Nonholonomic constraints in kk-symplectic Classical Field Theories

A $k$-symplectic framework for classical field theories subject to nonholonomic constraints is presented. If the constrained problem is regular one can construct a projection operator such that the solutions of the constrained problem are obtained by projecting the solutions of the free problem. Symmetries for the nonholonomic system are introduced and we show that for every such symmetry, there exist a nonholonomic momentum equation. The proposed formalism permits to introduce in a simple way many tools of nonholonomic mechanics to nonholonomic field theories.Comment: 27 page

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Symmetries in Classical Field Theory

The multisymplectic description of Classical Field Theories is revisited, including its relation with the presymplectic formalism on the space of Cauchy data. Both descriptions allow us to give a complete scheme of classification of infinitesimal symmetries, and to obtain the corresponding conservation laws.Comment: 70S05; 70H33; 55R10; 58A2

Osteomielitis subaguda en paciente con diabetes mellitus complicada

La osteomielitis subaguda es una infección hematógena del hueso definida como una forma de osteomielitis no supurativa esclerosante que habitualmente pasa desapercibida en estadios precoces dada su clínica insidiosa caracterizada por buen estado del paciente, así como una historia de dolor de larga evolución.Presentamos un caso de osteomielitis subaguda que, por la edad de presentación, la patología asociada del paciente y la localización de la misma, debe hacer replantearnos las distintas opciones de tratamiento asumiendo las posibles complicaciones y fracasos.Subacute osteomyelitis is a haematogenous infection of bone defined as a non-suppurative, sclerosing form of osteomyelitis which usually escapes detection in its early stages because of its insidious clinical features (good general condition of the patient and a long-lasting history of pain). We report one case of subacute osteomyelitis which, because of its location, the age at presentation and the patient's associated pathology should prompt consideration of the various therapeutic options and assumption of the possible complications and therapeutic failures

Multivector Field Formulation of Hamiltonian Field Theories: Equations and Symmetries

We state the intrinsic form of the Hamiltonian equations of first-order Classical Field theories in three equivalent geometrical ways: using multivector fields, jet fields and connections. Thus, these equations are given in a form similar to that in which the Hamiltonian equations of mechanics are usually given. Then, using multivector fields, we study several aspects of these equations, such as the existence and non-uniqueness of solutions, and the integrability problem. In particular, these problems are analyzed for the case of Hamiltonian systems defined in a submanifold of the multimomentum bundle. Furthermore, the existence of first integrals of these Hamiltonian equations is considered, and the relation between {\sl Cartan-Noether symmetries} and {\sl general symmetries} of the system is discussed. Noether's theorem is also stated in this context, both the ``classical'' version and its generalization to include higher-order Cartan-Noether symmetries. Finally, the equivalence between the Lagrangian and Hamiltonian formalisms is also discussed.Comment: Some minor mistakes are corrected. Bibliography is updated. To be published in J. Phys. A: Mathematical and Genera

Symmetries and conservation laws in the Gunther k-symplectic formalism of field theory

This paper is devoted to studying symmetries of k-symplectic Hamiltonian and Lagrangian first-order classical field theories. In particular, we define symmetries and Cartan symmetries and study the problem of associating conservation laws to these symmetries, stating and proving Noether's theorem in different situations for the Hamiltonian and Lagrangian cases. We also characterize equivalent Lagrangians, which lead to an introduction of Lagrangian gauge symmetries, as well as analyzing their relation with Cartan symmetries.Comment: 29 page

Non-standard connections in classical mechanics

In the jet-bundle description of first-order classical field theories there are some elements, such as the lagrangian energy and the construction of the hamiltonian formalism, which require the prior choice of a connection. Bearing these facts in mind, we analyze the situation in the jet-bundle description of time-dependent classical mechanics. So we prove that this connection-dependence also occurs in this case, although it is usually hidden by the use of the ``natural'' connection given by the trivial bundle structure of the phase spaces in consideration. However, we also prove that this dependence is dynamically irrelevant, except where the dynamical variation of the energy is concerned. In addition, the relationship between first integrals and connections is shown for a large enough class of lagrangians.Comment: 17 pages, Latex fil

Poliuquetos perforadores de conchas marinas y exóticos invasores

En esta contribución se enfatiza la importancia de los gusanos poliquetos perforadores de moluscos de interés comercial en México y del estudio de las especies exóticas invasoras. Asimismo, se presenta el estado del conocimiento de ambos rubros en México. Es necesario sensibilizar a los tomadores de decisiones sobre la necesidad de apoyar proyectos de investigación y contrataciones en los dos temas. Recomendamos modificar la sección de poliquetos de la Lista de especies exóticas invasoras en México, publicada en el Diario Oficial de la Federación en 2016

Development of Surface-Coated Polylactic Acid/Polyhydroxyalkanoate (PLA/PHA) Nanocomposites

This work reports on the design and development of nanocomposites based on a polymeric matrix containing biodegradable Polylactic Acid (PLA) and Polyhydroxyalkanoate (PHA) coated with either Graphite NanoPlatelets (GNP) or silver nanoparticles (AgNP). Nanocomposites were obtained by mechanical mixing under mild conditions and low load contents (<0.10 wt %). This favours physical adhesion of the additives onto the polymer surface, while the polymeric bulk matrix remains unaffected. Nanocomposite characterisation was performed via optical and focused ion beam microscopy, proving these nanocomposites are selectively modified only on the surface, leaving bulk polymer unaffected. Processability of these materials was proven by the fabrication of samples via injection moulding and mechanical characterisation. Nanocomposites showed enhanced Young modulus and yield strength, as well as better thermal properties when compared with the unmodified polymer. In the case of AgNP coated nanocomposites, the surface was found to be optically active, as observed in the increase of the resolution of Raman spectra, acquired at least 10 times, proving these nanocomposites are promising candidates as surface enhanced Raman spectroscopy (SERS) substrates

Classical field theory on Lie algebroids: Variational aspects

The variational formalism for classical field theories is extended to the setting of Lie algebroids. Given a Lagrangian function we study the problem of finding critical points of the action functional when we restrict the fields to be morphisms of Lie algebroids. In addition to the standard case, our formalism includes as particular examples the case of systems with symmetry (covariant Euler-Poincare and Lagrange Poincare cases), Sigma models or Chern-Simons theories.Comment: Talk deliverd at the 9th International Conference on Differential Geometry and its Applications, Prague, September 2004. References adde