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We consider a coupled system of partial differential equations describing the interactions between a closed free interface and two viscous incompressible fluids. The fluids are assumed to satisfy the incompressible Navier-Stokes equations…
Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…
The dynamics of a thin layer of liquid, between a flat solid substrate and an infinitely-thick layer of saturated vapor, is examined. The liquid and vapor are two phases of the same fluid, governed by the diffuse-interface model. The…
The theory of interfacial properties in liquid-liquid or liquid-vapour systems is nearly 200 years old. The advent of computational tools has greatly advanced the field, mainly through the use of Molecular Dynamics simulations. Despite the…
We establish short-time existence of a smooth solution to the surface diffusion equation with an elastic term and without an additional curvature regularization in three space dimensions. We also prove the asymptotic stability of strictly…
Diffusion-based generative models are extremely effective in generating high-quality images, with generated samples often surpassing the quality of those produced by other models under several metrics. One distinguishing feature of these…
We study the emergence of dynamical quantum phase transitions (DQPTs) in a half-filled one-dimensional lattice described by the extended Fermi-Hubbard model, based on tensor network simulations. Considering different initial states, namely…
The interaction between shear and double-diffusive convection (DDC) in the diffusive regime (cold fresh water on top of hot salty water) plays an important role in the heat and mass transport of polar region oceans. This study computes…
We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of…
We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account…
In hydrodynamic problems involving wave impact on structures, air compressibility is crucial for accurate pressure prediction when an air bubble is entrapped. In this work, the consistent $\delta^{+}$-SPH model, originally developed for…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
For molecular dynamics simulations of hard particles, we define dynamic neighbors as the distinct particles that collide with a given reference one during a specific time interval. This definition allows us to determine the distribution of…
We investigate the existence of a robust, i.e., continuous, representation of the conditional distribution in a stochastic filtering model for multidimensional correlated jump-diffusions. Even in the absence of jumps, it is known that in…
In conventional fluid mechanics, the chemical composition and thermodynamic state of a fluid-solid interface are not considered when establishing velocity-field boundary conditions. As a consequence, fluid simulations are usually not able…
Dissipative particle dynamics (DPD) is an effective mesoscopic particle model with a lower computational cost than molecular dynamics because of the soft potentials that it employs. However, the soft potential is not strong enough to…
We investigate two-phase flow in porous media and derive a two-scale model, which incorporates pore-scale phase distribution and surface tension into the effective behavior at the larger Darcy scale. The free-boundary problem at the pore…
The injection of liquid fuel at supercritical pressures is a relevant topic in combustion, but usually overlooked. In the past, the wrong assumption whereby the liquid experiments a fast transition to a supercritical state was made, thus…
From the Navier-Stokes-Korteweg (NSK) equations, the exact relations between the fundamental surface physical quantities for two-phase viscous flow with diffuse interface are derived, including density gradient, shear stress, vorticity,…
In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylinder…