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We derive the probability density of a diffusion process generated by nonergodic velocity fluctuations in presence of a weak potential, using the Liouville equation approach. The velocity of the diffusing particle undergoes dichotomic…
We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be…
Systems are studied in which transport is possible due to large extension with open boundaries in certain directions but the particles responsible for transport can disappear from it by leaving it in other directions, by chemical reaction…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time…
When very small particles are suspended in a fluid in motion, they tend to follow the flow. How such tracer particles are mixed, transported, and dispersed by turbulent flow has been successfully described by statistical models. Heavy…
It is now well established that microswimmers can be sorted or segregated fabricating suitable microfluidic devices or using external fields. A natural question is how these techniques can be employed for dividing swimmers of different…
We show some computations related to the motion by mean curvature flow of a submanifold inside an ambient Riemannian manifold evolving by Ricci or backward Ricci flow. Special emphasis is given to the possible generalization of Huisken's…
We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates…
Using simulations, we examine the average velocity as a function of applied drift force for active matter particles moving through a random obstacle array. We find that for low drift force, there is an initial flow regime where the mobility…
In this paper, we derive explicit formulas for the surface averaged first exit time of a discrete random walk on a finite lattice. We consider a wide class of random walks and lattices, including random walks in a non-trivial potential…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
We consider two scalar conservation laws with non-local flux functions, describing traffic flow on roads with rough conditions. In the first model, the velocity of the car depends on an averaged downstream density, while in the second model…
We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the…
We study a generalization of the standard trapping problem of random walk theory in which particles move subdiffusively on a one-dimensional lattice. We consider the cases in which the lattice is filled with a one-sided and a two-sided…
In this paper we analyze some aspects of {\em exponential flights}, a stochastic process that governs the evolution of many random transport phenomena, such as neutron propagation, chemical/biological species migration, or electron motion.…
Turbulent fluid flows exhibit a complex small-scale structure with frequently occurring extreme velocity gradients. Particles probing such swirling and straining regions respond with an intricate shape-dependent orientational dynamics,…
We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study…