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The chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifier-thickener units. This model appears in two variants for cylindrical and variable cross-sectional area units, respectively (Models 1 and 2). In both cases, the governing… (More)

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… (More)

We consider scalar conservation laws with the spatially varying flux H(x)f (u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L 1 contraction semigroups, one for each… (More)

Multi-species kinematic flow models lead to strongly coupled, nonlinear systems of first-order, spatially one-dimensional conservation laws. The number of unknowns (the concentrations of the species) may be arbitrarily high. Models of this class include a multi-species generalization of the Lighthill–Whitham–Richards traffic model and a model for the… (More)

We present fully adaptive multiresolution methods for a class of spatially two-dimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate diffusion term that controls the degree of spatial coherence and serves as a mechanism for obtaining… (More)

Polydisperse suspensions consist of small particles which are dispersed in a viscous fluid, and which belong to a finite number N of species that differ in size or density. Spatially one-dimensional kinematic models for the sedimentation of such mixtures are given by systems of N non-linear first-order conservation laws for the vector Φ of the N local… (More)

The classical Lighthill-Witham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The evolution of the car density φ = φ(x, t) can then be described by the initial value problem φt + `… (More)

A finite volume method for solving the monodomain and bidomain models for the electrical activity of myocardial tissue is presented. These models consist of a parabolic PDE and a system of a parabolic and an elliptic PDE, respectively, for certain electric potentials, coupled to an ODE for the gating variable. The existence and uniqueness of the approximate… (More)