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We describe the bifurcation diagrams of almost toric integrable Hamiltonian systems on a four dimensional symplectic manifold M, not necessarily compact. We prove that, under a weak assumption, the connectivity of the fibers of the induced singular Lagrang ...
Multisymplectic variational integrators are structure-preserving numerical schemes especially designed for PDEs derived from covariant spacetime Hamilton principles. The goal of this paper is to study the properties of the temporal and spatial discrete evo ...
This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in two and three dimensions in the quasistatic regime. Two key figures of CALR are (i) the localized resonance and (ii) the connection between the localized resonance a ...
This paper develops the theory of multisymplectic variational integrators for nonsmooth continuum mechanics with constraints. Typical problems are the impact of an elastic body on a rigid plate or the collision of two elastic bodies. The integrators are ob ...
A compact Kahler manifold X is shown to be simply connected if its 'symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective connected holomorphic m ...
In this paper we show that the incompressible Euler equation on the Sobolev space H-s(R-n), s> n/2+1, can be expressed in Lagrangian coordinates as a geodesic equation on an infinite dimensional manifold. Moreover the Christoffel map describing the geodesi ...
In the context of robotic control, synergies can form an elementary unit of behavior. By specifying task-dependent coordination behaviors at a low control level, one can achieve task-specific disturbance rejection. In this work we present an approach to le ...
Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...
The goal of this paper is to derive a structure preserving integrator for geometrically exact beam dynamics, by using a Lie group variational integrator. Both spatial and temporal discretization are implemented in a geometry preserving manner. The resultin ...