相关论文: Dimension-splitting for simplifying diffusion in l…
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…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We develop diffusion models for lattice gauge theories which build on the concept of stochastic quantization. This framework is applied to $U(1)$ gauge theory in $1+1$ dimensions. We show that a model trained at one small inverse coupling…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Physics-guided sampling with diffusion priors has recently shown strong performance in solving complex systems of partial differential equations (PDEs) from sparse observations. However, these methods are typically evaluated on benchmark…
We consider one component lattice gases with a local dynamics and a stationary product Bernoulli measure. We give upper and lower bounds on the diffusivity at an equilibrium point depending on the dimension and the local behavior of the…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
Developments in dynamical systems theory provides new support for the discretisation of \pde{}s and other microscale systems. By systematically resolving subgrid microscale dynamics the new approach constructs asymptotically accurate,…
The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…
Three-dimensional molecular generators based on diffusion models can now reach near-crystallographic accuracy, yet they remain fragmented across tasks. SMILES-only inputs, two-stage pretrain-finetune pipelines, and one-task-one-model…
We investigate the aging behavior of lattice-gas models with constrained dynamics in which particle exchange with a reservoir is allowed. Such models provide a particularly simple interpretation of aging phenomena as a slow approach to…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
The object of the present article is a 1d lattice-gas system comprised of soft-particles, wherein particles interact only if they occupy the same or a neighboring site, as a simple representation of penetrable particles of soft condensed…
We consider the coagulation dynamics A+A -> A and the annihilation dynamics A+A -> 0 for particles moving subdiffusively in one dimension, both on a lattice and in a continuum. The analysis combines the "anomalous kinetics" and "anomalous…
Dimensionally split advection schemes are attractive for atmospheric modelling due to their efficiency and accuracy in each spatial dimension. Accurate long time-steps can be achieved without significant cost using the flux-form…
Diffusion models have shown remarkable success across a wide range of generative tasks. However, they often suffer from spatially inconsistent generation, arguably due to the inherent locality of their denoising mechanisms. This can yield…
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method…
Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is…