3,539 research outputs found
Asymptotic Expansions for lambda_d of the Dimer and Monomer-Dimer Problems
In the past few years we have derived asymptotic expansions for lambda_d of
the dimer problem and lambda_d(p) of the monomer-dimer problem. The many
expansions so far computed are collected herein. We shine a light on results in
two dimensions inspired by the work of M. E. Fisher. Much of the work reported
here was joint with Shmuel Friedland.Comment: 4 page
Exact asymptotics of monomer-dimer model on rectangular semi-infinite lattices
By using the asymptotic theory of Pemantle and Wilson, exact asymptotic
expansions of the free energy of the monomer-dimer model on rectangular lattices in terms of dimer density are obtained for small values
of , at both high and low dimer density limits. In the high dimer density
limit, the theoretical results confirm the dependence of the free energy on the
parity of , a result obtained previously by computational methods. In the
low dimer density limit, the free energy on a cylinder
lattice strip has exactly the same first terms in the series expansion as
that of infinite lattice.Comment: 9 pages, 6 table
An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem
Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer
lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower
bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q).
The upper bound is based on a conjecture claiming that the p monomer-dimer
entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We
compute the first three terms in the formal asymptotic expansion of
(lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching
conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,
Complementary algorithms for graphs and percolation
A pair of complementary algorithms are presented. One of the pair is a fast
method for connecting graphs with an edge. The other is a fast method for
removing edges from a graph. Both algorithms employ the same tree based graph
representation and so, in concert, can arbitrarily modify any graph. Since the
clusters of a percolation model may be described as simple connected graphs, an
efficient Monte Carlo scheme can be constructed that uses the algorithms to
sweep the occupation probability back and forth between two turning points.
This approach concentrates computational sampling time within a region of
interest. A high precision value of pc = 0.59274603(9) was thus obtained, by
Mersenne twister, for the two dimensional square site percolation threshold.Comment: 5 pages, 3 figures, poster version presented at statphys23 (2007
Monomer-dimer model in two-dimensional rectangular lattices with fixed dimer density
The classical monomer-dimer model in two-dimensional lattices has been shown
to belong to the \emph{``#P-complete''} class, which indicates the problem is
computationally ``intractable''. We use exact computational method to
investigate the number of ways to arrange dimers on
two-dimensional rectangular lattice strips with fixed dimer density . For
any dimer density , we find a logarithmic correction term in the
finite-size correction of the free energy per lattice site. The coefficient of
the logarithmic correction term is exactly -1/2. This logarithmic correction
term is explained by the newly developed asymptotic theory of Pemantle and
Wilson. The sequence of the free energy of lattice strips with cylinder
boundary condition converges so fast that very accurate free energy
for large lattices can be obtained. For example, for a half-filled lattice,
, while and . For , is accurate at least to 10 decimal
digits. The function reaches the maximum value at , with 11 correct digits. This is also
the \md constant for two-dimensional rectangular lattices. The asymptotic
expressions of free energy near close packing are investigated for finite and
infinite lattice widths. For lattices with finite width, dependence on the
parity of the lattice width is found. For infinite lattices, the data support
the functional form obtained previously through series expansions.Comment: 15 pages, 5 figures, 5 table
Inversion of stellar statistics equation for the Galactic Bulge
A method based on Lucy (1974, AJ 79, 745) iterative algorithm is developed to
invert the equation of stellar statistics for the Galactic bulge and is then
applied to the K-band star counts from the Two-Micron Galactic Survey in a
number of off-plane regions (10 deg.>|b|>2 deg., |l|<15 deg.).
The top end of the K-band luminosity function is derived and the morphology
of the stellar density function is fitted to triaxial ellipsoids, assuming a
non-variable luminosity function within the bulge. The results, which have
already been outlined by Lopez-Corredoira et al.(1997, MNRAS 292, L15), are
shown in this paper with a full explanation of the steps of the inversion: the
luminosity function shows a sharp decrease brighter than M_K=-8.0 mag when
compared with the disc population; the bulge fits triaxial ellipsoids with the
major axis in the Galactic plane at an angle with the line of sight to the
Galactic centre of 12 deg. in the first quadrant; the axial ratios are
1:0.54:0.33, and the distance of the Sun from the centre of the triaxial
ellipsoid is 7860 pc. The major-minor axial ratio of the ellipsoids is found
not to be constant. However, the interpretation of this is controversial. An
eccentricity of the true density-ellipsoid gradient and a population gradient
are two possible explanations.
The best fit for the stellar density, for 1300 pc<t<3000 pc, are calculated
for both cases, assuming an ellipsoidal distribution with constant axial
ratios, and when K_z is allowed to vary. From these, the total number of bulge
stars is ~ 3 10^{10} or ~ 4 10^{10}, respectively.Comment: 19 pages, 23 figures, accepted in MNRA
New Lower Bounds on the Self-Avoiding-Walk Connective Constant
We give an elementary new method for obtaining rigorous lower bounds on the
connective constant for self-avoiding walks on the hypercubic lattice .
The method is based on loop erasure and restoration, and does not require exact
enumeration data. Our bounds are best for high , and in fact agree with the
first four terms of the expansion for the connective constant. The bounds
are the best to date for dimensions , but do not produce good results
in two dimensions. For , respectively, our lower bound is within
2.4\%, 0.43\%, 0.12\%, 0.044\% of the value estimated by series extrapolation.Comment: 35 pages, 388480 bytes Postscript, NYU-TH-93/02/0
The Dialogic: art work as method
This paper discusses how the multisite artwork The Dialogic demonstrates an innovative, supportive and generative artwork-as-method which resists overly reductive, and prescriptive tendencies within practice-led research. It continues a dialogue between participants that has been ongoing since 2012. The Dialogic has been adapted through the work of multiple artists, and this iteration is offered as a dialogue between the artists John Hammersley and Rachelle Viader Knowles in response to reflections in the work of Simon Pope. The Dialogic emerged as a method-work which imbricates the artist in socially situated exchange across multiple contexts, enacts coauthored and co-produced meaning-making, and challenges assumptions about the separation of art and research and notions of the detached artist-researcher. Its innovative contribution to practice-led research is how it demonstrates dialogical art as the on-going re-construction of a community of support, sustained through a commitment to knowledge mobilization, continued exchange and engagement in which the artist and their work are ‘answerable’ for the choices and actions in their art-as-research. The work functions as a generative research tool. It demonstrates how semi-structured everyday conversational-exchange-as-art can simultaneously lead to the emergence of subconsciously held insights, construct a community of practice that helps shape thinking outside of institutional frameworks, and act as a situated literature review that may disrupt traditional frameworks of knowledge production normalized in much fine art research. The authors argue that this method is appropriate to dialogical art-as-research as it makes a necessary contribution to the practice-led research tool box. It offers a method of distributive authorship grounded in an emergent, situated and more provisional mode of meaning-making that facilitates generous, democratized, peer-to-peer co-mentorship and skill-sharing contributing to understandings of dialogical art as research. This they argue is an increasingly necessary counterpoint to the reduction of practice-led fine art research to a training in mechanistic methods, reductive evaluation, and singular concrete outcomes aimed at satisfying the artist-researcher as customer and consumer
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
Enumeration of self avoiding trails on a square lattice using a transfer matrix technique
We describe a new algebraic technique, utilising transfer matrices, for
enumerating self-avoiding lattice trails on the square lattice. We have
enumerated trails to 31 steps, and find increased evidence that trails are in
the self-avoiding walk universality class. Assuming that trails behave like , we find and .Comment: To be published in J. Phys. A:Math Gen. Pages: 16 Format: RevTe
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