Velocity Distribution in a Viscous Granular Gas

We investigate the velocity relaxation of a viscous one-dimensional granular gas, that is, one in which neither energy nor momentum is conserved in a collision. Of interest is the distribution of velocities in the gas as it cools, and the time dependence of the relaxation behavior. A Boltzmann equation of instantaneous binary collisions leads to a two-peaked distribution with each peak relaxing to zero velocity as 1/t while each peak also narrows as 1/t. Numerical simulations of grains on a line also lead to a double-peaked distribution that narrows as 1/t. A Maxwell approximation leads to a single-peaked distribution about zero velocity with power-law wings. This distribution narrows exponentially. In either case, the relaxing distribution is not of Maxwell-Boltzmann form

Is Self-Sufficiency for Women’s Collegiate Athletics a Hoop Dream? Willingness to Pay for Men’s and Women’s Basketball Tickets

Universities spend almost $2 billion subsidizing their collegiate sports programs. Even the most popular women’s sport, basketball, fails to break even. An application of Becker’s theory of customer discrimination is used to calculate the relative preference for men’s basketball for both men and women. Median willingness to pay for men’s basketball relative to women’s basketball is 180% greater for men and 37% greater for women. Pricing each sport at its revenue maximizing price, revenues from women’s basketball are only 43% of that for men, even at a school with historically strong demand for women’s sports

Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum

The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing operators which, in turn, give rise to a non-Hermitian radial Hamiltonian. The set of eigenvalues of this new Hamiltonian is exactly the same as the energy spectrum of the radial oscillator and the new square-integrable eigenfunctions are complex Darboux-deformations of the associated Laguerre polynomials.Comment: 13 pages, 7 figure

Pulse propagation in decorated granular chains: An analytical approach

We study pulse propagation in one-dimensional chains of spherical granules decorated with small grains placed between large granules. The effect of the small granules can be captured by replacing the decorated chains by undecorated chains of large granules of appropriately renormalized mass and effective interaction between the large granules. This allows us to obtain simple analytic expressions for the pulse propagation properties using a generalization of the binary collision approximation introduced in our earlier work [Phys. Rev. E in print (2009); Phys. Rev. E {\bf 69}, 037601 (2004)]Comment: 10 pages and 12 figure

Robustness of the European power grids under intentional attack

The power grid defines one of the most important technological networks of our times and sustains our complex society. It has evolved for more than a century into an extremely huge and seemingly robust and well understood system. But it becomes extremely fragile as well, when unexpected, usually minimal, failures turn into unknown dynamical behaviours leading, for example, to sudden and massive blackouts. Here we explore the fragility of the European power grid under the effect of selective node removal. A mean field analysis of fragility against attacks is presented together with the observed patterns. Deviations from the theoretical conditions for network percolation (and fragmentation) under attacks are analysed and correlated with non topological reliability measures.Comment: 7 pages, 4 figure

Cellular connectivity for UAVs: Network modeling, performance analysis, and design guidelines

The growing use of aerial user equipments (UEs) in various applications requires ubiquitous and reliable connectivity for safe control and data exchange between these devices and ground stations. Key questions that need to be addressed when planning the deployment of aerial UEs are whether the cellular network is a suitable candidate for enabling such connectivity and how the inclusion of aerial UEs might impact the overall network efficiency. This paper provides an in-depth analysis of user and network-level performance of a cellular network that serves both unmanned aerial vehicles (UAVs) and ground users in the downlink. Our results show that the favorable propagation conditions that UAVs enjoy due to their height often backfire on them, as the increased load-dependent co-channel interference received from neighboring ground base stations (BSs) is not compensated by the improved signal strength. When compared with a ground user in an urban area, our analysis shows that a UAV flying at 100 m can experience a throughput decrease of a factor 10 and a coverage drop from 76% to 30%. Motivated by these findings, we develop UAV and network-based solutions to enable an adequate integration of UAVs into cellular networks. In particular, we show that an optimal tilting of the UAV antenna can increase the coverage from 23% to 89% and throughput from 3.5 to 5.8 b/s/Hz, outperforming ground UEs. Furthermore, our findings reveal that depending on the UAV altitude and its antenna configuration, the aerial user performance can scale with respect to the network density better than that of a ground user. Finally, our results show that network densification and the use of microcells limit the UAV performance. Although UAV usage has the potential to increase the area spectral efficiency (ASE) of cellular networks with a moderate number of cells, they might hamper the development of future ultradense networks

Observation of two-wave structure in strongly nonlinear dissipative granular chains

In a strongly nonlinear viscous granular chain under conditions of loading that exclude stationary waves (e.g., impact by a single grain) we observe a pulse that consists of two interconnected but distinct parts. One is a leading narrow "primary pulse" with properties similar to a solitary wave in a "sonic vacuum." It arises from strong nonlinearity and discreteness in the absence of dissipation, but now decays due to viscosity. The other is a broad, much more persistent shock-like "secondary pulse" trailing the primary pulse and caused by viscous dissipation. The medium behind the primary pulse is transformed from a "sonic vacuum" to a medium with finite sound speed. When the rapidly decaying primary pulse dies, the secondary pulse continues to propagate in the "sonic vacuum," with an oscillatory front if the viscosity is relatively small, until its eventual (but very slow) disintegration. Beyond a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shock-like attenuating pulse which now exhibits a nonoscillatory front

A Hamiltonian functional for the linearized Einstein vacuum field equations

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained.Comment: 5 pages, accepted in J. Phys.: Conf. Serie