Some remarks on the symplectic pairing on the moduli space of representations of the fundamental group of surfaces

This work grew out of an attempt to understand a conjectural remark made by Professor Kyoji Saito to the author about a possible link between the Fox-calculus description of the symplectic structure on the moduli space of representations of the fundamental group of surfaces into a Lie group and pairs of mutually dual sets of generators of the fundamental group. In fact in his paper [3] , Prof. Kyoji Saito gives an explicit description of the system of dual generators of the fundamental group.

Assignment of fundamental vibrations of. ,N'-dimethylthiourea,

The infrared spectra of symmetric N,N′-dimethylthiourea (s-DMTU) and its N-deuterated (s-DMTU-d2) species have been measured. The fundamental frequencies have been assigned by comparison with the assignments in structurally related molecules and the infrared band shifts on N-deuteration, S-methylation, available Raman data and with the aid of theoretical band assignments from normal coordinate treatments for s-DMTU-d0 and -d2. A force field is derived for s-DMTU by transferring the force constants chiefly from N-methylthiourea and the subsequent refinement of the force constants by a least squares procedure.

Spool valve mechanism used in a 20 K Gifford-McMahon cycle cryorefrigerator and its effect on the P-V diagram

The design and fabrication of a spool valve for a two-stage Gifford-McMahon cycle cryorefrigerator is described. The effect of this valve on the P-V diagram and practical methods of reducing the P-V degradation are also discussed.

The averaging principle and the diagram technique

Rae and Davidson have found a striking connection between the averaging method generalised by Kruskal and the diagram technique used by the Brussels school in statistical mechanics. They have considered conservative systems whose evolution is governed by the Liouville equation. In this paper we have considered a class of dissipative systems whose evolution is governed not by the Liouville equation but by the last-multiplier equation of Jacobi whose Fourier transform has been shown to be the Hopf equation. The application of the diagram technique to the interaction representation of the Jacobi equation reveals the presence of two kinds of interactions, namely the transition from one mode to another and the persistence of a mode. The first kind occurs in the treatment of conservative systems while the latter type is unique to dissipative fields and is precisely the one that determines the asymptotic Jacobi equation. The dynamical equations of motion equivalent to this limiting Jacobi equation have been shown to be the same as averaged equations.

Long-range Coulomb interactions and nanoscale electronic inhomogeneities in correlated oxides

Electronic, magnetic, or structural inhomogeneities ranging in size from nanoscopic to mesoscopic scales seem endemic and are possibly generic to colossal magnetoresistance manganites and other transition metal oxides. They are hence of great current interest and understanding them is of fundamental importance. We show here that an extension, to include long-range Coulomb interactions, of a quantum two-fluid l-b model proposed recently for manganites [Phys. Rev. Lett. 92, 157203 (2004)] leads to an excellent description of such inhomogeneities. In the l-b model two very different kinds of electronic states, one localized and polaronic (l) and the other extended or broad band (b) coexist. For model parameters appropriate to manganites and even within a simple dynamical mean-field theory (DMFT) framework, it describes many of the unusual phenomena seen in manganites, including colossal magnetoresistance (CMR), qualitatively and quantitatively. However, in the absence of long-ranged Coulomb interaction, a system described by such a model would actually phase separate, into macroscopic regions of l and b electrons, respectively. As we show in this paper, in the presence of Coulomb interactions, the macroscopic phase separation gets suppressed and instead nanometer scale regions of polarons interspersed with band electron puddles appear, constituting a kind of quantum Coulomb glass. We characterize the size scales and distribution of the inhomogeneity using computer simulations. For realistic values of the long-range Coulomb interaction parameter V-0, our results for the thresholds for occupancy of the b states are in agreement with, and hence support, the earlier approach mentioned above based on a configuration averaged DMFT treatment which neglects V-0; but the present work has features that cannot be addressed in the DMFT framework. Our work points to an interplay of strong correlations, long-range Coulomb interaction, and dopant ion disorder, all inevitably present in transition metal oxides as the origin of nanoscale inhomogeneities rather than disorder frustrated phase competition as is generally believed. As regards manganites, it argues against explanations for CMR based on disorder frustrated phase separation and for an intrinsic origin of CMR. Based on this, we argue that the observed micrometer (meso) scale inhomogeneities owe their existence to extrinsic causes, e.g., strain due to cracks and defects. We suggest possible experiments to validate our speculation.

