In this paper we construct, analyze and implement a new procedure for the spectral approximations of nonlinear conservation laws. It is well known that using spectral methods for nonlinear conservation laws will result in the formation of the Gibbs phenomenon once spontaneous shock discontinuities appear in the solution. These spurious oscillations will in turn lead to loss of resolution and re...

Abstract. We discuss the Cucker-Smale’s (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S particle model and prove it exhibits time-asymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynami...

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In this paper, we propose an algorithm for the measure of local and global contrast in digital images. It applies locally, at various sub-sampled levels, a simplified computation of local contrast based on DOG and finally it recombines all the values to obtain a global measure. The proposed method comes from the modification of a previous algorithm with a different local measure of contrast and...

We present results of the application of the anisotropic hydrodynamics (aHydro) framework to (2+1)dimensional boost-invariant systems. The necessary aHydro dynamical equations are derived by taking moments of the Boltzmann equation using a momentum-space anisotropic one-particle distribution function. We present a derivation of the necessary equations and then proceed to numerical solutions of ...

In the seminal paper E. Tadmor, S. Nezzar and L. Vese, A multiscale image representation using hierarchical \((BV, L^2)\) decompositions, Multiscale Model. Simul., 2(4), 554–579, (2004), authors introduce a decomposition model providing of given into sum scale-varying components. line with this framework, we extend approach to case registration, task which consists mapping salient features an o...

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...

In this project, we develop a Hierarchical Decomposition algorithm to solve the `1-Regularized Least Square problem: min x∈Rn {||x||`1 ∣∣Ax = b}. With the new approach, we show a systemic approach on how to select a family of regularization parameters λ’s in order to improve accuracy while retaining the sparsity of our approximation. 1 Background: A Constrained `0 Minimization In the recent dec...