The behavior of elastic waves in a three-dimensional isotropic incompressible material is studied. Unlike compressible elastodynamics, where there are nonlinear interactions of shear and pressure waves, with incompressible elastodynamics the only waves present are shear waves. In an isotropic system, shear waves are linearly degenerate, and therefore global solutions to the perturbative incompr...

As V. I. Arnold observed in the 1960s, the Euler equations of incompressible fluid flow correspond formally to geodesic equations in a group of volume-preserving diffeomorphisms. Working in an Eulerian framework, we study incompressible flows of shapes as critical paths for action (kinetic energy) along transport paths constrained to be shape densities (characteristic functions). The formal geo...

A new two-distribution lattice Boltzmann equation (LBE) algorithm is presented to solve the laminar diffusion flames within the context of Burke–Schumann flame sheet model. One distribution models the transport of the Schvab–Zeldovich coupling function, or the mixture fraction to combine the energy and species equations. The other distribution models the quasi-incompressible Navier–Stokes equat...

Application of the computer simulation for solving the incompressible flow problems motivates developing efficient and accurate numerical models. The set of Inviscid Incompressible Euler equations can be applied for wide range of engineering applications. For the steady state problems, the equation of continuity can be simultaneously solved with the equations of motion in a coupled manner using...

B-spline based deformable model is commonly used in recovering three-dimensional (3D) cardiac motion from tagged MRI due to its compact description, localized continuity and control flexibility. However, existing approaches usually ignore an important well-known fact that myocardial tissue is incompressible. In this paper, we propose to reconstruct 3D cardiac motion from tagged MRI using an inc...

In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler equations: a standard relaxation approximation, but with a diffusive scaling, and the Euler-Poisson equations in the quasineutral regime.

We prove that the product of an arbitrary projective homogeneous variety Y by an orthogonal, symplectic, or unitary Grassmannian X is 2-incompressible if and only if the varieties XF (Y ) and YF (X) are so. Some new properties of incompressible Grassmannians are established on the way.

Let Σ be a compact surface and let I be the unit interval. This paper gives a standard form for all 2-sided incompressible surfaces in the 3-manifold Σ×I. Since Σ × I is a handlebody when Σ has boundary, this standard form applies to incompressible surfaces in a handlebody.