Steady state spurious errors in shock-capturing numerical schemes

The behavior of the steady state spurious error modes of the MacCormack scheme and the upwind scheme of Warming and Beam was obtained from a linearized difference equation for the steady state error. It was shown that the spurious errors can exist either as an eigensolution of the homogeneous part of this difference equation or because of excitation from large discretization errors near oblique shocks. It was found that the upwind scheme does not permit spurious oscillations on the upstream side of shocks. Examples are given for the inviscid Burgers' equation and for one and two dimensional gasdynamic flows

The cardiac bidomain model and homogenization

We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface.Comment: To appear in Networks and Heterogeneous Media, Special Issue on Mathematical Methods for Systems Biolog

Acoustic Tweezing and Patterning of Concentration Fields in Microfluidics

We demonstrate theoretically that acoustic forces acting on inhomogeneous fluids can be used to pattern and manipulate solute concentration fields into spatio-temporally controllable configurations stabilized against gravity. A theoretical framework describing the dynamics of concentration fields that weakly perturb the fluid density and speed of sound is presented and applied to study manipulation of concentration fields in rectangular-channel acoustic eigenmodes and in Bessel-function acoustic vortices. In the first example, methods to obtain horizontal and vertical multi-layer stratification of the concentration field at the end of a flow-through channel are presented. In the second example, we demonstrate acoustic tweezing and spatio-temporal manipulation of a local high-concentration region in a lower-concentration medium, thereby extending the realm of acoustic tweezing to include concentration fields.Comment: Revtex, 9 pages, 5 eps figure

Well-posedness theory for stochastically forced conservation laws on Riemannian manifolds

We investigate a class of scalar conservation laws on manifolds driven by multiplicative Gaussian (Ito) noise. The Cauchy problem defined on a Riemannian manifold is shown to be well-posed. We prove existence of generalized kinetic solutions using the vanishing viscosity method. A rigidity result is derived, which implies that generalized solutions are kinetic solutions and that kinetic solutions are uniquely determined by their initial data ($L^1$ contraction principle). Deprived of noise, the equations we consider coincide with those analyzed by Ben-Artzi and LeFloch (2007), who worked with Kruzkov-DiPerna solutions. In the Euclidian case, the stochastic equations agree with those examined by Debussche and Vovelle (2010).Comment: Submitted for publication on 23.09.1

Modelling Fresh Strawberry Supply "From-Farm-to-Fork" as a Complex Adaptive Network

 The purpose of this study is to model and thereby enable simulation of the complete business entity of fresh food supply. A case narrative of fresh strawberry supply provides basis for this modelling. Lamming et al. (2000) point to the importance of discerning industry-specific product features (or particularities) regarding managing supply networks when discussing elements in "an initial classification of a supply network" while Fisher (1997) and Christopher et al. (2006, 2009) point to the lack of adopting SCM models to variations in products and market types as an important source of SCM failure. In this study we have chosen to move along a research path towards developing an adapted approach to model end-to-end fresh food supply influenced by a combination of SCM, system dynamics and complex adaptive network thinking...