Integrability of graph combinatorics via random walks and heaps of dimers

We investigate the integrability of the discrete non-linear equation governing the dependence on geodesic distance of planar graphs with inner vertices of even valences. This equation follows from a bijection between graphs and blossom trees and is expressed in terms of generating functions for random walks. We construct explicitly an infinite set of conserved quantities for this equation, also involving suitable combinations of random walk generating functions. The proof of their conservation, i.e. their eventual independence on the geodesic distance, relies on the connection between random walks and heaps of dimers. The values of the conserved quantities are identified with generating functions for graphs with fixed numbers of external legs. Alternative equivalent choices for the set of conserved quantities are also discussed and some applications are presented.Comment: 38 pages, 15 figures, uses epsf, lanlmac and hyperbasic

Heterogeneidade física de um latossolo argiloso manejado sob sistema plantio direto.

bitstream/CNPT-2010/40741/1/p-bp70.pd

Numerical Simulations of Dynamos Generated in Spherical Couette Flows

We numerically investigate the efficiency of a spherical Couette flow at generating a self-sustained magnetic field. No dynamo action occurs for axisymmetric flow while we always found a dynamo when non-axisymmetric hydrodynamical instabilities are excited. Without rotation of the outer sphere, typical critical magnetic Reynolds numbers $Rm_c$ are of the order of a few thousands. They increase as the mechanical forcing imposed by the inner core on the flow increases (Reynolds number $Re$). Namely, no dynamo is found if the magnetic Prandtl number $Pm=Rm/Re$ is less than a critical value $Pm_c\sim 1$. Oscillating quadrupolar dynamos are present in the vicinity of the dynamo onset. Saturated magnetic fields obtained in supercritical regimes (either $Re>2 Re_c$ or $Pm>2Pm_c$) correspond to the equipartition between magnetic and kinetic energies. A global rotation of the system (Ekman numbers $E=10^{-3}, 10^{-4}$) yields to a slight decrease (factor 2) of the critical magnetic Prandtl number, but we find a peculiar regime where dynamo action may be obtained for relatively low magnetic Reynolds numbers ($Rm_c\sim 300$). In this dynamical regime (Rossby number $Ro\sim -1$, spheres in opposite direction) at a moderate Ekman number ($E=10^{-3}$), a enhanced shear layer around the inner core might explain the decrease of the dynamo threshold. For lower $E$ ($E=10^{-4}$) this internal shear layer becomes unstable, leading to small scales fluctuations, and the favorable dynamo regime is lost. We also model the effect of ferromagnetic boundary conditions. Their presence have only a small impact on the dynamo onset but clearly enhance the saturated magnetic field in the ferromagnetic parts. Implications for experimental studies are discussed

Combinatorics of bicubic maps with hard particles

We present a purely combinatorial solution of the problem of enumerating planar bicubic maps with hard particles. This is done by use of a bijection with a particular class of blossom trees with particles, obtained by an appropriate cutting of the maps. Although these trees have no simple local characterization, we prove that their enumeration may be performed upon introducing a larger class of "admissible" trees with possibly doubly-occupied edges and summing them with appropriate signed weights. The proof relies on an extension of the cutting procedure allowing for the presence on the maps of special non-sectile edges. The admissible trees are characterized by simple local rules, allowing eventually for an exact enumeration of planar bicubic maps with hard particles. We also discuss generalizations for maps with particles subject to more general exclusion rules and show how to re-derive the enumeration of quartic maps with Ising spins in the present framework of admissible trees. We finally comment on a possible interpretation in terms of branching processes.Comment: 41 pages, 19 figures, tex, lanlmac, hyperbasics, epsf. Introduction and discussion/conclusion extended, minor corrections, references adde

Distance statistics in large toroidal maps

We compute a number of distance-dependent universal scaling functions characterizing the distance statistics of large maps of genus one. In particular, we obtain explicitly the probability distribution for the length of the shortest non-contractible loop passing via a random point in the map, and that for the distance between two random points. Our results are derived in the context of bipartite toroidal quadrangulations, using their coding by well-labeled 1-trees, which are maps of genus one with a single face and appropriate integer vertex labels. Within this framework, the distributions above are simply obtained as scaling limits of appropriate generating functions for well-labeled 1-trees, all expressible in terms of a small number of basic scaling functions for well-labeled plane trees.Comment: 24 pages, 9 figures, minor corrections, new added reference

Binding Energy and the Fundamental Plane of Globular Clusters

A physical description of the fundamental plane of Galactic globular clusters is developed which explains all empirical trends and correlations in a large number of cluster observables and provides a small but complete set of truly independent constraints on theories of cluster formation and evolution in the Milky Way. Within the theoretical framework of single-mass, isotropic King models, it is shown that (1) 39 regular (non--core-collapsed) globulars with measured core velocity dispersions share a common V-band mass-to-light ratio of 1.45 +/- 0.10, and (2) a complete sample of 109 regular globulars reveals a very strong correlation between cluster binding energy and total luminosity, regulated by Galactocentric position: E_b \propto (L^{2.05} r_{\rm gc}^{-0.4}). The observational scatter about either of these two constraints can be attributed fully to random measurement errors, making them the defining equations of a fundamental plane for globular clusters. A third, weaker correlation, between total luminosity and the King-model concentration parameter, c, is then related to the (non-random) distribution of globulars on the plane. The equations of the FP are used to derive expressions for any cluster observable in terms of only L, r_{\rm gc}, and c. Results are obtained for generic King models and applied specifically to the globular cluster system of the Milky Way.Comment: 60 pages with 19 figures, submitted to Ap

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Synthesis of 4-Piperidinoflavan

A study of the reaction of flavylium perchlorate with piperidine showed that piperidine perchlorate was formed plus two other compounds. One of these appears to be 4-piperidinoflavene which should be reducible to 4-piperidinoflavan. This compound had not been described previously, hence its synthesis was undertaken. Flavanone was prepared according to the method of Kostanecki (1). Catalytic reduction of flavanone with hydrogen and a platinum catalyst gave a 79% yield of a compound melting at 145- 147°. This corresponds to the, B-isomer of 4-hydroxyflavan originally obtained by Karrar, Yen and Reichstein (2) as the result of a titanous chloride reduction of flavanone. Mozingo and Adkins (3) also obtained this ,B-isomer by catalytic reduction of flavanone but used copper-chromium oxide at 120° and hydrogen at 100-200 atm. Treatment of the 4-hydroxyflavan with phosphorus tribromide at 0° gave a 52% yield of 4-bromoflavan. An ether solution of this bromo-compound reacted with two equivalents of piperidine to form piperidinium hydrobromide and {3-4 piperidinoflavan. Upon recrystallization from ether, colorless needles were obtained melting at 137-138° which had the correct analysis for this compound

Global existence of classical solutions to the Vlasov-Poisson system in a three dimensional, cosmological setting

The initial value problem for the Vlasov-Poisson system is by now well understood in the case of an isolated system where, by definition, the distribution function of the particles as well as the gravitational potential vanish at spatial infinity. Here we start with homogeneous solutions, which have a spatially constant, non-zero mass density and which describe the mass distribution in a Newtonian model of the universe. These homogeneous states can be constructed explicitly, and we consider deviations from such homogeneous states, which then satisfy a modified version of the Vlasov-Poisson system. We prove global existence and uniqueness of classical solutions to the corresponding initial value problem for initial data which represent spatially periodic deviations from homogeneous states.Comment: 23 pages, Latex, report #