20,881 research outputs found
The Expected Duration of Gamma-Ray Bursts in the Impulsive Hydrodynamic Models
Depending upon the various models and assumptions, the existing literature on
Gamma Ray Bursts (GRBs) mentions that the gross theoretical value of the
duration of the burst in the hydrodynamical models is tau~r^2/(eta^2 c), where
r is the radius at which the blastwave associated with the fireball (FB)
becomes radiative and sufficiently strong. Here eta = E/Mc^2, c is the speed of
light, E is initial lab frame energy of the FB, and M is the baryonic mass of
the same (Rees and Meszaros 1992). However, within the same basic framework,
some authors (like Katz and Piran) have given tau ~ r^2 /(eta c). We intend to
remove this confusion by considering this problem at a level deeper than what
has been considered so far. Our analysis shows that none of the previously
quoted expressions are exactly correct and in case the FB is produced
impulsively and the radiative processes responsible for the generation of the
GRB are sufficiently fast, its expected duration would be tau ~ar^2/(eta^2 c),
where a~O(10^1). We further discuss the probable change, if any, of this
expression, in case the FB propagates in an anisotropic fashion. We also
discuss some associated points in the context of the Meszaros and Rees
scenario.Comment: 21 pages, LATEX (AAMS4.STY -enclosed), 1 ps. Fig. Accepted in
Astrophysical Journa
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The scheduling of sparse matrix-vector multiplication on a massively parallel dap computer
An efficient data structure is presented which supports general unstructured sparse matrix-vector multiplications on a Distributed Array of Processors (DAP). This approach seeks to reduce the inter-processor data movements and organises the operations in batches of massively parallel steps by a heuristic scheduling procedure performed on the host computer.
The resulting data structure is of particular relevance to iterative schemes for solving linear systems. Performance results for matrices taken from well known Linear Programming (LP) test problems are presented and analysed
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Experimental investigation of an interior search method within a simple framework
A steepest gradient method for solving Linear Programming (LP) problems, followed by a procedure for purifying a non-basic solution to an improved extreme point solution have been embedded within an otherwise simplex based optimiser. The algorithm is designed to be hybrid in nature and exploits many aspects of sparse matrix and revised simplex technology. The interior search step terminates at a boundary point which is usually non-basic. This is then followed by a series of minor pivotal steps which lead to a basic feasible solution with a superior objective function value. It is concluded that the procedures discussed in this paper are likely to have three possible applications, which are
(i) improving a non-basic feasible solution to a superior extreme point solution,
(iii) an improved starting point for the revised simplex method, and
(iii) an efficient implementation of the multiple price strategy of the revised simplex method
Dimension zero at all scales
We consider the notion of dimension in four categories: the category of
(unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and
the category of (unbounded) separable metric spaces and (metrically proper)
uniform maps. A unified treatment is given to the large scale dimension and the
small scale dimension. We show that in all categories a space has dimension
zero if and only if it is equivalent to an ultrametric space. Also,
0-dimensional spaces are characterized by means of retractions to subspaces.
There is a universal zero-dimensional space in all categories. In the Lipschitz
Category spaces of dimension zero are characterized by means of extensions of
maps to the unit 0-sphere. Any countable group of asymptotic dimension zero is
coarsely equivalent to a direct sum of cyclic groups. We construct uncountably
many examples of coarsely inequivalent ultrametric spaces.Comment: 17 pages, To appear in Topology and its Application
Can planetesimals form by collisional fusion?
As a test bed for the growth of protoplanetary bodies in a turbulent
circumstellar disk we examine the fate of a boulder using direct numerical
simulations of particle seeded gas flowing around it. We provide an accurate
description of the flow by imposing no-slip and non-penetrating boundary
conditions on the boulder surface using the immersed boundary method pioneered
by Peskin (2002). Advected by the turbulent disk flow, the dust grains collide
with the boulder and we compute the probability density function (PDF) of the
normal component of the collisional velocity. Through this examination of the
statistics of collisional velocities we test the recently developed concept of
collisional fusion which provides a physical basis for a range of collisional
velocities exhibiting perfect sticking. A boulder can then grow sufficiently
rapidly to settle into a Keplerian orbit on disk evolution time scales.Comment: Astrophysical Journal, in pres
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