Renormalization Group Analysis of a Quivering String Model of Posture Control

Scaling concepts and renormalization group (RG) methods are applied to a simple linear model of human posture control consisting of a trembling or quivering string subject to damping and restoring forces. The string is driven by uncorrelated white Gaussian noise intended to model the corrections of the physiological control system. We find that adding a weak quadratic nonlinearity to the posture control model opens up a rich and complicated phase space (representing the dynamics) with various non-trivial fixed points and basins of attraction. The transition from diffusive to saturated regimes of the linear model is understood as a crossover phenomenon, and the robustness of the linear model with respect to weak non-linearities is confirmed. Correlations in posture fluctuations are obtained in both the time and space domain. There is an attractive fixed point identified with falling. The scaling of the correlations in the front-back displacement, which can be measured in the laboratory, is predicted for both the large-separation (along the string) and long-time regimes of posture control.Comment: 20 pages, 13 figures, RevTeX, accepted for publication in PR

Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Search for the h_c meson in B^+- ->h_c K^+-

We report a search for the $h_c$ meson via the decay chain $B^{\pm}\to h_c K^{\pm}$, \etac \gamma with $\eta_c \to K_S^0 K^{\pm} \pi^{\mp}$ and $p\bar{p}$. No significant signals are observed. We obtain upper limits on the branching fractions for $B^{\pm} \to \eta_c\gamma K^{\pm}$ in bins of the $\eta_c\gamma$ invariant mass. The results are based on an analysis of 253 fb$^{-1}$ of data collected by the Belle detector at the KEKB $e^+e^-$ collider.Comment: 12 pages, 6 figures, submitted to Phys. Rev.

Non-isothermal model for the direct isotropic/smectic-A liquid crystalline transition

An extension to a high-order model for the direct isotropic/smectic-A liquid crystalline phase transition was derived to take into account thermal effects including anisotropic thermal diffusion and latent heat of phase-ordering. Multi-scale multi-transport simulations of the non-isothermal model were compared to isothermal simulation, showing that the presented model extension corrects the standard Landau-de Gennes prediction from constant growth to diffusion-limited growth, under shallow quench/undercooling conditions. Non-isothermal simulations, where meta-stable nematic pre-ordering precedes smectic-A growth, were also conducted and novel non-monotonic phase-transformation kinetics observed.Comment: First revision: 20 pages, 7 figure

Oriented Matroids -- Combinatorial Structures Underlying Loop Quantum Gravity

We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence vertices of a graph in 3-dimensional Riemannian space, and can be represented by sign strings containing relative orientations of embedded edges. We demonstrate that these signature factors are a special representation of the general mathematical concept of an oriented matroid. Moreover, we show that oriented matroids can also be used to describe the topology (connectedness) of directed graphs. Hence the mathematical methods developed for oriented matroids can be applied to the difficult combinatorics of embedded graphs underlying the construction of LQG. As a first application we revisit the analysis of [4-5], and find that enumeration of all possible sign configurations used there is equivalent to enumerating all realizable oriented matroids of rank 3, and thus can be greatly simplified. We find that for 7-valent vertices having no coplanar triples of edge tangents, the smallest non-zero eigenvalue of the volume spectrum does not grow as one increases the maximum spin \jmax at the vertex, for any orientation of the edge tangents. This indicates that, in contrast to the area operator, considering large \jmax does not necessarily imply large volume eigenvalues. In addition we give an outlook to possible starting points for rewriting the combinatorics of LQG in terms of oriented matroids.Comment: 43 pages, 26 figures, LaTeX. Version published in CQG. Typos corrected, presentation slightly extende