In this paper, we study on knots and closed incompressible surfaces in the 3-sphere via Morse functions. We show that both of knots and closed incompressible surfaces can be isotoped into a ”related Morse position” simultaneously. As an application, we have following results. • Smallness of Montesinos tangles with length two • Classification of closed incompressible and meridionally incompressi...

Predicting particle dispersion in recirculating two-phase flows is a key issue for reacting flows and a potential application of Large Eddy Simulation (LES) methods. In this study, Euler/Euler and Euler/Lagrange LES approaches are compared in the bluff body configuration from Borée et al. [1] where glass beads are injected into a complex recirculating flow. These tests are performed for non-rea...

In the last decade or so, the lattice Boltzmann (LB) method has emerged as a new and effective numerical technique of computational fluid dynamics (CFD).(1-5) Modeling of the incompressible Navier-Stokes equation is among many of its wide applications. Indeed, the lattice Boltzmann equation (LBE) was first proposed to simulate the incompressible NavierStokes equations.(1) The incompressible Nav...

In this work, some nonconforming elements on arbitrary quadrilateral meshes in solving incompressible elastic equations are analyzed. A uniform optimal convergence rate is established at the incompressible limit ν = 0.5 for both displacement and stresses (or pressure in the case of incompressible flow).

Culler and Shalen, and later Yoshida, give ways to construct incompressible surfaces in 3-manifolds from ideal points of the character and deformation varieties, respectively. We work in the case of hyperbolic punctured torus bundles, for which the incompressible surfaces were classi ed by Floyd and Hatcher. We convert non ber incompressible surfaces from their form to the form output by Yoshid...

This work focuses on numerically modelling the dynamics of a single phase fluid at varying densities and pressures. We explore the potential of incompressible flow simulation methods in modelling compressible flow, with an eye towards computer animation applications. The methods developed capture the interesting thermodynamic effects of compressible flow, and reduce to the standard Marker and C...

We consider compressible and almost incompressible elasticity on the compu13 tational domain Ω ⊂ IR3 which is partitioned into a number of subdomains. We 14 introduce nodes in the interior of the subdomains and on the interface. We distribute 15 the material parameters such that in a neighborhood of the interface we have com16 pressible and in the interior of a subdomain we have almost incompre...

This paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic–plastic solids, such as metals. An updated Lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation. This formulation circumvents the restriction on the displacement and pressure ...

Over the past few decades, the importance of the incompressible surface in the study of 3-manifold topology has become apparent. In fact, nearly all of the important outstanding conjectures in the eld have been proved, for 3-manifolds containing incompressible surfaces (see, e.g., [20],[22]). Faced with such success, it becomes important to know just what 3-manifolds could contain an incompress...