Symplectic-energy-momentum preserving variational integrators

The purpose of this paper is to develop variational integrators for conservative mechanical systems that are symplectic and energy and momentum conserving. To do this, a space–time view of variational integrators is employed and time step adaptation is used to impose the constraint of conservation of energy. Criteria for the solvability of the time steps and some numerical examples are given

Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

Vortex-antivortex annihilation in mesoscopic superconductors with a central pinning center

In this work we solved the time-dependent Ginzburg-Landau equations, TDGL, to simulate two superconducting systems with different lateral sizes and with an antidot inserted in the center. Then, by cycling the external magnetic field, the creation and annihilation dynamics of a vortex-antivortex pair was studied as well as the range of temperatures for which such processes could occur. We verified that in the annihilation process both vortex and antivortex acquire an elongated format while an accelerated motion takes place.Comment: 4 pages, 5 figures, work presented in Vortex VII

Variational integrators, the Newmark scheme, and dissipative systems

Variational methods are a class of symplectic-momentum integrators for ODEs. Using these schemes, it is shown that the classical Newmark algorithm is structure preserving in a non-obvious way, thus explaining the observed numerical behavior. Modifications to variational methods to include forcing and dissipation are also proposed, extending the advantages of structure preserving integrators to non-conservative systems

Nonsmooth Lagrangian mechanics and variational collision integrators

Variational techniques are used to analyze the problem of rigid-body dynamics with impacts. The theory of smooth Lagrangian mechanics is extended to a nonsmooth context appropriate for collisions, and it is shown in what sense the system is symplectic and satisfies a Noether-style momentum conservation theorem. Discretizations of this nonsmooth mechanics are developed by using the methodology of variational discrete mechanics. This leads to variational integrators which are symplectic-momentum preserving and are consistent with the jump conditions given in the continuous theory. Specific examples of these methods are tested numerically, and the long-time stable energy behavior typical of variational methods is demonstrated

La diversidad funcional en comunidades animales: una revisión que hace énfasis en los vertebrados

La diversidad funcional es la variedad de funciones que desempeñan las especies en los ecosistemas. Su estudio en comunidades animales todavía es incipiente y, por ello, el objetivo de esta revisión es aportar información de referencia sobre los conceptos básicos relativos a la cuantificación de la diversidad funcional y sus aplicaciones en vertebrados, así como los avances realizados al respecto. Los peces y las aves, seguidos de los mamíferos, han sido los grupos más estudiados. Los anfibios y los reptiles han recibido menos atención, aun cuando tienen un alto potencial para el estudio de la diversidad funcional. Existen protocolos para la medición directa y estandarizada de los rasgos funcionales en aves, anfibios y peces dulceacuícolas. Con respecto a los mamíferos y los reptiles, no existen guías a seguir y los rasgos funcionales generalmente se toman de la literatura. Para complementar y promover la medición de rasgos funcionales en vertebrados, se presenta una lista de rasgos que se podrían utilizar para analizar la diversidad funcional en diferentes subgrupos de mamíferos y en reptiles.Functional diversity in animal communities: a review with emphasis on vertebrates Functional diversity is the variety of functional roles that species have in ecosystems. As its study in animal communities is still emerging, the aim of this review is to provide an informative reference on the basic concepts and advances in the quantification of functional diversity and its applications to vertebrates. The most studied groups to date are fish and birds, followed by mammals. Amphibians and reptiles have received less attention despite their high potential for the study of functional diversity. Protocols are available for the direct and standardized measure of functional traits in birds, amphibians and freshwater fish. No guides are yet available, however, for mammals and reptiles and functional traits are usually taken from the literature. To complement and to promote the measurement of functional traits in vertebrates, we provide a list of potential traits for the analysis of functional diversity in different subgroups of mammals and in reptiles.La diversidad funcional es la variedad de funciones que desempeñan las especies en los ecosistemas. Su estudio en comunidades animales todavía es incipiente y, por ello, el objetivo de esta revisión es aportar información de referencia sobre los conceptos básicos relativos a la cuantificación de la diversidad funcional y sus aplicaciones en vertebrados, así como los avances realizados al respecto. Los peces y las aves, seguidos de los mamíferos, han sido los grupos más estudiados. Los anfibios y los reptiles han recibido menos atención, aun cuando tienen un alto potencial para el estudio de la diversidad funcional. Existen protocolos para la medición directa y estandarizada de los rasgos funcionales en aves, anfibios y peces dulceacuícolas. Con respecto a los mamíferos y los reptiles, no existen guías a seguir y los rasgos funcionales generalmente se toman de la literatura. Para complementar y promover la medición de rasgos funcionales en vertebrados, se presenta una lista de rasgos que se podrían utilizar para analizar la diversidad funcional en diferentes subgrupos de mamíferos y en reptiles