6,290 research outputs found

    Time-Independent Gravitational Fields in the BGK Scheme for Hydrodynamics

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    We incorporate a time-independent gravitational field into the BGK scheme for numerical hydrodynamics. In the BGK scheme the gas evolves via an approximation to the collisional Boltzmann equation, namely the Bhatnagar-Gross-Krook (BGK) equation. Time-dependent hydrodynamical fluxes are computed from local solutions of the BGK equation. By accounting for particle collisions, the fundamental mechanism for generating dissipation in gas flow, a scheme based on the BGK equation gives solutions to the Navier-Stokes equations: the fluxes carry both advective and dissipative terms. We perform numerical experiments in both 1D Cartesian geometries and axisymmetric cylindrical coordinates.Comment: 31 pages including 19 figures (For higher resolution figs. see http://www.mpia-hd.mpg.de/MPIA/Projects/THEORY/slyz), Accepted for publication in Astronomy and Astrophysics, Supplement Serie

    Barter relationships

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    We offer a simple economic model of repeated barter to explore current economic exchange in Russia: individuals trade with each other in a dynamic environment where the threat of dissolving the relationship constrains the incentives to cheat. We show how the value of future interactions affects the willingness of individuals to trade with each other; only when rates of interaction are large can trust compensate for an absence of money. Moreover, when trading relationships are asymmetric – either in the trading partners’ values for each other’s goods or in their relative bargaining power – the resulting barter allocations are distorted, as goods must be used for liquidity reasons. When third-party middlemen exist who can facilitate barter, they command a premium for their services, and have preferences for improved liquidity which may or may not correspond with the other traders in the barter economy. Fourth, we demonstrate that the restriction of trading to tight trading networks may be a socially efficient response to insufficient barter interactions. Finally, we consider how liquidity constraints affect pricing, and illustrate how the existence of a barter market can mute incentives to change prices in response to credit crunches.Barter, non-monetary exchange
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