Let F be an incompressible, meridionally incompressible and not boundary-parallel surface in the complement of an algebraic tangle (B, T ). Then F separates the strings of T in B and the boundary slope of F is uniquely determined by (B, T ) and hence we can define the slope of the algebraic tangle. In addition to the Conway’s tangle sum, we define a natural product of two tangles. The slopes an...

The incompressible limit of a compressible fluid, when the Mach number tends to zero, is a singular limit due to the fact that the governing equations change their type. The propagation rate of the pressure waves become infinite. Based on asymptotic results the multiple pressure variables (MPV-) method is reviewed as it may be used for the construction of numerical methods in this low Mach numb...

Incompressibility is established for threeand two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satis ed by the elastic compliances. These conditions make it straightforward to derive results for incompressible materials from those established for compressible materials. As an illustration, the explicit secular equation is obtained for surface waves i...

Interaction of incompressible and compress-ible MHD fluctuations on a one-dimensional plasma inho-mogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. An initially incompress-ible (Alfvénic) MHD fluctuation generates, by linear coupling , compressible (magnetoacoustic) fluctuations. In the initial stage of the interaction, the efficiency of the coupling is...

We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible NavierStokes equation: Real fluids are never perfectly incompressible, but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. ...

We show that the motion of a slightly compressible fluid is near that of an incompressible fluid. That is, for a given initial velocity field, the motion of a compressible fluid with large sound speed is near to that of an idealized incompressible fluid. We consider the compressible fluid motion in Lagrangian coordinates and show that it can be defined by two functions giving the kinetic and po...

Abstract We propose two Hybrid High-Order (HHO) methods for the incompressible Navier-Stokes equations and investigate their robustness with respect to Reynolds number. While both rely on a HHO formulation of viscous term, pressure-velocity coupling is fundamentally different, up point that approaches can be considered antithetical. The first method kinetic energy preserving, meaning skew-symme...

We describe a variational theory for incompressible ground states and charge gaps in the N=0 Landau level of graphene that accounts for the fourfold Landau level degeneracy and the short-range interactions that break SU(4) spin-valley invariance. Our approach explains the experimental finding that gaps at odd numerators are weak for 1<|ν|<2 and strong for 0<|ν|<1. We find that in the SU(4) inva...

In this paper we extend the conditions on quasi-thermal-incompressible materials presented in [1] so that they satisfy all the principles of thermodynamics, including the stability condition associated with the concavity of the chemical potential. We analyze the approximations under which a quasi-thermal-incompressible medium can be considered as incompressible. We find that the pressure cannot...