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Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…

We present an effective stochastic advection-diffusion-reaction (SADR) model that explains incomplete mixing typically observed in transport with bimolecular reactions. Unlike traditional advection-dispersion-reaction models, the SADR model…

The recently developed Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) is investigated for a wide range of model parameters including the parameter m representing the chain length and the thermodynamic temperature T and…

An approximate maximum likelihood method of estimation of diffusion parameters $(\vartheta,\sigma)$ based on discrete observations of a diffusion $X$ along fixed time-interval $[0,T]$ and Euler approximation of integrals is analyzed. We…

Gribov quantization is a method to improve the infrared dynamics of Yang-Mills theory. We study the thermodynamics and transport properties of a plasma consisting of gluons whose propagator is improved by the Gribov prescription. We first…

Trajectory prediction is a fundamental task in Autonomous Vehicles (AVs) and Intelligent Transportation Systems (ITS), supporting efficient motion planning and real-time traffic safety management. Diffusion models have recently demonstrated…

The viscosity and self-diffusion constant of a mesoscale hydrodynamic method, dissipative particle dynamics (DPD), are investigated. The viscosity of DPD with finite time step, including the Lowe-Anderson thermostat, is derived analytically…

The diffusion model presents a powerful ability to capture the entire (conditional) data distribution. However, due to the lack of sufficient training and data to learn to cover low-probability areas, the model will be penalized for failing…

Finding an initial noise vector that produces an input image when fed into the diffusion process (known as inversion) is an important problem in denoising diffusion models (DDMs), with applications for real image editing. The…

The gradient discretisation method (GDM) is a generic framework for designing and analysing numerical schemes for diffusion models. In this paper, we study the GDM for the porous medium equation, including fast diffusion and slow diffusion…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

The mean square displacement and instantaneous diffusion coefficient for different configurations of charged particles in stochastic motion are calculated by numerically solving the associated equations of motion. The method is suitable for…

In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…

Changes in hydration are central to the phenomenon of biomolecular recognition, but it has been difficult to properly frame and answer questions about their precise thermodynamic role. We address this problem by introducing Grid…

This paper introduces a new stochastic diffusion process to model the electricity production from natural gas sources (as a percentage of total electricity production) in the United States. The method employs trend function analysis to…

We study the measurement of transverse diffusion through beam echoes. We revisit earlier observations of echoes in RHIC and apply an updated theoretical model to these measurements. We consider three possible models for the diffusion…

Subsurface flows are commonly modeled by advection-diffusion equations. Insufficient measurements or uncertain material procurement may be accounted for by random coefficients. To represent, for example, transitions in heterogeneous media,…

We introduce a simple and efficient model to describe the potential energy surface of lithium diffusing in a solid-state ionic conductor. First, we assume that the Li atoms are fully ionized and we neglect the weak dependence of the…

We present the Bidimensional Exploration of the warm-Temperature Ionised gaS (BETIS) project, designed for the spatial and spectral study of the diffuse ionised gas (DIG) in a selection of nearby spiral galaxies observed with the MUSE…

Resetting or restart, when applied to a stochastic process, usually brings its dynamics to a time-independent stationary state. In turn, the optimal resetting rate makes the mean time to reach a target to be the shortest one. These and…