Related papers: Diffusion: Quiescence and Perturbation
From the exact single step evolution equation of the two-point correlation function of a particle distribution subjected to a stochastic displacement field $\bu(\bx)$, we derive different dynamical regimes when $\bu(\bx)$ is iterated to…
Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or with a Gaussian distributed…
The stability of cortical function depends critically on proper regulation. Under conditions of migraine and stroke a breakdown of transmembrane chemical gradients can spread through cortical tissue. A concomitant component of this emergent…
The challenges of graph stream algorithms are twofold. First, each edge needs to be processed only once, and second, it needs to work on highly constrained memory. Diffusion degree is a measure of node centrality that can be calculated (for…
We introduce a simple model of deterministic particles in weakly disordered media which exhibits a transition from normal to anomalous diffusion. The model consists of a set of non-interacting overdamped particles moving on a disordered…
We survey recent results of normal and anomalous diffusion of two types of random motions with long memory in ${\Bbb R}^d$ or ${\Bbb Z}^d$. The first class consists of random walks on ${\Bbb Z}^d$ in divergence-free random drift field,…
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…
Originating from the diffusion phenomenon in physics that describes particle movement, the diffusion generative models inherit the characteristics of stochastic random walk in the data space along the denoising trajectory. However, the…
Diffusion models have significantly advanced the field of generative modeling. However, training a diffusion model is computationally expensive, creating a pressing need to adapt off-the-shelf diffusion models for downstream generation…
We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the…
Recently, text-guided image editing has achieved significant success. However, existing methods can only apply simple textures like wood or gold when changing the texture of an object. Complex textures such as cloud or fire pose a…
By analyzing the displacement statistics of an assembly of horizontally vibrated bidisperse frictional grains in the vicinity of the jamming transition experimentally studied before, we establish that their superdiffusive motion is a…
Diffusion models are proficient at generating high-quality images. They are however effective only when operating at the resolution used during training. Inference at a scaled resolution leads to repetitive patterns and structural…
We introduce the pushy random walk, where a walker can push multiple obstacles, thereby penetrating large distances in environments with finite obstacle density. This process provides a minimal model for experimentally observed interactions…
Denoising diffusion models represent a recent emerging topic in computer vision, demonstrating remarkable results in the area of generative modeling. A diffusion model is a deep generative model that is based on two stages, a forward…
We perform molecular dynamic simulations of liquid nanoparticles deposited on a disordered substrate. The motion of the nanoparticle is characterised by a 'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$), analysis…
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing…
A conditional diffusion model has been developed to analyze intricate conductance fluctuations called universal conductance fluctuations or quantum fingerprints appearing in quantum transport phenomena. The model reconstructs impurity…
Accretion disc theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was emitted to the sides of the disc. One of the most important new invention of this theory was a…
Turbulence acting on mixes of gas and particles generally evenly diffuses the latter through the former. However, in the presence of background gas temperature gradients a phenomenon known as turbulent thermal diffusion appears as a…