相关论文: Continuation for thin film hydrodynamics and relat…

We present and study a Particle method for the stationary solutions of a class of transport equations. This method is inspired by non-stationary Particle methods, the time variable being replaced by one spatial variable. Particles…

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation.…

Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…

We study the asymptotic behaviour of a system of nonlinear reaction--diffusion--advection equations in a domain consisting of two bulk regions connected via microscopic channels distributed within a thin membrane. Both the width of the…

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important…

This article continues the research initiated in [17]. We derive explicit formulae for the leading order profiles of eleven types of stationary solutions to a one-dimensional two-layer thin-film liquid model considered with an…

We consider a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities. The model aims to be analogous to a discrete algorithm used in works by T. Vicsek et al. In this paper we…

This paper investigates a variational approach to viscous flows with contact line dynamics based on energy-dissipation modeling. The corresponding model is reduced to a thin-film equation and its variational structure is also constructed…

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

We present a 2D parallel implementation of the modified Cahn-Hilliard equation for the simulation of a biofilm in an aqueous enviroment. Biofilms are attached microbial communities made of many different components and can have both…

Motivated by the viewpoint of integrable systems, we study commuting flows of 2-component quasilinear equations, reducing to investigate the solutions of the wave equation with non-constant speed. In this paper, we apply the reduction…

The shallow water equations describing the motion of thin liquid film on the rotating cylinder surface are obtained. These equations are the analog of the modified Boussinesq equations for shallow water and the Korteweg-de Vries equation.…

The effects of thermal fluctuations on nanoscale flows are captured by a numerical scheme that is underpinned by fluctuating hydrodynamics. A stochastic lubrication equation (SLE) is solved on non-uniform adaptive grids to study a series of…

We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization…

Wavy film flow of incompressible Newtonian fluid down an inclined plane is considered. The question is posed as to the parametric conditions under which the description of evolution can be approximately reduced for all time to a single…

The paper is concerned with the mathematical analysis of a class of thermodynamically consistent kinetic models for nonisothermal flows of dilute polymeric fluids, based on the identification of energy storage mechanisms and entropy…

The scalar auxiliary variable (SAV) approach of Shen et al. (2018), which presents a novel way to discretize a large class of gradient flows, has been extended and improved by many authors for general dissipative systems. In this work we…

We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. and…

We find solutions that describe the levelling of a thin fluid film, comprising a non-Newtonian power-law fluid, that coats a substrate and evolves under the influence of surface tension. We consider the evolution from both periodic and…

Recently, fractional derivatives have been employed to analyze various systems in engineering, physics, finance and hidrology. For instance, they have been used to investigate anomalous diffusion processes which are present in different…