Related papers: Local modification of subdiffusion by initial Fick…

Systems describing the long-range interaction between individuals have attracted a lot of attention in the last years, in particular in relation with living systems. These systems are quadratic, written under the form of transport equations…

Based on Fick's 2nd law the development of moving particle semi-implicit method for predicting diffusion process is proposed in this study

In this paper, we generalize the theory of the invariant subspace method to (m + 1)-dimensional non-linear time-fractional partial differential equations for the first time. More specifically, the applicability and efficacy of the method…

This paper addresses the issue of inversion in cases where (1) the observation system is modeled by a linear transformation and additive noise, (2) the problem is ill-posed and regularization is introduced in a Bayesian framework by an a…

Fickian yet non-Gaussian diffusion (FnGD) has gained popularity in the recent times owing to it's ubiquity in a variety of complex fluids. However, whether FnGD can be observed experimentally in molecular fuids is still obscure with very…

This work investigates how we can extend the invariant subspace method to two-dimensional time-fractional non-linear PDEs. More precisely, the systematic study has been provided for constructing the various dimensions of the invariant…

In this work, we theoretically and numerically discuss the time fractional subdiffusion-normal transport equation, which depicts a crossover from sub-diffusion (as $t\rightarrow 0$) to normal diffusion (as $t\rightarrow \infty$). Firstly,…

Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial…

The microscopic theory of atomic diffusion kinetics is used for f.c.c. substitutional solid solutions. Within this approach, the short-range order relaxation is due to the atomic migration. Experimental data on the time dependence of…

Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…

Diffusion models have shown superior performance on unsupervised anomaly detection tasks. Since trained with normal data only, diffusion models tend to reconstruct normal counterparts of test images with certain noises added. However, these…

The chemistry of molecular clouds has been studied for decades, with an increasingly general and sophisticated treatment of the reactions involved. Yet the treatment of turbulent diffusion has remained extremely sketchy, assuming simple…

We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…

Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…

Tracking experiments in dense biological tissues reveal a diversity of sources f or local energy injection at the cell scale. The effect of cell motility has been largely studied, but much less is known abo ut the effect of the observed…

Over the past decades, nonlocal models have been widely used to describe aggregation phenomena in biology, physics, engineering, and the social sciences. These are often derived as mean-field limits of attraction-repulsion agent-based…

The problem of identifying the diffusion parameter appearing in a nonlocal steady diffusion equation is considered. The identification problem is formulated as an optimal control problem having a matching functional as the objective of the…

Classical search algorithms have long underpinned modern artificial intelligence. In this work, we tackle the challenge of inference-time control in diffusion models -- adapting generated outputs to meet diverse test-time objectives --…

We develop diffusion models for simulating lattice gauge theories, where stochastic quantization is explicitly incorporated as a physical condition for sampling. We demonstrate the applicability of this novel sampler to U(1) gauge theory in…

Diffusion models have been increasingly used as strong generative priors for solving inverse problems such as super-resolution in medical imaging. However, these approaches typically utilize a diffusion prior trained at a single scale,…