Related papers: Perturbation theorems for Hele-Shaw flows and thei…
We numerically study, under a Gowdy symmetry assumption, nonlinear perturbations of the decelerated FLRW fluid solutions to the Einstein-Euler system toward the future for linear equations of state $p=K\rho$ with $0\leq K\leq 1$. This…
Evolution of scalar perturbations in a universe containing solid matter with positive pressure is studied. Solution for pure solid is found and matched with solution for ideal fluid, including the case when the pressure to energy density…
We present new solutions to the strong explosion problem in a non power law density profi{}le. The unperturbed self similar solutions developed by Sedov, Taylor and Von Neumann describe strong Newtonian shocks propagating into a cold gas…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
We introduce a discrete numerical method based on the diffusion-limited aggregation (DLA) approach to simulate two-fluid Hele-Shaw flow subject to the Saffman-Taylor interfacial instability, in the case where the displaced fluid is…
A new approach to study the scaling behavior of the scalar theory near the Gaussian fixed point in $d$-dimensions is presented. For a class of initial data an explicit use of the Green's function of the evolution equation is made. It is…
This paper is motivated by the study of Lyapunov functionals for four equations describing free surface flows in fluid dynamics: the Hele-Shaw and Mullins-Sekerka equations together with their lubrication approximations, the Boussinesq and…
A Streamline Upwind Petrov-Galerkin (SUPG) finite element method for transient convection-diffusion-reaction equation in time-dependent domains is proposed. In particular, a convection dominated transient scalar problem is considered. The…
We investigate the interplay between Horava-Lifshitz (HL) gravity and more general theories where the local Hamiltonian constraint is lost, for example due to the time variability of the Lagrangian (e.g. via its parameters) where time is…
This paper investigates shear flow in a Hele-Shaw cell, driven by varying horizontal buoyancy forces resulting from a horizontal density gradient induced by a scalar field. By employing asymptotic methods and taking the dependence of…
The onset of convection in a horizontal layer of fluid heated from below in the presence of a gravity field varying across the layer is investigated. The eigenvalue problem governing the linear stability of the mechanical equilibria of the…
We assess experimentally the scaling laws that characterize the mixing region produced by the Rayleigh-Taylor instability in a confined porous medium. In particular, we wish to assess experimentally the existence of a superlinear scaling…
Reaction cross diffusion systems are a two species generalization of the porous media equation. These systems play an important role in the mechanical modeling of living tissues and tumor growth. Due to their mixed parabolic-hyperbolic…
Eulerian hydrodynamical simulations are a powerful and popular tool for modeling fluids in astrophysical systems. In this work, we critically examine recent claims that these methods violate Galilean invariance of the Euler equations. We…
The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability…
Local polarization effects, induced by mono and divalent positive ions in water, influence (and in turn are influenced by) the large scale structural properties of the solvent. Experiments can only distinguish this process of interplay in a…
A large population limit of the parabolic-parabolic Patlak-Keller-Segel (PKS) system with degenerate, nonlinear diffusion, e.g., of porous medium-type $-\frac{m}{m-1}\mathrm{div}(\rho \nabla \rho^{m-1})$, is studied. We show,…
We construct a new Godunov type relativistic hydrodynamics code in Milne coordinates, using a Riemann solver based on the two-shock approximation which is stable under the existence of large shock waves. We check the correctness of the…
We analyze the stability of stationary solutions of a singular Vlasov type hydrodynamic equation (HE). This equation was derived (under suitable assumptions) as the hydrodynamical scaling limit of the Hamiltonian evolution of a system…
As an experimental model to mimic the flow of bio-fluids in the cell and the flow in tiny blood capillaries, we study the co-moving shear flow of dilute polymeric solutions. An inflection point shear flow profile is created by parallel…