Related papers: Fractional diffusion on a fractal grid comb
Recently, a perturbative model of non-linear fiber propagation in uncompensated optical transmission systems has been proposed, called GN-model [1]. Here, an extended and more detailed version of the GN-model derivation [1] is reported,…
Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially…
Much of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a…
Understanding the physics of the integrable spin-1/2 XXZ chain has witnessed substantial progress, due to the development and application of sophisticated analytical and numerical techniques. In particular, infinite-temperature…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under…
{\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…
We present an analytical diffusion-expansion Forbush decrease (FD) model ForbMod which is based on the widely used approach of the initially empty, closed magnetic structure (i.e. flux rope) which fills up slowly with particles by…
A fundamental problem in plasma physics, space science, and astrophysics is the transport of energetic particles interacting with stochastic magnetic fields. In particular the motion of particles across a large scale magnetic field is…
Anomalous diffusion occurs at very different scales in nature, from atomic systems to motions in cell organelles, biological tissues or ecology, and also in artificial materials, such as cement. Being able to accurately measure the…
The global existence of bounded solutions to reaction-diffusion systems with fractional diffusion in the whole space $\mathbb R^N$ is investigated. The systems are assumed to preserve the non-negativity of initial data and to dissipate…
The simplest transport problem, namely maxflow, is investigated on critical percolation clusters in two and three dimensions, using a combination of extremal statistics arguments and exact numerical computations, for power-law distributed…
Fractional Brownian motion (fBm) is a ubiquitous diffusion process in which the memory effects of the stochastic transport result in the mean squared particle displacement following a power law, $\langle {\Delta r}^2 \rangle \sim…
We derive a renormalization method to calculate the spectral dimension $\bar{d}$ of deterministic self-similar networks with arbitrary base units and branching constants. The generality of the method allows the affect of a multitude of…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
Symmetries strongly influence transport properties of quantum many-body systems, and can lead to deviations from the generic case of diffusion. In this work, we study the impact of time-reversal symmetry breaking on the transport and its…
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…
The widespread use of GPS devices has driven advances in spatiotemporal data mining, enabling machine learning models to simulate human decision making and generate realistic trajectories, addressing both data collection costs and privacy…
The problem of spin diffusion is studied numerically in one-dimensional classical Heisenberg model using a deterministic odd even spin precession dynamics. We demonstrate that spin diffusion in this model, like energy diffusion, is normal…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…