Related papers: Effect of diffusion in simple discontinuous absorb…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
Demixing of binary fluids subjected to slow temperature ramps shows repeated waves of nucleation which arise as a consequence of the competition between generation of supersaturation by the temperature ramp and relaxation of supersaturation…
In the context of non-convex optimization, we let the temperature of a Langevin diffusion to depend on the diffusion's own density function. The rationale is that the induced density captures to some extent the landscape imposed by the…
Group-based reinforcement can induce discontinuous transitions from inactive to active phases in higher-order contagion models. However, these results are typically obtained on static interaction structures or within mean-field…
The process by which one may take a discrete model of a biophysical process and construct a continuous model based on it is of mathematical interest as well as being of practical use. In this paper, we first study the singular limit of a…
The increased model capacity of Diffusion Transformers (DiTs) and the demand for generating higher resolutions of images and videos have led to a significant rise in inference latency, impacting real-time performance adversely. While prior…
We study diffusion of hardcore particles on a one dimensional periodic lattice subjected to a constraint that the separation between any two consecutive particles does not increase beyond a fixed value $(n+1);$ initial separation larger…
The thin interface limit aims at minimizing the effects arising from a numerical interface thickness, inherent in diffuse interface models of solidification and microstructure evolution such as the phase field model. While the original…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
Generative modeling within constrained sets is essential for scientific and engineering applications involving physical, geometric, or safety requirements (e.g., molecular generation, robotics). We present a unified framework for…
Many driven systems alternate between bursts of activity and quiescence and can become trapped in an absorbing state, such as complete inactivity in reaction-diffusion processes or extinction in predator-prey dynamics. It is generally…
We explore the effects that quenched disorder has on discontinuous nonequilibrium phase transitions into absorbing states. We focus our analysis on the Naming Game model, a nonequilibrium low-dimensional system with different absorbing…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…
Nonequilibrium hyperuniformity can arise either as a steady-state property of driven active fluids or as a critical signature at continuous absorbing transition points in two and three dimensions. Whether analogous structural order exists…
We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density…
Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by…
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 a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assumptions on the Hamiltonian, a weak Lyapunov structure, and a…
Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…
We study anomalous diffusion for one-dimensional systems described by a generalized Langevin equation. We show that superdiffusion can be classified in slow superdiffusion and fast superdiffusion. For fast superdiffusion we prove that the…