Two-Band Eliashberg Theory in Doped MgB $_{2}$_{2}: Experimental Tc and Superconductive Gaps

The variation of the critical temperature and of the superconductive gaps as functions of doping (Al, C) in the diboride MgB has been studied in the framework of the two-band Eliashberg theory and traditional phonon coupling mechanism. We have solved the two-band Eliashberg equations using first-principle calculations or simple assumptions for the variation of the relevant physical quantities. We have found that the experimental curves can be exactly explained only if the Coulomb pseudopotential changes with x by tuning the Fermi level toward the σ band edge. We also found that a small amount of impurities changes the structural properties of the material, so we cannot treat the Mg and MgB systems as a contamination with Al or C of MgB, but as new materials. Finally, we compare the predictions of our theory with the available experimental data.     

Linear Response Theory Around a Localized Impurity in the Pseudogap Regime of an Anisotropic Superconductor

We compare and contrast the polarizability of a d-wave superconductor in the pseudogap regime, within the precursor pairing scenario (dPG), and of a d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Our study is motivated by STM imaging experiments around an isolated impurity, which may in principle distinguish between precursor pairing and dDW order in the pseudogap regime of the high- superconductors. In both cases, the -dependence of the polarizability is characterized by an azimuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave vector , albeit imperfect, due to a nonzero value of the hopping ratio in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also reflected by the dependence of the retarded polarizability.     

Finite piecewise polynomial parametrization of plane rational algebraic curves

We present an algorithm with the following characteristics: given a real non-polynomial rational parametrization of a plane curve and a tolerance , is decomposed as union of finitely many intervals, and for each interval I of the partition, with the exception of some isolating intervals, the algorithm generates a polynomial parametrization . Moreover, as an option, one may also input a natural number N and then the algorithm returns polynomial parametrizations with degrees smaller or equal to N. In addition, we present an error analysis where we prove that the curve piece is in the offset region of at distance at most , and conversely. Authors partially supported by the Spanish “Ministerio de Educación y Ciencia” under the Project MTM2005-08690-C02-01, and by the “Dirección General de Universidades de la Consejería de Educación de la CAM y la Universidad de Alcalá” under the project CAM-UAH2005/053.     

Excitonic Collective Mode and Negative Compressibility in Electron Liquids

A highly self-consistent theory maintaining the exact functional relations between the electron self-energy and the vertex part is employed to calculate the dielectric function very accurately in the homogeneous electron gas in two- and three-dimensions. By investigating the full dynamical properties of thus obtained, we find that the softening of excitonic collective modes is responsible for making the compressibility of the system negative at sufficiently low densities.     

Bi2212 c-Axis Twist Bicrystal and Artificial and Natural Cross-Whisker Josephson Junctions: Strong Evidence for s-Wave Superconductivity and Incoherent c-Axis Tunneling

We discuss the latest data from c-axis twist Josephson junction experiments on Bi₂Sr₂CaCu₂O (Bi2212) bicrystals and on artificially and naturally formed cross whiskers. All three experiments provide strong evidence for a dominant s-wave order parameter for . The bicrystal and natural cross-whisker data also provide strong evidence for incoherent c-axis tunneling across the intrinsic Bi2212 junctions, consistent with a strongly inhomogeneous material.     

Effect of solidification cooling rate and phosphorus inoculation on number per unit volume of primary silicon particles in hypereutectic aluminium—silicon alloys

Collected data on derived number per unit volume of primary silicon particles in hypereutectic Al-Si alloys show a power relationship with solidification cooling rate of the form where typically and mm^-3 (K/s)^-1 in the absence of phosphorus and mm^-3 (K/s)^-1 in its prescence. Significantly lower apparent values of from one set of results appear to stem from measurement of a mean long dimension rather than diameter of particle sections as well as lower measured undercoolings than in Bridgman experiments at similar .     

Pseudogap State of Underdoped Cuprate Hts as a Display of The Jahn–Teller Pseudoeffect

For underdoped quasi-two dimensional cuprate antiferromagnets within the framework of the two-component model of charge carriers (holes and Zhang–Rice polarons) it is considered two near-degenerate states of hole molecular orbitals of one-site cluster Cu²⁺O₄ ²⁻ and two-site cluster Cu²⁺O₄ ²⁻+Cu²⁺O₄ ² in CuO₂ planes. It is shown that the vibronic mixing of these near-degenerate states with near energies separated by the energy barrier , leads to transition of the system to the pseudogap state with new quasilocal and local states of charge carriers. The supposition that the pseudogap state is a consequence of the Jahn–Teller pseudoeffect and that barrier is stipulated by magnetic interaction is discussed.     

