26 research outputs found
Rapid Accurate Calculation of the s-Wave Scattering Length
Transformation of the conventional radial Schr\"odinger equation defined on
the interval into an equivalent form defined on the finite
domain allows the s-wave scattering length to be
exactly expressed in terms of a logarithmic derivative of the transformed wave
function at the outer boundary point , which corresponds to
. In particular, for an arbitrary interaction potential that dies off
as fast as for , the modified wave function obtained
by using the two-parameter mapping function has no singularities, and
For
a well bound potential with equilibrium distance , the optimal mapping
parameters are and . An
outward integration procedure based on Johnson's log-derivative algorithm
[B.R.\ Johnson, J.\ Comp.\ Phys., \textbf{13}, 445 (1973)] combined with a
Richardson extrapolation procedure is shown to readily yield high precision
-values both for model Lennard-Jones () potentials and for realistic
published potentials for the Xe--e, Cs_2(a\,^3\Sigma_u^+) and
He_2(X\,^1\Sigma_g^+) systems. Use of this same transformed
Schr{\"o}dinger equation was previously shown [V.V. Meshkov et al., Phys.\
Rev.\ A, {\bf 78}, 052510 (2008)] to ensure the efficient calculation of all
bound levels supported by a potential, including those lying extremely close to
dissociation.Comment: 12 pages, 9 figures, to appear in J. Chem. Phy
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An introduction to chordal graphs and clique trees
Clique trees and chordal graphs have carved out a niche for themselves in recent work on sparse matrix algorithms, due primarily to research questions associated with advanced computer architectures. This paper is a unified and elementary introduction to the standard characterizations of chordal graphs and clique trees. The pace is leisurely, as detailed proofs of all results are included. We also briefly discuss applications of chordal graphs and clique trees in sparse matrix computations
A Self-stabilizing Algorithm for Edge Monitoring Problem
International audienceSelf-monitoring is a simple and effective mechanism for the security of wireless sensor networks (WSNs), especially to cope against compromised nodes. A node v can monitor an edge e if both end-nodes of e are neighbors of v; i.e., e together with v forms a triangle in thegraph. Moreover, some edges need more than one monitor. Finding a set of monitoring nodes satisfying all monitoring constraints is called the edge-monitoring problem. The minimum edge-monitoring problem is long known to be NP-complete. In this paper, we present a novelsilent self-stabilizing algorithm for computing a minimal edge-monitoring set. Correctness and termination are proven for the unfair distributed scheduler
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On finding minimum-diameter clique trees
It is well-known that any chordal graph can be represented as a clique tree (acyclic hypergraph, join tree). Since some chordal graphs have many distinct clique tree representations, it is interesting to consider which one is most desirable under various circumstances. A clique tree of minimum diameter (or height) is sometimes a natural candidate when choosing clique trees to be processed in a parallel computing environment. This paper introduces a linear time algorithm for computing a minimum-diameter clique tree. The new algorithm is an analogue of the natural greedy algorithm for rooting an ordinary tree in order to minimize its height. It has potential application in the development of parallel algorithms for both knowledge-based systems and the solution of sparse linear systems of equations. 31 refs., 7 figs
A self-stabilizing 2/3-approximation algorithm for the maximum matching problem
International audienceThe matching problem asks for a large set of disjoint edges in a graph. It is a problem that has received considerable attention in both the sequential and self-stabilizing literature. Previous work has resulted in self-stabilizing algorithms for computing a maximal (-approximation) matching in a general graph, as well as computing a -approximation on more specific graph types. In the following we present the first self-stabilizing algorithm for finding a -approximation to the maximum matching problem in a general graph. We show that our new algorithm stabilizes in at most exponential time under a distributed adversarial daemon, and rounds under a distributed fair daemon, where is the number of nodes in the graph
Finding contractions and induced minors in chordal graphs via disjoint paths.
The k-Disjoint Paths problem, which takes as input a graph G and k pairs of specified vertices (s i ,t i ), asks whether G contains k mutually vertex-disjoint paths P i such that P i connects s i and t i , for i = 1,…,k. We study a natural variant of this problem, where the vertices of P i must belong to a specified vertex subset U i for i = 1,…,k. In contrast to the original problem, which is polynomial-time solvable for any fixed integer k, we show that this variant is NP-complete even for k = 2. On the positive side, we prove that the problem becomes polynomial-time solvable for any fixed integer k if the input graph is chordal. We use this result to show that, for any fixed graph H, the problems H-Contractibility and H-Induced Minor can be solved in polynomial time on chordal graphs. These problems are to decide whether an input graph G contains H as a contraction or as an induced minor, respectively