Anomalous Lorentz and CPT violation from a local Chern-Simons-like term in the effective gauge-field action

We consider four-dimensional chiral gauge theories defined over a spacetime manifold with topology $\mathbb{R}^3 \times S^1$ and periodic boundary conditions over the compact dimension. The effective gauge-field action is calculated for Abelian $U(1)$ gauge fields $A_{\mu}(x)$ which depend on all four spacetime coordinates (including the coordinate $x^{4}\in S^1$ of the compact dimension) and have vanishing components $A_{4}(x)$ (implying trivial holonomies in the 4-direction). Our calculation shows that the effective gauge-field action contains a local Chern-Simons-like term which violates Lorentz and CPT invariance. This result is established perturbatively with a generalized Pauli-Villars regularization and nonperturbatively with a lattice regularization based on Ginsparg-Wilson fermions.Comment: 48 pages, v7: published versio

Statistics of the Kolkata Paise Restaurant Problem

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent tries get to dinner in the best restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents and assume that each follow the same probabilistic or stochastic strategy dependent on the information of the past successes in the game. We show that some 'naive' strategies lead to much better utilization of the services than some relatively 'smarter' strategies. We also show that the service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not; with probability decreasing inversely in the past crowd size). The numerical results for utilization fraction of the services in some limiting cases are analytically examined.Comment: 10 pages, 3 figs; accepted in New J Phy

Thermal elastohydrodynamic lubrication of line contacts

A numerical solution to the problem of thermal elastohydrodynamic lubrication of line contacts was obtained by using a finite difference formulation. The solution procedure consists of simultaneous solution of the thermal Reynolds equation, the elasticity equation, and the energy equation subject to appropriate boundary conditions. Pressure distribution, film shape, and temperature distribution were obtained for fully flooded conjunctions, a paraffinic lubricant, and various dimensionless speed parameters while the dimensionless load and materials parameters were held constant. Reduction in the minimum film thickness due to thermal effects (as a ratio of thermal to isothermal minimum film thickness) is given by a simple formula as a function of the thermal loading parameter Q: H(min)/H(min,I) = 10/10+ Q(0.4). Plots of pressure distribution, film shape, temperature distribution, and flow are shown for some representative cases

Simultaneous stabilization and simultaneous pole placement by nonswitching dynamic compensation

The 'simultaneous stabilization problem' is defined and theorems are proposed for its solution. The problem consists in answering the question: given an r-tuple G sub 1(s), G sub r(s) of p x m proper transfer functions, does there exist a compensator K(s) such that the closed loop systems G sub 1(s) (I+K(s)G sub 1(s)) (-1), G sub r(s) (I+K(s) G sub r(s)) (-1) are (internally) stable. This question arises in reliability theory, where G sub 2(s), G sub r(s) represents a plant G sub 1(s) operating in various modes of failure and K(s) is a nonswitching stabilizing compensator. It is important in the stability analysis and design of a plant which can be switched into various operating modes. The simultaneous stabilization problem can also apply to the stabilization of a nonlinear system which is linearized at several equilibria. Conditions are defined for pole placement and the generalized Sylvestor matrix is discussed

Three flavour Quark matter in chiral colour dielectric model

We investigate the properties of quark matter at finite density and temperature using the nonlinear chiral extension of Colour Dielectric Model (CCM). Assuming that the square of the meson fields devlop non- zero vacuum expectation value, the thermodynamic potential for interacting three flavour matter has been calculated. It is found that $$and$$ remain zero in the medium whereas $$ changes in the medium. As a result, $u$ and $d$ quark masses decrease monotonically as the temperature and density of the quark matter is increased.In the present model, the deconfinement density and temperature is found to be lower compared to lattice results. We also study the behaviour of pressure and energy density above critical temperature.Comment: Latex file. 5 figures available on request. To appear in Phys. Rev.

Growth of preferential attachment random graphs via continuous-time branching processes

A version of ``preferential attachment'' random graphs, corresponding to linear ``weights'' with random ``edge additions,'' which generalizes some previously considered models, is studied. This graph model is embedded in a continuous-time branching scheme and, using the branching process apparatus, several results on the graph model asymptotics are obtained, some extending previous results, such as growth rates for a typical degree and the maximal degree, behavior of the vertex where the maximal degree is attained, and a law of large numbers for the empirical distribution of degrees which shows certain ``scale-free'' or ``power-law'' behaviors.Comment: 20 page

Study of QCD generalized ghost dark energy in FRW universe

A phenomenological generalized ghost dark energy model has been studied under the framework of FRW universe. In ghost dark energy model the energy density depends linearly on Hubble parameter (H) but in this dark energy model, the energy density contains a the sub-leading term which is depends on $\mathcal{O} (H^2)$, so the energy density takes the form $\rho_D=\alpha H+ \beta H^2$, where $\alpha$ and $\beta$ are the constants. The solutions of the Friedman equation of our model leads to a stable universe. We have fitted our model with the present observational data including Stern data set. With the help of best fit results we find the adiabatic sound speed remains positive throughout the cosmic evolution, that claims the stability of the model. The flipping of the signature of deceleration parameter at the value of scale factor $a=0.5$ indicates that the universe is at the stage of acceleration i.e. de Sitter phase of the universe at late time. Our model shows that the acceleration of the universe begin at redshift $z_{ace}\approx 0.617$ and the model is also consistent with the current observational data.Comment: 9 pages, 9 figure

Multi-Channel Scheduling for Fast Convergecast in Wireless Sensor Networks

We explore the following fundamental question - how fast can information be collected from a wireless sensor network? We consider a number of design parameters such as, power control, time and frequency scheduling, and routing. There are essentially two factors that hinder efficient data collection - interference and the half-duplex single-transceiver radios. We show that while power control helps in reducing the number of transmission slots to complete a convergecast under a single frequency channel, scheduling transmissions on different frequency channels is more efficient in mitigating the effects of interference (empirically, 6 channels suffice for most 100-node networks). With these observations, we define a receiver-based channel assignment problem, and prove it to be NP-complete on general graphs. We then introduce a greedy channel assignment algorithm that efficiently eliminates interference, and compare its performance with other existing schemes via simulations. Once the interference is completely eliminated, we show that with half-duplex single-transceiver radios the achievable schedule length is lower-bounded by max(2nk − 1,N), where nk is the maximum number of nodes on any subtree and N is the number of nodes in the network. We modify an existing distributed time slot assignment algorithm to achieve this bound when a suitable balanced routing scheme is employed. Through extensive simulations, we demonstrate that convergecast can be completed within up to 50% less time slots, in 100-node networks, using multiple channels as compared to that with single-channel communication. Finally, we also demonstrate further improvements that are possible when the sink is equipped with multiple transceivers or when there are multiple sinks to collect data