Patrícia Santos

Quasi-coordinates from the point of view of Lie algebroid structures

A geometrical description of the Lagrangian dynamics in quasi-coordinates on the tangent bundle, using the Lie algebroid framework, is given. Linear nonholonomic systems on Lie algebroids are solved in local coordinates adapted to the constraints, through Lagrangian multipliers and Gibbs–Appell generalized methods.

Coaxial electrospun PCL/Gelatin-MA fibers as scaffolds for vascular tissue engineering

Coaxial electrospinning is a technique that allows the production of nanofibers with a core-shell structure. Such fibers present several advantages as materials for the preparation of scaffolds, namely due to the possibility of combining a core with the desired mechanical properties with a shell prepared from biocompatible materials that will establish proper interactions with the host. Herein, core-shell fibrous meshes, composed of a polycaprolactone (PCL) core and a functionalized gelatin shell, were prepared by coaxial electrospinning and then photocrosslinked under UV light aiming to be used in vascular tissue regeneration. The suitability of the meshes for the pretended biomedical application was evaluated by assessing their chemical/physical properties as well as their haemo and biocompatibility in vitro. The obtained results revealed that meshes shell prepared with a higher content of gelatin showed fibers with diameters presenting a unimodal distribution and a mean value of 600nm. Moreover, those fibers with higher content of gelatin also displayed lower water contact angles, and therefore higher hydrophilicities. Such features are crucial for the good biologic performance displayed by these meshes, when in contact with blood and with Normal Human Dermal Fibroblasts cells.

SOME APPLICATIONS OF QUASI-VELOCITIES IN OPTIMAL CONTROL

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently [20]. We also provide several examples to illustrate our construction.

Reduction of Lie algebroid structures

Based on the ideas of Marsden–Ratiu, a reduction method for Lie algebroids is developed in such a way that the canonical projection onto the reduced Lie algebroid is a homomorphism of Lie algebroids. A relation between Poisson reduction and Lie algebroid reduction is established. Reduction of Lie algebroids with symmetry is also studied using this method.

Conformal Killing vector fields and a virial theorem

The virial theorem is formulated both intrinsically and in local coordinates for a Lagrangian system of mechanical type on a Riemann manifold. An import case studied in this paper is that of an affine virial function associated to a vector field on the configuration manifold. The special cases of a virial function associated to a Killing, a homothetic and a conformal Killing vector field are considered and the corresponding virial theorems are established for this type of functions.

Virial theorem in quasi-coordinates and Lie algebroid formalism

In this paper, the geometric approach to the virial theorem (VT) developed in [J. F. Carinena, F. Falceto and M. F. Ranada, A geometric approach to a generalized virial theorem, J. Phys. A: Math. Theor. 45 (2012) 395210, 19 pp.] is written in terms of quasi-velocities (see [J. F. Carinena, J. Nunes da Costa and P. Santos, Quasi-coordinates from the point of view of Lie algebroid structures, J. Phys. A: Math. Theor. 40 (2007) 10031–10048]). A generalization of the VT for mechanical systems on Lie algebroids is also given, using the geometric tools of Lagrangian and Hamiltonian mechanics on the prolongation of the Lie algebroid.

Internal deformation of Lie algebroids and symplectic realizations

Given a Lie algebroid and a bundle over its base which is endowed with a localizable Poisson structure and a flat connection, we construct an extended bundle whose dual is endowed with an almost-Poisson structure that is a quadratic Poisson structure when a certain compatibility property is satisfied. This new formalism on Lie algebroids describes systems with internal degrees of freedom.

Amphibia, Anura, Hylodidae, Megaelosia apuana Pombal, Prado and Canedo, 2003: distribution extension, new state record and geographic distribution map

In this study we report the first record of the giant torrent frog Megaelosia apuana in the state of Minas Gerais, southeastern Brazil. The finding of this species at Reserva Particular do Patrimonio Natural (RPPN) Mata do Sossego, municipality of Simonesia, east of Minas Gerais extends its geographic distribution by 120 km from the type locality, and 45 km northwest from its westernmost known record. A geographic distribution map is presented.

Amphibia, Anura, Leiuperidae, Physalaemus feioi Cassini, Cruz and Caramaschi, 2010: distribution extension

We provide new records of the recently described frog Physalaemus feioi in the state of Minas Gerais, southeastern Brazil. Records presented here extend the distribution of P. feioi around 113 km straight north from Parque Estadual da Serra do Brigadeiro, the previously northernmost known record for the species.

Mussurana montana (Franco, Marques & Puorto, 1997) (Serpentes: Dipsadidae): noteworthy records and an updated distribution map

Mussurana montana xa0is a poorly known dipsadid snake endemic to elevated areas in the Atlantic Forest of southeastern Brazil. After the examination of specimens deposited in scientific collections, we update the distribution range of M. montana xa0with five new locality records, including its first record from the state of Rio de Janeiro, and a new northernmost and easternmost record in the state of Minas Gerais. These new data reinforce the distribution of M. montana within the mountain ranges of Serra da Mantiqueira and Serra do Mar, from 750–1,610 m above sea level.