Related papers: On diffusion in narrow random channels
We develop an analytical theory for diffusive random lasers by coupling the transport theory of the disordered medium to the semiclassical laser rate equations, accounting for (coherent) stimulated and (incoherent) spontaneous emission.…
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…
Diffusion is a fundamental physical phenomenon with critical applications in fields such as metallurgy, cell biology, and population dynamics. While standard diffusion is well-understood, anomalous diffusion often requires complex non-local…
Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…
We present a conception of the slow diffusion processes in the Euclidean spaces $\Bbb R^m, \; m\ge 1$, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow…
The existing kinetic theory of gases is based on an analytical approach that becomes intractable for all but the simplest molecules. Here we propose a simple numerical scheme to compute the transport properties of molecular gases in the…
Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state ``burnt-bridge'' models.…
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven-diffusive systems may be described by urn models. We consider a class of one-dimensional urn models whereby particles hop from an…
We present a theoretical investigation of thermal fluctuation statistics in a molecular motor. Energy transfer in the motor is described using a multidimensional discrete master equation with nearest-neighbor hopping. In this theory, energy…
Traditional theories of the NMR autocorrelation function for intramolecular dipole pairs assume single-exponential decay, yet the calculated autocorrelation of realistic systems display a rich, multi-exponential behavior resulting in…
We present a combined experimental and theoretical study of the self-diffusion of ammonia on exfoliated graphite. Using neutron time-of-flight spectroscopy we are able to resolve the ultrafast diffusion process of adsorbed ammonia, NH$_3$,…
The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
Long DNA molecules can be mapped by cutting them with restriction enzymes inside a narrow channel. Once cut, the individual fragments thus produced move away from each other due to diffusion and entropic effects. We investigate how long it…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
Starting from a unit mass on a vertex of a graph, we investigate the minimum number of "\emph{controlled diffusion}" steps needed to transport a constant mass $p$ outside of the ball of radius $n$. In a step of a controlled diffusion…
Dynamic properties of molecular motors whose motion is powered by interactions with specific lattice bonds are studied theoretically with the help of discrete-state stochastic "burnt-bridge" models. Molecular motors are depicted as random…
We present a novel approach for generating motion primitives for kinodynamic motion planning using diffusion models. The motions generated by our approach are adapted to each problem instance by utilizing problem-specific parameters,…
Diffusion and rectification of Brownian particles powered by a rotating wheel are numerically investigated in a two-dimensional channel. The nonequilibrium driving comes from the rotating wheel, which can break thermodynamical equilibrium…