83,710 research outputs found
Variational integrators and time-dependent lagrangian systems
This paper presents a method to construct variational integrators for
time-dependent lagrangian systems. The resulting algorithms are symplectic,
preserve the momentum map associated with a Lie group of symmetries and also
describe the energy variation.Comment: 8 page
Towards a Hamilton-Jacobi Theory for Nonholonomic Mechanical Systems
In this paper we obtain a Hamilton-Jacobi theory for nonholonomic mechanical
systems. The results are applied to a large class of nonholonomic mechanical
systems, the so-called \v{C}aplygin systems.Comment: 13 pages, added references, fixed typos, comparison with previous
approaches and some explanations added. To appear in J. Phys.
The blocks of the Brauer algebra in characteristic zero
We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra
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
A new geometric setting for classical field theories
A new geometrical setting for classical field theories is introduced. This
description is strongly inspired in the one due to Skinner and Rusk for
singular lagrangians systems. For a singular field theory a constraint
algorithm is developed that gives a final constraint submanifold where a
well-defined dynamics exists. The main advantage of this algorithm is that the
second order condition is automatically included.Comment: 22 page
Towards standard methods for benchmark quality ab initio thermochemistry --- W1 and W2 theory
Two new schemes for computing molecular total atomization energies (TAEs)
and/or heats of formation () of first-and second-row
compounds to very high accuracy are presented. The more affordable scheme, W1
(Weizmann-1) theory, yields a mean absolute error of 0.30 kcal/mol and includes
only a single, molecule-independent, empirical parameter. It requires CCSD
(coupled cluster with all single and double substitutions) calculations in
and basis sets, while CCSD(T) [i.e. CCSD with a
quasiperturbative treatment of connected triple excitations] calculations are
only required in and basis sets. On workstation computers and
using conventional coupled cluster algorithms, systems as large as benzene can
be treated, while larger systems are feasible using direct coupled cluster
methods. The more rigorous scheme, W2 (Weizmann-2) theory, contains no
empirical parameters at all and yields a mean absolute error of 0.23 kcal/mol,
which is lowered to 0.18 kcal/mol for molecules dominated by dynamical
correlation. It involves CCSD calculations in and basis sets
and CCSD(T) calculations in and basis sets. On workstation
computers, molecules with up to three heavy atoms can be treated using
conventional coupled cluster algorithms, while larger systems can still be
treated using a direct CCSD code. Both schemes include corrections for scalar
relativistic effects, which are found to be vital for accurate results on
second-row compounds.Comment: J. Chem. Phys., in press; text 30 pages RevTeX; tables 10 pages, HTML
and PostScript versions both included Reason for replacement: fixed typos in
Table II in proo
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