Higher order Moreau’s sweeping process: mathematical formulation and numerical simulation

Higher order Moreau's sweeping process: mathematical formulation and numerical simulation

In this paper we present an extension of Moreau’s sweeping process for higher order systems. The dynamical framework is carefully introduced, qualitative, dissipativity, stability, existence, regularity and uniqueness results are given. The time-discretization of these nonsmooth systems with a timestepping algorithm is also presented. This differential inclusion can be seen as a mathematical fo...

Convergence Order of a Numerical Scheme for Sweeping Process

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An overview of Non Smooth Dynamical Systems. Higher order Moreau’s sweeping process, numerical methods and links with Optimization

The Non Smooth Dynamical Systems (NSDS) are a very special kind of dynamical systems characterized by their nonsmoothness in the evolution with respect to time and by a set of non smooth generalized equations. The so-called Moreau’s Sweeping Process[9, 10] is a special kind of differential inclusion with a maximal monotone operator[5] which appears to be a very nice formulation for the unilater...

Higher order process engineering

A cell cycle model for somitogenesis: mathematical formulation and numerical simulation.

After many years of research, the mechanisms that generate a periodic pattern of repeated elements (somites) along the length of the embryonic body axis is still one of the major unresolved problems in developmental biology. Here we present a mathematical formulation of the cell cycle model for somitogenesis proposed in Development105 (1989), 119-130. Somite precursor cells in the node are asyn...