Dual Isomonodromic Deformations and Moment Maps to Loop Algebras

The Hamiltonian structure of the monodromy preserving deformation equations of Jimbo {\it et al } is explained in terms of parameter dependent pairs of moment maps from a symplectic vector space to the dual spaces of two different loop algebras. The nonautonomous Hamiltonian systems generating the deformations are obtained by pulling back spectral invariants on Poisson subspaces consisting of elements that are rational in the loop parameter and identifying the deformation parameters with those determining the moment maps. This construction is shown to lead to ``dual'' pairs of matrix differential operators whose monodromy is preserved under the same family of deformations. As illustrative examples, involving discrete and continuous reductions, a higher rank generalization of the Hamiltonian equations governing the correlation functions for an impenetrable Bose gas is obtained, as well as dual pairs of isomonodromy representations for the equations of the Painleve transcendents $P_{V}$ and $P_{VI}$.Comment: preprint CRM-1844 (1993), 28 pgs. (Corrected date and abstract.

A utility survey and market assessment on repowering in the electric power industry

Section 1 of this report provides a background about the DOE High Performance Power Systems (HIPPS) program. There are two kinds of HIPPS cycles under development. One team is led by the Foster Wheeler Development Corporation, the other team is led by the United Technologies Research Center. These cycles are described. Section 2 summarizes the feedback from the survey of the repowering needs of ten electric utility companies. The survey verified that the utility company planners favor a repowering for a first-of-a-kind demonstration of a new technology rather than an all-new-site application. These planners list the major factor in considering a unit as a repowering candidate as plant age: they identify plants built between 1955 and 1965 as the most likely candidates. Other important factors include the following: the need to reduce operating costs; the need to perform major maintenance/replacement of the boiler; and the need to reduce emissions. Section 3 reports the results of the market assessment. Using the size and age preferences identified in the survey, a market assessment was conducted (with the aid of a power plant data base) to estimate the number and characteristics of US generating units which constitute the current, primary potential market for coal-based repowering. Nearly 250 units in the US meet the criteria determined to be the potential repowering market

Middle Convolution and Harnad Duality

We interpret the additive middle convolution operation in terms of the Harnad duality, and as an application, generalize the operation to have a multi-parameter and act on irregular singular systems.Comment: 50 pages; v2: Submitted version once revised according to referees' comment

Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential

The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an elliptic function potential models a quasi-one-dimensional repulsive dilute gas Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. All trivial-phase stable solutions are deformations of the ground state of the linear Schr\"odinger equation. Our results show that a large number of condensed atoms is sufficient to form a stable, periodic condensate. Physically, this implies stability of states near the Thomas-Fermi limit.Comment: 12 pages, 17 figure

Surface Effects in Magnetic Microtraps

We have investigated Bose-Einstein condensates and ultra cold atoms in the vicinity of a surface of a magnetic microtrap. The atoms are prepared along copper conductors at distances to the surface between 300 um and 20 um. In this range, the lifetime decreases from 20 s to 0.7 s showing a linear dependence on the distance to the surface. The atoms manifest a weak thermal coupling to the surface, with measured heating rates remaining below 500 nK/s. In addition, we observe a periodic fragmentation of the condensate and thermal clouds when the surface is approached.Comment: 4 pages, 4 figures; v2: corrected references; v3: final versio

Couplings of light I=0 scalar mesons to simple operators in the complex plane

The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the K\Kbar threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omn\`es dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.Comment: 31 pages, 5 figure

Comparison of different stomatal conductance algorithms for ozone flux modelling

A multiplicative and a semi-mechanistic, BWB-type [Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatalconductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggens, J. (Ed.), Progress in Photosynthesis Research, vol. IV. Martinus Nijhoff, Dordrecht, pp. 221–224.] algorithm for calculating stomatalconductance (gs) at the leaf level have been parameterised for two crop and two tree species to test their use in regional scale ozone deposition modelling. The algorithms were tested against measured, site-specific data for durum wheat, grapevine, beech and birch of different European provenances. A direct comparison of both algorithms showed a similar performance in predicting hourly means and daily time-courses of gs, whereas the multiplicative algorithm outperformed the BWB-type algorithm in modelling seasonal time-courses due to the inclusion of a phenology function. The re-parameterisation of the algorithms for local conditions in order to validate ozone deposition modelling on a European scale reveals the higher input requirements of the BWB-type algorithm as compared to the multiplicative algorithm because of the need of the former to model net photosynthesis (An

Radiative decays with light scalar mesons and singlet-octet mixing in ChPT

We study different types of radiative decays involving f0(980) and a0(980) mesons within a unified ChPT-based approach at one-loop level. Light scalar resonances which are seen in pi pi, pi eta, K K-bar channels of phi(1020) radiative decays and in J/psi decays are responsible for key questions of low-energy dynamics in the strong interaction sector, and decays phi(1020) -> gamma a0(980), phi(1020) -> gamma f0(980), a0(980) -> gamma gamma, f0(980) -> gamma gamma are of interest for current experimental programs in Juelich, Frascati and Novosibirsk. From theoretical point of view it is important to verify whether light scalar mesons are members of some flavor octet or nonet. We find a value of mixing angle dictated by consistency with experiment and coupling structures of ChPT Lagrangian. Decay widths f0(980)/a0(980) -> gamma rho(770)/omega(782), which are not studied experimentally yet, are predicted. We also obtain several relations between widths, which hold independently of coupling constants and represent a fingerprint of the model.Comment: 18 pages, 8 figures; misprints in text and tables corrected, discussion extended, references added; version accepted for publication in Eur.Phys.J.

f0(980) meson as a K bar K molecule in a phenomenological Lagrangian approach

We discuss a possible interpretation of the f0(980) meson as a hadronic molecule - a bound state of K and bar K mesons. Using a phenomenological Lagrangian approach we calculate the strong f0(980) to pi pi and electromagnetic f0(980) to gamma gamma decays. The compositeness condition provides a self-consistent method to determine the coupling constant between f0 and its constituents, K and bar K. Form factors governing the decays of the f0(980) are calculated by evaluating the kaon loop integrals. The predicted f0(980) to pi pi and f0(980) to gamma gamma decay widths are in good agreement with available data and results of other theoretical approaches.Comment: 21 pages, 11 figures, revised version accepted for publication in Eur. Phys. J.

On the role of the magnetic dipolar interaction in cold and ultracold collisions: Numerical and analytical results for NH(3Σ−^3\Sigma^-) + NH(3Σ−^3\Sigma^-)

We present a detailed analysis of the role of the magnetic dipole-dipole interaction in cold and ultracold collisions. We focus on collisions between magnetically trapped NH molecules, but the theory is general for any two paramagnetic species for which the electronic spin and its space-fixed projection are (approximately) good quantum numbers. It is shown that dipolar spin relaxation is directly associated with magnetic-dipole induced avoided crossings that occur between different adiabatic potential curves. For a given collision energy and magnetic field strength, the cross-section contributions from different scattering channels depend strongly on whether or not the corresponding avoided crossings are energetically accessible. We find that the crossings become lower in energy as the magnetic field decreases, so that higher partial-wave scattering becomes increasingly important \textit{below} a certain magnetic field strength. In addition, we derive analytical cross-section expressions for dipolar spin relaxation based on the Born approximation and distorted-wave Born approximation. The validity regions of these analytical expressions are determined by comparison with the NH + NH cross sections obtained from full coupled-channel calculations. We find that the Born approximation is accurate over a wide range of energies and field strengths, but breaks down at high energies and high magnetic fields. The analytical distorted-wave Born approximation gives more accurate results in the case of s-wave scattering, but shows some significant discrepancies for the higher partial-wave channels. We thus conclude that the Born approximation gives generally more meaningful results than the distorted-wave Born approximation at the collision energies and fields considered in this work.Comment: Accepted by Eur. Phys. J. D for publication in Special Issue on Cold Quantum Matter - Achievements and Prospects (2011