Computer experiment on deformation of nanocrystals of the chromium-niobium system. Part 1. Atomic-structural rearrangements

Molecular-dynamic simulation of the process of stretching of chromium and niobium nanocrystals and chromium-niobium bicrystals was performed to a pair-potential approximation. Atomic mechanism of deformation and fracture is illustrated, which depends on the crystal orientation with respect to the acting force . In the case of the initial orientation (100) , the reorientation mechanism (100) (110) is in action. In a bicrystal, it is niobium that deforms first and then the relay-race transfer of deformation from Nb to Cr takes place. With the initial configuration (110) , the fragmentation of the crystal and grain-boundary rearrangements are observed. Niobium crystallite in a bicrystal deforms only within the limits of elastic deformation whereas the deformation of chromium is of brittle-ductile mode. With the initial configuration (111) , the mechanism of pure brittle fracture is observed. In all cases, fracture of a bicrystal occurs along the interphase boundary. The causes of such atomic-structural transformations are explained.Translated from Problemy Prochnosti, No. 1, pp. 5–23, January–February, 2005.     

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

Laminar thermal boundary layer on a continuous accelerated sheet extruded in an ambient fluid

Summary Exact boundary layer similarity solutions are developed for flow, friction and heat transfer on a continuously accelerated sheet extruded in an ambient fluid of a lower temperature.Melt-spinning, polymer and glass industries and the cooling of extruded metallic plates are practical applications of this problem.Results for skin-friction and heat-transfer coefficients are given. Larger acceleration is accompanied by larger skin-friction and heat-transfer coefficients. Rapid cooling of the sheet is accompanied by a larger Nusselt number.Nomenclature sheet width - c dimensionless constant - c _f local skin friction coefficient - F dimensionless transformed stream function - G dimensionless transformed temperature - local heat transfer coefficient - fluid thermal conductivity - length of deformation zone - m exponent of surface speed variation - q exponent of surface temperature variation - T dimensionless temperature - sheet surface temperature - solidification temperature - ambient temperature - sheet thickness - u velocity component along the sheet - u _s sheet surface velocity - wind up velocity - v velocity component normal to the sheet - x dimensionless coordinate along the sheet - y dimensionless coordinate normal to the sheet - Nu Nusselt number, - Pr Prandtl number, - Re Reynolds number, - =Re^–0.5 - dimensionless similarity coordinate - dynamic viscosity - kinematic viscosity - fluid mass density - sheet mass density - wall shear stress - dimensionless stream function With 3 Figures     

Effect of boundary plane on the atomic structure of [0001] Σ 7 tilt grain boundaries in ZnO

The atomic structure of [0001] Σ 7 tilt grain boundaries with { }‖ { }, { }‖ { }, and { }‖ { } boundary planes in ZnO was investigated through high-resolution transmission electron microscopy observation of fiber-textured thin films and atomistic calculations. These boundaries were found to comprise three kinds of common structural units that are characterized by fourfold- to eightfold-coordinated channels along the [0001] direction in contrast to sixfold-coordinated channels in wurtzite structure. The boundary structural units are very similar to the multiple core structures of edge dislocations with Burgers vectors of 1/3 < > . Transformation between two of the three configurations can easily occur through an atom flipping corresponding to dislocation glide. Depending on the orientation of boundary planes with respect to the Burgers vectors, the dislocation-like units exhibit straight or zigzag arrangements with periodicities corresponding to the Σ 7 misorientation.     

Multiband superconductivity: A mapping to the extended attractive Hubbard model

Following our recent work which shows that purely repulsive multiband systems effectively reduce to the extended attractive Hubbard model having the on-site repulsion along with nearest-neighbor and next-nearst-neighbor attraction for the cuprate structures, we study the latter model in the mean-field theory.T _c against band filling for various symmetries of pairing is numerically calculated. The results show that, for the region of and expected for the mapping from the original multiband model,T _c has maximum values of the order of 100 K, which is consistent with the experimental results. For certain values of parameters,s- and -wave pairing have similar values of T_c, which may suggest the possibility of a mixed phase of the two.The numerical calculations were done on the HITAC S3800 in the University of Tokyo Computer Centre. This work was in part supported by a Grant-in-Aid from the Ministry of Education, Science, and Culture, Japan.     

