Hamiltonian structure of Hamiltonian chaos

From a kinematical point of view, the geometrical information of hamiltonian chaos is given by the (un)stable directions, while the dynamical information is given by the Lyapunov exponents. The finite time Lyapunov exponents are of particular importance in physics. The spatial variations of the finite time Lyapunov exponent and its associated (un)stable direction are related. Both of them are found to be determined by a new hamiltonian of same number of degrees of freedom as the original one. This new hamiltonian defines a flow field with characteristically chaotic trajectories. The direction and the magnitude of the phase flow field give the (un)stable direction and the finite time Lyapunov exponent of the original hamiltonian. Our analysis was based on a $1{1\over 2}$ degree of freedom hamiltonian system

High-pT pi0 Production with Respect to the Reaction Plane Using the PHENIX Detector at RHIC

The origin of the azimuthal anisotropy in particle yields at high pT (pT > 5 GeV/c) in RHIC collisions remains an intriguing puzzle. Traditional flow and parton energy loss models have failed to completely explain the large v2 observed at high pT. Measurement of this parameter at high pT will help to gain an understanding of the interplay between flow, recombination and energy loss, and the role they play in the transition from soft to hard physics. Neutral mesons measured in the PHENIX experiment provide an ideal observable for such studies. We present recent measurements of \piz yields with respect to the reaction plane, and discuss the impact current models have on our understanding of these mechanisms.Comment: Contribnution to the proceedings of Hot Quarks 2006, 15-20 May 2006, Villasimius, Sardini

Commentary CeNTech:nanotechnological research and application

The Centre for Nanotechnology (CeNTech), Münster, Germany, represents one of the first dedicated nanotechnology centres in Germany providing space and infrastructure for application, research and development in the area of nanotechnology. It offers an optimised environment for entrepreneurs to fur-ther develop their research ideas into marketable products as well as excellent conditions for application ori-ented research and further education. Three years after the opening of the CeNTech building most of the ex-pectations are fulfilled. The article describes the general aspects of the CeNTech concept and reviews its de-velopment in the first years

Twenty-First Century Climate Change and Submerged Aquatic Vegetation in a Temperate Estuary: The Case of Chesapeake Bay

Introduction: The Chesapeake Bay was once renowned for expansive meadows of submerged aquatic vegetation (SAV). However, only 10% of the original meadows survive. Future restoration effortswill be complicated by accelerating climate change, including physiological stressors such as a predicted mean temperature increase of 2-6°C and a 50-160% increase in CO2 concentrations. Outcomes: As the Chesapeake Bay begins to exhibit characteristics of a subtropical estuary, summer heat waves will become more frequent and severe. Warming alone would eventually eliminate eelgrass (Zostera marina) from the region. It will favor native heat-tolerant species such as widgeon grass (Ruppia maritima) while facilitating colonization by non-native seagrasses (e.g., Halodule spp.). Intensifying human activity will also fuel coastal zone acidification and the resulting high CO2/low pH conditions may benefit SAV via a CO2 fertilization effect. . Discussion: Acidification is known to offset the effects of thermal stress and may have similar effects in estuaries, assuming water clarity is sufficient to support CO2-stimulated photosynthesis and plants are not overgrown by epiphytes. However, coastal zone acidification is variable, driven mostly by local biological processes that may or may not always counterbalance the effects of regional warming. This precarious equipoise between two forces - thermal stress and acidification - will be critically important because it may ultimately determine the fate of cool-water plants such as Zostera marina in the Chesapeake Bay. Conclusion: The combined impacts of warming, coastal zone acidification, water clarity, and overgrowth of competing algae will determine the fate of SAV communities in rapidly changing temperate estuaries

Covariant derivative expansion of fermionic effective action at high temperatures

We derive the fermionic contribution to the 1-loop effective action for A_4 and A_i fields at high temperatures, assuming that gluon fields are slowly varying but allowing for an arbitrary amplitude of A_4.Comment: RevTex 4, 11 pages, 3 figures. Version 2: Typos corrected; magnetic fields restricted to parallel sector. Version accepted for publication in PR

Covariant derivative expansion of Yang-Mills effective action at high temperatures

Integrating out fast varying quantum fluctuations about Yang--Mills fields A_i and A_4, we arrive at the effective action for those fields at high temperatures. Assuming that the fields A_i and A_4 are slowly varying but that the amplitude of A_4 is arbitrary, we find a non-trivial effective gauge invariant action both in the electric and magnetic sectors. Our results can be used for studying correlation functions at high temperatures beyond the dimensional reduction approximation, as well as for estimating quantum weights of classical static configurations such as dyons.Comment: Minor changes. References added. Paper accepted for publication in Phys.Rev.

Hamiltonization of Nonholonomic Systems and the Inverse Problem of the Calculus of Variations

We introduce a method which allows one to recover the equations of motion of a class of nonholonomic systems by finding instead an unconstrained Hamiltonian system on the full phase space, and to restrict the resulting canonical equations to an appropriate submanifold of phase space. We focus first on the Lagrangian picture of the method and deduce the corresponding Hamiltonian from the Legendre transformation. We illustrate the method with several examples and we discuss its relationship to the Pontryagin maximum principle.Comment: 23 pages, accepted for publication in Rep. Math. Phy

Moving constraints as stabilizing controls in classical mechanics

The paper analyzes a Lagrangian system which is controlled by directly assigning some of the coordinates as functions of time, by means of frictionless constraints. In a natural system of coordinates, the equations of motions contain terms which are linear or quadratic w.r.t.time derivatives of the control functions. After reviewing the basic equations, we explain the significance of the quadratic terms, related to geodesics orthogonal to a given foliation. We then study the problem of stabilization of the system to a given point, by means of oscillating controls. This problem is first reduced to the weak stability for a related convex-valued differential inclusion, then studied by Lyapunov functions methods. In the last sections, we illustrate the results by means of various mechanical examples.Comment: 52 pages, 4 figure

Bounds and optimisation of orbital angular momentum bandwidths within parametric down-conversion systems

The measurement of high-dimensional entangled states of orbital angular momentum prepared by spontaneous parametric down-conversion can be considered in two separate stages: a generation stage and a detection stage. Given a certain number of generated modes, the number of measured modes is determined by the measurement apparatus. We derive a simple relationship between the generation and detection parameters and the number of measured entangled modes.Comment: 6 pages, 4 figure