Correlation functions for the Z-invariant Ising model

The correlation functions of the Z-invariant Ising model are calculated explicitly using the Vertex Operators language developed by the Kyoto school.Comment: Latex Document, minor change and new Reference adde

Energy and global warming impacts of HFC refrigerants and emerging technologies: TEWI-III

The use of hydrofluorocarbons (BFCs) which were developed as alternative refrigerants and insulating foam blowing agents to replace chlorofluorocarbons (CFCs) is now being affected by scientific investigations of greenhouse warming and questions about the effects of refrigerants and blowing agents on global warming. A Total Equivalent Warming Impact (TEWI) assessment analyzes the environmental affects of these halogenated working fluids in energy consuming applications by combining a direct effect resulting from the inadvertent release of HFCs to the atmosphere with an indirect effect resulting from the combustion of fossil fuels needed to provide the energy to operate equipment using these compounds as working fluids. TEWI is a more balanced measure of environmental impact because it is not based solely on the global warming potential (GWP) of the working fluid. It also shows the environmental benefit of efficient technologies that result in less CO{sub 2} generation and eventual emission to the earth`s atmosphere. The goal of TEWI is to assess total global warming impact of all the gases released to the atmosphere, including CO{sub 2} emissions from energy conversion. Alternative chemicals and technologies have been proposed as substitutes for HFCs in the vapor-compression cycle for refrigeration and air conditioning and for polymer foams in appliance and building insulations which claim substantial environmental benefits. Among these alternatives are: (1) Hydrocarbon (HC) refrigerants and blowing agents which have zero ozone depleting potential and a negligible global warming potential, (2) CO{sub 2} as a refrigerant and blowing agent, (3) Ammonia (NH{sub 3}) vapor compression systems, (4) Absorption chiller and heat pumping cycles using ammonia/water or lithium bromide/water, and (5) Evacuated panel insulations. This paper summarizes major results and conclusions of the detailed final report on the TEWI-111 study

Phase coexistence of gradient Gibbs states

We consider the (scalar) gradient fields $\eta=(\eta_b)$--with $b$ denoting the nearest-neighbor edges in $\Z^2$--that are distributed according to the Gibbs measure proportional to \texte^{-\beta H(\eta)}\nu(\textd\eta). Here $H=\sum_bV(\eta_b)$ is the Hamiltonian, $V$ is a symmetric potential, $\beta>0$ is the inverse temperature, and $\nu$ is the Lebesgue measure on the linear space defined by imposing the loop condition $\eta_{b_1}+\eta_{b_2}=\eta_{b_3}+\eta_{b_4}$ for each plaquette $(b_1,b_2,b_3,b_4)$ in $\Z^2$. For convex $V$, Funaki and Spohn have shown that ergodic infinite-volume Gibbs measures are characterized by their tilt. We describe a mechanism by which the gradient Gibbs measures with non-convex $V$ undergo a structural, order-disorder phase transition at some intermediate value of inverse temperature $\beta$. At the transition point, there are at least two distinct gradient measures with zero tilt, i.e., $E \eta_b=0$.Comment: 3 figs, PTRF style files include

Using a cognitive architecture to examine what develops

Different theories of development propose alternative mechanisms by which development occurs. Cognitive architectures can be used to examine the influence of each proposed mechanism of development while keeping all other mechanisms constant. An ACT-R computational model that matched adult behavior in solving a 21-block pyramid puzzle was created. The model was modified in three ways that corresponded to mechanisms of development proposed by developmental theories. The results showed that all the modifications (two of capacity and one of strategy choice) could approximate the behavior of 7-year-old children on the task. The strategy-choice modification provided the closest match on the two central measures of task behavior (time taken per layer, r = .99, and construction attempts per layer, r = .73). Modifying cognitive architectures is a fruitful way to compare and test potential developmental mechanisms, and can therefore help in specifying “what develops.

An alternative order parameter for the 4-state Potts model

We have investigated the dynamic critical behavior of the two-dimensional 4-state Potts model using an alternative order parameter first used by Vanderzande [J. Phys. A: Math. Gen. \textbf{20}, L549 (1987)] in the study of the Z(5) model. We have estimated the global persistence exponent $\theta_g$ by following the time evolution of the probability $P(t)$ that the considered order parameter does not change its sign up to time $t$. We have also obtained the critical exponents $\theta$, $z$, $\nu$, and $\beta$ using this alternative definition of the order parameter and our results are in complete agreement with available values found in literature.Comment: 6 pages, 6 figure

Adsorption of Reactive Particles on a Random Catalytic Chain: An Exact Solution

We study equilibrium properties of a catalytically-activated annihilation $A + A \to 0$ reaction taking place on a one-dimensional chain of length $N$ ($N \to \infty$) in which some segments (placed at random, with mean concentration $p$) possess special, catalytic properties. Annihilation reaction takes place, as soon as any two $A$ particles land onto two vacant sites at the extremities of the catalytic segment, or when any $A$ particle lands onto a vacant site on a catalytic segment while the site at the other extremity of this segment is already occupied by another $A$ particle. Non-catalytic segments are inert with respect to reaction and here two adsorbed $A$ particles harmlessly coexist. For both "annealed" and "quenched" disorder in placement of the catalytic segments, we calculate exactly the disorder-average pressure per site. Explicit asymptotic formulae for the particle mean density and the compressibility are also presented.Comment: AMSTeX, 27 pages + 4 figure

