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Several classes of physical systems exhibit ultraslow diffusion for which the mean squared displacement at long times grows as a power of the logarithm of time ("strong anomaly") and share the interesting property that the probability…
We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $\phi$ and mean-square velocity fluctuations $\langle v^2\rangle$ the…
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…
We describe non-conventional localization of the midband E=0 state in square and cubic finite bipartite lattices with off-diagonal disorder by solving numerically the linear equations for the corresponding amplitudes. This state is shown to…
The leading Pollicott-Ruelle resonance is calculated analytically for a general class of two-dimensional area-preserving maps. Its wave number dependence determines the normal transport coefficients. In particular, a general exact formula…
We argue that at moderately large momentum transfer -t <10 GeV^2, hadronic form factors and wide-angle Compton scattering amplitudes are dominated by mechanism corresponding to overlap of soft wave functions. We show that the soft…
{\bf Purpose}: To develop a geometry-governed diffusion framework that explains differential tissue response under FLASH ultra-high dose rate (UHDR) irradiation by explicitly accounting for structural heterogeneity and anomalous transport…
Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modelling axons as straight cylinders. Axons do…
We address the problem of random search for a target in an environment with space-dependent diffusion coefficient $D(x)$. From a general form of the diffusion differential operator that includes It\^o, Stratonovich, and…
We explore the nature of anomalous diffusion of wave packets in disorder-free incommensurate multi-walled carbon nanotubes. The spectrum-averaged diffusion exponent is obtained by calculating the multifractal dimension of the energy…
We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
Consider the linear Boltzmann equation of radiative transfer in a half-space, with constant scattering coefficient $\sigma$. Assume that, on the boundary of the half-space, the radiation intensity satisfies the Lambert (i.e. diffuse)…
The frequency correlations of light in complex photonic media are of interest as a tool for characterizing the dynamical aspects of light diffusion. We demonstrate here that the frequency correlation shows a pronounced angle dependence both…
Transport by normal diffusion can be decomposed into the so-called hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with two degrees of freedom, the fine scale structure of these hydrodynamic…
We consider dense random packing of disks with a power-law distribution of radii and investigate their correlation properties. We study the corresponding structure factor, mass-radius relation and pair distribution function of the disk…
The probability density function (PDF) and cumulative distribution function of the sum of L independent but not necessarily identically distributed squared \eta-\mu variates, applicable to the output statistics of maximal ratio combining…
We relate ordinary and skewed parton distributions to soft overlap contributions to elastic form factors and large angle Compton scattering, using light-cone wave functions in a Fock state expansion of the nucleon. With a simple ansatz for…
We derive the transmission coefficient, $T(\omega)$, for grazing incidence of crystals with spatial dispersion accounting for the excitation of multiple modes with different wave vectors ${\bf k}$ for a given frequency $\omega$. The…