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

Constitutive behavior of as-cast A356

The constitutive behavior of aluminum alloy A356 in the as-cast condition has been characterized using compression tests performed over a wide range of deformation temperatures (30-500{\deg}C) and strain rates (\approx0.1-10 /s). This work is intended to support the development of process models for a wide range of conditions including those relevant to casting, forging and machining. The flow stress behavior as a function of temperature and strain rate has been fit to a modified Johnson-Cook and extended Ludwik-Hollomon expression. The data has also been assessed with both the strain-independent Kocks-Mecking and Zener-Hollomon frameworks. The predicted plastic flow stress for each expression are compared. The results indicate that the extended Ludwik-Hollomon is best suited to describe small strain conditions (stage III hardening), while the Kocks-Mecking is best employed for large strain (stage IV). At elevated temperatures, it was found that the Zener-Hollomon model provides the best prediction of flow stress.Comment: 34 pages, 12 figure

Geometrical vs. Fortuin-Kasteleyn Clusters in the Two-Dimensional qq-State Potts Model

The tricritical behavior of the two-dimensional $q$-state Potts model with vacancies for $1\leq q \leq4$ is argued to be encoded in the fractal structure of the geometrical spin clusters of the pure model. The close connection between the critical properties of the pure model and the tricritical properties of the diluted model is shown to be reflected in an intimate relation between Fortuin-Kasteleyn and geometrical clusters: The same transformation mapping the two critical regimes onto each other also maps the two cluster types onto each other. The map conserves the central charge, so that both cluster types are in the same universality class. The geometrical picture is supported by a Monte Carlo simulation of the high-temperature representation of the Ising model ($q=2$). In this new numerical approach, closed graph configurations are generated by means of a Metropolis update algorithm, involving single plaquettes.Comment: 23 pages, 11 figures, 2nd version: references added, introduction partly rewritten, error estimates improve

CO, 13CO and [CI] in Galaxy Centers

Measurements of [CI], (J=2-1) 13CO and (J=4-3) 12CO emission from quiescent, starburst and active galaxy centers reveal a distinct pattern characterized by relatively strong [CI] emission. The [CI] to 13CO emission ratio increases with central [CI] luminosity. It is lowest in quiescent and mild starburst centers and highest for strong starburst centers and active nuclei. Neutral C abundances are close to, or even exceed, CO abundances. The emission is characteristic of warm and dense gas rather than either hot tenuous or cold very dense gas. The relative intensities of CO, [CI], [CII] and far-infrared emission suggest that the dominant excitation mechanism in galaxy centers may be different from that in Photon-Dominated Regions (PDRs).Comment: 6 pages, to appear in the Proceedings of the 2004 European Workshop: "Dense Molecular Gas around Protostars and in Galactic Nuclei", Eds. Y.Hagiwara, W.A.Baan, H.J.van Langevelde, 2004, a special issue of ApSS, Kluwe

The Primordial Inflation Explorer (PIXIE): A Nulling Polarimeter for Cosmic Microwave Background Observations

The Primordial Inflation Explorer (PIXIE) is an Explorer-class mission to measure the gravity-wave signature of primordial inflation through its distinctive imprint on the linear polarization of the cosmic microwave background. The instrument consists of a polarizing Michelson interferometer configured as a nulling polarimeter to measure the difference spectrum between orthogonal linear polarizations from two co-aligned beams. Either input can view the sky or a temperature-controlled absolute reference blackbody calibrator. PIXIE will map the absolute intensity and linear polarization (Stokes I, Q, and U parameters) over the full sky in 400 spectral channels spanning 2.5 decades in frequency from 30 GHz to 6 THz (1 cm to 50 um wavelength). Multi-moded optics provide background-limited sensitivity using only 4 detectors, while the highly symmetric design and multiple signal modulations provide robust rejection of potential systematic errors. The principal science goal is the detection and characterization of linear polarization from an inflationary epoch in the early universe, with tensor-to-scalar ratio r < 10^{-3} at 5 standard deviations. The rich PIXIE data set will also constrain physical processes ranging from Big Bang cosmology to the nature of the first stars to physical conditions within the interstellar medium of the Galaxy.Comment: 37 pages including 17 figures. Submitted to the Journal of Cosmology and Astroparticle Physic

Rigidity percolation in a field

Rigidity Percolation with g degrees of freedom per site is analyzed on randomly diluted Erdos-Renyi graphs with average connectivity gamma, in the presence of a field h. In the (gamma,h) plane, the rigid and flexible phases are separated by a line of first-order transitions whose location is determined exactly. This line ends at a critical point with classical critical exponents. Analytic expressions are given for the densities n_f of uncanceled degrees of freedom and gamma_r of redundant bonds. Upon crossing the coexistence line, n_f and gamma_r are continuous, although their first derivatives are discontinuous. We extend, for the case of nonzero field, a recently proposed hypothesis, namely that the density of uncanceled degrees of freedom is a ``free energy'' for Rigidity Percolation. Analytic expressions are obtained for the energy, entropy, and specific heat. Some analogies with a liquid-vapor transition are discussed. Particularizing to zero field, we find that the existence of a (g+1)-core is a necessary condition for rigidity percolation with g degrees of freedom. At the transition point gamma_c, Maxwell counting of degrees of freedom is exact on the rigid cluster and on the (g+1)-rigid-core, i.e. the average coordination of these subgraphs is exactly 2g, although gamma_r, the average coordination of the whole system, is smaller than 2g. gamma_c is found to converge to 2g for large g, i.e. in this limit Maxwell counting is exact globally as well. This paper is dedicated to Dietrich Stauffer, on the occasion of his 60th birthday.Comment: RevTeX4, psfig, 16 pages. Equation numbering corrected. Minor typos correcte

