Hyalotekite, (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2)(Si,B)(2)O28F, a Tectosilicate Related to Scapolite: New Structure Refinement, Phase Transitions and a Short-Range Ordered 3B Superstructure

Hyalotekite, a framework silicate of composition (Ba,Pb,K)(4)(Ca,Y)(2)Si-8(B,Be)(2) (Si,B)(2)O28F, is found in relatively high-temperature(greater than or equal to 500 degrees C) Mn skarns at Langban, Sweden, and peralkaline pegmatites at Dara-i-Pioz, Tajikistan. A new paragenesis at Dara-i-Pioz is pegmatite consisting of the Ba borosilicates leucosphenite and tienshanite, as well as caesium kupletskite, aegirine, pyrochlore, microcline and quartz. Hyalotekite has been partially replaced by barylite and danburite. This hyalotekite contains 1.29-1.78 wt.% Y2O3, equivalent to 0.172-0.238 Y pfu or 8-11% Y on the Ca site; its Pb/(Pb+Ba) ratio ranges 0.36-0.44. Electron microprobe F contents of Langban and Dara-i-Pioz hyalotekite range 1.04-1.45 wt.%, consistent with full occupancy of the F site. A new refinement of the structure factor data used in the original structural determination of a Langban hyalotekite resulted in a structural formula, (Pb1.96Ba1.86K0.18)Ca-2(B1.76Be0.24)(Si1.56B0.44)Si8O28F, consistent with chemical data and all cations with positive-definite thermal parameters, although with a slight excess of positive charge (+57.14 as opposed to the ideal +57.00). An unusual feature of the hyalotekite framework is that 4 of 28 oxygens are non-bridging; by merging these 4 oxygens into two, the framework topology of scapolite is obtained. The triclinic symmetry of hyalotekite observed at room temperature is obtained from a hypothetical tetragonal parent structure via a sequence of displacive phase transitions. Some of these transitions are associated with cation ordering, either Pb-Ba ordering in the large cation sites, or B-Be and Si-B ordering on tetrahedral sites. Others are largely displacive but affect the coordination of the large cations (Pb, Ba, K, Ca). High-resolution electron microscopy suggests that the undulatory extinction characteristic of hyalotekite is due to a fine mosaic microstructure. This suggests that at least one of these transitions occurs in nature during cooling, and that it is first order with a large volume change. A diffuse superstructure observed by electron diffraction implies the existence of a further stage of short-range cation ordering which probably involves both (Pb,K)-Ba and (BeSi,BB)-BSi.

Phase Transitions of YbBr2

The crystalline phases of YbBr2 were investigated by powder neutron diffraction between 1.5 K and the melting point at 955 K (682 °C). The low temperature SrI2 phase is observed up to 550 K, the α-PbO2 phase between 260 K and 750 K, the CaCl2 phase between 690 K and 790 K, and the rutile phase from 790 K to the melting point. All observed phase transitions are first order, except for the second order CaCl2 to rutile transition. The transition temperatures and enthalpies were determined by differential scanning calorimetry.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Light-induced phase-delay of the chicken pineal circadian clock is associated with the induction of cE4bp4, a potential transcriptional repressor of cPer2 gene

The chicken pineal gland contains the autonomous circadian oscillator together with the photic-input pathway. We searched for chicken pineal genes that are induced by light in a time-of-day-dependent manner, and isolated chicken homolog of bZIP transcription factor E4bp4 (cE4bp4) showing high similarity to vrille, one of the Drosophila clock genes. cE4bp4 was expressed rhythmically in the pineal gland with a peak at very early (subjective) night under both 12-h light/12-h dark cycle and constant dark conditions, and the phase was nearly opposite to the expression rhythm of cPer2, a chicken pineal clock gene. Luciferase reporter gene assays showed that cE4BP4 represses cPer2 promoter through a E4BP4-recognition sequence present in the 5′-flanking region, indicating that cE4BP4 can down-regulate the chick pineal cPer2 expression. In vivo light-perturbation studies showed that the prolongation of the light period to early subjective night maintained the high level expression of the pineal cE4bp4, and presumably as a consequence delayed the onset of the induction of the pineal cPer2 expression in the next morning. These light-dependent changes in the mRNA levels of the pineal cE4bp4 and cPer2 were followed by a phase-delay of the subsequent cycles of cE4bp4/cPer2 expression, suggesting that cE4BP4 plays an important role in the phase-delaying process as a light-dependent suppressor of cPer2 gene.

