11,665 research outputs found
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 -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
itself acquires a finite thermodynamic average
besides two-point Green's function 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
and 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 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 , where is the
natural shear stress on the ground (that is observed before constructing the
wind farm) and 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 .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 -
and -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 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 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
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