Aspects of reduction and transformation of Lagrangian systems with symmetry

This paper contains results on geometric Routh reduction and it is a continuation of a previous paper where a new class of transformations is introduced between Lagrangian systems obtained after Routh reduction. In general, these reduced Lagrangian systems have magnetic force terms and are singular in the sense that the Lagrangian does not depend on some velocity components. The main purpose of this paper is to show that the Routh reduction process itself is entirely captured by the application of such a new transformation on the initial Lagrangian system with symmetry.Comment: To appear in Journal of Geometric Mechanic

Reduced dynamics and Lagrangian submanifolds of symplectic manifolds

In this paper, we will see that the symplectic creed by Weinstein "everything is a Lagrangian submanifold" also holds for Hamilton-Poincar\'e and Lagrange-Poincar\'e reduction. In fact, we show that solutions of the Hamilton-Poincar\'e equations and of the Lagrange-Poincar\'e equations are in one-to-one correspondence with distinguished curves in a Lagrangian submanifold of a symplectic manifold. For this purpose, we will combine the concept of a Tulczyjew triple with Marsden-Weinstein symplectic reduction.Comment: 26 page

Routh reduction and the class of magnetic Lagrangian systems

In this paper, some new aspects related to Routh reduction of Lagrangian systems with symmetry are discussed. The main result of this paper is the introduction of a new concept of transformation that is applicable to systems obtained after Routh reduction of Lagrangian systems with symmetry, so-called magnetic Lagrangian systems. We use these transformations in order to show that, under suitable conditions, the reduction with respect to a (full) semi-direct product group is equivalent to the reduction with respect to an Abelian normal subgroup. The results in this paper are closely related to the more general theory of Routh reduction by stages.Comment: 23 page

Lagrangian Lie subalgebroids generating dynamics for second-order mechanical systems on Lie algebroids

The study of mechanical systems on Lie algebroids permits an understanding of the dynamics described by a Lagrangian or Hamiltonian function for a wide range of mechanical systems in a unified framework. Systems defined in tangent bundles, Lie algebras, principal bundles, reduced systems, and constrained are included in such description. In this paper, we investigate how to derive the dynamics associated with a Lagrangian system defined on the set of admissible elements of a given Lie algebroid using Tulczyjew’s triple on Lie algebroids and constructing a Lagrangian Lie subalgebroid of a symplectic Lie algebroid, by building on the geometric formalism for mechanics on Lie algebroids developed by M. de León, J.C. Marrero and E. Martínez on “Lagrangian submanifolds and dynamics on Lie algebroids”publishe

PenNuc: Monte Carlo simulation of the decay of radionuclides

The Fortran subroutine package PenNuc that performs Monte Carlo simulation of the decay of radioactive nuclides is described. The adopted nuclear decay characteristics (possible disintegration modes and branching ratios, energies and half-lives of nuclear energy levels, types and energies of emitted particles) are from the NUCLEIDE evaluated database ( http://www.nucleide.org/DDEP_WG/DDEPdata.htm) in the specific format PenNuc. The initial energies of electrons and positrons emitted in beta disintegrations are sampled from their continuous spectra by means of the RITA (rational inverse transform with aliasing) algorithm, which is described in the Appendix. Electronic relaxation of the residual ion after electron capture and internal conversion is simulated by using the data and sampling methods of the PENELOPE code system. At each call the subroutines deliver a list of state variables of the particles (photons, electrons, positrons and alphas) emitted in a random decay path of the considered radionuclide down to a metastable level or to the ground state of the daughter nucleus. The distribution package includes a main program that simulates the emission spectrum of a radionuclide and, optionally, produces a list of particles emitted in a prescribed number of decays

Estratigrafía y estructura de los materiales permotriásicos del sector Gijón - La Collada (Asturias)

[ES] Una campaña de investigación geológico-minera del yacimiento carbonífero de «Mina La Camocha» ha aportado nuevos y abundantes datos del Pérmico de la Orla Cantábrica. Al no aflorar en ningún punto el Carbonífero investigado con fines mineros, se realizó una campaña de exploración profunda que contó con líneas sísmicas, sondeos geológico-mineros de superficie e interior y sondeos de investigación hidrogeológica. Todos ellos han permitido reconocer en varios puntos la cobertera permotriásica completa, aportando numerosas precisiones y la discriminación de unidades que generalmente no afloran. Se distinguen y caracterizan ocho unidades litoestratigráficas locales con rango de miembro, que se datan mediante correlación regional. En las unidades basales se observan importantes cambios de facies y de potencia relacionados con la configuración geodinámica inicial de la cuenca. Se propone un modelo de evolución ambiental de ésta. La investigación realizada permite situar y acotar en edad las principales fallas que en determinados momentos han condicionado la sedimentación, distinguiéndose fallas alpinas y tardihercínicas. Del estudio de estos materiales considerados pérmicos, ha resultado un mejor conocimiento de la Formación Caravia («Saxoniense») en la subcuenca de Gijón-Villaviciosa.[EN] A geological and mining investigation campaign, of the buried «La Camocha Mine» coalfield, has indirectly provided several new data of the Cantabrian seaside Permian rocks (Asturias, N. Spain). As the Carboniferous investigated with mining purposes, does not crop out in the studicd area, the eampaign was carried out including seismie Enes, surface and underground inclined geological, and hydrogeological research diamond drilí boreholes. AII of them recognised the complete permotriassic cover, providing several findings of different units, generally non-outcropping. Eight local lithostratigraphic units with member rank are distinguished, characterized and dated as Permian through regional correlations. Important thickness and facies changes are observed within basal units. These are related with the initial geodynamic setting of the sedimentary basin. An environmental evolution is proposed. The investigation developed has enabled to precisely situate and limit the age of the main faults that in some specific periods have constraint sedimentation, and furthermore, alpine and late hercynian fractures are distinguished. The study of these Permian sequences is enhancing the knowledge of the Caravia Fm. (Saxonian) in the Gijón-Villaviciosa sub-basin.Peer reviewe