Discrete variational integrators and optimal control theory

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.Comment: 17 page

Tulczyjew's triples and lagrangian submanifolds in classical field theories

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.Comment: 29 page

Geometric numerical integration of nonholonomic systems and optimal control problems

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 200

Relative production rates of 6^{6}He, 9^{9}Be, 12^{12}C in astrophysical environments

We assume an environment of neutrons and $\alpha$-particles of given density and temperature where nuclear syntheses into $^{6}$He, $^{9}$Be and $^{12}$C are possible. We investigate the resulting relative abundance as a function of density and temperature. When the relative abundance of $\alpha$-particles $Y_{\alpha}$ is between 0.2 and 0.9, or larger than 0.9, the largest production is $^{9}$Be or $^{12}$C, respectively. When $Y_{\alpha}<0.2$ $^{6}$He is mostly frequently produced for temperatures above about 2 GK whereas the $^{9}$Be production dominates at smaller temperatures.Comment: 5 pages, 4 figure

Extended D=3D=3 Bargmann supergravity from a Lie algebra expansion

In this paper we show how the method of Lie algebra expansions may be used to obtain, in a simple way, both the extended Bargmann Lie superalgebra and the Chern-Simons action associated to it in three dimensions, starting from $D=3$, $\mathcal{N}=2$ superPoincar\'e and its corresponding Chern-Simons supergravity.Comment: 17 page