Related papers: Diffusion-limited aggregation with jumps and fligh…
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…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Computer simulations are used to generate two-dimensional diffusion-limited deposits of dipoles. The structure of these deposits is analyzed by measuring some global quantities: the density of the deposit and the lateral correlation…
Brownian particles that are replicated and annihilated at equal rate have strongly correlated positions, forming a few compact clusters separated by large gaps. We characterize the distribution of the particles at a given time, using a…
Recently, diffusion models have achieved great success in image synthesis. However, when it comes to the layout-to-image generation where an image often has a complex scene of multiple objects, how to make strong control over both the…
In this paper, we present an effective data augmentation framework leveraging the Large Language Model (LLM) and Diffusion Model (DM) to tackle the challenges inherent in data-scarce scenarios. Recently, DMs have opened up the possibility…
Over the past few years the displacement statistics of self-propelled particles has been intensely studied, revealing their long-time diffusive behavior. Here, we demonstrate that a concerted combination of boundary conditions and switching…
Diffusion-based data augmentation (DiffDA) has emerged as a promising approach to improving classification performance under data scarcity. However, existing works vary significantly in task configurations, model choices, and experimental…
We investigate three types of Internal Diffusion Limited Aggregation (IDLA) models. These models are based on simple random walks on $\mathbf{Z}^2$ with infinitely many sources that are the points of the vertical axis…
The basic science responsible for the fascinating shapes of ice crystals and snowflakes is still not understood. Insufficient knowledge of the interaction potentials and the lack of relevant experimental access to the growth process are to…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
We study discontinuous percolation transitions (PT) in the diffusion-limited cluster aggregation model of the sol-gel transition as an example of real physical systems, in which the number of aggregation events is regarded as the number of…
We extend a previous analysis [PRL {\bf 80}, 4693 (1998)] of breakdown of dynamical scale invariance in the coarsening of two-dimensional DLAs (diffusion-limited aggregates) as described by the Cahn-Hilliard equation. Existence of a second…
We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and…
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…
A new model that describes adsorption and clustering of particles on a surface is introduced. A {\it clustering} transition is found which separates between a phase of weakly correlated particle distributions and a phase of strongly…
A theoretical approach to describing transport of an entire ensemble of clusters with different sizes as a single species in gas has been developed. The major assumption is an existence of local partial chemical equilibrium between the…
Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…