Symplectic structures associated to Lie-Poisson groups

The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a Lie group are considered. For the natural Poisson brackets the symplectic leaves in these manifolds are classified and the corresponding symplectic forms are described. Thus the construction of the Kirillov symplectic form is generalized for Lie-Poisson groups.Comment: 30 page

Beetroot Juice Does Not Enhance Altitude Running Performance in Well-Trained Athletes

We hypothesized that acute dietary nitrate (NO3-) provided as concentrated beetroot juice supplement would improve endurance running performance of well-trained runners in normobaric hypoxia. Ten male runners (mean (SD): sea level V�O2max 66 (7) mL.kg^-1.min^-1, 10 km personal best 36 (2) min) completed incremental exercise to exhaustion at 4000 m and a 10 km treadmill time trial at 2500 m simulated altitude on separate days, after supplementation with ~7 mmol NO3- and a placebo, 2.5 h before exercise. Oxygen cost, arterial oxygen saturation, heart rate and ratings of perceived exertion (RPE) were determined during the incremental exercise test. Differences between treatments were determined using means [95% confidence intervals], paired sample t-tests and a probability of individual response analysis. NO3- supplementation increased plasma [nitrite] (NO3-, 473 (226) nM vs. placebo, 61 (37) nM, P < 0.001) but did not alter time to exhaustion during the incremental test (NO3-, 402 (80) s vs. placebo 393 (62) s, P = 0.5) or time to complete the 10 km time trial (NO3-, 2862 (233) s vs. placebo, 2874 (265) s, P = 0.6). Further, no practically meaningful beneficial effect on time trial performance was observed as the 11 [-60 to 38] s improvement was less than the a priori determined minimum important difference (51 s), and only three runners experienced a ´likely, probable´ performance improvement. NO3- also did not alter oxygen cost, arterial oxygen saturation, heart rate or RPE. Acute dietary NO3- supplementation did not consistently enhance running performance of well-trained athletes in normobaric hypoxia

Symplectic structure of the moduli space of flat connections on a Riemann surface

We consider canonical symplectic structure on the moduli space of flat {\g}-connections on a Riemann surface of genus $g$ with $n$ marked points. For {\g} being a semisimple Lie algebra we obtain an explicit efficient formula for this symplectic form and prove that it may be represented as a sum of $n$ copies of Kirillov symplectic form on the orbit of dressing transformations in the Poisson-Lie group $G^{*}$ and $g$ copies of the symplectic structure on the Heisenberg double of the Poisson-Lie group $G$ (the pair ($G,G^{*}$) corresponds to the Lie algebra {\g}).Comment: 20 page

Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

The role of discharge variability in determining alluvial stratigraphy

We illustrate the potential for using physics-based modeling to link alluvial stratigraphy to large river morphology and dynamics. Model simulations, validated using ground penetrating radar data from the Río Paraná, Argentina, demonstrate a strong relationship between bar-scale set thickness and channel depth, which applies across a wide range of river patterns and bar types. We show that hydrologic regime, indexed by discharge variability and flood duration, exerts a first-order influence on morphodynamics and hence bar set thickness, and that planform morphology alone may be a misleading variable for interpreting deposits. Indeed, our results illustrate that rivers evolving under contrasting hydrologic regimes may have very similar morphology, yet be characterized by marked differences in stratigraphy. This realization represents an important limitation on the application of established theory that links river topography to alluvial deposits, and highlights the need to obtain field evidence of discharge variability when developing paleoenvironmental reconstructions. Model simulations demonstrate the potential for deriving such evidence using metrics of paleocurrent variance

Differential Geometry applied to Acoustics : Non Linear Propagation in Reissner Beams

Although acoustics is one of the disciplines of mechanics, its "geometrization" is still limited to a few areas. As shown in the work on nonlinear propagation in Reissner beams, it seems that an interpretation of the theories of acoustics through the concepts of differential geometry can help to address the non-linear phenomena in their intrinsic qualities. This results in a field of research aimed at establishing and solving dynamic models purged of any artificial nonlinearity by taking advantage of symmetry properties underlying the use of Lie groups. The geometric constructions needed for reduction are presented in the context of the "covariant" approach.Comment: Submitted to GSI2013 - Geometric Science of Informatio

Supergauge interactions and electroweak baryogenesis

We present a complete treatment of the diffusion processes for supersymmetric electroweak baryogenesis that characterizes transport dynamics ahead of the phase transition bubble wall within the symmetric phase. In particular, we generalize existing approaches to distinguish between chemical potentials of particles and their superpartners. This allows us to test the assumption of superequilibrium (equal chemical potentials for particles and sparticles) that has usually been made in earlier studies. We show that in the Minimal Supersymmetric Standard Model, superequilibrium is generically maintained -- even in the absence of fast supergauge interactions -- due to the presence of Yukawa interactions. We provide both analytic arguments as well as illustrative numerical examples. We also extend the latter to regions where analytical approximations are not available since down-type Yukawa couplings or supergauge interactions only incompletely equilibrate. We further comment on cases of broken superequilibrium wherein a heavy superpartner decouples from the electroweak plasma, causing a kinematic bottleneck in the chain of equilibrating reactions. Such situations may be relevant for baryogenesis within extensions of the MSSM. We also provide a compendium of inputs required to characterize the symmetric phase transport dynamics.Comment: 49 pages, 9 figure

QUANTIZATION OF A CLASS OF PIECEWISE AFFINE TRANSFORMATIONS ON THE TORUS

We present a unified framework for the quantization of a family of discrete dynamical systems of varying degrees of "chaoticity". The systems to be quantized are piecewise affine maps on the two-torus, viewed as phase space, and include the automorphisms, translations and skew translations. We then treat some discontinuous transformations such as the Baker map and the sawtooth-like maps. Our approach extends some ideas from geometric quantization and it is both conceptually and calculationally simple.Comment: no. 28 pages in AMSTE

The leading Ruelle resonances of chaotic maps

The leading Ruelle resonances of typical chaotic maps, the perturbed cat map and the standard map, are calculated by variation. It is found that, excluding the resonance associated with the invariant density, the next subleading resonances are, approximately, the roots of the equation $z^4=\gamma$, where $\gamma$ is a positive number which characterizes the amount of stochasticity of the map. The results are verified by numerical computations, and the implications to the form factor of the corresponding quantum maps are discussed.Comment: 5 pages, 4 figures included. To appear in Phys. Rev.

Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fail