We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finite-size particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper in...

Let A be an n × n subgaussian matrix (entries are i.i.d. subgaussian r.v’s with variance 1). There are two reasons for the invertibility of A, depending on the nature of the unit vector on which A is acting – either compressible or incompressible. We recall that compressible vectors are those whose distance is at most some constant ρ from the set of (δn)-sparse vectors, and incompressible vecto...

Numerical manifold method was applied to directly solve Navier-Stokes N-S equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite elemen...

We construct the weakly nonlinear-dissipative approximate system for the general compressible Navier-Stokes system in a periodic domain. It was shown in [11] that because the Navier-Stokes system has an entropy structure, its approximate system will have Leray-like global weak solutions. These solutions decompose into an incompressible part governed by an incompressible Navier-Stokes system, an...

Transverse vibrations can induce the non-linear compression of a thin film air to levitate objects, via squeeze effect. This phenomenon is well captured by Reynolds' lubrication theory, however, same theory fails describe this levitation when fluid incompressible. In case, computation predicts no steady-state levitation, contradicting documented experimental evidence. letter, we uncover main so...

For every total recursive time bound t, a constant fraction of all compressible (low Kolmogorov complexity) strings is t-bounded incompressible (high time-bounded Kolmogorov complexity); there are uncountably many infinite sequences of which every initial segment of length n is compressible to log n yet t-bounded incompressible below 1 4n − log n; and there are a countably infinite number of re...

In this paper, we present some numerical studies on two partitioned fluid-structure interaction solvers: a preconditioned GMRES solver and a Newton based solver, for the fluid-structure interaction problems employing a nearly incompressible elasticity model in a classical mixed displacementpressure formulation. Both are highly relying on robust and efficient solvers for the fluid and structure ...

— The occurrence of incompressible quantum fluid states of a two dimensional system is a result of electron–electron interactions in a highly degenerate fractionally filled Landau level. Novel quasiparticles (QP’s) called composite Fermions (CF’s) have allowed a simple single particle description of the most prominent incompressible states. Residual interactions among these QP’s are investigate...