We propose three novel methods for recovering edges in piecewise smooth functions from their possibly incomplete and noisy spectral information. The proposed methods utilize three different approaches: #1. the randomly-based sparse Inverse Fast Fourier Transform (sIFT); #2. the Total Variation-based (TV) compressive sensing; and #3. the modified zero crossing. The different approaches share a c...

Here we outline a modification of the second order central difference scheme based on staggered spatial grids due to Nessyahu and Tadmor [H. Nessyahu, E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws, J. Comput. Phys. 87 (1990) 408] to a non-staggered scheme for one-dimensional hyperbolic systems which can additionally include source terms. With this modification...

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 of the unacceptable first-order convergence in rate. The purpos...

Tibetan wild barley is a treasure trove of useful genes for crop improvement including abiotic stress tolerance, like drought. Root hair of single-celled structures plays an important role in water and nutrition uptake. Polyethylene-glycol-induced drought stress hydroponic/petri-dish experiments were performed, where root hair morphology and transcriptional characteristics of two contrasting Ti...

has been one of the most outstanding open problems. It plays a very important role in understanding the core problems in hydrodynamics such as the onset of turbulence (people have also tried to understand turbulence through studying weak solutions; see Scheffer, 1993 or Shnirelman, 1997). Much effort has been made to answer this question; see, e.g., Beale et al. (1984), Ebin et al. (1970), Cafl...

The numerical method we consider is based on the nonstaggered central scheme proposed by Jiang, Levy, Lin, Osher, and Tadmor (SIAM J. Numer. Anal. 35, 2147(1998)) that was obtained by conversion of the standard central NT scheme to the nonstaggered mesh. The generalization we propose is connected with the numerical evaluation of the geometrical source term. The presented scheme is applied to th...

We consider weak solutions of (hyperbolic or hyperbolic-elliptic) systems of conservation laws in one-space dimension and their approximation by finite difference schemes in conservative form. The systems under consideration are endowed with an entropy-entropy flux pair. We introduce a general approach to construct second and third order accurate, fully discrete (in both space and time) entropy...

We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under conideration include the kinetic Cucker-Smale equation [6, 7] with possibly non-symmetric flocking potential, the Cucker-Smale equation with additional strong local alignment, and a newly proposed model by Motsch and Tadmor [14]. The main tools employed in the analysis are the velocity...

This paper describes how one can use the spectral vanishing viscosity method pro posed by Tadmor in multidomain solution of hyperbolic systems Interface conditions are derived using a variational approach and open boundary conditions are derived using the approach used in for incomplete parabolic systems Introduction Filtering of the solution is a very common technique when using spectral metho...