Related papers: Anomalous diffusion in the dynamics of complex pro…
Anomalous diffusion, which shows a deviation of transport dynamics from the framework of standard Brownian motion, is involved in the evolution of various physical, chemical, biological, and economic systems. The study of such random…
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching we unveil a rich transport dynamics including…
As the labor force decreases, the demand for labor-saving automatic anomalous sound detection technology that conducts maintenance of industrial equipment has grown. Conventional approaches detect anomalies based on the reconstruction…
We present analytical results for the biased diffusion of particles moving under a constant force in a randomly layered medium. The influence of this medium on the particle dynamics is modeled by a piecewise constant random force. The…
Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…
Anomaly detection, the technique of identifying abnormal samples using only normal samples, has attracted widespread interest in industry. Existing one-model-per-category methods often struggle with limited generalization capabilities due…
Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied…
In hydrology, the degradation coefficient is one of the key parameters to describe the water quality change and to determine the water carrying capacity. This paper is devoted to identify the degradation coefficient in an anomalous…
In this work we show that under specific anomalous diffusion conditions, chemical systems can produce well-ordered self-similar concentration patterns through a diffusion-driven instability. We also find spiral patterns and patterns with…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
In many-particle diffusions, particles that move the furthest and fastest can play an outsized role in physical phenomena. A theoretical understanding of the behavior of such extreme particles is nascent. A classical model, in the spirit of…
We study generalised anomalous diffusion processes whose diffusion coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position $x$ of the test particle and the process time $t$. This process thus combines the features of…
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…
We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…
In classical diffusion, particle step-sizes have a Gaussian distribution. However, in superdiffusion, they have power-law tails, with transport dominated by rare, long L\'evy flights. Similarly, if the time interval between scattering…
We introduced simple microscopic non-Markovian walk models which describe underlying mechanism of anomalous diffusions. In the models, we considered the competitions between randomness and memory effects of previous history by introducing…
Strong anomalous diffusion phenomena are often observed in complex physical and biological systems, which are characterized by the nonlinear spectrum of exponents $q\nu(q)$ by measuring the absolute $q$-th moment $\langle |x|^q\rangle$.…
We investigate the dynamics of a single tracer exploring a course of fixed obstacles in the vicinity of the percolation transition for particles confined to the infinite cluster. The mean-square displacement displays anomalous transport,…
The superdiffusion behavior, i.e. $<x^2(t)> \sim t^{2 \nu}$, with $\nu > 1/2$, in general is not completely characherized by a unique exponent. We study some systems exhibiting strong anomalous diffusion, i.e. $<|x(t)|^q> \sim t^{q \nu(q)}$…
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic…