Investigation into the role of the Laurent property in integrability

We study the Laurent property for autonomous and nonautonomous discrete equations. First we show, without relying on the caterpillar lemma, the Laurent property for the Hirota-Miwa and the discrete BKP equations. Next we introduce the notion of reductions and gauge transformations for discrete bilinear equations and we prove that these preserve the Laurent property. Using these two techniques, we obtain the explicit condition on the coefficients of a nonautonomous discrete bilinear equation for it to possess the Laurent property. Finally we study the denominators of the iterates of an equation with the Laurent property and we show that any reduction to a mapping on a one-dimensional lattice of a nonautonomous Hirota-Miwa equation or discrete BKP equation, with the Laurent property, has zero algebraic entropy

Entropy in Nonequilibrium Statistical Mechanics

Entropy in nonequilibrium statistical mechanics is investigated theoretically so as to extend the well-established equilibrium framework to open nonequilibrium systems. We first derive a microscopic expression of nonequilibrium entropy for an assembly of identical bosons/fermions interacting via a two-body potential. This is performed by starting from the Dyson equation on the Keldysh contour and following closely the procedure of Ivanov, Knoll and Voskresensky [Nucl. Phys. A {\bf 672} (2000) 313]. The obtained expression is identical in form with an exact expression of equilibrium entropy and obeys an equation of motion which satisfies the $H$-theorem in a limiting case. Thus, entropy can be defined unambiguously in nonequilibrium systems so as to embrace equilibrium statistical mechanics. This expression, however, differs from the one obtained by Ivanov {\em et al}., and we show explicitly that their ``memory corrections'' are not necessary. Based on our expression of nonequilibrium entropy, we then propose the following principle of maximum entropy for nonequilibrium steady states: ``The state which is realized most probably among possible steady states without time evolution is the one that makes entropy maximum as a function of mechanical variables, such as the total particle number, energy, momentum, energy flux, etc.'' During the course of the study, we also develop a compact real-time perturbation expansion in terms of the matrix Keldysh Green's function.Comment: 20 pages, 5 figures; addendum included in the revised versio

Pathfinder flight of the Polarized Gamma-ray Observer (PoGOLite) in 2013

The Polarized Gamma-ray Observer (PoGOLite) is a balloon-borne instrument that can measure polarization in the energy range 25--240 keV. The instrument adopts an array of well-type "phoswich" detectors in order to suppress backgrounds. Based on the anisotropy of Compton scattering angles resulting from polarized gamma-rays, the polarization of the observed source can be reconstructed. During July 12-26 of 2013, a successful near-circumpolar pathfinder flight was conducted from Esrange, Sweden, to Norilsk, Russia. During this two-week flight, several observations of the Crab were conducted. Here, we present the PoGOLite instrument and summarize the 2013 flight.Comment: 2014 Fermi Symposium proceedings - eConf C14102.

Effective action for Bose-Einstein condensates

We clarify basic properties of an effective action (i.e., self-consistent perturbation expansion) for interacting Bose-Einstein condensates, where field $\psi$ itself acquires a finite thermodynamic average $\langle \psi\rangle$ besides two-point Green's function $\hat G$ to form an off-diagonal long-range order. It is shown that the action can be expressed concisely order by order in terms of the interaction vertex and a special combination of $\langle\psi\rangle$ and $\hat G$ so as to satisfy both Noether's theorem and Goldstone's theorem (I) corresponding to the first proof. The self-energy is predicted to have a one-particle-reducible structure due to $\langle \psi\rangle\neq 0$ to transform the Bogoliubov mode into a bubbling mode with a substantial decay rate.Comment: 9 pages, 10 figure

Generalisation of the two-scale momentum theory for coupled wind turbine/farm optimisation

An extended theoretical approach is proposed to predict the average power of wind turbines in a large finite-size wind farm. The approach is based on the two-scale momentum theory proposed recently for the modelling of ideal very large wind farms, but the theory is now generalised by introducing the effect of additional pressure difference induced by the farm between the upstream and downstream sides of the farm, making the approach applicable to real wind farms that are large but not as large as the size of the relevant atmospheric system driving the flow over the farm. To validate the generalised theoretical model, 3D Reynolds-averaged Navier-Stokes simulations of boundary layer flow over a large array (25 x 25) of actuator (drag) discs are conducted at eight different conditions. The results suggest that the generalised model could be embedded in a regional-scale atmospheric model to predict the average power of a given wind farm effectively. This approach may also be combined with the blade element momentum (BEM) theory for coupled wind turbine/farm optimisation.Comment: 25th National Symposium on Wind Engineering, Tokyo, Japan, 3-5 December 2018 (accepted for publication, 6 pages, 6 figures

