Interacting queues in heavy traffic

We consider a system of parallel queues with Poisson arrivals and exponentially distributed service requirements. The various queues are coupled through their service rates, causing a complex dynamic interaction. Specifically, the system consists of one primary queue and several secondary queues whose service rates depend on whether the primary queue is empty or not. Conversely, the service rate of the primary queue depends on which of the secondary queues are empty. An important special case arises when the service rates satisfy a specific relationship so that the various queues form a work-conserving system. This case is, in fact, equivalent to a so-called Generalized Processor Sharing (GPS) system. GPS-based scheduling algorithms have emerged as popular mechanisms for achieving service differentiation while providing statistical multiplexing gains. We consider a heavy-traffic scenario, and assume that each of the secondary queues is underloaded when the primary queue is busy. Using a perturbation procedure, we derive the lowest-order asymptotic approximation to the joint stationary distribution of the queue lengths, in terms of a small positive parameter measuring the closeness of the system to instability. Heuristic derivations of these results are presented. We also pursue two extensions: (i) the more general work-conserving case where the service rate of a secondary queue may depend on its own length, and is a slowly varying function of the length of the primary queue; and (ii) the non-work-conserving case where the service rate of a secondary queue may depend on its own length, but not on the length of the primary queue

1/N expansion formalism for high-spin states

The 1/$N$ expansion solutions for the interacting boson model are extended to higher orders using computer algebra. The analytic results are compared with those obtained from an exact diagonalization of the Hamiltonian and are shown to be very accurate. The extended formulas for level energies and E2 transitions will be useful in the analysis of high-spin states in both normal and superdeformed nuclei.Comment: 11 pages, Latex, 3 figures available upon reques

Asymptotic Expansions for the Conditional Sojourn Time Distribution in the M/M/1M/M/1-PS Queue

We consider the $M/M/1$ queue with processor sharing. We study the conditional sojourn time distribution, conditioned on the customer's service requirement, in various asymptotic limits. These include large time and/or large service request, and heavy traffic, where the arrival rate is only slightly less than the service rate. The asymptotic formulas relate to, and extend, some results of Morrison \cite{MO} and Flatto \cite{FL}.Comment: 30 pages, 3 figures and 1 tabl

Hunting for dark matter and new physics with GECCO

We outline the science opportunities in the areas of searches for dark matter and new physics offered by a proposed future MeV gamma-ray telescope, the Galactic Explorer with a Coded Aperture Mask Compton Telescope (GECCO). We point out that such an instrument would play a critical role in opening up a discovery window for particle dark matter with mass in the MeV or sub-MeV range, in disentangling the origin of the mysterious 511 keV line emission in the Galactic Center region, and in potentially discovering Hawking evaporation from light primordial black holes

Systematic model behavior of adsorption on flat surfaces

A low density film on a flat surface is described by an expansion involving the first four virial coefficients. The first coefficient (alone) yields the Henry's law regime, while the next three correct for the effects of interactions. The results permit exploration of the idea of universal adsorption behavior, which is compared with experimental data for a number of systems

Remote Sensing D/H Ratios in Methane Ice: Temperature-Dependent Absorption Coefficients of CH3D in Methane Ice and in Nitrogen Ice

The existence of strong absorption bands of singly deuterated methane (CH3D) at wavelengths where normal methane (CH4) absorbs comparatively weakly could enable remote measurement of D/H ratios in methane ice on outer solar system bodies. We performed laboratory transmission spectroscopy experiments, recording spectra at wavelengths from 1 to 6 \mum to study CH3D bands at 2.47, 2.87, and 4.56 \mum, wavelengths where ordinary methane absorption is weak. We report temperature-dependent absorption coefficients of these bands when the CH3D is diluted in CH4 ice and also when it is dissolved in N2 ice, and describe how these absorption coefficients can be combined with data from the literature to simulate arbitrary D/H ratio absorption coefficients for CH4 ice and for CH4 in N2 ice. We anticipate these results motivating new telescopic observations to measure D/H ratios in CH4 ice on Triton, Pluto, Eris, and Makemake.Comment: 17 pages, 7 figure

Finite time singularities in a class of hydrodynamic models

Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\cal L}\sim\int k^\alpha|{\bf v_k}|^2d^3{\bf k}$ in 3D Fourier representation, where $\alpha$ is a constant, $0<\alpha< 1$. Unlike the case $\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\alpha$ results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for the nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically. They describe the formation of a finite time singularity, with all length scales decreasing like $(t^*-t)^{1/(2-\alpha)}$, where $t^*$ is the singularity time.Comment: LaTeX, 17 pages, 3 eps figures. This version is close to the journal pape

Occupational exposures to solvents and metals are associated with fixed airflow obstruction

peer-reviewedOur study is the first to investigate the associations between exposures to solvents and metals using lifetime work history calendars and fixed airflow obstruction (AO). We have shown that increasing cumulative exposure-unit years to chlorinated solvents is associated with fixed AO. We found that women were at increased risk of fixed AO with increasing cumulative exposed-unit-years to chlorinated solvents but not men