We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...

Adaptive Finite Element Simulation of Currents at Mi roele trodes to a Guaranteed A ura y. Appli ation to Channel Mi roband Ele trodes. Kathryn Harriman David Gavaghan Paul Houston David Kay Endre S uli We extend our earlier work (see K. Harriman et al., Te hni al Report NA99/19) on adaptive nite element methods for dis ele trodes to the ase of rea tion me hanisms to the in reasingly popular h...

when a direct voltage is applied under low injection conditions. In Equation (1) o is the angular frequency o= 2pf, where f is the frequency, R0=(dI/ dV)ÿ1, tp is the lifetime of the hole minority carriers, w is the length of the lower doped n bulk region, Lp is the minority carrier di€usion length for holes, with tp=Lp /Dp, where Dp is the di€usion coecient, and ®nally tw=w /Dp is a character...

This work provides the rst detailed investigation of the disturbed di usion scheme FOS/C introduced in [17] as a type of di usion distance measure within a graph partitioning framework related to Lloyd's k-means algorithm [14]. After outlining connections to distance measures proposed in machine learning, we show that FOS/C can be related to random walks despite its disturbance. Its convergence...

When the supply of intermittent renewable energies like wind and solar is high, the electricity price is low. Conversely, prices are high when their supply is low. This reduces the pro t potential in renewable energies and, therefore, incentives to invest in renewable capacities. Nevertheless, we show that perfect competition and dynamic pricing lead to e cient choices of renewable and fossil c...

Understanding the nature of di usion in complex and compact systems, such as alloyed metals, remains a serious challenge in contemporary materials science. Since these processes take place in the bulk, direct observation, using any of the scanning probes, is ruled out and most experimental probes have to be indirect. On the simulation side, progress has been hampered by the long time scale typi...

Figure 83: (a) The network of [263] contains three populations of excitatory cells; each selective population responds preferentially to one stimulus, the third is nonselective to both stimuli. A fourth population of interneurons provides overall inhibition. Excitatory (NMDAand AMPA-mediated) and inhibitory (GABAA-mediated) synapses are denoted by filled and open ovals respectively. All cells r...

A generalization of the Gurtin{MacCamy model for an S{I{R epidemic is described. The new model, which includes di usion away from overcrowded regions, retains many of the interesting qualitative features of previous models. In addition, the global{in{time existence of solutions is proved for a special case. Qualitative properties of the solution are discussed and illustrated with a numerical ex...

This paper proposes a new class of nonlinear PDEs called the Gibbs Reaction And Di usion Equation GRADE for a variety of applications in computer vision image processing and graphics In two previous papers the authors have been studying a minimax entropy theory based on which a new class of Gibbs distributions are learned in a fully non parametric form from a set of observed images such as text...

We motivate and analyze a reaction-advection-di usion model for the dynamics of a phytoplankton species. The reproductive rate of the phytoplankton is determined by the local light intensity. The light intensity decreases with depth due to absorption by water and phytoplankton. Phytoplankton is transported by turbulent di usion in a water column of given depth. Furthermore, it might be sinking ...