Phase diagram of vortex matter in layered superconductors with tilted columnar pinning centers

We study the vortex matter phase diagram of a layered superconductor in the presence of columnar pinning defects, tilted with respect to the normal to the layers. We use numerical minimization of the free energy written as a functional of the time-averaged vortex density of the Ramakrishnan-Yussouff form, supplemented by the appropriate pinning potential. We study the case where the pin density is smaller than the areal vortex density. At lower pin concentrations, we find, for temperatures of the order of the melting temperature of the unpinned lattice, a Bose glass type phase which at lower temperatures converts, via a first-order transition, to a Bragg glass, while, at higher temperatures, it crosses over to an interstitial liquid. At somewhat higher concentrations, no transition to a Bragg glass is found even at the lowest temperatures studied. While qualitatively the behavior we find is similar to that obtained using the same procedures for columnar pins normal to the layers, there are important and observable quantitative differences, which we discuss.

Negative sequence compensation within fundamental positive sequence reference frame for a stiff micro-grid generation in a wind power system using slip ring induction machine

An isolated wind power generation scheme using slip ring induction machine (SRIM) is proposed. The proposed scheme maintains constant load voltage and frequency irrespective of the wind speed or load variation. The power circuit consists of two back-to-back connected inverters with a common dc link, where one inverter is directly connected to the rotor side of SRIM and the other inverter is connected to the stator side of the SRIM through LC filter. Developing a negative sequence compensation method to ensure that, even under the presence of unbalanced load, the generator experiences almost balanced three-phase current and most of the unbalanced current is directed through the stator side converter is the focus here. The SRIM controller varies the speed of the generator with variation in the wind speed to extract maximum power. The difference of the generated power and the load power is either stored in or extracted from a battery bank, which is interfaced to the common dc link through a multiphase bidirectional fly-back dc-dc converter. The SRIM control scheme, maximum power point extraction algorithm and the fly-back converter topology are incorporated from available literature. The proposed scheme is both simulated and experimentally verified.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Phase diagram of the system Ca-Ti-O at 1200 K

Phase relations in the system Ca-Ti-O have been established by equilibration of several samples at 1200 K for prolonged periods and identification of phases in quenched samples by optical and scanning electron microscopy, XRD and EDS. Samples representing 20 compositions in the ternary system were analyzed. There was negligible solid solubility of Ca in the phases along the binary Ti-O, and of Ti in CaO. Four ternary oxides were identified: CaTiO3, Ca4Ti3O10 and Ca3Ti2O7 containing tetravalent titanium, and CaTi2O4 containing trivalent titanium. Tie-lines link calcium titanite (CaTi2O4) with the three calcium titanates (CaTiO3, Ca4Ti3O10 and Ca3Ti2O7), CaO, oxygen excess TiO1+delta and stoichiometric TiO. Tie-lines connect CaTiO3 with TiO2-x, Magneli phases TinO2n-1 (28 >= n >= 4), Ti3O5, Ti2O3 and TiO1+delta. CaO was found to coexist with TiO, and Ti-O solid solutions alpha and beta. The phase diagram is useful for understanding the mechanisms and kinetics of direct calciothermic reduction of TiO2 to metal and electrochemical reduction of TiO2 using graphite anode and molten CaCl2 electrolyte.

Phase Diagram for the System RuO2-TiO2 in Air

There are conflicting reports in the literature regarding solid solubility in the system RuO2-TiO2. To resolve this issue a few experiments were conducted in air at 1673, 1723, and 1773 K. The results show limited terminal solid solubility. There is an extended solid-state miscibility gap that intersects the decomposition curve for the RuO2-rich solid solution generating a peritectoid reaction at 1698 K. The measured equilibrium compositions of the solid solutions are used to develop a thermodynamic description of the oxide solid solution with rutile structure. Using the subregular solution model, the enthalpy of mixing can be represented by the expression, Delta H-M/J center dot mol(-1) = XTiO2XRuO2 ( 34,100X(TiO2) + 30,750X(RuO2)). The binodal and spinodal curves and T-X phase diagram in air are computed using this datum and Gibbs energy of formation of RuO2 available in the literature. The computed results suggest that equilibrium was not attained during solubility measurements at lower temperatures reported in the literature.

