Unified formalism for higher-order non-autonomous dynamical systems

This work is devoted to giving a geometric framework for describing higher-order non-autonomous mechanical systems. The starting point is to extend the Lagrangian-Hamiltonian unified formalism of Skinner and Rusk for these kinds of systems, generalizing previous developments for higher-order autonomous mechanical systems and first-order non-autonomous mechanical systems. Then, we use this unified formulation to derive the standard Lagrangian and Hamiltonian formalisms, including the Legendre-Ostrogradsky map and the Euler-Lagrange and the Hamilton equations, both for regular and singular systems. As applications of our model, two examples of regular and singular physical systems are studied.Comment: 43 pp. We have corrected and clarified the statement of Propositions 2 and 3. A remark is added after Proposition

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

Predicting global geographical distribution of "Lolium rigidum" under climate change

“Lolium rigidum Gaud.” (vallico) es una de las malezas más extendidas y perjudiciales en los cultivos de cereales de invierno. Un modelo bioclimático para esta especie fue desarrollado utilizando CLIMEX. El modelo fue validado con los registros de esta especie en Estados Unidos y Oceanía y utilizado para predecir la distribución potencial global de “L. rigidum” bajo el clima actual y dos escenarios de cambio climático. Las proyección en virtud de las condiciones climáticas actuales indican que “L. rigidum” no ocupa todo el área disponible para su expansión. Considerando los escenarios climáticos futuros, el área potencial de expansión aumentará 3,79% y 5,06% bajo los escenarios moderado y extremo, respectivamente. La proyección del modelo mostró un avance gradual de “L. rigidum” en Norteamérica, Europa, Sudamérica y Asia, mientras que en África y Oceanía se prevé una regresión. Estos resultados proporcionan Los conocimientos necesarios para identificar y poner de relieve las posibles zonas de riesgo de invasión.“Lolium rigidum” Gaud. (rigid ryegrass) is one of the most extended and harmful weeds in winter cereal crops. A bioclimatic model for this species was developed using CLIMEX. The model was validated with records from North America and Oceania and used to assess the global potential distribution of “L. rigidum” under the current climate and under two climate change scenarios. The projection under current climate conditions indicated that “L. rigidum” does not occupy the full extent of the climatically suitable area available to it. Under future climate scenarios, the infested potential area will increase 3.79% in the low-emission CO2 scenario and 5.06% under the most extreme scenario. The model projection showed a gradual advance of rigid ryegrass in North America, Europe, South America and Asia, whilst in Africa and Oceania it indicated regression. These results provide the necessary knowledge for identifying and highlighting the potential invasion risk areas

Unambiguous Formalism for Higher-Order Lagrangian Field Theories

The aim of this paper is to propose an unambiguous intrinsic formalism for higher-order field theories which avoids the arbitrariness in the generalization of the conventional description of field theories, which implies the existence of different Cartan forms and Legendre transformations. We propose a differential-geometric setting for the dynamics of a higher-order field theory, based on the Skinner and Rusk formalism for mechanics. This approach incorporates aspects of both, the Lagrangian and the Hamiltonian description, since the field equations are formulated using the Lagrangian on a higher-order jet bundle and the canonical multisymplectic form on its dual. As both of these objects are uniquely defined, the Skinner-Rusk approach has the advantage that it does not suffer from the arbitrariness in conventional descriptions. The result is that we obtain a unique and global intrinsic version of the Euler-Lagrange equations for higher-order field theories. Several examples illustrate our construction.Comment: 21 pages; 4 diagrams; (this version) corrected typos; moved paragraphs; publishe

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

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

X-ray diffraction, cements and environment, three worlds in one

This keynote lecture will be focused on the strategies for reducing CO2 emissions in the cement production. Concretely, the production of ecocements with optimised formulations that yield reductions in CO2 emissions of up to 25%, when compared to OPC production. Phase assemblage has to be carefully optimised to be competitive and these new ecocements should develop compressive strengths of at least 50 MPa at 28 days of hydration. Optimised compositions of several ecocements will be discussed, but all of them are ye'elimite or calcium sulphoaluminate containing ones: belite-ye'elimite-ferrite (BYF), belite-alite-ye'elimite (BAY) and ye'elimite rich ones (CSA). The clinkering temperature of BYF and BAY has to be established to obtain the targeted phase assemblages. Moreover, the stabilisation of alpha-forms of belite is needed to develop high mechanical strengths at early ages. The benefits of the use of waste materials (such as fly ash or slag) as additions to ecocements are three-fold: lower CO2 emissions due to clinker replacement; valorisation of “useless” products that need a lot of landscape and the consequent efficient consumption of raw materials; and to enhance mechanical properties of the corresponding mortars. The design of appropriate CSA, BYF and BAY mortars, with the final aim of knowing and controlling the hydration mechanisms, will be presented. Particularly, the role of i) type and amount of set regulator (gypsum, anhydrite, etc.), ii) water/cement ratio (w/c); iii) superplasticiser; and iv) pozzolanic additions will be discussed. The role of these parameters in the microstructure and hydraulic behaviour has been investigated through traditional techniques as well as advanced synchrotron characterisation. The formers include laboratory/synchrotron X-ray powder diffraction combined with Rietveld methodology (to obtain phase assemblage), electron microscopy techniques for paste microstructure determination, rheological studies (to control the effect of the different additives, w/c ratio and setting time retarders) and mechanical tests (setting times, compressive strengths and dimensional stability). The latters comprise a group of techniques available at synchrotrons such as: i) high temperature x-ray diffraction for clinkering studies and ii) total scattering data to be analysed by pair distribution function, PDF.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. PhD D. Londono-Zuluaga thanks Colciencias and Enlaza Mundos program PhD grant. Spanish MINECO (BIA2014-57658-C2-2-R, which is co-funded by FEDER, BIA2014-57658-C2-1-R and I3 (IEDI-2016-0079) grants) are acknowledged