stochastic differential equations (SDEs) by prescribing arbitrary absolutely continuous marginal distributions. Our approach uses a copula-based transformation…
We address truncated states of continuous variable systems and analyze their statistical properties numerically by generating random states in finite-dimensional Hilbert spaces. In particular, we focus to the distribution of purity and…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
We investigate the dynamic behavior of optical vortices, or phase singularities, in random wavefields and demonstrate the direct experimental observation of the anomalous diffusion of optical vortices. The observed subdiffusion of optical…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
The velocity distribution of spheres rolling on a slightly tilted rectangular two dimensional surface is obtained by high speed imaging. The particles are excited by periodic forcing of one of the side walls. Our data suggests that strongly…
We demonstrate that the Einstein relation for the diffusion of a particle in the random energy landscape with the Gaussian density of states is an exclusive 1D property and does not hold in higher dimensions. We also consider the analytical…
The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-squared displacement (MSD) grows linearly with time.…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
Solitons in a strongly nonlocal nonlinear medium have attracted considerable attention in recent years due to their unique and distinctive characteristics from those observed in the local nonlinear medium. In this work, we investigate the…
The diffusing-diffusivity mechanism proposed by Chubynsky and Slater [PRL 113, 098302, 2014] predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the…
The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…
The genus statistics is studied using large $N$-body simulations for several cosmological models. We consider the effects of nonlinear gravitational evolution, smoothing the particle data in fully nonlinear regime, and the redshift-space…
We consider a non acoustic chain of harmonic oscillators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the…