Antifreeze glycoproteins inhibit leakage from liposomes during thermotropic phase transitions.

Antifreeze glycoproteins (AFGPs), found in the blood of polar fish at concentrations as high as 35 g/liter, are known to prevent ice crystal growth and depress the freezing temperature of the blood. Previously, Rubinsky et al. [Rubinsky, B., Mattioli, M., Arav, A., Barboni, B. & Fletcher, G. L. (1992) Am. J. Physiol. 262, R542-R545] provided evidence that AFGPs block ion fluxes across membranes during cooling, an effect that they ascribed to interactions with ion channels. We investigated the effects of AFGPs on the leakage of a trapped marker from liposomes during chilling. As these liposomes are cooled through the transition temperature, they leak approximately 50% of their contents. Addition of less than 1 mg/ml of AFGP prevents up to 100% of this leakage, both during chilling and warming through the phase transition. This is a general effect that we show here applies to liposomes composed of phospholipids with transition temperatures ranging from 12 degrees C to 41 degrees C. Because these results were obtained with liposomes composed of phospholipids alone, we conclude that the stabilizing effects of AFGPs on intact cells during chilling reported by Rubinsky et al. may be due to a nonspecific effect on the lipid components of native membranes. There are other proteins that prevent leakage, but only under specialized conditions. For instance, antifreeze proteins, bovine serum albumin, and ovomucoid all either have no effect or actually induce leakage. Following precipitation with acetone, all three proteins inhibited leakage, although not to the extent seen with AFGPs. Alternatively, there are proteins such as ovotransferrin that have no effect on leakage, either before or after acetone precipitation.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

Phase Transitions in Disordered Systems: The Example of the Random-Field Ising Model in Four Dimensions

By performing a high-statistics simulation of the D = 4 random-field Ising model at zero temperature for different shapes of the random-field distribution, we show that the model is ruled by a single universality class. We compute to a high accuracy the complete set of critical exponents for this class, including the correction-to-scaling exponent. Our results indicate that in four dimensions (i) dimensional reduction as predicted by the perturbative renormalization group does not hold and (ii) three independent critical exponents are needed to describe the transition.

Phase transitions and memory effects in the dynamics of Boolean networks

The generating functional method is employed to investigate the synchronous dynamics of Boolean networks, providing an exact result for the system dynamics via a set of macroscopic order parameters. The topology of the networks studied and its constituent Boolean functions represent the system's quenched disorder and are sampled from a given distribution. The framework accommodates a variety of topologies and Boolean function distributions and can be used to study both the noisy and noiseless regimes; it enables one to calculate correlation functions at different times that are inaccessible via commonly used approximations. It is also used to determine conditions for the annealed approximation to be valid, explore phases of the system under different levels of noise and obtain results for models with strong memory effects, where existing approximations break down. Links between Boolean networks and general Boolean formulas are identified and results common to both system types are highlighted. © 2012 Copyright Taylor and Francis Group, LLC.

Computing with noise: phase transitions in Boolean formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.

Phase transitions in wave turbulence

We consider turbulence within the Gross-Pitaevsky model and look into the creation of a coherent condensate via an inverse cascade originating at small scales. The growth of the condensate leads to a spontaneous breakdown of statistical symmetries of overcondensate fluctuations: First, isotropy is broken, then a series of phase transitions marks the changing symmetry from twofold to threefold to fourfold. We describe respective anisotropic flux flows in the k space. At the highest level reached, we observe a short-range positional and long-range orientational order (as in a hexatic phase). In other words, the more one pumps the system, the more ordered the system becomes. The phase transitions happen when the system is pumped by an instability term and does not occur when pumped by a random force. We thus demonstrate nonuniversality of an inverse-cascade turbulence with respect to the nature of small-scale forcing.