5,723 research outputs found
Isomorphism versus commensurability for a class of finitely presented groups
We construct a class of finitely presented groups where the isomorphism problem is solvable but the commensurability problem is unsolvable. Conversely, we construct a class of finitely presented groups within which the commensurability problem is solvable but the isomorphism problem is unsolvable. These are first examples of such a contrastive complexity behaviour with respect to the isomorphism problem
Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning
We show that linear congruential pseudo-random-number generators can cause
systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm,
if the lattice size is a multiple of a very large power of 2 and one random
number is used per bond. These systematic errors arise from correlations within
a single bond-update half-sweep. The errors can be eliminated (or at least
radically reduced) by updating the bonds in a random order or in an aperiodic
manner. It also helps to use a generator of large modulus (e.g. 60 or more
bits).Comment: Revtex4, 4 page
SUE: A Special Purpose Computer for Spin Glass Models
The use of last generation Programmable Electronic Components makes possible
the construction of very powerful and competitive special purpose computers. We
have designed, constructed and tested a three-dimensional Spin Glass model
dedicated machine, which consists of 12 identical boards. Each single board can
simulate 8 different systems, updating all the systems at every clock cycle.
The update speed of the whole machine is 217ps/spin with 48 MHz clock
frequency. A device devoted to fast random number generation has been developed
and included in every board. The on-board reprogrammability permits us to
change easily the lattice size, or even the update algorithm or the action. We
present here a detailed description of the machine and the first runs using the
Heat Bath algorithm.Comment: Submitted to Computer Physics Communications, 19 pages, 5 figures,
references adde
Topological fluid mechanics of point vortex motions
Topological techniques are used to study the motions of systems of point
vortices in the infinite plane, in singly-periodic arrays, and in
doubly-periodic lattices. The reduction of each system using its symmetries is
described in detail. Restricting to three vortices with zero net circulation,
each reduced system is described by a one degree of freedom Hamiltonian. The
phase portrait of this reduced system is subdivided into regimes using the
separatrix motions, and a braid representing the topology of all vortex motions
in each regime is computed. This braid also describes the isotopy class of the
advection homeomorphism induced by the vortex motion. The Thurston-Nielsen
theory is then used to analyse these isotopy classes, and in certain cases
strong conclusions about the dynamics of the advection can be made
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