Semiclassical analysis of Wigner 3j3j-symbol

We analyze the asymptotics of the Wigner $3j$-symbol as a matrix element connecting eigenfunctions of a pair of integrable systems, obtained by lifting the problem of the addition of angular momenta into the space of Schwinger's oscillators. A novel element is the appearance of compact Lagrangian manifolds that are not tori, due to the fact that the observables defining the quantum states are noncommuting. These manifolds can be quantized by generalized Bohr-Sommerfeld rules and yield all the correct quantum numbers. The geometry of the classical angular momentum vectors emerges in a clear manner. Efficient methods for computing amplitude determinants in terms of Poisson brackets are developed and illustrated.Comment: 7 figure file

Semiclassical transmission across transition states

It is shown that the probability of quantum-mechanical transmission across a phase space bottleneck can be compactly approximated using an operator derived from a complex Poincar\'e return map. This result uniformly incorporates tunnelling effects with classically-allowed transmission and generalises a result previously derived for a classically small region of phase space.Comment: To appear in Nonlinearit

Thermodynamics of an ideal generalized gas:II Means of order α\alpha

The property that power means are monotonically increasing functions of their order is shown to be the basis of the second laws not only for processes involving heat conduction but also for processes involving deformations. In an $L$-potentail equilibration the final state will be one of maximum entropy, while in an entropy equilibrium the final state will be one of minimum $L$. A metric space is connected with the power means, and the distance between means of different order is related to the Carnot efficiency. In the ideal classical gas limit, the average change in the entropy is shown to be proportional to the difference between the Shannon and R\'enyi entropies for nonextensive systems that are multifractal in nature. The $L$-potential, like the internal energy, is a Schur convex function of the empirical temperature, which satisfies Jensen's inequality, and serves as a measure of the tendency to uniformity in processes involving pure thermal conduction.Comment: 8 page

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

Star products made (somewhat) easier

We develop an approach to the deformation quantization on the real plane with an arbitrary Poisson structure which based on Weyl symmetrically ordered operator products. By using a polydifferential representation for deformed coordinates $\hat x^j$ we are able to formulate a simple and effective iterative procedure which allowed us to calculate the fourth order star product (and may be extended to the fifth order at the expense of tedious but otherwise straightforward calculations). Modulo some cohomology issues which we do not consider here, the method gives an explicit and physics-friendly description of the star products.Comment: 20 pages, v2, v3: comments and references adde

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.Comment: 33 pages, 8 figure

Optimisation and control of a hydraulic power take-off unit for a wave energy converter in irregular waves

The optimisation of a wave energy converter hydraulic power take-off for sea states of varying wave amplitude, direction and frequency is a significant problem. Sub-optimal configuration can result in very inefficient energy conversion, so understanding the design trade-offs is key to the success of the technology. This work focuses on a generic point absorber type wave energy converter. Previous work by the authors has considered the optimisation of this device for regular waves to gain an understanding of the fundamental issues. This work extends the analysis to the more realistic case of irregular waves. Simulations are performed using an irregular wave input to predict how the power take-off will operate in real sea conditions. Work is also presented on a motor speed control strategy to maintain the maximum flow of electrical power to the grid, assuming the use of a doubly fed induction generator. Finally, the sizing of key components in the power take-off is considered in an attempt to maximise power take-off efficiency and generated power. </jats:p

Strategies for active tuning of Wave Energy Converter hydraulic power take-off mechanisms

This paper presents a study of practically implementable active tuning methodsfor a Wave Energy Converter (WEC) power take-off (PTO). It is distinguished from other simulation studies by the level of detail and realism in the inputs and the PTO model. Wave data recorded at the European Marine Energy Centre is used to derive input data for a detailed component level model of a hydraulic PTO. A methodology is presented for obtaining the optimum PTO damping co-efficient for a given sea state, and an open loop active tuning method is used to adjust the PTO parameters to achieve this optimum damping in service. The investigation shows that tuning of a hydraulic PTO to an estimated wave frequency is a difficult task due to sea state estimation errors and the complex dynamics of a realistic PTO. Preview knowledge of the future waves was shown to provide no meaningful improvement in energy capture for the device under investigation. Significantly, power gains observed in similar work using simplified linear PTO models or simplified sea states are not seen here, demonstrating that over-simplification of the PTO during the simulation phase of WEC development could lead to incorrect design decisions and subsequent additional delay and cost

Morphoanatomical characters for the recognition of two species of asclepias in the province of Santa Fe, Argentina

We disclose a morpho-anatomical study of Asclepias curassavica L. and Asclepias mellodora St.-Hil., collected in the Province of Santa Fe, Argentina. Whole plants of both species are commercialized for external and internal use due to its attributed therapeutic properties. For each entity we provide synonyms, folk names, morphological description, common and uncommon anatomical characteristics of roots, stems and leaves. These features were analyzed by optical and scanning electron microscopy. Photomicrographs are included in order to provide adequate differentiation between entitiesColegio de Farmacéuticos de la Provincia de Buenos Aire