Related papers: Anomalous diffusion via iterative quantitative hom…
Laboratory experiments reveal that variations in bottom topography can qualitatively alter the distribution of randomized surface waves. A normally-distributed, unidirectional wave field becomes highly skewed and non-Gaussian upon…
We analyze a family of fourth-order non-linear diffusion models corresponding to local approximations of 4-wave kinetic equations of weak wave turbulence. We focus on a class of parameters for which a dual cascade behaviour is expected with…
We study diffusion processes in anomalous spacetimes regarded as models of quantum geometry. Several types of diffusion equation and their solutions are presented and the associated stochastic processes are identified. These results are…
This paper derives the Fokker-Planck (FP) equation for a particle moving in potential by a randomly modulated dipole. The FP equation describes the anomalous diffusion observed in the companion paper [1] and breaks the conservation of the…
Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the…
A relation between the effective diffusion coefficient in a lattice with random site energies and random trasition rates and the macroscopic conductivity in a random resistor network allows for elucidating possible sources of anomalous…
A general link between geometry and intermittency in passive scalar turbulence is established. Intermittency is qualitatively traced back to events where tracer particles stay for anomalousy long times in degenerate geometries characterized…
Anomaly localization in images -- identifying regions that deviate from normal patterns -- is vital in applications such as medical diagnosis and industrial inspection. A recent trend is the use of image generation models in anomaly…
Three-dimensional turbulence simulations are used to show that the turbulent root mean square velocity is an upper bound of the speed of turbulent diffusion. There is a close analogy to magnetic diffusion where the maximum diffusion speed…
Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause…
This study examines anomalous diffusion and dynamical phase transitions in a nonlinear bouncer model with short-range interactions leading to velocity-dependent (adiabatic) collisions. By varying a control parameter, transitions between…
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…
This paper investigates the performance of diffusion models for video anomaly detection (VAD) within the most challenging but also the most operational scenario in which the data annotations are not used. As being sparse, diverse,…
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 aim of this paper is to derive the averaged governing equations for non-degenerated oscillatory flows, in which the magnitudes of mean velocity and oscillating velocity are similar. We derive the averaged equations for a scalar passive…
Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…
For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…
In many physical situations involving diverse length scales, waves or rays representing them travel through media characterized by spatially smooth, random, modest refactive index variations. "Primary" diffraction (by individual…
Heterogeneous dynamics commonly emerges in anomalous diffusion with intermittent transitions of diffusion states but proves challenging to identify using conventional statistical methods. To effectively capture these transient changes of…