Staggered grid finite volume methods (also called central schemes) were introduced in one dimension by Nessyahu and Tadmor in 1990 in order to avoid the necessity of having information on solutions of Riemann problems for the evaluation of numerical fluxes. We consider the general case in multidimensions and on general staggered grids which have to satisfy only an overlap assumption. We interpr...

A novel approach for multiscale image processing based on integro-differential equations (IDEs) was proposed in [E. Tadmor and P. Athavale, Inverse Probl. Imaging, 3 (2009), pp. 693–710]. These IDEs, which stem naturally from multiscale (BV,L) hierarchical decompositions, yield inverse scale representations of images in the sense that the BV -dual norms of their residuals are inversely proporti...

We continue our study of hydrodynamic models of self-organized evolution of agents with singular interaction kernelφ(x) = |x|−(1+α). Following ourworks Shvydkoy and Tadmor (2017) [1,2]which focused on the range 1 ≤ α < 2, and Do et al. (2017) which covered the range 0 < α < 1, in this paper we revisit the latter case and give a short(-er) proof of global in time existence of smooth solutions, t...

The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] can effectively reduce spurious oscillations without local characteristic decomposition for numerical capturing of discontinuous solutions. However, there are still small remaining overshoots/undershoots in the vicinity of discontinuities. HR with partial neighboring cells [Xu, Liu and Shu, JCP ’09] essentially overcom...

The decomposition of images into their meaningful components is one of the major tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical decomposition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a discrete variational framework that makes ...

We study theL1-stability and error estimates of general approximate solutions for the Cauchy problem associated with multidimensional Hamilton-Jacobi (H-J) equations. For strictly convex Hamiltonians, we obtain a priori error estimates in terms of the truncation errors and the initial perturbation errors. We then demonstrate this general theory for two types of approximations: approximate solut...

The multi scale approach was pioneered by Tadmor, Ortiz and Phillips [1] for atomistic-based quasi-continuum analysis of dislocations and hardening plasticity of polycrystalline metals. In that case, the structural failure is due to necking, which is caused by nonlinear geometric effects of finite strain, or to sharp fracture, which is modelled separately (see also [2]). There can be no dispute...

The acculturation complexity model suggests that immersion into dissonant cultures promotes cognitive skills in biculturals (Tadmor and Tetlock, 2006). In the present study, we examined links between identity acculturation and executive functioning (EF). Turkish-German immigrant origin children (N = 225; M = 11 years, SD = 1.6 years, 99 males) were given questions about their identification wit...

We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments (“sedimentation with compression” or “sedimentation-consolidation process”). For N solid particle species, this ...