We study the stabilizing effect of rotational forcing in the nonlinear setting of twodimensional shallow-water and more general models of compressible Euler equations. In [Phys. D, 188 (2004), pp. 262–276] Liu and Tadmor have shown that the pressureless version of these equations admit a global smooth solution for a large set of subcritical initial configurations. In the present work we prove t...

We introduce a new high-resolution central scheme for multidimensional Hamilton–Jacobi equations. The scheme retains the simplicity of the non-oscillatory central schemes developed by C.-T. Lin and E. Tadmor (in press, SIAM J. Sci. Comput.), yet it enjoys a smaller amount of numerical viscosity, independent of 1/1t. By letting 1t ↓ 0 we obtain a new second-order central scheme in the particular...

A multiscale image registration technique is presented for the registration of medical images that contain significant levels of noise. An overview of the medical image registration problem is presented, and various registration techniques are discussed. Experiments using mean squares, normalized correlation, and mutual information optimal linear registration are presented that determine the no...

We discuss the reconstruction of piecewise smooth data from its (pseudo-) spectral information. Spectral projections enjoy superior resolution provided the data is globally smooth, while the presence of jump discontinuities is responsible for spurious O(1) Gibbs oscillations in the neighborhood of edges and an overall deterioration to the unacceptable first-order convergence rate. The purpose i...

In this thesis, the following type Tikhonov regularization problem will be systematically studied: (ut, vt) := argmin u+v=f {‖v‖X + t‖u‖Y }, where Y is a smooth space such as a BV space or a Sobolev space and X is the space in which we measure distortion. Examples of the above problem occur in denoising in image processing, in numerically treating inverse problems, and in the sparse recovery pr...

This work concerns the numerical approximation of a multicomponent compressible Euler system for fluid mixture in multiple space dimensions on unstructured meshes with high-order discontinuous Galerkin spectral element method (DGSEM). We first derive an entropy stable (ES) and robust (i.e., that preserves positivity partial densities internal energy) three-point finite volume scheme using relax...

Entropy-Stable (ES) schemes, specifically those built from [Tadmor \textit{Math. Comput.} 49 (1987) 91], have been gaining interest over the past decade, especially in context of under-resolved simulations compressible turbulent flows using high-order methods. These schemes are attractive because they can provide stability a global and nonlinear sense (consistency with thermodynamics). However,...

In this paper, an investigation on the relation between state-building and Near Eastern religion is attempted. Analyzing the city-state of Ḥaṭrā (Iraq, close to Kirkuk), it is demonstrated that pre-Islamic state craft in the region was dependent on the initiative of the Parthian monarchy in Iran. The kings of the Arsacid dynasty attempted to bestow the local Arabic tribes in the Jazira with a c...

The nonlinear shallow water equations (SWEs) are widely used to model the unsteady flows in rivers and coastal areas. In this work, we present a novel class of locally conservative, entropy stable well-balanced discontinuous Galerkin (DG) methods for equation with non-flat bottom topography. major novelty our work is use velocity field as an independent solution unknown DG scheme, which closely...

During the recent decades there was an enormous amount of activity related to the construction and analysis of modern algorithms for the approximate solution of nonlinear hyperbolic conservation laws and related problems. To present some aspects of this successful activity, we discuss the analytical tools which are used in the development of convergence theories for these algorithms. These incl...