a r t i c l e i n f o a b s t r a c t We developed a graphical user interface, MATLAB based program to calculate the translational diffusion coefficients in three dimensions for a single diffusing particle, suspended inside a fluid. When the particles are not spherical, in addition to their translational motion also a rotational freedom is considered for them and in addition to the previous tra...

Heat conduction [1] is usually modeled as a diffusion process embodied in heat conduction equation. The traditional numerical methods [2, 3] for heat conduction problems such as the finite difference or finite element are well developed. However, these methods are based on discretized mesh systems, thus they are inherently limited in the geometry treatment. This chapter describes the Monte Carl...

The transport of variably sized colloids (polydisperse) in a fracture with uniform aperture is investigated by a particle-tracking model that treats colloids as discrete particles with unique transport properties while accounting for either matrix diffusion or irreversible colloid deposition. For the special case of a monodisperse colloid suspension the particle-tracking model is in perfect agr...

1: Diffusion coefficient D(a) of the map depicted in the lower right corner. Shown are two pieces of the periodically continued map plus a trajectory segment of a diffusing particle. The slope a determining the average step lengths of a walker serves as a control parameter. The dashed lines represent random walk solutions for D(a), the inset depicts a blowup for the initial region of the main g...

The diffusion of a Janus rod-shaped nanoparticle in a dense Lennard-Jones fluid is studied using molecular dynamics (MD) simulations. The Janus particle is modeled as a rigid cylinder whose atoms at each end have different interaction energies with fluid molecules, thus comprising wetting and nonwetting surfaces. We found that both rotational and translational diffusion coefficients are larger ...

Our previous results indicated that the plasma membrane of cultured normal rat kidney fibroblastic cell is compartmentalized for diffusion of receptor molecules, and that long-range diffusion is the result of successive intercompartmental jumps (Sako, Y. and Kusumi, A. 1994. J. Cell Biol. 125:1251-1264). In the present study, we characterized the properties of intercompartmental boundaries by t...

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, an accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum-likelihood estimator...

We construct a system of interacting two-sided Bessel processes on the unit interval and show that the associated empirical measure process converges to the Wasserstein Diffusion [27], assuming that Markov uniqueness holds for the generating Wasserstein Dirichlet form. The proof is based on the variational convergence of an associated sequence of Dirichlet forms in the generalized Mosco sense o...

The one-dimensional reaction diffusion process AA → A and A∅A → AAA is exactly solvable through the empty interval method if the diffusion rate equals the coagulation rate. Independently of the particle production rate, the model is always in the universality class of diffusion-annihilation. This allows us to check analytically the universality of finite-size scaling in a non-equilibrium critic...

We consider diffusion on substrate with a frozen disorder. While in ordered state the moving particle meets always the same energy barrier in amorphous state there is a more or less broad distribution of the height of barriers. The effective activation energy Eeff that controls the diffusion process is not equal to the average activation energy barrier. Actually, Eeff is the highest barrier tha...