On perfect nonlinear functions (Π)

Perfect nonlinear functions are of importance in cryptography. By using Galois ring, relative trace and investigating the character values of corresponding relative difference sets, we present a construction of perfect nonlinear functions from to , where m′ is a divisor of 2m, and a construction of perfect nonlinear functions from to where 2m is possibly larger than the largest divisor of n. Meanwhile we prove that there exists a perfect nonlinear function from to if and only if p = 2, and there doesn’t exist a perfect nonlinear function from to if m > n and l(l is odd) is self-conjugate modulo 2 ^k (k ≥ 1).      

Microstructure and microwave properties of {CaT{i}O}<Subscript>3</Subscript>–LaGaO<Subscript>3</Subscript> {solid solutions}

The phase assemblage, microstructure and microwave (MW) properties of xCaTiO₃-(1-x)LaGaO₃ (CT-LG) ceramics prepared by solid state synthesis from raw oxides and carbonates have been investigated. LG was predominantly single phase perovskite with space group, Pnma, but a small quantity of pyrochlore structured La₂Zr₂O₇ second phase was present due to the contamination from the ZrO₂ milling media. At MW frequencies, the temperature coefficient of resonant frequency (τ_{f}) of LG was --80~ppm/\({\circ}\)C, its permittivity, \(\varepsilon_{r} {=} \)27 and MW quality factor, \(Q^{*}f_{o} {=} \)97,000 (@5~GHz). As CT concentration increased, \(\tau_{f}\) and \(\varepsilon_{r}\) increased to The phase assemblage, microstructure and microwave (MW) properties of xCaTiO₃-(1-x)LaGaO₃ (CT-LG) ceramics prepared by solid state synthesis from raw oxides and carbonates have been investigated. LG was predominantly single phase perovskite with space group, Pnma, but a small quantity of pyrochlore structured La₂Zr₂O₇ second phase was present due to the contamination from the ZrO₂ milling media. At MW frequencies, the temperature coefficient of resonant frequency (τ_{f}) of LG was --80~ppm/ C, its permittivity, 27 and MW quality factor, 97,000 (@5~GHz). As CT concentration increased, and increased to $+$850~ppm/ C and 160, respectively but decreased to 20,000. Zero was achieved at 0.65 with 47, and 40,000, properties comparable with commercial compositions. However, for 0.5, a different second phase was observed which was rich in Ca and Ga. Electron diffraction patterns could be indexed according to a body centred cubic lattice, 12.5 ?. It is suggested that the presence of second phases in the CT-LG compounds may, in part, be responsible for the deterioration in .     

Implication of Striped Hole Structurization on the Evolution of Cuprate Electronic Properties with Doping

The striped hole structurization in cuprate CuO₂ layers is discussed in the framework of the earlier introduced string model implying the direct overlap of O 2p-like orbitals. In the lightly doped compounds with the mean hole density , each dopant ion and the nearest quantized hole orbital of rank η can be viewed as a pseudoatom. The growth of above 1/24 stimulates condensation of the pseudoatoms into pancakes where some part of hole orbitals is expected to be collectivizing into bosonic stripes (BS). The formation of BS among the fermion-like hole surroundings has to be displayed in electronic spectra first as a bulge, and then as the coherent peak flanking to the broad hump of incoherent origin (the so called “peak-dip-hump structure”). Accumulating and broadening BS with increase of give rise to percolation superconductivity below a border of critical temperatures . It is shown, that the cuprate characteristics calculated without fitting parameters are consistent with measurements.      

Lead-strontium titanate glass ceramics: I – crystallization and microstructure

The crystallization behaviour of glasses in the system [(Pb Sr ) O·TiO₂]-[2SiO₂· B₂O₃]-[K₂O]-[BaO] (0.2 ≤ x ≤ 0.9) have been studied. Perovskite titanate was found to be the major phase in all the glass ceramic samples investigated. The actual composition of crystalline phases could not be confirmed on the basis of shift in the X-ray diffraction (XRD) peak positions because of similar effects due to solid solution formation and strain due to crystal clamping. Comparison of the observed intensities of various XRD peaks of the perovskite titanate phase with the calculated intensities for (Pb Sr )TiO₃ with same lead/strontium ratio confirmed the formation of lead strontium titanate solid solution. Microstructural characteristics of various glass ceramics are also discussed. The advantages of using K₂O and BaO as additives instead of only K₂O are also discussed.     

