The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we...

The hydrodynamic limit of a kinetic Cucker-Smale flocking model is investigated. The starting point is the model considered in [17], which in addition to free-transport of individuals and a standard Cucker-Smale alignment operator, includes Brownian noise and strong local alignment. The latter was derived in [18] as the singular limit of an alignment operator first introduced by Motsch and Tadm...

We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure, allowing the use of some nonlinear test functions in the analysis. The existence of a solution to and the convergence of the scheme are proved under very general ...

One reason which makes Roe’s Riemann solver attractive is its low computational cost. But the main drawback with Roe’s approximate Riemann solver is that non-physical expansion shocks can occur in the sonic points, it has been early remarked that for this particular situation. The Roe flux does not satisfy the entropy condition. In this paper an elegant response has been proposed by combining H...

Title of dissertation: NOVEL INTEGRO-DIFFERENTIAL SCHEMES FOR MULTISCALE IMAGE REPRESENTATION Prashant Athavale, Doctor of Philosophy, 2009 Dissertation directed by: Professor Eitan Tadmor Department of Applied Mathematics & Statistics and Scientific Computation Multiscale representation of a given image is the problem of constructing a family of images, where each image in this family represen...

Abstract This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by Liouville (continuity) equation that have been originally proposed R.W. Brockett with purpose determining an efficient and robust strategy for dynamical systems. A methodology solving these presented based on a Lagrange optimization framework where controls are characterized as s...

To this end, we introduce general families of entropy-conservative schemes, interesting in their own right. The present treatment of such schemes extends our earlier recipe for construction of entropy-conservative schemes, introduced in Tadmor (1987b). The new families of entropy-conservative schemes offer two main advantages, namely, (i) their numerical fluxes admit an explicit, closed-form ex...

The aim of this paper is to present a streamlined and fully three-dimensional version of the quasicontinuum (QC) theory of Tadmor et al. [18, 19] and to analyze its accuracy and convergence characteristics. Specifically, we assess the effect of the summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we...

Among the efficient numerical methods based on atomistic models, the quasicontinuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices (Tadmor et al, 1999). Another existing numerical approach to modeling multilattices is homogenization. In the present paper we revie...