Related papers: Diffusion Limited Aggregation with modified local …
Discrete diffusion models have emerged as a powerful class of models and a promising route to fast language generation, but practical implementations typically rely on factored reverse transitions ignoring cross-token dependencies and…
The single-file problem of N particles in one spatial dimension is analyzed, when each particle has a randomly distributed diffusion constant D sampled in a density $\rho(D)$. The averaged one-particle distributions of the edge particles…
We use molecular dynamics simulations to study a model of the gelation transition with a dynamic bond forming procedure. After establishing evidence for 3D percolation as the static universality class, we turn our attention to the dynamics…
We consider a single-species diffusion-limited annihilation reaction with reactants confined to a two-dimensional surface with one arbitrarily large dimension and the other comparable in size to interparticle distances. This situation could…
In this paper, we study pattern formations in an aggregation and diffusion cell migration model with Dirichlet boundary condition. The formal continuum limit of the model is a nonlinear parabolic equation with a diffusivity which can become…
Diffusion Policy has shown great performance in robotic manipulation tasks under stochastic perturbations, due to its ability to model multimodal action distributions. Nonetheless, its reliance on a computationally expensive reverse-time…
A simple model of irreversible aggregation under differential sedimentation of particles in a fluid is presented. The structure of the aggregates produced by this process is found to feed back on the dynamics in such a way as to stabilise…
We propose a unifying theoretical framework for the analysis of first-passage time distributions in two important classes of stochastic processes in which the diffusivity of a particle evolves randomly in time. In the first class of…
An overview of the author's papers on the new approach to the Brownian coagulation theory and its generalization to the diffusion-limited reaction rate theory is presented. The traditional diffusion approach of the Smoluchowski theory for…
We use a macromodel of a flow-driven deterministic lateral displacement (DLD) microfluidic system to investigate conditions leading to size-separation of suspended particles. This model system can be easily reconfigured to establish an…
The DCA$^+$ algortihm was recently introduced to extend the dynamic cluster approximation (DCA) with a continuous lattice self-energy in order to achieve better convergence with cluster size. Here we extend the DCA$^+$ algorithm to the…
During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its…
Diffusion of a two component fluid is studied in the framework of differential equations, but where these equations are systematically derived from a well-defined microscopic model. The model has a finite carrying capacity imposed upon it…
A mode-coupling theory for the slow single-particle dynamics in fluids adsorbed in disordered porous media is derived, which complements previous work on the collective dynamics [V. Krakoviack, Phys. Rev. E 75, 031503 (2007)]. Its…
We investigate the single-file dynamics of a tagged particle in a system consisting of N hardcore interacting particles (the particles cannot pass each other) which are diffusing in a one-dimensional system where the particles have…
As one of the leading acceleration mechanisms in laser-driven underdense plasmas, direct laser acceleration (DLA) is capable of producing high-energy-density electron beams in a plasma channel for many applications. However, the mechanism…
We study a two-lane model of two-species of particles that perform biased diffusion. Extensive numerical simulations show that when bias q is strong enough oppositely drifting particles form some clusters that block each other. Coarsening…
Diffusion models have recently emerged as effective generative frameworks for trajectory optimization, capable of producing high-quality and diverse solutions. However, training these models in a purely data-driven manner without explicit…
We examine a discrete model of sticky particles initially subjected to acceleration. We propose a novel generalized variational principle for characterizing clusters (i.e., particle agglomerations) under decreasing acceleration function.…
A simple, discrete, parametric model is proposed to describe conditional (correlated) deposition of particles on a surface and formation of a connecting (percolating) cluster. The surface changes spontaneously its properties (phase…