Related papers: The Shortest Path Across the Mesoscopic System
Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of…
We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to…
In the classical transport theory, the coefficients such as the diffusion, thermal conductivity and viscosity of fluid are usually expressed in a form proportional to the mean free path of molecules. We point out that this may cause a great…
In this paper, I derive a closed expression for how precisely a small-scaled system can follow a pre-defined trajectory, while keeping its dissipation below a fixed limit. The total amount of dissipation is approximately inversely…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
A random hopping on a fractal network with dimension slightly above one, $d = 1 + \epsilon$, is considered as a model of transport for conducting polymers with nonmetallic conductivity. Within the real space renormalization group method of…
Many theoretical treatments of transport in heterogeneous Darcy flows consider advection only. When local-scale dispersion is neglected, flux-weighting persists over time; mean Lagrangian and Eulerian flow velocity distributions relate…
A theory of the dynamical conductance of mesoscopic conductors is presented. It is applied to mesoscopic capacitors, resonant double barriers, ballistic wires, metallic diffusive wires, and to the Corbino disk and the Hall bar in quantizing…
We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect…
We combine theory, numerical calculations, and experiments to accurately predict the motion of anisotropic particles in shallow microfluidic channels, in which the particles are strongly confined in the vertical direction. We formulate an…
In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF…
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We…
Properties of networks are often characterized in terms of features such as node degree distributions, average path lengths, diameters, or clustering coefficients. Here, we study shortest path length distributions. On the one hand, average…
We present a stochastic approach for charge transport in transistors. In this approach, the electron and hole densities are governed by diffusion-reaction stochastic differential equations satisfying local detailed balance and the electric…
A Gaussian process (GP)-based methodology is proposed to emulate complex dynamical computer models (or simulators). The method relies on emulating the numerical flow map of the system over an initial (short) time step, where the flow map is…
We introduce simple conditions ensuring that invariant distributions of a Feller Markov chain on a compact Riemannian manifold are absolutely continuous with a lower semi-continuous, continuous or smooth density with respect to the…
The low-T part of the phase diagram in self-assembling systems is correctly predicted by the known versions of the density functional theory (DFT). The high-T part obtained in DFT, however, does not agree with simulations even on the…
In this paper, we consider a diffusion process pertaining to a chain of distributed control systems with small random perturbation. The distributed control system is formed by n subsystems that satisfy an appropriate Hormander condition,…
We consider a controlled-diffusion process pertaining to a chain of distributed systems with random perturbations that satisfies a weak H\"ormander type condition. In particular, we consider a stochastic control problem with the following…
We have developed a theory for inhomogeneous systems that allows for incorporation of effects of mesoscopic fluctuations. A hierarchy of equations relating the correlation and direct correlation functions for the local excess $\phi({\bf…