Related papers: Diffusion in a Curved Tube
The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the…
A thin tube is an $n$-dimensional space which is very thin in $n-1$ directions, compared to the remaining direction, for example the $\epsilon$-neighborhood of a curve or an embedded graph in $\R^n$ for small $\epsilon$. The Laplacian on…
In this paper the distribution of charged particles is constructed under the approximation of ambipolar diffusion. The results of mathematical modelling in two-dimensional case taking into account the velocities of the system are presented.
Diffusion-driven patterns appear on curved surfaces in many settings, initiated by unstable modes of an underlying Laplacian operator. On a flat surface or perfect sphere, the patterns are degenerate, reflecting translational/rotational…
We present a simple model for the development of shear layers between parallel flows in confining channels. Such flows are important across a wide range of topics from diffusers, nozzles and ducts to urban air flow and geophysical fluid…
The self-diffusion process of a hard sphere fluid confined by two parallel plates separated by a distance on the order of the particle diameter is studied. The starting point is a closed kinetic equation for the distribution function that…
The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence…
The remaining dynamical degrees of freedom of molecular fluids confined into capillaries of nano to sub-nanometer diameter are of fundamental relevance for future developments in the field of nanofluidics. These properties cannot be simply…
The frictionless, directional propagation of particles at the boundary of topological materials is one of the most striking phenomena in transport. These chiral edge modes lie at the heart of the integer and fractional quantum Hall effects,…
We study the diffusive behavior of biased Brownian particles in a two dimensional confined geometry filled with the freezing obstacles. The transport properties of these particles are investigated for various values of the obstacles density…
Diffusive transport is characterized by the scaling law $(length)^{2}\propto(time)$. In this letter we show that this relationship is significantly altered in curved analogue spacetimes. This circumstance provides an opportunity to tailor…
We show that the diffusion of a single file of particles moving in a fluctuating modulated 1D channel is enhanced with respect to the one in a bald pipe. This effect, induced by the fluctuations of the modulation, is favored by the…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We define the Dyson diffusion process on a curved smooth closed contour in the plane and derive the Fokker-Planck equation for probability density. Its stationary solution is shown to be the Boltzmann weight for the logarithmic gas confined…
We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the…
We study the transport properties of a system of active particles moving at constant speed in an heterogeneous two-dimensional space. The spatial heterogeneity is modeled by a random distribution of obstacles, which the active particles…
In the spirit of the thin-layer quantization scheme, we give the effective Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the…
The aim of the thesis is to present and analyze two particular problems of transport in porous media flow. The first of them is related to the process of saturation of porous building materials. Recently, M. K\"untz and P. Laval\'ee, using…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…