Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Microcanonical temperature for a classical field: application to Bose-Einstein condensation

We show that the projected Gross-Pitaevskii equation (PGPE) can be mapped exactly onto Hamilton's equations of motion for classical position and momentum variables. Making use of this mapping, we adapt techniques developed in statistical mechanics to calculate the temperature and chemical potential of a classical Bose field in the microcanonical ensemble. We apply the method to simulations of the PGPE, which can be used to represent the highly occupied modes of Bose condensed gases at finite temperature. The method is rigorous, valid beyond the realms of perturbation theory, and agrees with an earlier method of temperature measurement for the same system. Using this method we show that the critical temperature for condensation in a homogeneous Bose gas on a lattice with a UV cutoff increases with the interaction strength. We discuss how to determine the temperature shift for the Bose gas in the continuum limit using this type of calculation, and obtain a result in agreement with more sophisticated Monte Carlo simulations. We also consider the behaviour of the specific heat.Comment: v1: 9 pages, 5 figures, revtex 4. v2: additional text in response to referee's comments, now 11 pages, to appear in Phys. Rev.

Nurses\u27 Alumnae Association Bulletin - Volume 2 Number 3

The Jefferson Nurse Letter from the President Delegates to Biennial Convention Attention Blood Transfusion - Plasma Unit Life in the Army Nurse Corps Secretary\u27s Report Elected to New Office 1892-1942 Progress or Alumnae Association 1892-1942 Report of the School of Nursing Staff News Please Change My Address Air Cooled Red Cross Report Fingerprinting Graduates in the U.S. Army and Navy Degrees Received Promotions Jubilee Report Engagements Marriages Births New Positions - 1941-1942 New Positions on the Nursing Staff of the Hospita

Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

Fractal Scales in a Schwarzschild Atmosphere

Recently, Glass and Krisch have extended the Vaidya radiating metric to include both a radiation fluid and a string fluid [1999 Class. Quantum Grav. vol 16, 1175]. Mass diffusion in the extended Schwarzschild atmosphere was studied. The continuous solutions of classical diffusive transport are believed to describe the envelope of underlying fractal behavior. In this work we examine the classical picture at scales on which fractal behavior might be evident.Comment: to appear in Class. Quantum Gra

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.Comment: More comments for the quantitative estimation of chaos are added, and some inappropriate terms are changed. This will appear on Class. Quant. Gra

Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, a re used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation between the analytic structure of the zeta function, where a branch cut plays an important role, and the asymptotic dynamics of the system. We find a diverging diffusion constant $D(t) \sim \log t$ and a phase transition for the generalized Lyapunov exponents.Comment: 14 pages LaTeX, figs 2-3 on .uu file, fig 1 available from autho

Ruelle-Perron-Frobenius spectrum for Anosov maps

We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (Information on the existence of an SRB measure, its smoothness properties and statistical properties readily follow from such a result.) In dimension $d=2$ we show that the transfer operator associated to smooth random perturbations of the map is close, in a proper sense, to the unperturbed transfer operator. This allows to obtain easily very strong spectral stability results, which in turn imply spectral stability results for smooth deterministic perturbations as well. Finally, we are able to implement an Ulam type finite rank approximation scheme thus reducing the study of the spectral properties of the transfer operator to a finite dimensional problem.Comment: 58 pages, LaTe

A New Method for Computing Topological Pressure

The topological pressure introduced by Ruelle and similar quantities describe dynamical multifractal properties of dynamical systems. These are important characteristics of mesoscopic systems in the classical regime. Original definition of these quantities are based on the symbolic description of the dynamics. It is hard or impossible to find symbolic description and generating partition to a general dynamical system, therefore these quantities are often not accessible for further studies. Here we present a new method by which the symbolic description can be omitted. We apply the method for a mixing and an intermittent system.Comment: 8 pages LaTeX with revtex.sty, the 4 postscript figures are included using psfig.tex to appear in PR

Hamiltonian dynamics and geometry of phase transitions in classical XY models

The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of thermodynamical observables in place of ensemble averages, qualitatively new information is derived from the temperature dependence of Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests to consider other observables of geometric meaning tightly related with the largest Lyapunov exponent. The numerical computation of these observables - unusual in the study of phase transitions - sheds a new light on the microscopic dynamical counterpart of thermodynamics also pointing to the existence of some major change in the geometry of the mechanical manifolds at the thermodynamical transition. Through the microcanonical definition of the entropy, a relationship between thermodynamics and the extrinsic geometry of the constant energy surfaces $\Sigma_E$ of phase space can be naturally established. In this framework, an approximate formula is worked out, determining a highly non-trivial relationship between temperature and topology of the $\Sigma_E$. Whence it can be understood that the appearance of a phase transition must be tightly related to a suitable major topology change of the $\Sigma_E$. This contributes to the understanding of the origin of phase transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22 PostScript figure