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We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a…
The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…
The possible functional forms of the effective conductivity sigma_e of the randomly inhomogeneous two-phase systems at arbitrary values of concentrations are discussed. Two explicit approximate expressions for effective conductivity are…
Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and…
Using Langevin dynamics, we have investigated the dynamics of vortices in a disordered two dimensional superconductor subjected to a uniform driving current. The results provide direct numerical evidence for a dynamical phase transition…
We consider flux penetration to a 2D superconducting cylinder. We show that in the low field limit the kinetics is deterministic. In the strong field limit the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder…
Electron transport through a single-level quantum dot weakly coupled to Luttinger liquid leads is considered in the master equation approach. It is shown that for a weak or moderately strong interaction the differential conductance…
We adopt a stochastic approach to study the charge transport in transistors. In this approach, the hole and electron densities are ruled by diffusion-reaction stochastic partial differential equations satisfying local detailed balance…
We have studied numerically the fluctuations of the conductance, $g$, in two-dimensional, three-dimensional and four-dimensional disordered non-interacting systems. We have checked that the variance of $\ln g$ varies with the lateral sample…
We have considered the conductivity properties of a two dimensional electron gas (2DEG) in two different kinds of inhomogeneous magnetic fields, i.e. a disordered distribution of magnetic flux vortices, and a periodic array of magnetic flux…
The analytical theory for the voltage-current characteristics of the large inductance (L>100 pH) high-T_c DC SQUIDs that has been developed previously is consistently compared with the computer simulations and the experiment. The…
We develop a full microscopic theory for the optical conductivity, $\sigma(\omega)$, of a dirty current-carrying superconductor. Within the Keldysh sigma model formalism, we obtain the general analytical expression for $\sigma(\omega)$,…
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed…
In ultra-pure conductors, collective motion of charge carriers at relatively high temperatures may become hydrodynamic such that electronic transport may be described similarly to a viscous flow. In confined geometries (e.g., in ultra-high…
Here we present the calculations of incoherent current flowing through the two-site molecular device as well as the DNA-based junction within the rate-equation approach. Few interesting phenomena are discussed in detail. Structural…
We use a theoretical model to explore how fluid dynamics, in particular, the pressure gradient and wall shear stress in a channel, affect the deposition of particles flowing in a microfluidic network. Experiments on transport of colloidal…
Two-dimensional (2D) materials are a new class of materials with interesting physical properties and applications ranging from nanoelectronics to sensing and photonics. In addition to graphene, the most studied 2D material, monolayers of…
We have generalized the semi-analytic approach of special flow to the description of flows of passive particles taking into account internal noise. The model is represented by a series of recurrence relations. The recurrence relations are…
We study the multifractal properties of the current distribution of the three-dimensional random resistor network at the percolation threshold. For lattices ranging in size from $8^3$ to $80^3$ we measure the second, fourth and sixth…
Density functional calculations for the electronic conductance of single molecules are now common. We examine the methodology from a rigorous point of view, discussing where it can be expected to work, and where it should fail. When…