Variation of texture anisotropy and hardness with build parameters and wall height in directed-energy-deposited 316L steel

Directed energy deposition (DED) is an emerging technology with repair applications in critical aerospace components. Mechanical properties of DED components have been shown to vary significantly through a part, making it difficult to achieve the level of process control required for these applications. Using thermal data captured in-situ, cooling rates and melt pool dimensions were calculated and related to the final grain structure, captured by EBSD. The changes in cooling rate explain the microstructural variation between different processing parameters and through the build height. A new approach, using a cumulative anisotropy factor was implemented and correlates the variation in hardness with grain structure. Two regimes were found depending on the linear heat input in 316L, with high linear heat input resulting in great amounts of mechanical anisotropy on the component level. The relationships between thermal signature and mechanical properties suggest close control of anisotropy could be achieved by monitoring and controlling the melt pool size using a coaxial camera

The critical Z-invariant Ising model via dimers: locality property

We study a large class of critical two-dimensional Ising models, namely critical Z-invariant Ising models. Fisher [Fis66] introduced a correspondence between the Ising model and the dimer model on a decorated graph, thus setting dimer techniques as a powerful tool for understanding the Ising model. In this paper, we give a full description of the dimer model corresponding to the critical Z-invariant Ising model, consisting of explicit expressions which only depend on the local geometry of the underlying isoradial graph. Our main result is an explicit local formula for the inverse Kasteleyn matrix, in the spirit of [Ken02], as a contour integral of the discrete exponential function of [Mer01a,Ken02] multiplied by a local function. Using results of [BdT08] and techniques of [dT07b,Ken02], this yields an explicit local formula for a natural Gibbs measure, and a local formula for the free energy. As a corollary, we recover Baxter's formula for the free energy of the critical Z-invariant Ising model [Bax89], and thus a new proof of it. The latter is equal, up to a constant, to the logarithm of the normalized determinant of the Laplacian obtained in [Ken02].Comment: 55 pages, 29 figure

Confirmation of Anomalous Dynamical Arrest in attractive colloids: a molecular dynamics study

Previous theoretical, along with early simulation and experimental, studies have indicated that particles with a short-ranged attraction exhibit a range of new dynamical arrest phenomena. These include very pronounced reentrance in the dynamical arrest curve, a logarithmic singularity in the density correlation functions, and the existence of `attractive' and `repulsive' glasses. Here we carry out extensive molecular dynamics calculations on dense systems interacting via a square-well potential. This is one of the simplest systems with the required properties, and may be regarded as canonical for interpreting the phase diagram, and now also the dynamical arrest. We confirm the theoretical predictions for re-entrance, logarithmic singularity, and give the first direct evidence of the coexistence, independent of theory, of the two coexisting glasses. We now regard the previous predictions of these phenomena as having been established.Comment: 15 pages,15 figures; submitted to Phys. Rev.

Iba-1-/CD68+ microglia are a prominent feature of age-associated deep subcortical white matter lesions.

Deep subcortical lesions (DSCL) of the brain, are present in ~60% of the ageing population, and are linked to cognitive decline and depression. DSCL are associated with demyelination, blood brain barrier (BBB) dysfunction, and microgliosis. Microglia are the main immune cell of the brain. Under physiological conditions microglia have a ramified morphology, and react to pathology with a change to a more rounded morphology as well as showing protein expression alterations. This study builds on previous characterisations of DSCL and radiologically 'normal-appearing' white matter (NAWM) by performing a detailed characterisation of a range of microglial markers in addition to markers of vascular integrity. The Cognitive Function and Ageing Study (CFAS) provided control white matter (WM), NAWM and DSCL human post mortem tissue for immunohistochemistry using microglial markers (Iba-1, CD68 and MHCII), a vascular basement membrane marker (collagen IV) and markers of BBB integrity (fibrinogen and aquaporin 4). The immunoreactive profile of CD68 increased in a stepwise manner from control WM to NAWM to DSCL. This correlated with a shift from small, ramified cells, to larger, more rounded microglia. While there was greater Iba-1 immunoreactivity in NAWM compared to controls, in DSCL, Iba-1 levels were reduced to control levels. A prominent feature of these DSCL was a population of Iba-1-/CD68+ microglia. There were increases in collagen IV, but no change in BBB integrity. Overall the study shows significant differences in the immunoreactive profile of microglial markers. Whether this is a cause or effect of lesion development remains to be elucidated. Identifying microglia subpopulations based on their morphology and molecular markers may ultimately help decipher their function and role in neurodegeneration. Furthermore, this study demonstrates that Iba-1 is not a pan-microglial marker, and that a combination of several microglial markers is required to fully characterise the microglial phenotype