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Editorial

Olga Krupková (2010)

Communications in Mathematics

Electrowetting of a 3D drop: numerical modelling with electrostatic vector fields

Patrick Ciarlet Jr., Claire Scheid (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The electrowetting process is commonly used to handle very small amounts of liquid on a solid surface. This process can be modelled mathematically with the help of the shape optimization theory. However, solving numerically the resulting shape optimization problem is a very complex issue, even for reduced models that occur in simplified geometries. Recently, the second author obtained convincing results in the 2D axisymmetric case. In this paper, we propose and analyze a method that is suitable...

Epitaxially strained elastic films: the case of anisotropic surface energies

Marco Bonacini (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In the context of a variational model for the epitaxial growth of strained elastic films, we study the effects of the presence of anisotropic surface energies in the determination of equilibrium configurations. We show that the threshold effect that describes the stability of flat morphologies in the isotropic case remains valid for weak anisotropies, but is no longer present in the case of highly anisotropic surface energies, where we show that the flat configuration is always a local minimizer...

Equazioni di bilancio della meccanica dei continui nell’ambito della teoria geometrica della misura

Alessandro Musesti (2004)

Bollettino dell'Unione Matematica Italiana

Si dà una presentazione della formulazione delle equazioni di bilancio della Meccanica dei Continui tramite l'approccio insiemistico (flussi e interazioni di Cauchy) e quello distribuzionale (potenze virtuali), illustrando i progressi ottenuti nell'indebolimento delle ipotesi, fino a comprendere campi tensoriali a divergenza misura. Si mostra poi come l'approccio attraverso il Principio delle potenze virtuali permetta di individuare il tensore degli sforzi anche nel caso di un corpo continuo dotato...

Equivalent formulation and numerical analysis of a fire confinement problem

Alberto Bressan, Tao Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a class of variational problems for differential inclusions, related to the control of wild fires. The area burned by the fire at time t> 0 is modelled as the reachable set for a differential inclusion x ˙ ∈F(x), starting from an initial set R0. To block the fire, a barrier can be constructed progressively in time. For each t> 0, the portion of the wall constructed within time t is described by a rectifiable set γ(t) ⊂ 2 . In this paper we show that the search for blocking strategies...

Espaces variationnels et mécanique

Joseph Klein (1962)

Annales de l'institut Fourier

Ce travail est essentiellement consacré aux systèmes dynamiques Σ non conservatifs, la force généralisée dépendant à la fois des paramètres de position x α et de vitesse y α . V désignant l’espace-temps de configuration, V l’espace fibré des vecteurs tangents, W celui des directions tangentes à V , on caractérise Σ par son lagrangien homogène L et le tenseur-force S antisymétrique dont le produit contracté par le vecteur vitesse donne le vecteur force généralisé.Dans la première partie, on étudie l’algèbre...

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