In this work we compare two semidiscrete schemes for the solution of hy-perbolic conservation laws, namely the relaxation [JX95] and the Kurganov Tadmor central scheme [KT00]. We are particularly interested in their behavior under small time steps, in view of future applications to convection diffusion problems. The schemes are tested on two benchmark problems, with one space variable. 1 Motiva...

We study the global well-posedness of Euler--Monge--Ampère (EMA) system. obtain a sharp, explicit critical threshold in space initial configurations which guarantees regularity EMA system with radially symmetric data. The result is obtained using two independent approaches---one spectral dynamics Liu and Tadmor [Comm. Math. Phys., 228 (2002), pp. 435--466] other based on geometric approach Bren...

Drought is a serious threat for sustainable agriculture. Barley represents a species well adapted to environmental stresses including drought. To elucidate the adaptive mechanism of barley on transcriptional level we evaluated transcriptomic changes of two contrasting barley cultivars upon drought using the microarray technique on the level of leaves and crowns. Using bioinformatic tools, diffe...

In [1] and some following publications, Tadmor and Gelb took up a well known property of conjugate Fourier series in 1-d, namely the property to detect jump discontinuities in given spectral data. In fact, this property of conjugate series is known for quite a long time. The research in papers around the year 1910 shows that there were also other means of detecting jumps observed and analysed. ...

We present a new finite-difference formulation to update the conformation tensor in dumbbell models (e.g., Oldroyd-B, FENE-P, Giesekus) that guarantees positive eigenvalues of the tensor (i.e., the tensor remains positive definite) and prevents over-extension for finite-extensible models. The formulation is a generalization of the second-order, central difference scheme developed by Kurganov an...

We present a new family of high-resolution, nonoscillatory semidiscrete central schemes for the approximate solution of the ideal magnetohydrodynamics (MHD) equations. This is the second part of our work, where we are passing from the fully discrete staggered schemes in [J. Balbás, E. Tadmor, and C.-C. Wu, J. Comput. Phys., 201 (2004), pp. 261–285] to the semidiscrete formulation advocated in [...

We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated oscillations. We quantify the weak convergence in W−1,∞ to the ’expected’ averages and obtain a sharp W−1,∞-convergence rate of order O(ε) – the small scale of the modulated oscillations. Moreover, in case the solution operator of the equation is compact, this weak...

Based on Nessyahu and Tadmor’s nonoscillatory central difference schemes for one-dimensional hyperbolic conservation laws [16], for higher dimensions several finite volume extensions and numerical results on structured and unstructured grids have been presented. The experiments show the wide applicability of these multidimensional schemes. The theoretical arguments which support this are some m...

In 1994, Lions, Perthame and Tadmor conjectured the maximal smoothing effect for multidimensional scalar conservation laws in Sobolev spaces. For strictly smooth convex flux and the one-dimensional case we detail the proof of this conjecture in the framework of Sobolev fractional spaces W s,1, and in fractional BV spaces: BV s. The BV s smoothing effect is more precise and optimal. It implies t...

Copyright: © 2013 Tadmor T. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Much effort is being invested in advancing the knowledge on cancer immunology, cancer microenvironment, and their interactions both w...