A rigorous control of logarithmic corrections in four-dimensional ϕ4 spin systems

Using Gawedzki and Kupiainen's rigorous block spin transformation method, we study critical phenomena in ⁴ spin systems in four dimensions. In Part I of this work we investigate in detail the renormalization group trajectory of the system not exactly at the critical point.     

Spin interaction with an ideal Fermi gas

We consider the equilibrium dynamics of a system consisting of a spin interacting with an ideal Fermi gas on the lattice , 3. We present two examples: when this system is unitarily equivalent to an ideal Fermi gas or to a spin in an ideal Fermi gas without interaction between them.     

On the statistical mechanics of the traveling salesman problem

We consider the statistical mechanics of the traveling salesman problem (TSP) and develop some representations to study it. In one representation the mean field theory has a simple form and brings out some of the essential features of the problem. It shows that the system has spontaneous symmetry breaking at any nonzero temperature. In general the phase progressively changes as one decreases the temperature. At low temperatures the mean field theory solution is very sensitive to any small perturbations, due to the divergence of some local susceptibilities. This critical region extends down to zero temperature. We perform the quenched average for a nonmetric TSP in the second representation and the resulting problem is more complicated than the infinite-range spin-glass problem, suggesting that the free energy landscape may be more complex. The role played by frustration in this problem appears explicitly through the localization property of a random matrix, which resembles the tight binding matrix of an electron in a random lattice.     

Characterization of SiO2-P2O5-ZrO2 Sol-Gel/NAFION™ Composite Membranes

Composite membranes were prepared by (a) infiltrating NAFION with SiO₂-P₂O₅-ZrO₂ sol, and (b) recasting a film using NAFION solution containing SiO₂-P₂O₅-ZrO₂ sol. The membranes were characterized by Differential Thermal Analysis and ac-impedance spectroscopy as a function of relative humidity. The influences of the heat treatment (80°C–150°C) and cleaning on the electrical properties were investigated. The incorporation of SiO₂-P₂O₅-ZrO₂ gels into NAFION lead to improvements in its thermal stability and proton conductivity.     

Heat conductivity of three periodic Hard Disks via nonequilibrium molecular dynamics

We use a driving field, of the type first suggested by Evans, to generate a steady heat current in the simplest possible system, a two-dimensional periodic fluid of three hard disks. Hard-disk motion equations can be conveniently derived from repulsive constant-force or linear-force potentials by considering the infinitely repulsive limit of these potentials. We show that the isoenergetic and isokinetic forms of the nonequilibrium equations of motion generate steady-state heat conductivities differing by terms of order 1/N, whereN is the number of particles. The resulting conductivities appear to vary as the logarithm of the driving field strength. Even at low fields, the three-body periodic-system results lie well below Enskog's infinite-system prediction.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.     

First radical cation salts of 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene (BDA-TTP) with copper(II) metal complex anions: β-(BDA-TTP)4Cu2Cl6 and (BDA-TTP)2CuCl4

New radical cation salts based on 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene (BDA-TTP) with copper(II) metal complex anions, β-(BDA-TTP)₄Cu₂Cl₆ and (BDA-TTP)₂CuCl₄, were synthesized and structurally characterized. Single crystals were prepared by electrochemical oxidation of BDA-TTP under galvanostatic conditions. X-ray diffraction study demonstrated that the salts have a layered structure, in which the conducting BDA-TTP layers alternate with the [Cu₂Cl₆]²⁻ or [CuCl₄]²⁻ anions. Both salts show the semiconductor-type temperature dependence of the conductivity. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 48–54, January, 2007.     

Phase transition and mixed oxide-proton conductivity in germanium oxy-apatites

La_9.75□_0.25(Ge₆O₂₄)O_2.62 oxy-apatite shows a phase transition from triclinic to hexagonal symmetry at approximately 1020 K that has been characterised by high-temperature synchrotron X-ray and neutron powder diffraction, and ionic conductivity measurements. The crystal structure at 1073 K has been determined from joint Rietveld refinements of synchrotron X-ray and neutron powder diffraction data. The study shows that hexagonal-La_9.75□_0.25(Ge₆O₂₄)O_2.62 contains interstitial oxygen at the position previously reported for other oxy-germanates. Changes in the oxide conductivity associated with this structural transition are discussed. The thermal analyses showed a weight loss on heating close to 600 K very likely due to water release. The synchrotron thermodiffractometric study shows an anomaly in the cell parameters evolution at that temperature, which indicates that this residual water is located into the apatite channels. The electrical characterisation under different atmospheres (dry and wet synthetic air) indicates that there is a significant proton contribution to the overall conductivity below 600 K, mainly under wet atmosphere.     

Aspects of thermal conductivity relative to heat flow

Summary The various techniques and methodologies of thermal conductivity measurement have been conventionally based on the determination of the rate of directional heat flow through a material having a unit temperature differential between its opposing faces. The constancy of this rate depends on the material density, its thermal resistance and the heat flow path itself. The last of these variables contributes most significantly to the true value of steady-state axial and radial heat dissipation depending on the magnitude of transient thermal diffusivity along these directions. The purpose of this paper is to exemplify the above features by defined parameters of heat flow measurement by existing methodologies. No new method is proposed here. Importantly, the relationship between the rate of heat transfer, total heat transferred and thermal conductivity at a given temperature under steady-state conditions for a fixed heat flow path will be illustrated.     

Thermal properties of sodium acetylacetonate

Sodium acetylacetonate was prepared by the interaction of acetyl acetone with sodium hydroxide. The thermal conductivity, phonon velocity, mean free path, Yong's modulus, and the thermal expansion coefficient were studied. The thermal conductivity of the material decreases with increasing temperature due to the thermal lattice scattering of phonons. The velocity of phonons is also decreased due to the perturbation of thermal phonons. The linear thermal expansion coefficient increases with temperature due to the weakness of the attractive forces between the small Na⁺ cations and bulkier acetylacetonate anions in the lattice.

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Zusammenfassung Natriumacetylacetonat wurde durch die Wechselwirkung zwischen Acetylaceton und Natriumhydroxid gewonnen. Es wurde die Wärmeleitfähigkeit, die Phononengeschwindigkeit, die mittlere freie Wegstrecke, das Elastizitätsmodul und der Wärmeausdehnungskoeffizient untersucht. Die Wärmeleitfähigkeit der Substanz nimmt wegen der thermischen Gitterstreuung der Phononen mit steigender Temparatur ab. Die Geschwindigkeit der Phononen nimmt auf Grund der Perturbierung der thermischen Phononen ebenfalls ab. Der lineare Wärmeausdehnungskoeffizient steigt mit zunehmender Temperatur an, was auf die schwachen Anziehungskräfte zwischen den kleinen Na⁺ Ionen und den massigen Acetylacetonat-Anionen im Gitter zurückzuführen ist.