Quasivelocities and Optimal Control for Underactuated Mechanical Systems

This paper is concerned with the application of the theory of quasivelocities for optimal control for underactuated mechanical systems. Using this theory, we convert the original problem in a variational second-order lagrangian system subjected to constraints. The equations of motion are geometrically derived using an adaptation of the classical Skinner and Rusk formalism.Comment: 8 page

Lepton Flavor Violation in B Decays?

The LHCb Collaboration's measurement of R_K = B(B+ -> K+ mu+ mu-)/B(B+ -> K+ e+e-) lies 2.6 sigma below the Standard Model prediction. Several groups suggest this deficit to result from new lepton non-universal interactions of muons. But non-universal leptonic interactions imply lepton flavor violation in B decays at rates much larger than are expected in the Standard Model. A simple model shows that these rates could lie just below current limits. An interesting consequence of our model, that B(B_s -> mu+ mu-)_{exp}/B(B_s -> mu+ mu-)_{SM} = R_K = 0.75, is compatible with recent measurements of these rates. We stress the importance of searches for lepton flavor violations, especially for B -> K mu e, K mu tau and B_s -> mu e, mu tau.Comment: 8 pages. Discussion of P'5 added; some discussion sharpened; discussion of decays with tau's modified; references adde

A new method to find the potential center of N-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and com- pared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolu- tion of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Fil: Aguilar, L. A.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Cruz, F.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Carpintero, Daniel Diego. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Sporopollenin, the least known yet toughest natural biopolymer

© 2015 Mackenzie, Boa, Diego-Taboada, Atkin and Sathyapalan. Sporopollenin is highly cross-linked polymer composed of carbon, hydrogen, and oxygen that is extraordinarily stable and has been found chemically intact in sedimentary rocks some 500 million years old. It makes up the outer shell (exine) of plant spores and pollen and when extracted it is in the form of an empty exine or microcapsule. The exines resemble the spores and pollen from which they are extracted, in size and morphology. Also, from any one plant such characteristics are incredible uniform. The exines can be used as microcapsules or simply as micron-sized particles due to the variety of functional groups on their surfaces. The loading of a material into the chamber of the exine microcapsule is via multi-directional nano-diameter sized channels. The exines can be filled with a variety of polar and non-polar materials. Enzymes can be encapsulated within the shells and still remain active. In vivo studies in humans have shown that an encapsulated active substance can have a substantially increased bioavailability than if it is taken alone. The sporopollenin exine surface possesses phenolic, alkane, alkene, ketone, lactone, and carboxylic acid groups. Therefore, it can be derivatized in a number of ways, which has given rise to applications in areas, such as solid supported for peptide synthesis, catalysis, and ion-exchange chromatography. Also, the presence of the phenolic groups on sporopollenin endows it with antioxidant activity

Statistical Behavior Of Domain Systems

We study the statistical behavior of two out of equilibrium systems. The first one is a quasi one-dimensional gas with two species of particles under the action of an external field which drives each species in opposite directions. The second one is a one-dimensional spin system with nearest neighbor interactions also under the influence of an external driving force. Both systems show a dynamical scaling with domain formation. The statistical behavior of these domains is compared with models based on the coalescing random walk and the interacting random walk. We find that the scaling domain size distribution of the gas and the spin systems is well fitted by the Wigner surmise, which lead us to explore a possible connection between these systems and the circular orthogonal ensemble of random matrices. However, the study of the correlation function of the domain edges, show that the statistical behavior of the domains in both gas and spin systems, is not completely well described by circular orthogonal ensemble, nor it is by other models proposed such as the coalescing random walk and the interacting random walk. Nevertheless, we find that a simple model of independent intervals describe more closely the statistical behavior of the domains formed in these systems.Comment: v2: minor change