3-D kinematical conservation laws (KCL) are equations of evolution of a propagating surface Ωt in three space dimensions and were first derived in 1995 by Giles, Prasad and Ravindran [15] assuming the motion of the surface to be isotropic. We start with a brief introduction to 3-D KCL and mention some properties relevant to this paper. The 3-D KCL, a system of 6 conservation laws, is an under-d...

We propose a biophysical model of Escherichia coli that predicts growth rate and an effective cellular composition from an effective, coarse-grained representation of its genome. We assume that E. coli is in a state of balanced exponential steadystate growth, growing in a temporally and spatially constant environment, rich in resources. We apply this model to a series of past measurements, wher...

Abstract. We discuss the Cucker-Smale’s (C-S) particle model for flocking, deriving precise conditions for flocking to occur when pairwise interactions are sufficiently strong long range. We then derive a Vlasov-type kinetic model for the C-S particle model and prove it exhibits time-asymptotic flocking behavior for arbitrary compactly supported initial data. Finally, we introduce a hydrodynami...

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This work concerns the numerical approximation of a multicomponent compressible Euler system for fluid mixture in multiple space dimensions on unstructured meshes with high-order discontinuous Galerkin spectral element method (DGSEM). We first derive an entropy stable (ES) and robust (i.e., that preserves positivity partial densities internal energy) three-point finite volume scheme using relax...

Second-order accurate upwind and centered schemes are presented in a framework that facilitates their analysis and comparison. The upwind scheme employed consists of a reconstruction step (Van Leer 1977) followed by an upwind step (Roe 1981). The two centered schemes are of Lax-Friedrichs (L-F) type. They are the nonstaggered versions of the N-T scheme (called ORD in Nessyahu-Tadmor 1990) and t...