Related papers: Effective transient behaviour of inclusions in dif…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
Coulomb drag between parallel two-dimensional electronic layers is an excellent tool for the study of electron-electron interactions. In actual experiments, the layers display spatial charge density fluctuations due to imperfections such as…
For the rendering of multiple scattering effects in participating media, methods based on the diffusion approximation are an extremely efficient alternative to Monte Carlo path tracing. However, in sufficiently transparent regions,…
The application of diffusion transformers is suffering from their significant inference costs. Recently, feature caching has been proposed to solve this problem by reusing features from previous timesteps, thereby skipping computation in…
We investigate the effective diffusion of a tracer immersed in an active particle bath consisting of self-propelled particles. Utilising the Dean's method developed for the equilibrium bath and extending it to the nonequilibrium situation,…
The transport and dispersion of multiple species of charged ions are central to many biological and physical processes, including electrokinetic ion separation. However, most theoretical studies of dispersion in channels have focused on…
Diffusion models have been successfully adapted to text generation tasks by mapping the discrete text into the continuous space. However, there exist nonnegligible gaps between training and inference, owing to the absence of the forward…
Diffusion-based inpainting is a powerful tool for the reconstruction of images from sparse data. Its quality strongly depends on the choice of known data. Optimising their spatial location -- the inpainting mask -- is challenging. A…
Transition graphs capture the memory and sequential response of multistable media, by specifying their evolution under external driving. Microscopically, collections of bistable elements, or hysterons, provide a powerful model for these…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
The approach to calculating the effective dielectric and magnetic response in bounded composite materials is developed. The method is essentially based on the renormalisation of the dielectric matrix parameters to account for the surface…
Under inhomogeneous flow, dense suspensions exhibit complex behaviour that violates the conventional homogenous rheology. Specifically, one finds flowing regions with a macroscopic friction coefficient below the yielding criterion, and…
Diffusion models have shown remarkable performance in generation problems over various domains including images, videos, text, and audio. A practical bottleneck of diffusion models is their sampling speed, due to the repeated evaluation of…
We provide a general framework for learning diffusion bridges that transport prior to target distributions. It includes existing diffusion models for generative modeling, but also underdamped versions with degenerate diffusion matrices,…
We study measures of the amount of time required for transient flow in heterogeneous porous media to effectively reach steady state, also known as the response time. Here, we develop a new approach that extends the concept of mean action…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
The purpose of this article is to investigate the emergence of cross-diffusion in the time evolution of two slow-fast species in competition. A class of triangular cross-diffusion system is obtained as the singular limit of a fast…
Discrete state space diffusion models have shown significant advantages in applications involving discrete data, such as text and image generation. It has also been observed that their performance is highly sensitive to the choice of rate…
Autoregressive models (ARMs) are hindered by slow sequential inference. While masked diffusion models (MDMs) offer a parallel alternative, they suffer from critical drawbacks: high computational overhead from precluding Key-Value (KV)…