Global stability map of the flow in a horizontal concentric cylinder forced by natural convection.

There are a large number of studies in the literature on natural convection in the annulus between horizontal concentric cylinders. However, not many publications dealing with global stability analysis in this kind of flow have been published. For a fixed diameter ratio L/Di = (Ro − Ri)/2Ri, being Ri and Ro the inner and outer cylinder radii respectively, and assuming Boussinesq approximation, the solution only depends on Prandtl (P r ≡ ν/α) and Rayleigh (Ra ≡ g β L3 (Ti − To)/(ν α)) numbers. A spectral collocation code has been developed to solve the problem by means of Chebyshev and Fourier differentiation matrices for L/Di = 0.8 and it has been validated with classical experimental results. Steady solutions have been sought within the range P r ∈ [1e−2, 1] and Ra ∈ [1e-2, 5e6]. As a result, a steady solution Pr-Ra map (consisting of 149 x 75 points) has been traced, where the different families of similar solutions found are detailed, mainly characterized by presenting single or multiple plumes. In addition, two main double-solution regions have been found

Anomalous shell effect in the transition from a circular to a triangular billiard

We apply periodic orbit theory to a two-dimensional non-integrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-two bifurcation of the triangular periodic orbit. Gutzwiller's semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system. We also discuss the role of discrete symmetry for the large shell effect obtained here.Comment: 14 pages REVTeX4, 16 figures, version to appear in Phys. Rev. E. Qualities of some figures are lowered to reduce their sizes. Original figures are available at http://www.phys.nitech.ac.jp/~arita/papers/tricirc

Gibbs and Quantum Discrete Spaces

Gibbs measure is one of the central objects of the modern probability, mathematical statistical physics and euclidean quantum field theory. Here we define and study its natural generalization for the case when the space, where the random field is defined is itself random. Moreover, this randomness is not given apriori and independently of the configuration, but rather they depend on each other, and both are given by Gibbs procedure; We call the resulting object a Gibbs family because it parametrizes Gibbs fields on different graphs in the support of the distribution. We study also quantum (KMS) analog of Gibbs families. Various applications to discrete quantum gravity are given.Comment: 37 pages, 2 figure

Symmetry Breaking and Bifurcations in the Periodic Orbit Theory: II -- Spheroidal Cavity --

We derive a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences and discontinuities occurring at bifurcation points and in the spherical limit, the trace integrals over the action-angle variables are performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell energies are in good agreement with quantum-mechanical results. We find that the births of three-dimensional orbits through the bifurcations of planar orbits in the equatorial plane lead to considerable enhancement of shell effect for superdeformed shapes.Comment: 49 pages, 18 figures, using PTPTeX.cls(included), submitted to Prog. Theor. Phy