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We expand upon a new theoretical framework for Diffusion Limited Aggregation and associated Dielectric Breakdown Models in two dimensions [R. C. Ball and E. Somfai, Phys. Rev. Lett. 89, 135503 (2002)]. Key steps are understanding how these…
The present article proposes a diffuse interface model for compressible multicomponent flows with transport phenomena of mass, momentum and energy (i.e., mass diffusion, viscous dissipation and heat conduction). The model is reduced from…
Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…
Diffusion-based and neural communication are two interesting domains in molecular communication. Both of them have distinct advantages and are exploited separately in many works. However, in some cases, neural and diffusion-based ways have…
Charge transport in disordered two-dimensional (2D) systems showcases a myriad of unique phenomenologies that highlight different aspects of the underlying quantum dynamics. Electrons in such systems undergo a crossover from ballistic…
Diffusion-induced Ramsey narrowing that appears when atoms can leave the interaction region and repeatedly return without lost of coherence is investigated using strong collisions approximation. The effective diffusion equation is obtained…
Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…
In this paper an analytical model is introduced to describe the impulse response of the diffusive channel between a pointwise transmitter and a given fully-absorbing (FA) receiver in a molecular communication (MC) system. The presence of…
Inverse design problems are common in engineering and materials science. The forward direction, i.e., computing output quantities from design parameters, typically requires running a numerical simulation, such as a FEM, as an intermediate…
Defects are inevitable during the manufacturing processes of materials. Presence of these defects and their dynamics significantly influence the responses of materials. A thorough understanding of dislocation dynamics of different types of…
A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…
Diffusion models are the mainstream approach for time series generation tasks. However, existing diffusion models for time series generation require retraining the entire framework to introduce specific conditional guidance. There also…
Local drug delivery has received much recognition in recent years, yet it is still unpredictable how drug efficacy depends on physicochemical properties and delivery kinetics. The purpose of the current study is to provide a useful…
As a class of generative artificial intelligence frameworks inspired by statistical physics, diffusion models have shown extraordinary performance in synthesizing complicated data distributions through a denoising process gradually guided…
We consider a simple model of particle transport on the line defined by a dynamical map F satisfying F(x+1) = 1 + F(x) for all x in R and F(x) = ax + b for |x| < 0.5. Its two parameters a (`slope') and b (`bias') are respectively symmetric…
Diffusion models have emerged as a powerful new family of deep generative models with record-breaking performance in many applications, including image synthesis, video generation, and molecule design. In this survey, we provide an overview…
Diffusion Models are probabilistic models that create realistic samples by simulating the diffusion process, gradually adding and removing noise from data. These models have gained popularity in domains such as image processing, speech…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
We explain how to use diffusion models to learn inverse renormalization group flows of statistical and quantum field theories. Diffusion models are a class of machine learning models which have been used to generate samples from complex…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…