Related papers: A Coordinate Free Formulation of Effective Diffusi…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
This paper focuses on the derivation of the distribution of diffused particles absorbed by an agent in a bounded environment. In particular, we analogously consider to derive the impulse response of a molecular communication channel in 2-D…
A diffusion process for charge distributions in a phase space is examined. The corresponding charge moves in a force field and under an action of a random field. There are the diffusion motions for coordinates and for momenta. In our model,…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…
The advection-diffusion equation can be approximated by a one-dimensional diffusion equation in Lagrangian coordinates along the directions of compression of fluid elements (the stable manifold). This result holds in any number of…
Rectification and diffusion of non-interacting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient.…
What is the optimal way to approximate a high-dimensional diffusion process by one in which the coordinates are independent? This paper presents a construction, called the \emph{independent projection}, which is optimal for two natural…
We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…
We study the diffusion equation on the surface of a 4D sphere and obtain a Kubo formula for the diffusion coefficient.
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
In this paper we study the problem of the numerical calculation (by Monte Carlo Methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity filed, in the limit of vanishing molecular diffusion. In this…
We describe an exact and highly efficient numerical algorithm for solving a special but important class of convection-diffusion equations. These equations occur in many problems in physics, chemistry, or biology, and they are usually hard…
A practical correction formula relating the self-diffusion coefficient of dense liquids from molecular dynamics simulations with periodic boundary conditions to the self-diffusion coefficient in the thermodynamic limit is discussed. This…
Translational diffusion coefficients are routinely estimated from molecular dynamics simulations. Linear fits to mean squared displacement (MSD) curves have become the de facto standard, from simple liquids to complex biomacromolecules.…
Diffusion Models (DMs) have demonstrated state-of-the-art performance in content generation without requiring adversarial training. These models are trained using a two-step process. First, a forward - diffusion - process gradually adds…
In this paper we study the problem of computing the effective diffusivity for a particle moving in chaotic and stochastic flows. In addition we numerically investigate the residual diffusion phenomenon in chaotic advection. The residual…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
Surface-active molecules supplied from a particle fixed at the water surface create a spatial gradient of the molecule concentration, resulting in Marangoni convection. Convective flow transports the molecules far from the particle,…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…