879 research outputs found
Theory of Computation of Multidimensional Entropy with an Application to the Monomer-Dimer Problem
We outline the most recent theory for the computation of the exponential
growth rate of the number of configurations on a multi-dimensional grid. As an
application we compute the monomer-dimer constant for the 2-dimensional grid to
8 decimal digits, agreeing with the heuristic computations of Baxter, and for
the 3-dimensional grid with an error smaller than 1.35%.Comment: 35 pages, one pstricks and two eps figures, submitte
The plasma dynamics of hypersonic spacecraft: Applications of laboratory simulations and active in situ experiments
Attempts to gain an understanding of spacecraft plasma dynamics via experimental investigation of the interaction between artificially synthesized, collisionless, flowing plasmas and laboratory test bodies date back to the early 1960's. In the past 25 years, a number of researchers have succeeded in simulating certain limited aspects of the complex spacecraft-space plasma interaction reasonably well. Theoretical treatments have also provided limited models of the phenomena. Several active experiments were recently conducted from the space shuttle that specifically attempted to observe the Orbiter-ionospheric interaction. These experiments have contributed greatly to an appreciation for the complexity of spacecraft-space plasma interaction but, so far, have answered few questions. Therefore, even though the plasma dynamics of hypersonic spacecraft is fundamental to space technology, it remains largely an open issue. A brief overview is provided of the primary results from previous ground-based experimental investigations and the preliminary results of investigations conducted on the STS-3 and Spacelab 2 missions. In addition, several, as yet unexplained, aspects of the spacecraft-space plasma interaction are suggested for future research
On pro-isomorphic zeta functions of -groups of even Hirsch length
Pro-isomorphic zeta functions of finitely generated nilpotent groups form one
of the group-theoretic generalisations of the Riemann zeta functions. They are
Dirichlet generating functions enumerating finite-index subgroups whose
profinite completion is isomorphic to that of the ambient group. We study
pro-isomorphic zeta functions of -groups; these form the building blocks
of finitely generated class two nilpotent groups with centre of rank two, up to
commensurability. These groups were classified by Grunewald and Segal, and can
be indexed by primary polynomials whose companion matrices define commutator
relations. We provide a key step towards the elucidation of the pro-isomorphic
zeta functions of -groups of even Hirsch length by describing the
automorphism groups of the associated graded Lie rings. Utilizing this
description of the automorphism groups, we calculate the local pro-isomorphic
zeta functions of groups associated to the polynomials and . In both
cases, the local zeta functions are uniform in the prime~ and satisfy
functional equations.Comment: 29 page
Cones of closed alternating walks and trails
Consider a graph whose edges have been colored red and blue. Assign a
nonnegative real weight to every edge so that at every vertex, the sum of the
weights of the incident red edges equals the sum of the weights of the incident
blue edges. The set of all such assignments forms a convex polyhedral cone in
the edge space, called the \emph{alternating cone}. The integral (respectively,
) vectors in the alternating cone are sums of characteristic vectors
of closed alternating walks (respectively, trails). We study the basic
properties of the alternating cone, determine its dimension and extreme rays,
and relate its dimension to the majorization order on degree sequences. We
consider whether the alternating cone has integral vectors in a given box, and
use residual graph techniques to reduce this problem to searching for a closed
alternating trail through a given edge. The latter problem, called alternating
reachability, is solved in a companion paper along with related results.Comment: Minor rephrasing, new pictures, 14 page
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