Geometric aspects of nonholonomic field theories

A geometric model for nonholonomic Lagrangian field theory is studied. The multisymplectic approach to such a theory as well as the corresponding Cauchy formalism are discussed. It is shown that in both formulations, the relevant equations for the constrained system can be recovered by a suitable projection of the equations for the underlying free (i.e. unconstrained) Lagrangian system.Comment: 29 pages; typos remove

Discrete Nonholonomic Lagrangian Systems on Lie Groupoids

This paper studies the construction of geometric integrators for nonholonomic systems. We derive the nonholonomic discrete Euler-Lagrange equations in a setting which permits to deduce geometric integrators for continuous nonholonomic systems (reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile robot).Comment: 45 page

Climate vulnerability assessment of the Espeletia Complex on Páramo Sky Islands in the Northern Andes

Some of the largest impacts of climate change are expected in the environmentally heterogeneous and species rich high mountain ecosystems. Among those, the Neotropical alpine grassland above the tree line (c. 2,800 m), known as Páramo, is the fastest evolving biodiversity hotspot on earth, and one of the most threatened. Yet, predicting climate responses of typically slow-growing, long-lived plant linages in this unique high mountain ecosystem remains challenging. Here we coupled climate sensitivity modeling and adaptive potential inferences to efficiently assess climate vulnerability of Espeletia, Páramo’s most iconic, predominant and rapidly evolving plant complex. In order to estimate climate sensitivity, we first modeled the distribution of 28 Espeletia taxa under a niche conservatism scenario using altitude and five current (1970–2000) and future (2050 RCP 8.5) bioclimatic variables across 36 different Páramo complexes in the northern Andes (49% of the world’s Páramo area). As an alternative to range shifts via migration, we also computed the adaptive capacity of these Páramo complexes by considering three enhancing factors of the biodiversity’s adaptive potential as well as three environmental limiting factors of the populations’ plastic response. These predictors showed that diverse Páramos in the Eastern Cordillera were more vulnerable likely because the counteracting effects of the adaptive potential (r = −0.93 ± 0.01) were not sufficient to buffer higher distribution losses (r = 0.39 ± 0.01). Agriculture (r = −0.48 ± 0.01), mining (r = −0.36 ± 0.01), and rural population density (r = −0.23 ± 0.01) also weakened the adaptive capacity. These results speak for a limited persistence via migration in the short-term responses of Espeletia to climate change, even though the past population dynamics in concert with glacial cycling is indicative of a predominant role of range shifts. Furthermore, changing climate, together with a general inability to adapt, may eventually constrain the rapid diversification in the Espeletia complex. Our integrative modeling illustrates how future climate may impact plant populations in a mega diverse and highly threatened ecosystem such as the Páramo, and encourages carrying out similar estimates in diverse plant complexes across other high mountain and island-like ecosystems

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

Soil temperature determines the reaction of olive cultivars to verticillium dahliae pathotypes

