Related papers: Molecular theory of anomalous diffusion - Applicat…
In contrast to normal diffusion, there is no canonical model for reactions between chemical species which move by anomalous subdiffusion. Indeed, the type of mesoscopic equation describing reaction-subdiffusion depends on subtle assumptions…
A ubiquitous observation in cell biology is that diffusion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This…
The purpose of this tutorial is to introduce the main concepts behind normal and anomalous diffusion. Starting from simple, but well known experiments, a series of mathematical modeling tools are introduced, and the relation between them is…
Polydimethylsiloxane (PDMS) is a glassy polymer widely used in biomedical engineering, namely in microfluidics applications. However, PDMS is known to interact with hydrophobic chemicals. This interaction is exacerbated at the scale of…
Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…
The angular and frequency correlation functions of the transmission coefficient for light propagation through a strongly scattering amplifying medium are considered. It is found that just as in the case of an elastic scattering medium the…
According to a traditional point of view Boltzmann entropy is intimately related to linear Fokker-Planck equations (Smoluchowski, Klein-Kramers, and Rayleigh equations) that describe a well-known nonequilibrium phenomenon: (normal) Brownian…
This work reports the results of the theoretical investigation of nonlinear dynamics and spiral wave breakup in a generalized two-variable model of cardiac action potential accounting for thermo-electric coupling and diffusion…
Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…
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 study a nonlinear pseudodifferential equation describing the dynamics of dislocations. The long time asymptotics of solutions is described by the self-similar profiles.
Recent advancements in diffusion models have demonstrated significant success in unsupervised anomaly segmentation. For anomaly segmentation, these models are first trained on normal data; then, an anomalous image is noised to an…
Fully describing light propagation in a rotating, anisotropic medium with thermal nonlinearity requires modeling the interplay between nonlinear refraction, birefringence, and the nonlinear group index. Incorporating these factors into a…
Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…
Infiltration of diffusing particles from one material to another where the diffusion mechanism is either normal or anomalous is a widely observed phenomena. When the diffusion is anomalous we find interesting behaviors: diffusion may lead…
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of…
The authors investigate the solution of a nonlinear reaction-diffusion equation connected with nonlinear waves. The equation discussed is more general than the one discussed recently by Manne, Hurd, and Kenkre (2000). The results are…
We consider anomalous diffusion for molecular communication with a passive receiver. We first consider the probability density function of molecules' location at a given time in a space of arbitrary dimension. The expected number of…
The problem of anomalous diffusion in momentum space is considered for plasma-like systems on the basis of a new collision integral, which is appropriate for consideration of the probability transition function (PTF) with long tails in…