New developments in geometric mechanics

We review the concept of a graded bundle, which is a generalisation of a vector bundle, its linearisation, and a double structure of this kind. We then present applications of these structures in geometric mechanics including systems with higher order Lagrangian and the Plateau problem.Comment: 16 pages, conference proceedings "Geometry of Jets and Fields" (Bedlewo, 10-16 May, 2015

Temperature dependent fluctuations in the two-dimensional XY model

We present a detailed investigation of the probability density function (PDF) of order parameter fluctuations in the finite two-dimensional XY (2dXY) model. In the low temperature critical phase of this model, the PDF approaches a universal non-Gaussian limit distribution in the limit T-->0. Our analysis resolves the question of temperature dependence of the PDF in this regime, for which conflicting results have been reported. We show analytically that a weak temperature dependence results from the inclusion of multiple loop graphs in a previously-derived graphical expansion. This is confirmed by numerical simulations on two controlled approximations to the 2dXY model: the Harmonic and ``Harmonic XY'' models. The Harmonic model has no Kosterlitz-Thouless-Berezinskii (KTB) transition and the PDF becomes progressively less skewed with increasing temperature until it closely approximates a Gaussian function above T ~ 4\pi. Near to that temperature we find some evidence of a phase transition, although our observations appear to exclude a thermodynamic singularity.Comment: 15 pages, 5 figures and 1 tabl

Relevance of soft modes for order parameter fluctuations in the Two-Dimensional XY model

We analyse the spin wave approximation for the 2D-XY model, directly in reciprocal space. In this limit the model is diagonal and the normal modes are statistically independent. Despite this simplicity non-trivial critical properties are observed and exploited. We confirm that the observed asymmetry for the probability density function for order parameter fluctuations comes from the divergence of the mode amplitudes across the Brillouin zone. We show that the asymmetry is a many body effect despite the importance played by the zone centre. The precise form of the function is dependent on the details of the Gibbs measure, giving weight to the idea that an effective Gibbs measure should exist in non-equilibrium systems, if a similar distribution is observed.Comment: 12 pages, 9 figure

Direct Improvement of Hamiltonian Lattice Gauge Theory

We demonstrate that a direct approach to improving Hamiltonian lattice gauge theory is possible. Our approach is to correct errors in the Kogut-Susskind Hamiltonian by incorporating additional gauge invariant terms. The coefficients of these terms are chosen so that the order $a^2$ classical errors vanish. We conclude with a brief discussion of tadpole improvement in Hamiltonian lattice gauge theory.Comment: 9 page

Generalised extreme value statistics and sum of correlated variables

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and (generally) correlated random variables with a sum distributed according to one of the three (k-dependent) asymptotic distributions of extreme value statistics, namely the Gumbel, Frechet and Weibull distributions. These classes, as well as the limit distributions, are naturally extended to real values of k, thus providing a clear interpretation to the onset of Gumbel distributions with non-integer index k in the statistics of global observables. This is one of the very few known generalisations of the central limit theorem to non-independent random variables. Finally, in the context of a simple physical model, we relate the index k to the ratio of the correlation length to the system size, which remains finite in strongly correlated systems.Comment: To appear in J.Phys.

Project Cerberus: Flyby Mission to Pluto

The goal of the Cerberus Project was to design a feasible and cost-effective unmanned flyby mission to Pluto. The requirements in the request for proposal for an unmanned probe to Pluto are presented and were met. The design stresses proven technology that will avoid show stoppers which could halt mission progress. Cerberus also utilizes the latest advances in the spacecraft industry to meet the stringent demands of the mission. The topics covered include: (1) mission management, planning, and costing; (2) structures; (3) power and propulsion; (4) attitude, articulation, and control; (5) command, control, and communication; and (6) scientific instrumentation

Galactic bulge formation as a maximum intensity starburst

Properties of normal galactic star formation, including the density dependence, threshold density, turbulent scaling relations, and clustering properties, are applied to the formation of galactic bulges. One important difference is that the bulge potential well is too deep to have allowed self-regulation or blow-out by the pressures from young stars, unlike galactic disks or dwarf galaxies. As a result, bulge formation should have been at the maximum rate, which is such that most of the gas would get converted into stars in only a few dynamical time scales, or ~10^8 years. The gas accretion phase can be longer than this, but once the critical density is reached, which depends primarily on the total virial density from dark matter, the formation of stars in the bulge should have been extremely rapid. Such three-dimensional star formation should also have formed many clusters, like normal disk star formation today. Some of these clusters may have survived as old globulars, but most got dispersed, although they might still be observable as concentrated streams in phase space.Comment: 10 pages, 1 figure, scheduled for ApJ, vol. 517, May 20, 199

Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?

Critical finite-size scaling functions for the order parameter distribution of the two and three dimensional Ising model are investigated. Within a recently introduced classification theory of phase transitions, the universal part of the critical finite-size scaling functions has been derived by employing a scaling limit that differs from the traditional finite-size scaling limit. In this paper the analytical predictions are compared with Monte Carlo simulations. We find good agreement between the analytical expression and the simulation results. The agreement is consistent with the possibility that the functional form of the critical finite-size scaling function for the order parameter distribution is determined uniquely by only a few universal parameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as uuencoded gzipped tar file. To appear in J. Phys. A

K-Band Galaxy Counts in the South Galactic Pole Region

We present new K-band galaxy number counts from K=13 to 20.5 obtained from $K'$-band surveys in the south galactic pole region, which cover 180.8 arcmin$^2$ to a limiting magnitude of K=19, and 2.21 arcmin$^2$ to K=21. These are currently the most precise K-band galaxy counts at $17.5<K<19.0$ because the area of coverage is largest among the existing surveys for this magnitude range. The completeness and photometry corrections are estimated from the recovery of simulated galaxy and stellar profiles added to the obtained field image. Many simulations were carried out to construct a probability matrix which corrects the galaxy counts at the faint-end magnitudes of the surveys so the corrected counts can be compared with other observations. The K-band star counts in the south galactic pole region to $K=17.25$ are also presented for use to constrain the vertical structure of the Galaxy.Comment: accepted for publication in ApJ. 26 pages with 4 figures, and 2 plates are not included. All documents and figures can be retrieved from http://merope.mtk.nao.ac.jp/~minezaki/mine_paper.htm