Accretion of Ghost Condensate by Black Holes

The intent of this letter is to point out that the accretion of a ghost condensate by black holes could be extremely efficient. We analyze steady-state spherically symmetric flows of the ghost fluid in the gravitational field of a Schwarzschild black hole and calculate the accretion rate. Unlike minimally coupled scalar field or quintessence, the accretion rate is set not by the cosmological energy density of the field, but by the energy scale of the ghost condensate theory. If hydrodynamical flow is established, it could be as high as tenth of a solar mass per second for 10MeV-scale ghost condensate accreting onto a stellar-sized black hole, which puts serious constraints on the parameters of the ghost condensate model.Comment: 5 pages, 3 figures, REVTeX 4.0; discussion expande

Lying Your Way to Better Traffic Engineering

To optimize the flow of traffic in IP networks, operators do traffic engineering (TE), i.e., tune routing-protocol parameters in response to traffic demands. TE in IP networks typically involves configuring static link weights and splitting traffic between the resulting shortest-paths via the Equal-Cost-MultiPath (ECMP) mechanism. Unfortunately, ECMP is a notoriously cumbersome and indirect means for optimizing traffic flow, often leading to poor network performance. Also, obtaining accurate knowledge of traffic demands as the input to TE is elusive, and traffic conditions can be highly variable, further complicating TE. We leverage recently proposed schemes for increasing ECMP's expressiveness via carefully disseminated bogus information ("lies") to design COYOTE, a readily deployable TE scheme for robust and efficient network utilization. COYOTE leverages new algorithmic ideas to configure (static) traffic splitting ratios that are optimized with respect to all (even adversarially chosen) traffic scenarios within the operator's "uncertainty bounds". Our experimental analyses show that COYOTE significantly outperforms today's prevalent TE schemes in a manner that is robust to traffic uncertainty and variation. We discuss experiments with a prototype implementation of COYOTE

Geometric Quantum Mechanics

The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given quantum system can be represented by specific geometrical features that are selected and preferentially identified in this complex manifold. Here we construct a number of examples of such geometrical features as they arise in the state spaces for spin-1/2, spin-1, and spin-3/2 systems, and for pairs of spin-1/2 systems. A study is undertaken on the geometry of entangled states, and a natural measure is assigned to the degree of entanglement of a given state for a general multi-particle system. The properties of this measure are analysed for the entangled states of a pair of spin-1/2 particles. With the specification of a quantum Hamiltonian, the resulting Schrodinger trajectory induces a Killing field, which is quasiergodic on a toroidal subspace of the energy surface. When the dynamical trajectory is lifted orthogonally to Hilbert space, it induces a geometric phase shift on the wave function. The uncertainty of an observable in a given state is the length of the gradient vector of the level surface of the expectation of the observable in that state, a fact that allows us to calculate higher order corrections to the Heisenberg relations. A general mixed state is determined by a probability density function on the state space, for which the associated first moment is the density matrix. The advantage of a general state is in its applicability in various attempts to go beyond the standard quantum theory.Comment: 27 pages. Extended with additional materia

A2 Toda theory in reduced WZNW framework and the representations of the W algebra

Using the reduced WZNW formulation we analyse the classical $W$ orbit content of the space of classical solutions of the $A_2$ Toda theory. We define the quantized Toda field as a periodic primary field of the $W$ algebra satisfying the quantized equations of motion. We show that this local operator can be constructed consistently only in a Hilbert space consisting of the representations corresponding to the minimal models of the $W$ algebra.Comment: 38 page

Two-variable linear programming: a graphical tool with mathematica

The didactical tool application is a CDF file. Download the CDF FREE Player at http://www.wolfram.com/cdf-player/ to run the application.This paper presents the GLP-Tool, an interactive tool for graphical linear programming involving two variables. The GLP-Tool is designed to solve user-defined linear programming problems with two variables. Implemented using the computer algebra system Mathematica, this interactive tool allows the user to dynamically explore different objective functions and constraint sets, and also perform post-optimal and sensitivity analysis. All the GLP-Tool functionalities are represented graphically and updated in real time. These interactive, dynamic, and graphical features make the GLP-Tool a powerful tool for teaching linear programming both in undergraduate and high school courses. After completing its development, we intend to make the GLP-Tool available at the Wolfram Demonstrations Project website

The shape dynamics description of gravity

Classical gravity can be described as a relational dynamical system without ever appealing to spacetime or its geometry. This description is the so-called shape dynamics description of gravity. The existence of relational first principles from which the shape dynamics description of gravity can be derived is a motivation to consider shape dynamics (rather than GR) as the fundamental description of gravity. Adopting this point of view leads to the question: What is the role of spacetime in the shape dynamics description of gravity? This question contains many aspects: Compatibility of shape dynamics with the description of gravity in terms of spacetime geometry, the role of local Minkowski space, universality of spacetime geometry and the nature of quantum particles, which can no longer be assumed to be irreducible representations of the Poincare group. In this contribution I derive effective spacetime structures by considering how matter fluctuations evolve along with shape dynamics. This evolution reveals an "experienced spacetime geometry." This leads (in an idealized approximation) to local Minkowski space and causal relations. The small scale structure of the emergent geometric picture depends on the specific probes used to experience spacetime, which limits the applicability of effective spacetime to describe shape dynamics. I conclude with discussing the nature of quantum fluctuations (particles) in shape dynamics and how local Minkowski spacetime emerges from the evolution of quantum particles.Comment: 16 pages Latex, no figures, arXiv version of a submission to the proceedings of Theory Canada