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Using high-resolution direct numerical simulations, the height and Reynolds number dependence of higher-order statistics of the energy dissipation rate and local enstrophy are examined in incompressible, fully-developed turbulent channel…
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
We study the crossing time statistic of diffusing point particles between the two ends of expanding and narrowing two-dimensional conical channels under a transverse external gravitational field. The theoretical expression for the mean…
A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is…
We investigate the escape behavior of systems governed by the one-dimensional nonlinear diffusion equation $\partial_t \rho = \partial_x[\partial_x U\rho] + D\partial^2_x \rho^\nu$, where the potential of the drift, $U(x)$, presents a…
In this paper escape rates and local escape rates for special flows are sudied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfills certain scaling, invariance, and…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
Narrow escape and narrow capture problems which describe the average times required to stop the motion of a randomly travelling particle within a domain have applications in various areas of science. While for general domains, it is known…
Many physical, chemical, and biological systems depend on the first passage time (FPT) of a diffusive searcher to a target. Typically, this FPT is much slower than the characteristic diffusion timescale. For example, this is the case if the…
We consider a particle which moves on the x axis and is subject to a constant force, such as gravity, plus a random force in the form of Gaussian white noise. We analyze the statistics of first arrival at point $x_1$ of a particle which…
Tilted (entropic) risk, obtained by applying a log-exponential transform to a base loss, is a well established tool in statistics and machine learning for emphasizing rare or high loss events while retaining a tractable optimization…
Tracer diffusion in single-file systems, where particles are restricted to move on a line without passing each other, has been a fertile ground to investigate anomalous diffusion and strong memory effects. While the long-time behavior of…
We study the single file diffusion problem on a one-dimensional lattice with a self-similar distribution of hopping rates. We find that the time dependence of the mean-square displacement of both a tagged particle and the center of mass of…
Transmission-constrained problems in power systems can be cast as polynomial optimization problems whose coefficients vary over time. We consider the complications therein and suggest several approaches. On the example of the…
For a spectrally positive strictly stable process with index in (1,2), the paper obtains i) the density of the time when the process makes first exit from an interval by hitting the interval's lower end point before jumping over its upper…
Single-file transport refers to the motion of particles in a narrow channel, such that they cannot bypass each other. This constraint leads to strong correlations between the particles, described by correlation profiles, which measure the…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
Advection and dispersion in highly heterogeneous environments involving interfacial discontinuities in the corresponding drift and dispersion rates are described through disparate examples from the physical and biological sciences. A…
The volume of phase space may grow super-exponentially ("explosively") with the number of degrees of freedom for certain types of complex systems such as those encountered in biology and neuroscience, where components interact and create…
In this letter we propose the use of physics techniques for entropy determination on constrained parameter optimization problems. The main feature of such techniques, the construction of an unbiased walk on energy space, suggests their use…