Chemostratigraphy of Neoproterozoic carbonates: implications for 'blind dating'

The delta C-13(carb) and Sr-87/Sr-86 secular variations in Neoproteozoic seawater have been used for the purpose of 'isotope stratigraphy' but there are a number of problems that can preclude its routine use. In particular, it cannot be used with confidence for 'blind dating'. The compilation of isotopic data on carbonate rocks reveals a high level of inconsistency between various carbon isotope age curves constructed for Neoproteozoic seawater, caused by a relatively high frequency of both global and local delta C-13(carb) fluctuations combined with few reliable age determinations. Further complication is caused by the unresolved problem as to whether two or four glaciations, and associated negative delta C-13(carb) excursions, can be reliably documented. Carbon isotope stratigraphy cannot be used alone for geological correlation and 'blind dating'. Strontium isotope stratigraphy is a more reliable and precise tool for stratigraphic correlations and indirect age determinations. Combining strontium and carbon isotope stratigraphy, several discrete ages within the 590-544 Myr interval, and two age-groups at 660-610 and 740-690 Myr can be resolved

A terminal assessment of stages theory : introducing a dynamic states approach to entrepreneurship

Stages of Growth models were the most frequent theoretical approach to understanding entrepreneurial business growth from 1962 to 2006; they built on the growth imperative and developmental models of that time. An analysis of the universe of such models (N=104) published in the management literature shows no consensus on basic constructs of the approach, nor is there any empirical confirmations of stages theory. However, by changing two propositions of the stages models, a new dynamic states approach is derived. The dynamic states approach has far greater explanatory power than its precursor, and is compatible with leading edge research in entrepreneurship

A multilevel neo-institutional analysis of infection prevention and control in English hospitals: coerced safety culture change?

Despite committed policy, regulative and professional efforts on healthcare safety, little is known about how such macro-interventions permeate organisations and shape culture over time. Informed by neo-institutional theory, we examined how inter-organisational influences shaped safety practices and inter-subjective meanings following efforts for coerced culture change. We traced macro-influences from 2000 to 2015 in infection prevention and control (IPC). Safety perceptions and meanings were inductively analysed from 130 in-depth qualitative interviews with senior- and middle-level managers from 30 English hospitals. A total of 869 institutional interventions were identified; 69% had a regulative component. In this context of forced implementation of safety practices, staff experienced inherent tensions concerning the scope of safety, their ability to be open and prioritisation of external mandates over local need. These tensions stemmed from conflicts among three co-existing institutional logics prevalent in the NHS. In response to requests for change, staff flexibly drew from a repertoire of cognitive, material and symbolic resources within and outside their organisations. They crafted 'strategies of action', guided by a situated assessment of first-hand practice experiences complementing collective evaluations of interventions such as 'pragmatic', 'sensible' and also 'legitimate'. Macro-institutional forces exerted influence either directly on individuals or indirectly by enriching the organisational cultural repertoire

Characterization of a New Phase and Its Effect on the Work Characteristics of a Near-Stoichiometric Ni30Pt20Ti50 High-Temperature Shape Memory Alloy (HTSMA)

A new phase observed in a nominal Ni30Pt20Ti50 (at.%) high temperature shape memory alloy has been characterized using transmission electron microscopy and 3-D atom probe tomography. This phase forms homogeneously in the B2 austenite matrix by a nucleation and growth mechanism and results in a concomitant increase in the martensitic transformation temperature of the base alloy. Although the structure of this phase typically contains a high density of faults making characterization difficult, it appears to be trigonal (-3m point group) with a(sub o) approx. 1.28 nm and c(sub o) approx. 1.4 nm. Precipitation of this phase increases the microhardness of the alloy substantially over that of the solution treated and quenched single-phase material. The effect of precipitation strengthening on the work characteristics of the alloy has been explored through load-biased strain-temperature testing in the solution-treated condition and after aging at 500 C for times ranging from 1 to 256 hours. Work output was found to increase in the aged alloy as a result of an increase in transformation strain, but was not very sensitive to aging time. The amount of permanent deformation that occurred during thermal cycling under load was small but increased with increasing aging time and stress. Nevertheless, the dimensional stability of the alloy at short aging times (1-4 hours) was still very good making it a potentially useful material for high-temperature actuator applications