Related papers: The Shortest Path Across the Mesoscopic System
We analyze the ergodicity of three one-dimensional Hamiltonian systems, with harmonic, quartic and Mexican-hat potentials, coupled to the logistic thermostat. As criteria for ergodicity we employ: the independence of the Lyapunov spectrum…
We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the…
An index of uniformity is developed as an alternative to the maximum-entropy principle for selecting continuous, differentiable probability distributions $\mathcal{P}$ subject to constraints $C$. The uniformity index developed in this paper…
Charge transport in amorphous semiconductors is considerably more complicated than process in crystalline materials due to abundant localized states. In addition to device-scale characterization, spatially resolved measurements are…
We present analytical results for the distribution of shortest path lengths between random pairs of nodes in configuration model networks. The results, which are based on recursion equations, are shown to be in good agreement with numerical…
This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with…
The interplay of Umklapp scattering from a periodic potential and other scattering processes determine the conductivity of (quasi) one-dimensional metals. We show that the transport at finite temperature is qualitatively and quantitatively…
A parametric method similar to autoregressive spectral estimators is proposed to determine the probability density function (pdf) of a random set. The method proceeds by maximizing the likelihood of the pdf, yielding estimates that perform…
The mathematical equivalence of the time-independent Schrodinger equation and the Helmholtz equation is exploited to provide a novel means of studying universal conductance fluctuations in ballistic chaotic mesoscopic systems using a…
The conductance coefficients of disordered mesoscopic devices with $n$ probes are investigated within the noninteracting electron approximation at zero temperature. The probes are eliminated from the theoretical description at the expense…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…
Statistics of molecular random walks in a fluid is considered with the help of the Bogolyubov equation for generating functional of distribution functions. An invariance group of solutions to this equation as functions of the fluid density…
A dephasing model in the spirit of Buttiker's fictitious probe model where infinite probes are distributed uniformly over the conductor is proposed. The dephasing rate enters into the model as an adjustable parameter and to compute the…
Experimental studies of the variation of the mean square displacement (MSD) of a particle in a confined colloid suspension that exhibits density variations on the scale length of the particle diameter are not in agreement with the…
The orbital angular momentum of electrons offers a promising, yet largely unexplored, degree of freedom for ultrafast, energy-efficient information processing. As the foundation of orbitronics, understanding how orbital currents propagate…
The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative density distribution (CDF) of a system state,…
We compare predictions from two familiar models of the metastable supercooled liquid respectively constructed with thermodynamic and dynamic approach. In the so called density functional theory (DFT) the free energy $F[\rho]$ of the liquid…
Mobility entropy is proposed to measure predictability of human movements, based on which, the upper and lower bound of prediction accuracy is deduced, but corresponding mathematical expressions of prediction accuracy keeps yet open. In…
The transport properties of discrete-time random walks on ring networks with deterministic shortcuts are investigated through analytical and numerical methods. The network consists of a periodic chain where each node is connected to its…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…