1 Department of Mathematics, Institute for Physical Science & Technology and Center for Scientific Computation And Mathematical Modeling (CSCAMM), University of Maryland College Park, MD 20742-3289 [email protected] 2 Department of Mathematics University of California Davis, CA 95616 [email protected] “Hyperbolic Problems: Theory, Numerics, Applications”, Proceedings of the 9th Inter...

A prototype modular single screw extruder fitted with a screw extracting device is used to monitor melting of an immiscible polymer blend (PP/PA6, with different weight ratios) in this popular type of processing equipment. As anticipated, the observed phenomena are much more complex than those involved in extruding PP or PA6, when the well known Maddock/Tadmor mechanism is valid. Consequently a...

Kurganov and Tadmor have developed a numerical scheme for solving the initial value problem for hyperbolic systems of conservation laws. They showed that in the scalar case their scheme satisfies a local maximum–minimum principle i.e., the solution at future is bounded above and below by the solution at current locally. In this paper we show that this scheme is positive in the sense of Friedric...

We study kinetic representations of flocking models. They arise from agent-based models for self-organized dynamics, such as Cucker-Smale [5] and Motsch-Tadmor [11] models. We prove the flocking behavior for the kinetic descriptions of flocking systems, which indicates a concentration in velocity variable in infinite time. We propose a discontinuous Galerkin method to treat the asymptotic δ -si...

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...

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 ...

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...

In the recent papers [4, 5] the authors study the existence of weak solutions and the hydrodynamic limit of kinetic flocking equations with strong local alignment. The introduction of a strong local alignment term to model flocking behavior was formally motivated in these papers as a limiting case of an alignment term proposed by Motsch and Tadmor [6]. In this paper, we rigorously justify this ...

There has been an enormous amount of work on error estimates for approximate solutions to scalar conservation laws. The methods of analysis include matching the traveling wave solutions, [8, 24]; matching the Green function of the linearized problem [21]; weak W convergence theory [32]; the Kruzkov-functional method [19]; and the energy-like method [34]. The results on error estimates include: ...