Pedestrian Solution of the Two-Dimensional Ising Model

The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2 fixed, minor beautification

The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of low-degree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.Comment: Graph Drawing 201

Love Among the Roses

It was on one summer\u27s eveningin the merry month of JuneI beheld a damsel sitting \u27Mid flower\u27s sweet perfumeShe had a novel readingjust as I was passing byAnd as she turned another pageI saw the brightest eye A bewitching smile was on her faceAs charming as the posies I felt the smart of Cupid\u27s dart\u27Twas love among the roses. CHORUSNow I hate to tell but then I must,Within her heart I place my trustShe was sitting in the garden WHere the little butterlfy reposesAnd how we met,I\u27ll ne\u27er forgwet,\u27Twas Love among the Roses. Now I passed her house next eveningThe clock had just struck eightAnd I saw my future happinessShe was standing by the garden gateShe smile as I approached herAnd I begged her to excuse May I view those pretty flowers She murmured if you chooseI spoke about the violetsThen finally made proposesThro\u27 the garden we walked of happiness talked\u27Twas love among the roses. I confess I love Matilda,Matilda, that\u27s her name,And there is a charm about her Which I never can explain She dresses up to fashion To her style there is no endAnd of course she must look dashingFor she wears a Grecian Bend But she\u27s left her home and where she\u27s goneMost everyone supposes For as dear as life is my little wife\u27Twas love among the roses

Thermodynamics for two flavor QCD

We conclude our analysis of the N_t=6 equation of state for two flavor QCD, first described at last year's conference. We have obtained new runs at am_q=0.025 and improved runs at am_q=0.0125. The results are extrapolated to m_q=0, and we extract the speed of sound as well. We also present evidence for a restoration of the SU(2) X SU(2) chiral symmetry just above the crossover, but not of the axial U(1) chiral symmetry.Comment: Poster presented at LATTICE96(finite temperature). 4 pages, LaTeX plus 5 encapsulated Postscript figure

Chapter 19: Vulnerability of coastal and estuarine habitats in the Great Barrier Reef to climate change

This chapter attempts to address the vulnerability of the CEM in the Great Barrier Reef region to global climate change. It does not consider individual habitats (eg reefs or seagrasses) but goes beyond the individual species and habitat assessments, to consider impacts on the whole coastal marine community complex, and the ecological processes that support its functioning.This is Chapter 19 of Climate change and the Great Barrier Reef: a vulnerability assessment. The entire book can be found at http://hdl.handle.net/11017/13

Conceptual design of an aircraft automated coating removal system

Paint stripping of the U.S. Air Force`s large transport aircrafts is currently a labor-intensive, manual process. Significant reductions in costs, personnel and turnaround time can be accomplished by the judicious use of automation in some process tasks. This paper presents the conceptual design of a coating removal systems for the tail surfaces of the C-5 plane. Emphasis is placed on the technology selection to optimize human-automation synergy with respect to overall costs, throughput, quality, safety, and reliability. Trade- offs between field-proven vs. research-requiring technologies, and between expected gain vs. cost and complexity, have led to a conceptual design which is semi-autonomous (relying on the human for task specification and disturbance handling) yet incorporates sensor- based automation (for sweep path generation and tracking, surface following, stripping quality control and tape/breach handling)

A Lattice Study of the Gluon Propagator in Momentum Space

We consider pure glue QCD at beta=5.7, beta=6.0 and beta=6.3. We evaluate the gluon propagator both in time at zero 3-momentum and in momentum space. From the former quantity we obtain evidence for a dynamically generated effective mass, which at beta=6.0 and beta=6.3 increases with the time separation of the sources, in agreement with earlier results. The momentum space propagator G(k) provides further evidence for mass generation. In particular, at beta=6.0, for k less than 1 GeV, the propagator G(k) can be fit to a continuum formula proposed by Gribov and others, which contains a mass scale b, presumably related to the hadronization mass scale. For higher momenta Gribov's model no longer provides a good fit, as G(k) tends rather to follow an inverse power law. The results at beta=6.3 are consistent with those at beta=6.0, but only the high momentum region is accessible on this lattice. We find b in the range of three to four hundred MeV and the exponent of the inverse power law about 2.7. On the other hand, at beta=5.7 (where we can only study momenta up to 1 GeV) G(k) is best fit to a simple massive boson propagator with mass m. We argue that such a discrepancy may be related to a lack of scaling for low momenta at beta=5.7. {}From our results, the study of correlation functions in momentum space looks promising, especially because the data points in Fourier space turn out to be much less correlated than in real space.Comment: 19 pages + 12 uuencoded PostScript picture

Axions and their Relatives

A review of the status of axions and axion-like particles is given. Special attention is devoted to the recent results of the PVLAS collaboration, which are in conflict with the CAST data and with the astrophysical constraints. Solutions to the puzzle and the implications for new physics are discussed. The question of axion-like particles being dark matter is also addressed.Comment: Updated version of an invited talk at the Axion Training (CERN, December 2005). To appear as a Lecture Notes in Physics (Springer-Verlag), edited by B. Beltran, M. Kuster and G. Raffel