19,844 research outputs found
Polyhedral representations of discrete differential manifolds
Any discrete differential manifold (finite set endowed with an algebraic
differential calculus) can be represented by appropriate polyhedron . This representation demonstrates the adequacy of the calculus of
discrete differential manifolds and links this approach with that based on
finitary substitutes of continuous spaces introduced by R.D.Sorkin.Comment: LaTeX, 35 Kb, submitted to JM
Local Axisymmetric Instability Criterion in the Thin, Rotating, Multicomponent Disk
Purely gravitational perturbations are considered in a thin rotating disk
composed of several gas and stellar components. The dispersion relation for the
axisymmetric density waves propagating through the disk is found and the
criterion for the local axisymmetric stability of the whole system is
formulated. In the appropriate limit of two-component gas we confirm the
findings of Jog & Solomon (1984) and extend consideration to the case when one
component is collisionless. Gravitational stability of the Galactic disk in the
Solar neighborhood based on the multicomponent instability condition is
explored using recent measurements of the stellar composition and kinematics in
the local Galactic disk obtained by Hipparcos satellite.Comment: 8 pages, 5 figures, 1 table, to be submitted to MNRA
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