相关论文: Accurate and efficient calculation of response tim…
We study the duration of "high-flow states" in freeway traffic, defined as the time periods for which traffic flows exceed a given flow threshold. Our empirical data are surprisingly well represented by a power law. Moreover, the power law…
Aggregations are emergent features common to many biological systems. Mathematical models to understand their emergence are consequently widespread, with the aggregation-diffusion equation being a prime example. Here we study the…
We assume that we observe $N$ independent copies of a diffusion process on a time-interval $[0,2T]$. For a given time $t$, we estimate the transition density $p_t(x,y)$, namely the conditional density of $X_{t + s}$ given $X_s = x$, under…
We consider the long-time behavior of the mean curvature flow in heterogeneous media with periodic fibrations, modeled as an additive driving force. Under appropriate assumptions on the forcing term, we show existence of generalized…
In this study, we investigate the appeared complexity of two-phase flow (air/water) in a heterogeneous soil where the supposed porous media is non-deformable media which is under the timedependent gas pressure. After obtaining of governing…
Consistency models imitate the multi-step sampling of score-based diffusion in a single forward pass of a neural network. They can be learned in two ways: consistency distillation and consistency training. The former relies on the true…
In this paper we propose the use of a continuous data assimilation algorithm for miscible flow models in a porous medium. In the absence of initial conditions for the model, observed sparse measurements are used to generate an approximation…
In this paper we investigate the porous medium equation with a fractional temporal derivative. We justify that the resulting equation emerges when we consider the waiting-time (or trapping) phenomenon that can happen in the medium. Our…
A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress…
This paper studies the large time behavior of aggregation-diffusion equations. For one spatial dimension with certain assumptions on the interaction potential, the diffusion index $m$, and the initial data, we prove the convergence to the…
In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant…
We study the stochastic dynamics of a particle with two distinct motility states. Each one is characterized by two parameters: one represents the average speed and the other represents the persistence quantifying the tendency to maintain…
Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the…
The first passage is a generic concept for quantifying when a random quantity such as the position of a diffusing molecule or the value of a stock crosses a preset threshold (target) for the first time. The last decade saw an enlightening…
Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability…
Non-equilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the Transient and Steady State forms of the Fluctuation Theorem. In the case of planar Poiseuille flow, we find that the Transient form,…
Sequential probabilistic inference from streaming observations requires modeling distributions over future trajectories as new observations arrive. Although diffusion and flow-matching models are effective at capturing high-dimensional,…
Deep learning models, in particular \textit{image} models, have recently gained generalisability and robustness. %are becoming more general and robust by the day. In this work, we propose to exploit such advances in the realm of…
The transport of single-phase fluid mixtures in porous media is described by cross-diffusion equations for the mass densities. The equations are obtained in a thermodynamic consistent way from mass balance, Darcy's law, and the van der…
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…