The ground state and the long-time evolution in the CMC Einstein flow

Let (g,K)(k) be a CMC (vacuum) Einstein flow over a compact three-manifold M with non-positive Yamabe invariant (Y(M)). As noted by Fischer and Moncrief, the reduced volume V(k)=(-k/3)^{3}Vol_{g(k)}(M) is monotonically decreasing in the expanding direction and bounded below by V_{\inf}=(-1/6)Y(M))^{3/2}. Inspired by this fact we define the ground state of the manifold M as "the limit" of any sequence of CMC states {(g_{i},K_{i})} satisfying: i. k_{i}=-3, ii. V_{i} --> V_{inf}, iii. Q_{0}((g_{i},K_{i}))< L where Q_{0} is the Bel-Robinson energy and L is any arbitrary positive constant. We prove that (as a geometric state) the ground state is equivalent to the Thurston geometrization of M. Ground states classify naturally into three types. We provide examples for each class, including a new ground state (the Double Cusp) that we analyze in detail. Finally consider a long time and cosmologically normalized flow (\g,\K)(s)=((-k/3)^{2}g,(-k/3))K) where s=-ln(-k) is in [a,\infty). We prove that if E_{1}=E_{1}((\g,\K))< L (where E_{1}=Q_{0}+Q_{1}, is the sum of the zero and first order Bel-Robinson energies) the flow (\g,\K)(s) persistently geometrizes the three-manifold M and the geometrization is the ground state if V --> V_{inf}.Comment: 40 pages. This article is an improved version of the second part of the First Version of arXiv:0705.307

Coherent instabilities of intense high-energy "white" charged-particle beams in the presence of nonlocal effects within the context of the Madelung fluid description

A hydrodynamical description of coherent instabilities that take place in the longitudinal dynamics of a charged-particle coasting beam in a high-energy accelerating machine is presented. This is done in the framework of the Madelung fluid picture provided by the Thermal Wave Model. The well known coherent instability charts in the complex plane of the longitudinal coupling impedance for monochromatic beams are recovered. The results are also interpreted in terms of the deterministic approach to modulational instability analysis usually given for monochromatic large amplitude wave train propagation governed by the nonlinear Schr\"odinger equation. The instability analysis is then extended to a non-monochromatic coasting beam with a given thermal equilibrium distribution, thought as a statistical ensemble of monochromatic incoherent coasting beams ("white" beam). In this hydrodynamical framework, the phenomenon of Landau damping is predicted without using any kinetic equation governing the phase space evolution of the system.Comment: 14 pages, 1 figur

Borel singularities at small x

D.I.S. at small Bjorken $x$ is considered within the dipole cascade formalism. The running coupling in impact parameter space is introduced in order to parametrize effects that arise from emission of large size dipoles. This results in a new evolution equation for the dipole cascade. Strong coupling effects are analyzed after transforming the evolution equation in Borel ($b$) space. The Borel singularities of the solution are discussed first for the universal part of the dipole cascade and then for the specific process of D.I.S. at small $x$. In the latter case the leading infrared renormalon is at $b=1/\beta_0$ indicating the presence of $1/Q^2$ power corrections for the small-$x$ structure functions.Comment: 5 pages, Latex (Talk presented at DIS'97, Chicago, IL

Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration

Radio metric data from the Pioneer 10/11, Galileo, and Ulysses spacecraft indicate an apparent anomalous, constant, acceleration acting on the spacecraft with a magnitude $\sim 8.5\times 10^{-8}$ cm/s$^2$, directed towards the Sun. Two independent codes and physical strategies have been used to analyze the data. A number of potential causes have been ruled out. We discuss future kinematic tests and possible origins of the signal.Comment: Revtex, 4 pages and 1 figure. Minor changes for publicatio

Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement

The behavior of ultracold atomic gases depends crucially on the two-body scattering properties of these systems. We develop a multichannel scattering theory for atom-atom collisions in quasi-one-dimensional (quasi-1D) geometries such as atomic waveguides or highly elongated traps. We apply our general framework to the low energy scattering of two spin-polarized fermions and show that tightly-confined fermions have infinitely strong interactions at a particular value of the 3D, free-space p-wave scattering volume. Moreover, we describe a mapping of this strongly interacting system of two quasi-1D fermions to a weakly interacting system of two 1D bosons.Comment: Submitted to Phys. Rev. Let

Spin-Charge separation in a model of two coupled chains

A model of interacting electrons living on two chains coupled by a transverse hopping $t_\perp$, is solved exactly by bosonization technique. It is shown that $t_\perp$ does modify the shape of the Fermi surface also in presence of interaction, although charge and spin excitations keep different velocities $u_\rho$, $u_\sigma$. Two different regimes occur: at short distances, $x\ll \xi = (u_\rho - u_\sigma)/4t_\perp$, the two chain model is not sensitive to $t_\perp$, while for larger separation $x\gg \xi$ inter--chain hopping is relevant and generates further singularities in the electron Green function besides those due to spin-charge decoupling. (2 figures not included. Figure requests: FABRIZIO@ITSSISSA)Comment: 12 pages, LATEX(REVTEX), SISSA 150/92/CM/M

Equilibrium properties of the Skylab CMG rotation law

The equilibrium properties of the control moment gyroscopes of the Skylab are discussed. A rotation law is developed to produce gimbal rates which distribute the angular momentum contributions among the control moment gyroscopes to avoid gimbal stop encounters. The implications for gimbal angle management under various angular momentum situations are described. Conditions were obtained for the existence of equilibria and corresponding stability properties

Competing epidemics on complex networks

Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same network at the same time, where infection with either disease gives an individual subsequent immunity to both. Using a combination of analytic and numerical methods, we derive the phase diagram of the system and estimates of the expected final numbers of individuals infected with each disease. The system shows an unusual dynamical transition between dominance of one disease and dominance of the other as a function of their relative rates of growth. Close to this transition the final outcomes show strong dependence on stochastic fluctuations in the early stages of growth, dependence that decreases with increasing network size, but does so sufficiently slowly as still to be easily visible in systems with millions or billions of individuals. In most regions of the phase diagram we find that one disease eventually dominates while the other reaches only a vanishing fraction of the network, but the system also displays a significant coexistence regime in which both diseases reach epidemic proportions and infect an extensive fraction of the network.Comment: 14 pages, 5 figure