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In this work we establish a link between two different phenomena that were studied in a large and growing number of biological, composite and soft media: the diffusion in compartmentalized environment and the Brownian yet non-Gaussian…
Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift…
We revisit the classic problem of the effective diffusion constant of a Brownian particle in a square lattice of reflecting impenetrable hard disks. This diffusion constant is also related to the effective conductivity of non-conducting and…
We present results for collective diffusion of adatoms on a stepped substrate with a submonolayer coverage. We study the combined effect of the additional binding at step edge, the Schwoebel barrier, the enhanced diffusion along step edges,…
Populations of swimming microorganisms produce fluid motions that lead to dramatically enhanced diffusion of tracer particles. Using simulations of suspensions of swimming particles in a periodic domain, we capture this effect and show that…
To study the effect of boundaries on diffusion of new products, we introduce two novel analytic tools: The indifference principle, which enables us to explicitly compute the aggregate diffusion on various networks, and the dominance…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
Nonergodicity observed in single-particle tracking experiments is usually modeled by transient trapping rather than spatial disorder. We introduce models of a particle diffusing in a medium consisting of regions with random sizes and random…
Living systems at the sub-cellular, cellular, and multi-cellular level are often crowded systems that contain active particles. The active motion of these particles can also propel passive particles, which typically results in enhanced…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…
In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of…
It is well-known under the name of `periodic homogenization' that, under a centering condition of the drift, a periodic diffusion process on R^d converges, under diffusive rescaling, to a d-dimensional Brownian motion. Existing proofs of…
Stable Diffusion is a popular Transformer-based model for image generation from text; it applies an image information creator to the input text and the visual knowledge is added in a step-by-step fashion to create an image that corresponds…
Diffusion of particles through an heterogenous obstacle line is modeled as a two-dimensional diffusion problem with a one--directional nonlinear convective drift and is examined using two-scale asymptotic analysis. At the scale where the…
Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new…
Diffusion processes in networks are increasingly used to model the spread of information and social influence. In several applications in computational sustainability such as the spread of wildlife, infectious diseases and traffic mobility…
Recent empirical studies have confirmed the key roles of complex contagion mechanisms such as memory, social reinforcement, and decay effects in information diffusion and behaviour spreading. Inspired by this fact, we here propose a new…
We show that a weakly absorbing, strongly scattering (white) medium can be made very strongly absorbing at any frequency within its strong-scattering bandwidth by optimizing the input electromagnetic field. For uniform absorption, results…
The diffusion model has demonstrated promising results in image generation, recently becoming mainstream and representing a notable advancement for many generative modeling tasks. Prior applications of the diffusion model for both fast…
While the mathematical foundations of score-based generative models are increasingly well understood for unconstrained Euclidean spaces, many practical applications involve data restricted to bounded domains. This paper provides a…