507 research outputs found
The structure of the hard sphere solid
We show that near densest-packing the perturbations of the HCP structure
yield higher entropy than perturbations of any other densest packing. The
difference between the various structures shows up in the correlations between
motions of nearest neighbors. In the HCP structure random motion of each sphere
impinges slightly less on the motion of its nearest neighbors than in the other
structures.Comment: For related papers see:
http://www.ma.utexas.edu/users/radin/papers.htm
Costs and effects of two public sector delivery channels for long-lasting insecticidal nets in Uganda.
BACKGROUND: In Uganda, long-lasting insecticidal nets (LLIN) have been predominantly delivered through two public sector channels: targeted campaigns or routine antenatal care (ANC) services. Their combination in a mixed-model strategy is being advocated to quickly increase LLIN coverage and maintain it over time, but there is little evidence on the efficiency of each system. This study evaluated the two delivery channels regarding LLIN retention and use, and estimated the associated costs, to contribute towards the evidence-base on LLIN delivery channels in Uganda. METHODS: Household surveys were conducted 5-7 months after LLIN distribution, combining questionnaires with visual verification of LLIN presence. Focus groups and interviews were conducted to further investigate determinants of LLIN retention and use. Campaign distribution was evaluated in Jinja and Adjumani while ANC distribution was evaluated only in the latter district. Costs were calculated from the provider perspective through retrospective analysis of expenditure data, and effects were estimated as cost per LLIN delivered and cost per treated-net-year (TNY). These effects were calculated for the total number of LLINs delivered and for those retained and used. RESULTS: After 5-7 months, over 90% of LLINs were still owned by recipients, and between 74% (Jinja) and 99% (ANC Adjumani) were being used. Costing results showed that delivery was cheapest for the campaign in Jinja and highest for the ANC channel, with economic delivery cost per net retained and used of USD 1.10 and USD 2.31, respectively. Financial delivery costs for the two channels were similar in the same location, USD 1.04 for campaign or USD 1.07 for ANC delivery in Adjumani, but differed between locations (USD 0.67 for campaign delivery in Jinja). Economic cost for ANC distribution were considerably higher (USD 2.27) compared to campaign costs (USD 1.23) in Adjumani. CONCLUSIONS: Targeted campaigns and routine ANC services can both achieve high LLIN retention and use among the target population. The comparatively higher economic cost of delivery through ANC facilities was at least partially due to the relatively short time this system had been in existence. Further studies comparing the cost of well-established ANC delivery with LLIN campaigns and other delivery channels are thus encouraged
The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary
We consider the dimer-monomer problem for the rectangular lattice. By mapping
the problem into one of close-packed dimers on an extended lattice, we rederive
the Tzeng-Wu solution for a single monomer on the boundary by evaluating a
Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by
identifying it as the product of the nonzero eigenvalues of the Kasteleyn
matrix.Comment: 4 Pages to appear in the Physical Review E (2006
Generation of folk song melodies using Bayes transforms
The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models
Logarithmic corrections in the free energy of monomer-dimer model on plane lattices with free boundaries
Using exact computations we study the classical hard-core monomer-dimer
models on m x n plane lattice strips with free boundaries. For an arbitrary
number v of monomers (or vacancies), we found a logarithmic correction term in
the finite-size correction of the free energy. The coefficient of the
logarithmic correction term depends on the number of monomers present (v) and
the parity of the width n of the lattice strip: the coefficient equals to v
when n is odd, and v/2 when n is even. The results are generalizations of the
previous results for a single monomer in an otherwise fully packed lattice of
dimers.Comment: 4 pages, 2 figure
Meanders and the Temperley-Lieb algebra
The statistics of meanders is studied in connection with the Temperley-Lieb
algebra. Each (multi-component) meander corresponds to a pair of reduced
elements of the algebra. The assignment of a weight per connected component
of meander translates into a bilinear form on the algebra, with a Gram matrix
encoding the fine structure of meander numbers. Here, we calculate the
associated Gram determinant as a function of , and make use of the
orthogonalization process to derive alternative expressions for meander numbers
as sums over correlated random walks.Comment: 85p, uuencoded, uses harvmac (l mode) and epsf, 88 figure
On the duality relation for correlation functions of the Potts model
We prove a recent conjecture on the duality relation for correlation
functions of the Potts model for boundary spins of a planar lattice.
Specifically, we deduce the explicit expression for the duality of the n-site
correlation functions, and establish sum rule identities in the form of the
M\"obius inversion of a partially ordered set. The strategy of the proof is by
first formulating the problem for the more general chiral Potts model. The
extension of our consideration to the many-component Potts models is also
given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.
Loop models and their critical points
Loop models have been widely studied in physics and mathematics, in problems
ranging from polymers to topological quantum computation to Schramm-Loewner
evolution. I present new loop models which have critical points described by
conformal field theories. Examples include both fully-packed and dilute loop
models with critical points described by the superconformal minimal models and
the SU(2)_2 WZW models. The dilute loop models are generalized to include
SU(2)_k models as well.Comment: 20 pages, 15 figure
Some Exact Results for Spanning Trees on Lattices
For -vertex, -dimensional lattices with , the number
of spanning trees grows asymptotically as
in the thermodynamic limit. We present an exact closed-form result for the
asymptotic growth constant for spanning trees on the
-dimensional body-centered cubic lattice. We also give an exact integral
expression for on the face-centered cubic lattice and an exact
closed-form expression for on the lattice.Comment: 7 pages, 1 tabl
Tetromino tilings and the Tutte polynomial
We consider tiling rectangles of size 4m x 4n by T-shaped tetrominoes. Each
tile is assigned a weight that depends on its orientation and position on the
lattice. For a particular choice of the weights, the generating function of
tilings is shown to be the evaluation of the multivariate Tutte polynomial
Z\_G(Q,v) (known also to physicists as the partition function of the Q-state
Potts model) on an (m-1) x (n-1) rectangle G, where the parameter Q and the
edge weights v can take arbitrary values depending on the tile weights.Comment: 8 pages, 6 figure
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