Limits to the power density of very large wind farms

A simple analysis is presented concerning an upper limit of the power density (power per unit land area) of a very large wind farm located at the bottom of a fully developed boundary layer. The analysis suggests that the limit of the power density is about 0.38 times $\tau_{w0}U_{F0}$, where $\tau_{w0}$ is the natural shear stress on the ground (that is observed before constructing the wind farm) and $U_{F0}$ is the natural or undisturbed wind speed averaged across the height of the farm to be constructed. Importantly, this implies that the maximum extractable power from such a very large wind farm will not be proportional to the cubic of the wind speed at the farm height, or even the farm height itself, but be proportional to $U_{F0}$.Comment: Author's original draft submitted to Wind Energy (7 pages, 2 figures

Detailed HBT measurements with respect to the event plane and collision energy in Au+Au collisions at PHENIX

The azimuthal dependence of 3D HBT radii relative to the event plane gives us information about the source shape at freeze-out. It also provides information on the system's evolution by comparing it to the initial source shape. In recent studies, higher harmonic event planes and flow have been measured at RHIC and the LHC, which result primarily from spatial fluctuations of the initial density across the collision area. If the shape caused by initial fluctuations still exists at freeze-out, the HBT measurement relative to higher order event plane may show these features. We present recent results of azimuthal HBT measurements relative to $2^{nd}$- and $3^{rd}$-order event planes in Au+Au 200 GeV collisions with the PHENIX experiment. Recent HBT measurements at lower energies will be also shown and compared with the 200 GeV result.Comment: 4 pages, 4 figures, proceedings of Quark Matter 2012 at Washington D.C., US

Final source eccentricity measured by HBT interferometry with the event shape selection

Azimuthal angle dependence of the pion source radii has been measured applying the event shape engineering technique at the PHENIX experiment. When events with higher magnitude of second-order flow vector are selected, the oscillation of the source radii is enhanced as well as $v_2$ which leads to the enhancement of the measured final source eccentricity. The event twist effect in the spatial source distribution in the final state has been also explored with AMPT model. Results indicate a possible twisted source due to the initial longitudinal fluctuations.Comment: 4 pages, 4 figures, Proceedings of Hot Quarks 2014 in Las Negras, Spain, Sep. 21-28, 201

3/2-Body Correlations and Coherence in Bose-Einstein Condensates

We construct a variational wave function for the ground state of weakly interacting bosons that gives a lower energy than the mean-field Girardeau-Arnowitt (or Hartree-Fock-Bogoliubov) theory. This improvement is brought about by incorporating the dynamical 3/2-body processes where one of two colliding non-condensed particles drops into the condensate and vice versa. The processes are also shown to transform the one-particle excitation spectrum into a bubbling mode with a finite lifetime even in the long-wavelength limit. These 3/2-body processes, which give rise to dynamical exchange of particles between the non-condensate reservoir and condensate absent in ideal gases, are identified as a key mechanism for realizing and sustaining macroscopic coherence in Bose-Einstein condensates.Comment: 12 pages, 7 figure

Decomposition of tensor products of Demazure crystals

A Demazure crystal is the basis at $q=0$ of a Demazure module. Demazure crystals play an important role in Schubert calculus because the character of a Demazure crystal in type A is identical to a key polynomial, which is closely related to Schubert polynomials. In this paper, we study tensor products of Demazure crystals. Each connected component of a tensor product of Demazure crystals need not be isomorphic to some Demazure crystal. We provide a necessary and sufficient condition for every connected component of a tensor product to be isomorphic to some Demazure crystal. Also, we obtain the explicit formula for connected components. As applications, we study the positivity for structure constants of products of key polynomials, and we obtain an equation of crystals, which is an analog of the Leibniz rule for Demazure operators.Comment: 32 page