Thermodynamic Properties and Phase Diagram for the System MoO2–TiO2

The activity of molybdenum dioxide (MoO2) in the MoO2–TiO2 solid solutions was measured at 1600 K using a solid-state cell incorporating yttria-doped thoria as the electrolyte. For two compositions, the emf was also measured as a function of temperature. The cell was designed such that the emf is directly related to the activity of MoO2 in the solid solution. The results show monotonic variation of activity with composition, suggesting a complete range of solid solutions between the end members and the occurrence of MoO2 with a tetragonal structure at 1600 K. A large positive deviation from Raoult's law was found. Excess Gibbs energy of mixing is an asymmetric function of composition and can be represented by the subregular solution model of Hardy as follows.The temperature dependence of the emf for two compositions is reasonably consistent with ideal entropy of mixing. A miscibility gap is indicated at a lower temperature with the critical point characterized by Tc (K)=1560 and . Recent studies indicate that MoO2 undergoes a transition from a monoclinic to tetragonal structure at 1533 K with a transition entropy of 9.91 J·(mol·K)−1. The solid solubility of TiO2 with rutile structure in MoO2 with a monoclinic structure is negligible. These features give rise to a eutectoid reaction at 1412 K. The topology of the computed phase diagram differs significantly from that suggested by Pejryd.

Growth, self-assembly and dynamics of nano-scale films at fluid interfaces

Ultrathin films at fluid interfaces are important not only from a fundamental point of view as 2D complex fluids but have also become increasingly relevant in the development of novel functional materials. There has been an explosion in the synthesis work in this area over the last decade, giving rise to many exotic nanostructures at fluid interfaces. However, the factors controlling particle nucleation, growth and self-assembly at interfaces are poorly understood on a quantitative level. We will outline some of the recent attempts in this direction. Some of the selected investigations examining the macroscopic mechanical properties of molecular and particulate films at fluid interfaces will be reviewed. We conclude with a discussion of the electronic properties of these films that have potential technological and biological applications.

Phase diagram and dielectric studies of binary organic materials

The phase equilibrium studies of organic system, involving resorcinol (R) and p-dimethylaminobenzaldehyde (DMAB), reveal the formation of a 1:1 molecular complex with two eutectics. The heat of mixing, entropy of fusion, roughness parameter, interfacial energy, and the excess thermodynamic functions were calculated based on enthalpy of fusion data determined via differential scanning calorimetric (DSC) method. X-ray powder diffraction studies confirm that the eutectics are not simple mechanical mixture of the components under investigation. The spectroscopic investigations (IR and NMR) suggest the occurrence of hydrogen bonding between the components forming the molecular complex. The dielectric measurements, carried out on hot-pressed addition compound (molecular complex), show higher dielectric constant at 320 K than that of individual components. The microstructural investigations of eutectic and addition compound indicate dendritic and faceted morphological features. (C) 2000 Elsevier Science B.V. All rights reserved.

Phase diagram of a hard-sphere system in a quenched random potential: A numerical study

We report numerical results for the phase diagram in the density-disorder plane of a hard-sphere system in the presence of quenched, random, pinning disorder. Local minima of a discretized version of the Ramakrishnan-Yussouff free energy functional are located numerically and their relative stability is studied as a function of the density and the strength of disorder. Regions in the phase diagram corresponding to liquid, glassy, and nearly crystalline states are mapped out, and the nature of the transitions is determined. The liquid to glass transition changes from first to second order as the strength of the disorder is increased. For weak disorder, the system undergoes a first-order crystallization transition as the density is increased. Beyond a critical value of the disorder strength, this transition is replaced by a continuous glass transition. Our numerical results are compared with those of analytical work on the same system. Implications of our results for the field-temperature phase diagram of type-II superconductors are discussed.

Macroscopic approach to multichannel disordered conductors

We present a theory of multichannel disordered conductors by directly studying the statistical distribution of the transfer matrix for the full system. The theory is based on the general properties of the scattering system: flux conservation, time-reversal invariance, and the appropriate combination requirement when two wires are put together. The distribution associated with systems of very small length is then selected on the basis of a maximum-entropy criterion; a fixed value is assumed for the diffusion coefficient that characterizes the evolution of the distribution as the length increases. We obtain a diffusion equation for the probability distribution and compute the average of a few relevant quantities.