Related papers: Transition state theory applied to self-diffusion …
Analytical equations were found for interdigitated electrodes, which considered reversible electrode reactions and pure diffusion within confined spaces. A conformal transformation, obtained by the use of Jacobian elliptic functions, was…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
Mathematically, it takes an infinite amount of time for the transient solution of a diffusion equation to transition from initial to steady state. Calculating a \textit{finite} transition time, defined as the time required for the transient…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
Discontinuous transitions into absorbing states require an effective mechanism that prevents the stabilization of low density states. They can be found in different systems, such as lattice models or stochastic differential equations (e.g.…
Self-diffusion of a sphere in a network of rods is analyzed theoretically. Hydrodynamic interactions are taken into account according to the model of Dhont et al., under the assumption that $\ka << 1$ and $\bar{a}/L<<1$, where $1/\kappa$ is…
We study by molecular dynamics computer simulation a binary soft-sphere mixture that shows a pronounced decoupling of the species' long-time dynamics. Anomalous, power-law-like diffusion of small particles arises, that can be understood as…
We provide some criteria on the stability of regime-switching diffusion processes. Both the state-independent and state-dependent regime-switching diffusion processes with switching in a finite state space and an infinite countable state…
We consider single-file diffusion in an open system with two species $A,B$ of particles. At the boundaries we assume different reservoir densities which drive the system into a non-equilibrium steady state. As a model we use an…
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this…
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,…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
The dynamics of two and five disk systems confined in a square has been studied using molecular dynamics simulations and compared with the predictions of transition state theory. We determine the partition functions Z and Z^\ddagger of…
We discuss the nature of phase transitions in self-gravitating systems both in the microcanonical and in the canonical ensemble. We avoid the divergence of the gravitational potential at short distances by considering the case of…
We study a mass transport model, where spherical particles diffusing on a ring can stochastically exchange volume $v$, with the constraint of a fixed total volume $V=\sum_{i=1}^N v_i$, $N$ being the total number of particles. The particles,…
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
Autocatalytic reaction system with a small number of molecules is studied numerically by stochastic particle simulations. A novel state due to fluctuation and discreteness in molecular numbers is found, characterized as extinction of…
To model a complex system intrinsically separated by a barrier, we use two random Hamiltonians, coupled to each other either by a tunneling matrix element or by an intermediate transition state. We study that model in the universal limit of…
The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…
The scaled particle theory is developed for the description of thermodynamical properties of a mixture of hard spheres and hard spherocylinders. Analytical expressions for free energy, pressure and chemical potentials are derived. From the…