Development of Verticillium wilt in olive, caused by the soil-borne fungus Verticillium dahliae, can be influenced by biotic and environmental factors. In this study we modeled i) the combined effects of biotic factors (i.e., pathotype virulence and cultivar susceptibility) and abiotic factors (i.e., soil temperature) on disease development and ii) the relationship between disease severity and several remote sensing parameters and plant stress indicators. Methodology: Plants of Arbequina and Picual olive cultivars inoculated with isolates of defoliating and non-defoliating V. dahliae pathotypes were grown in soil tanks with a range of soil temperatures from 16 to 32°C. Disease progression was correlated with plant stress parameters (i.e., leaf temperature, steady-state chlorophyll fluorescence, photochemical reflectance index, chlorophyll content, and ethylene production) and plant growth-related parameters (i.e., canopy length and dry weight). Findings: Disease development in plants infected with the defoliating pathotype was faster and more severe in Picual. Models estimated that infection with the defoliating pathotype was promoted by soil temperatures in a range of 16 to 24°C in cv. Picual and of 20 to 24°C in cv. Arbequina. In the non-defoliating pathotype, soil temperatures ranging from 16 to 20°C were estimated to be most favorable for infection. The relationship between stress-related parameters and disease severity determined by multinomial logistic regression and classification trees was able to detect the effects of V. dahliae infection and colonization on water flow that eventually cause water stress. Conclusions: Chlorophyll content, steady-state chlorophyll fluorescence, and leaf temperature were the best indicators for Verticillium wilt detection at early stages of disease development, while ethylene production and photochemical reflectance index were indicators for disease detection at advanced stages. These results provide a better understanding of the differential geographic distribution of V. dahliae pathotypes and to assess the potential effect of climate change on Verticillium wilt development.Financial support for this research was provided by Project P08-AGR-03528 from ‘‘Consejería de Economía, Innovación y Ciencia’’ of Junta de Andalucía and the European Social Fund (JANC), and projects AGL-2012-37521 (JANC) and AGL2012-40053-C03-01 (PJZT) from the Spanish ‘‘Ministerio de Economia y Competitividad’’ and the European Social Fund. R. Calderón is a recipient of research fellowship BES-2010-035511 from the Spanish ‘‘Ministerio de Ciencia e Innovación’’ and C. Lucena was a recipient of a JAE-DOC postdoctoral contract from ‘‘Consejo Superior de Investigaciones Científicas’’ (CSIC) co-funded by the European Social Fund. TPeer Reviewe

Comparison between FS-MPC control strategy for an UPS inverter application in α-β and abc frames

The voltage source inverter (VSI) of an uninterruptible power supply (UPS) is a system where the main objective is to obtain a high quality output sinusoidal voltage with independence on the output load. For this reason, it includes an output LC filter. The presence of the filter increases the complexity of the controller design thus it is necessary to evaluate the performance of the control strategy in terms of the output voltage quality and computational cost of the algorithm. In this paper, both analysis are developed for the finite states model predictive control (FS-MPC) of a VSI performed in the abc and α-βframes. Both algorithms are summarized and compared in order to establish an objective criteria to choose among them when a hardware implementation is developed. Simulation results are presented for both algorithms to validate the analysis

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

Reusing intravaginal progesterone releasing devices for oestrous synchoronization in ewes

In this study, the second use of an intravaginal progesterone-releasing device or controlled intravaginal drug release device (CIDR) was evaluated. After a first use of 11 days, the CIDR was again used for either nine or 12 days with 200 or 300 IU equine chorionic gonadotrophin (eCG) being injected on its removal. Sixty-four ewes were randomly distributed to four treatments (n=16/group): CIDR9+eCG200, CIDR9+eCG300, CIDR12+eCG200, and CIDR12+eCG300. The eCG was administered intramuscularly on withdrawal of the device. Thus, the experiment was a completely randomized design with a 2×2 factorial arrangement of treatments. Oestrus presentation did not differ between treatments (P =0.29). However, with the dose of 200 IU of eCG, oestrus presentation tended to increase (P =0.08). The onset and duration of oestrus, percentage of gestation, and return to oestrus did not differ between treatments (P >0.05). Progesterone concentration in serum was greater (P < 0.05) in ewes treated with CIDR12+eCG300. Prolificacy was greatest (1.44) with the CIDR12+eCG300 treatment and was different (P = 0.001) from the treatments CIDR9+eCG200 (1.21) and CIDR9+eCG300 (1.20), but not from the CIDR12+eCG200 treated ewes (1.31). The CIDR12+eCG300 treatement produced the highest percentage of twin births (45.8%) (P =0.001). Leaving the device in place for 12 days increased (P =0.001) the incidence of twin births. Use of the CIDR for a second time synchronized oestrus in ewes successfully with better fertility being obtained when the device was left in place for 12 days, and 300 IU of eCG was injected on its removal. Key words: gonadotropin, progesterone device, synchronizatio

Symmetry aspects of nonholonomic field theories

The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result), as well as a modified conservation law associated with spatial translations.Comment: 18 page