Load relaxation studies of germanium

A series of compressive load relaxation experiments were conducted on germanium single crystals in the temperature range 400 to 885° C. The curvature of the log-log data obtained from load relaxation tests changes from concave upward to concave downward as the test temperature increases at fixed stress level, or as the strain level increases at fixed temperature. At intermediate temperatures, 600° C, the transition from concave upward to concave downward curvature happens on a single relaxation curve. These observations are consistent with the two-branch rheological model proposed by Hart to explain the deformation behaviour of metals and were analysed in terms of this model. The transition from concave upward to concave downward curvature could be moved to higher temperature by doping germanium with gallium, which decreases the dislocation glide velocity relative to that in pure germanium. The transition could be shifted to lower temperature by compressing samples along [1 1] rather than [1 0] because the [1 1] orientation favours cross-slip while the [1 0] orientation does not. Dislocation dipoles and straight dislocations dominated the microstructure of samples which had concave upward log-log curves, while well-developed dislocation cell structures dominated the microstructure of samples which yielded concave downward curves. The observed changes in the curvature of the load relaxation curves and the dislocation structure both indicate the increased importance of dislocation climb with increasing temperature. When compared through the Orowan equation, the load relaxation results are in good agreement with published stress-dislocation velocity data.     

Higher approximations for supersonic flow past slowly oscillating bodies of revolution

Summary Supersonic flow past slowly oscillating pointed bodies of revolution is studied. Starting from the complete nonlinear potential equation an elementary linearized solution is discussed and it is shown how this solution together with the method of matched asymptotic expansions can be used to derive an elementary second-order slender body theory. This approach is further demonstrated for the oscillating cone and its range of validity is evaluated by comparison with other theoretical methods.

---

Zusammenfassung Es wird die Überschallströmung um langsam schwingende spitze Rotationskörper untersucht. Ausgehend von der vollständigen nichtlinearen Potentialgleichung wird zuerst eine elementare linearisierte Lösung besprochen und gezeigt, wie diese Lösung im Verein mit der Method of matched asymptotic expansions zur Herleitung einer elementaren Schlankkörpertheorie zweiter Ordnung verwendet werden kann. Die Theorie wird am Beispiel des schwingenden Kegels näher erläutert und mit anderen Methoden verglichen.

---

Symbols a Velocity of sound - c _N Normal force coefficient - Damping coefficient - F _(x) Dipole distribution - k Reduced frequency - M Mach number - R (x) Meridian profile - t Time - x, r, Cylindrical coordinates - - Ratio of specific heats - Amplitude of oscillation - Thickness ratio - Perturbation potential - Zero angle of attack potential - æ - Velocity potential - Out-of-phase potential - - In-phase potential - - Source coordinate With 4 Figures     

Thermomechanic behavior of a polymer upon its formation in a crystallization process: Theoretical principles,hypotheses, and mathematical model

A model of thermomechanic behavior of a polymer upon its formation in a crystallization process is proposed. Based on methods of nonequilibrium thermodynamics governing relationships are obtained which make it possible to establish the dependence of the final degree of crystallicity of the material on the history of the crystallization process and to explain the mechanism of formation of the remanent stresses in a polymer article.Notation u translation vector - v velocity vector - acceleration vector - absolute temperature - density - c specific heat capacity - deformation tensor - strain tensor - specific enthropy - U ^* internal energy - z specific free enthalpy - _i internal parameters of state - t time - q heat flux vector - matrix of heat conduction coefficients - W ^* energy dissipation - F vector of mass forces - the 4th rank tensor of elastic pliabilities - matrix of heat expansion coefficients - tensor of contribution of structural variations to deformation - function of equilibrium value ^* - p mean pressure - deviator of the tensor of deformations - spherical part of the deformation tensor - deviator of the tensor of stresses - K volume modulus - unity tensor - Q enthalpy of the crystallization process - Q _eq enthalpy of the equilibrium crystallization process - _g glass transition temperature - ^*() the curve obtained in the equilibrium crystallization process - f final degree of crystallicity Institute of Mechanics of Continuous Media of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Institute of Technical Chemistry of the Ural Branch of the Russian Academy of Sciences, Perm', Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 479–485, May–June, 1995.     

Analysis of a family of unstable lattice orientations in (110) channel die compression

Summary The family of f.c.c. crystal orientations defined by loading direction (110) and any channel die constraint direction between ( ) and ( ) is kinematically unstable. We establish that the experimentally observed finite rotation of the lattice about the loading axis, for initial orientations in this range, is uniquely predicted by the constraints and critical slip-system inequalities without regard to particular hardening theory. We further establish that experimental information on the changing constraint stress would serve to distinguish among theories. Predictions of three specific hardening rules, including classical Taylor hardening and the simple theory, are illustrated for initial constraint directions ( ) and ( ). For the first of these orientations the predictions include constraint stress, lattice rotation, active and latent hardening, and overall crystal shearing to a logarithmic compressive strain of 1.0.