3,039 research outputs found
Kirillov structures and reduction of Hamiltonian systems by scaling and standard symmetries
In this paper, we discuss the reduction of symplectic Hamiltonian systems by
scaling and standard symmetries which commute. We prove that such a reduction
process produces a so-called Kirillov Hamiltonian system. Moreover, we show
that if we reduce first by the scaling symmetries and then by the standard ones
or in the opposite order, we obtain equivalent Kirillov Hamiltonian systems. In
the particular case when the configuration space of the symplectic Hamiltonian
system is a Lie group G, which coincides with the symmetry group, the reduced
structure is an interesting Kirillov version of the Lie-Poisson structure on
the dual space of the Lie algebra of G. We also discuss a reconstruction
process for symplectic Hamiltonian systems which admit a scaling symmetry. All
the previous results are illustrated in detail with some interesting examples
EU polluting emissions: an empirical analysis
We provide an empirical study of the evolution of emissions of some specific air pollutants on a panel of EU member states from 1990 to 2000, and we relate observed patterns to macroeconomic performance. The ratio pollution emission to GDP, so-called emission intensity, has decreased over the period considered in most EU member states. However, a non-parametric analysis reveals that the relative positions of different countries in terms of GDP growth and reduction of emissions have remained basically unchanged. More specifically, remarkable differences can be detected between the richest and the poorest EU members notwithstanding. Also, more dispersion in emissions levels can be found in those countries with lower per capita GDP
Hamilton-Jacobi Theory in k-Symplectic Field Theories
In this paper we extend the geometric formalism of Hamilton-Jacobi theory for
Mechanics to the case of classical field theories in the k-symplectic
framework
Poisson-Jacobi reduction of homogeneous tensors
The notion of homogeneous tensors is discussed. We show that there is a
one-to-one correspondence between multivector fields on a manifold ,
homogeneous with respect to a vector field on , and first-order
polydifferential operators on a closed submanifold of codimension 1 such
that is transversal to . This correspondence relates the
Schouten-Nijenhuis bracket of multivector fields on to the Schouten-Jacobi
bracket of first-order polydifferential operators on and generalizes the
Poissonization of Jacobi manifolds. Actually, it can be viewed as a
super-Poissonization. This procedure of passing from a homogeneous multivector
field to a first-order polydifferential operator can be also understood as a
sort of reduction; in the standard case -- a half of a Poisson reduction. A
dual version of the above correspondence yields in particular the
correspondence between -homogeneous symplectic structures on and
contact structures on .Comment: 19 pages, minor corrections, final version to appear in J. Phys. A:
Math. Ge
Integrating palliative care and intensive care: different concepts and organizational models based on a mixed-methods study on professionals’ perspectives
info:eu-repo/semantics/acceptedVersio
A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids
This paper presents a geometric description of Lagrangian and Hamiltonian
systems on Lie affgebroids subject to affine nonholonomic constraints. We
define the notion of nonholonomically constrained system, and characterize
regularity conditions that guarantee that the dynamics of the system can be
obtained as a suitable projection of the unconstrained dynamics. It is shown
that one can define an almost aff-Poisson bracket on the constraint AV-bundle,
which plays a prominent role in the description of nonholonomic dynamics.
Moreover, these developments give a general description of nonholonomic systems
and the unified treatment permits to study nonholonomic systems after or before
reduction in the same framework. Also, it is not necessary to distinguish
between linear or affine constraints and the methods are valid for explicitly
time-dependent systems.Comment: 50 page
Momentum and energy preserving integrators for nonholonomic dynamics
In this paper, we propose a geometric integrator for nonholonomic mechanical
systems. It can be applied to discrete Lagrangian systems specified through a
discrete Lagrangian defined on QxQ, where Q is the configuration manifold, and
a (generally nonintegrable) distribution in TQ. In the proposed method, a
discretization of the constraints is not required. We show that the method
preserves the discrete nonholonomic momentum map, and also that the
nonholonomic constraints are preserved in average. We study in particular the
case where Q has a Lie group structure and the discrete Lagrangian and/or
nonholonomic constraints have various invariance properties, and show that the
method is also energy-preserving in some important cases.Comment: 18 pages, 6 figures; v2: example and figures added, minor correction
to example 2; v3: added section on nonholonomic Stoermer-Verlet metho
Hamiltonian dynamics and constrained variational calculus: continuous and discrete settings
The aim of this paper is to study the relationship between Hamiltonian
dynamics and constrained variational calculus. We describe both using the
notion of Lagrangian submanifolds of convenient symplectic manifolds and using
the so-called Tulczyjew's triples. The results are also extended to the case of
discrete dynamics and nonholonomic mechanics. Interesting applications to
geometrical integration of Hamiltonian systems are obtained.Comment: 33 page
Age validation in early stages of Sepia officinalis and its application to age estimation of Sepia species
Quality of Life Outcomes Following Organ-Sparing SBRT in Previously Irradiated Recurrent Head and Neck Cancer
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