In this paper, we present a novel Lagrangian formulation of the equations of motion for point vortices on the unit 2-sphere. We show first that no linear Lagrangian formulation exists directly on the 2-sphere but that a Lagrangian may be constructed by pulling back the dynamics to the 3-sphere by means of the Hopf fibration. We then use the isomorphism of the 3-sphere with the Lie group SU(2) t...

Adding a topological theta term to the action of $\mathcal{N}{=}\,1$ $D{=}4$ super Yang-Mills theory modifies its Nicolai map. For BPS value angle chiral version map emerges, which allows for considerable simplification compared non-chiral formulation. We exhibit these improvements all orders in perturbation and compute fourth order coupling on Laudau-gauge hypersurface. The second-order contri...

The FETI algorithms are numerically scalable iterative domain decomposition methods. These methods are well documented for solving equations arising from the Finite Element discretization of second or fourth order elasticity problems. The one level FETI method equipped with the Dirichlet preconditioner was shown to be numerically scalable for second order elasticity problems while the two level...

This article discusses a method that can aid in diagnosing root causes of product and process variability in complex manufacturing processes, when large amounts of multivariate in-process measurement data are available. A linear structured model, similar to the standard factor analysis model, is used to generically represent the variation patterns that result from the root causes. Blind source ...

Abstract   The present paper is devoted to implementation of the immersed boundary technique into the Fourier pseudo-spectral solution of the vorticity-velocity formulation of the two-dimensional incompressible Navier-Stokes equations. The immersed boundary conditions are implemented via direct modification of the convection and diffusion terms, and therefore, in contrast to some other similar ...

Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...

In this paper we construct high order weighted essentially non-oscillatory (WENO) schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. We present third order schemes using a combination of linear polynomials, and fourth order schemes using a combination of quadratic polynomials. Numerical examples are shown to demonstrate the accuracies and robustness of ...

The ultimate goal of this research is to construct a hybrid model for sound propagation in layered underwater environments with curved boundaries by employing a di↵erential formulation for inhomogeneous layers and a boundary integral formulation for homogeneous layers. The discretization of the new hybrid model is a combination of a finite di↵erence method for the Helmholtz equation for inhomog...