Thermally-driven Neutron Star Glitches

We examine the thermal and dynamical response of a neutron star to a sudden perturbation of the inner crust temperature. During the star's evolution, starquakes and other processes may deposit \gap 10^{42} ergs, causing significant internal heating and increased frictional coupling between the crust and the more rapidly rotating neutron superfluid the star is expected to contain. Through numerical simulation we study the propagation of the thermal wave created by the energy deposition, the induced motion of the interior superfluid, and the resulting spin evolution of the crust. We find that energy depositions of $\sim 10^{40}$ ergs produce gradual spin-ups above the timing noise level, while larger energy depositions produce sudden spin jumps resembling pulsar glitches. For a star with a temperature in the observed range of the Vela pulsar, an energy deposition of $\sim 10^{42}$ ergs produces a large spin-up taking place over minutes, similar to the Vela ``Christmas'' glitch. Comparable energy deposition in a younger and hotter ``Crab-like'' star produces a smaller spin-up taking place over $\sim 1$ day, similar to that seen during the partially time-resolved Crab glitch of 1989.Comment: 21 pages plus 17 figures, uuencode compressed Postscript. Accepted for publication in the Astrophysical Journa

The calculation of long-wave radiative transfer in planetary atmospheres

Equations, computer techniques, and model calculations of long wave radiative transfer in planetary atmosphere

The Absorption of Sound in Suspensions and Emulsions. I. Water Fog in Air

The suspended particles are approximated by spheres and the diffraction problem for a fluid sphere in a fluid medium is solved taking into consideration viscosity and thermal conduction. The results are discussed numerically for water droplets in air and a satisfactory agreement with Knudsen's attenuation measurements in water fog is found

An analytically solvable model of probabilistic network dynamics

We present a simple model of network dynamics that can be solved analytically for uniform networks. We obtain the dynamics of response of the system to perturbations. The analytical solution is an excellent approximation for random networks. A comparison with the scale-free network, though qualitatively similar, shows the effect of distinct topology.Comment: 4 pages, 1 figur

On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

Impact-induced devolatilization and hydrogen isotopic fractionation of serpentine: Implications for planetary accretion

Impact-induced devolatilization of porous serpentine was investigated using two independent experimental methods, the gas recovery and the solid recovery method, each yielding nearly identical results. For shock pressures near incipient devolatilization, the hydrogen isotopic composition of the evolved H2O is very close to that of the starting material. For shock pressures at which up to 12 percent impact-induced devolatilization occurs, the bulk evolved gas is significantly lower in deuterium than the starting material. There is also significant reduction of H2O to H2 in gases recovered at these higher shock pressures, probably caused by reaction of evolved H2O with the metal gas recovery fixture. Gaseous H2O-H2 isotopic fractionation suggests high temperature isotopic equilibrium between the gaseous species, indicating initiation of devolatilization at sites of greater than average energy deposition. Bulk gas-residual solid isotopic fractionations indicate nonequilibrium, kinetic control of gas-solid isotopic ratios. Impact-induced hydrogen isotopic fractionation of hydrous silicates during accretion can strongly affect the long-term planetary isotopic ratios of planetary bodies, leaving the interiors enriched in deuterium. Depending on the model used for extrapolation of the isotopic fractionation to devolatilization fractions greater than those investigated experimentally can result from this process