Related papers: Travelling waves near a critical point of a binary…
In mean-field theory, the non-local state of fluid molecules can be taken into account using a statistical method. The molecular model combined with a density expansion in Taylor series of the fourth order yields an internal energy value…
We consider a free boundary model of epithelial cell migration with logistic growth and nonlinear diffusion induced by mechanical interactions. Using numerical simulations, phase plane and perturbation analysis, we find and analyse…
The appearence of a new type of fast nonlinear traveling wave states in binary fluid convection with increasing Soret effect is elucidated and the parameter range of their bistability with the common slower ones is evaluated numerically.…
Starting from the kinetic approach for a mixture of reacting gases whose particles interact through elastic scattering and a bimolecular reversible chemical reaction, the equations that govern the dynamics of the system are obtained by…
The microscopic approach to the description of the phase behaviour and critical phenomena in binary fluid mixtures is proposed. It is based on the method of collective variables with a reference system. The physical nature of the order…
We consider the global bifurcation problem for spatially periodic traveling waves for two-dimensional gravity-capillary vortex sheets. The two fluids have arbitrary constant, non-negative densities (not both zero), the gravity parameter can…
It was recently observed that sand flowing down a vertical tube sometimes forms a traveling density pattern in which a number of regions with high density are separated from each other by regions of low density. In this work, we consider…
Binary fluid mixtures are examples of complex fluids whose microstructure and flow are strongly coupled. For pairs of simple fluids, the microstructure consists of droplets or bicontinuous demixed domains and the physics is controlled by…
Density waves were studied in a phase-separated binary complex plasma under microgravity conditions. For the big particles, waves were self-excited by the two-stream instability, while for small particles, they were excited by heartbeat…
We study density waves in the flows of granular particles through vertical tubes and hoppers using both analytic methods and molecular dynamics (MD) simulations. We construct equations of motion for quasi one-dimensional systems. The…
Nonlinear fronts between spatially extended traveling wave convection (TW) and quiescent fluid and spatially localized traveling waves (LTWs) are investigated in quantitative detail in the bistable regime of binary fluid mixtures heated…
We suppose that a rigid spherical particle is put into a binary fluid mixture with the critical composition in the homogeneous phase near the demixing critical point. A short-range interaction is assumed between each component and the…
The existence of travelling waves for a model of concentration waves of bacteria is investigated. The model consists in a kinetic equation for the biased motion of cells following a run-and-tumble process, coupled with two…
This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical…
Existence of non-negative weak solutions is shown for a full curvature thin-film model of a liquid thin film flowing down a vertical fibre. The proof is based on the application of a priori estimates derived for energy-entropy functionals.…
We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause…
We study travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration,…
We study bifurcations of periodic travelling waves in granular dimer chains from the anti-continuum limit, when the mass ratio between the light and heavy beads is zero. We show that every limiting periodic wave is uniquely continued with…
We study the motion of an interface between two irrotational, incompressible fluids, with elastic bending forces present; this is the hydroelastic wave problem. We prove a global bifurcation theorem for the existence of families of…
We prove the existence of a traveling wave solution for a boundary reaction diffusion equation when the reaction term is the combustion nonlinearity with ignition temperature. A key role in the proof is plaid by an explicit formula for…