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

The Computational Complexity of Knot and Link Problems

We consider the problem of deciding whether a polygonal knot in 3-dimensional Euclidean space is unknotted, capable of being continuously deformed without self-intersection so that it lies in a plane. We show that this problem, {\sc unknotting problem} is in {\bf NP}. We also consider the problem, {\sc unknotting problem} of determining whether two or more such polygons can be split, or continuously deformed without self-intersection so that they occupy both sides of a plane without intersecting it. We show that it also is in NP. Finally, we show that the problem of determining the genus of a polygonal knot (a generalization of the problem of determining whether it is unknotted) is in {\bf PSPACE}. We also give exponential worst-case running time bounds for deterministic algorithms to solve each of these problems. These algorithms are based on the use of normal surfaces and decision procedures due to W. Haken, with recent extensions by W. Jaco and J. L. Tollefson.Comment: 32 pages, 1 figur

The Black Box: Unraveling Family Business Succession

Using the family business succession, resource-based view of firms, familiness, and organizational clan literatures, this article develops a model based on the ability of the family business to use familiness, a specific bundle of attributes deriving from a family’s culture, as a competitive advantage for the family firm. In particular, this resource-based framework of family business shows how familiness can distinguish between family firms that succeed beyond the second generation and those that do not. Implications for future research are discussed

Downstream benefits vs upstream costs of land use change for water-yield and salt-load targets in the Macquarie Catchment, NSW

The net present value (NPV) of downstream economic benefits of changes in water-yield (W) and salt-load (S) of mean annual river flow received by a lower catchment from an upper catchment are described as a 3-dimensional (NPV,W, S) surface, where dNPV/dW > 0 and dNPV/d(S/W) < 0. Upstream changes in land use (i.e. forest clearing or forest establishment, which result in higher or lower water-yields, respectively) are driven by economic consequences for land owners. This paper defines conditions under which costs of strategic upstream land use changes could be exceeded by compensations afforded by downstream benefits from altered water-yields and/or lower salt loads. The paper presents methods, and preliminary calculations for an example river, quantifying the scope for such combinations, and raising the question of institutional designs to achieve mutually beneficial upstream and downstream outcomes. Examples refer to the Macquarie River downstream of Dubbo, NSW, and Little River, an upstream tributary.policy, markets, upstream, downstream, water, salinity, Land Economics/Use,

Planetary systems around close binary stars: the case of the very dusty, Sun-like, spectroscopic binary BD+20 307

Field star BD+20 307 is the dustiest known main sequence star, based on the fraction of its bolometric luminosity, 4%, that is emitted at infrared wavelengths. The particles that carry this large IR luminosity are unusually warm, comparable to the temperature of the zodiacal dust in the solar system, and their existence is likely to be a consequence of a fairly recent collision of large objects such as planets or planetary embryos. Thus, the age of BD+20 307 is potentially of interest in constraining the era of terrestrial planet formation. The present project was initiated with an attempt to derive this age using the Chandra X-ray Observatory to measure the X-ray flux of BD+20 307 in conjunction with extensive photometric and spectroscopic monitoring observations from Fairborn Observatory. However, the recent realization that BD+20 307 is a short period, double-line, spectroscopic binary whose components have very different lithium abundances, vitiates standard methods of age determination. We find the system to be metal-poor; this, combined with its measured lithium abundances, indicates that BD+20 307 may be several to many Gyr old. BD+20 307 affords astronomy a rare peek into a mature planetary system in orbit around a close binary star (because such systems are not amenable to study by the precision radial velocity technique).Comment: accepted for ApJ, December 10, 200

Spanning Trees on Lattices and Integration Identities

For a lattice $\Lambda$ with $n$ vertices and dimension $d$ equal or higher than two, the number of spanning trees $N_{ST}(\Lambda)$ grows asymptotically as $\exp(n z_\Lambda)$ in the thermodynamic limit. We present exact integral expressions for the asymptotic growth constant $z_\Lambda$ for spanning trees on several lattices. By taking different unit cells in the calculation, many integration identities can be obtained. We also give $z_{\Lambda (p)}$ on the homeomorphic expansion of $k$-regular lattices with $p$ vertices inserted on each edge.Comment: 15 pages, 3 figures, 1 tabl

Cavitation-induced force transition in confined viscous liquids under traction

We perform traction experiments on simple liquids highly confined between parallel plates. At small separation rates, we observe a simple response corresponding to a convergent Poiseuille flow. Dramatic changes in the force response occur at high separation rates, with the appearance of a force plateau followed by an abrupt drop. By direct observation in the course of the experiment, we show that cavitation accounts for these features which are reminiscent of the utmost complex behavior of adhesive films under traction. Surprisingly enough, this is observed here in purely viscous fluids.Comment: Submitted to Physical Review Letters on May 31, 2002. Related informations on http://www.crpp.u-bordeaux.fr/tack.htm

Homological Error Correction: Classical and Quantum Codes

We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming bound. In the quantum case, we show that for non-orientable surfaces it is impossible to construct homological codes based on qudits of dimension $D>2$, while for orientable surfaces with boundaries it is possible to construct them for arbitrary dimension $D$. We give a method to obtain planar homological codes based on the construction of quantum codes on compact surfaces without boundaries. We show how the original Shor's 9-qubit code can be visualized as a homological quantum code. We study the problem of constructing quantum codes with optimal encoding rate. In the particular case of toric codes we construct an optimal family and give an explicit proof of its optimality. For homological quantum codes on surfaces of arbitrary genus we also construct a family of codes asymptotically attaining the maximum possible encoding rate. We provide the tools of homology group theory for graphs embedded on surfaces in a self-contained manner.Comment: Revtex4 fil