Evolution of the Electronic Structure of Y-Bi-2212 from the Antiferromagnetic to the Superconducting Regime

The phase diagram of the cuprate superconductors at low doping and low temperatures in the non-superconducting state is dominated by magnetic correlations. When increasing the hole concentration in the CuO₂-planes from zero an antiferromagnetic (AF) insulating phase is followed for hole concentrations greater than approximately 0.08 by the superconducting phase. For the range of doping in between the situation is less clear and several models exist. For Bi₂Sr₂Y _x Ca_1–xCu₂O₈ in the range of Y-concentrations 0.9 < x < 0.0 the evolution of the electronic structure starting from the AF phase at x = 0.9, which in this respect can be regarded as the parent compound of the superconducting phase, and its gradual development into the superconducting range can be studied on one system. In this series the CuO₂-planes are kept embedded in a nearly identical environment for each hole concentration. Especially the results from the AF phase deviate from former reports attained mainly from oxychlorides.     

The “Paramagnetic” Meissner Effect in Superconductors

There are a number of publications concerning the observation of a paramagnetic signal in HTSC ceramic samples during field-cooling procedures. Some authors assume that this signal is connected with spontaneous currents and discuss the possibility of the existence of -junctions in Josephson media. In this work, it is shown that the paramagnetic signal could appear in the case of capture and compression of the magnetic flux in a sample during field-cooling procedures. The results of numerical calculation of the magnetic moment for different configurations of the sample and flux compression are presented. The unusual behavior of longtime relaxation of the magnetic moment in experiments on capture of magnetic flux is discussed.     

Maximizing pseudoconvex transportation problem: a special type

The paper discusses a non-concave fractional programming problem aiming at maximization of a pseudoconvex function under standard transportation conditions. The pseudoconvex function considered here is the product of two linear functions contrasted with a positive valued linear function. It has been established that optimal solution of the problem is attainable at an extreme point of the convex feasible region. The problem is shown to be related to indefinite quadratic programming which deals with maximization of a convex function over the given feasible region. It has been further established that the local maximum point of this quadratic programming problem is the global maximum point under certain conditions, and its optimal solution provides an upper bound on the optimal value of the main problem. The extreme point solutions of the indefinite quadratic program are ranked to tighten the bounds on the optimal value of the main problem and a convergent algorithm is developed to obtain the optimal solution.     

A field astrogravigeodetic standard for metrological tests on geodetic equipment

The paper discusses the scope for a qualitatively new field standard with improved accuracy based on relative GPS/GLONASS satellite measurements, with the object of performing metrological tests on a wide range of geodesic instruments under realistic conditions.Translated from Izmeritelnaya Tekhnika, No. 9, pp. 3–7, September, 2004.     

Observation ofd-wave interference pattern:Short junction is crucial

The properties of a one-dimensional 0--Josephson junction, consiting of ans-d junction or selected boundaries between three suitably orientedd-wave superconductors, are studied. It is shown that ad-wave type interference pattern can only be observed in the field-modulated critical current if the junction is short compared to the Josephson penetration depth. However, the behavior of a 0- junction is found to be indistinguishable from that of a 0-junction betweens-wave superconductors in the long junction limit, due to the formation of a -vortex.     

Two holes in the finite Hubbard lattice with a strong magnetic field: The phase diagram

The Nagaoka instability and the existence of off-diagonal long-range order (ODLRO) and superconductivity for two holes near half-filling in 1d, 2d, and 3d hypercubes with periodic boundary conditions are exactly proven in the Hubbard model immersed in a strong magnetic field. The upper critical field and criteria for stability of either the spin-flipped or excitonic phases as a function of interaction strength are found. The theory predicts the possibility of the ODLRO mechanism of superconductivity in the strong-repulsion Hubbard model in arbitrary dimensions.     

“Pseudogap” in High-Temperature Superconductors

It is shown that an existence of a pseudogap and peculiarities of its behavior under temperature and doping variation, both at doping above and below the optimal one, naturally follow from the impurity mechanism of high-temperature superconductivity, which is an additional argument in favor of it. Main attention is paid to the tunneling spectroscopy experimental data.     

Effects of measurement errors on sample monitoring reliability

Results are presented on the effects of measurement errors on items in routine production as regards the reliability of results on sampling inspection obtained by Monte Carlo simulation. The customers and the makers risks are examined in relation to the distributions of the measurement errors and the values of them.Translated from Izmeritelnaya Tekhnika, No. 12, pp. 8–11, December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

Vibration Diagnostics of a Damaged Inclined Cylindrical Shell

Free vibrations of an inclined cylindrical shell with a breathing crack are analyzed by the authors in view of the results of spectral diagnostics of transverse vibrations of a beam with a closing crack, which were obtained by A. A. Matveev and A. P. Bovsunovskii at the Institute of Problems of Strength of the National Academy of Sciences of Ukraine. Elastic characteristics of the shell are interpreted as a certain bilinear system. Data on the stiffness degradation due to the crack opening can be used for the selection of vibration damage indicators. We have obtained relationships between the relative stiffness degradation, crack depth, and crack location. It is demonstrated that the potential energy of tension of the shell median surface must be taken into account. We have found that the efficiency of detecting damages using vibration diagnostic methods improves with increasing shell thickness.     

Electronic Structure of Mn Acceptor Impurity Incorporated SrTiO3 Using Embedded Cluster Method

We have performed atomic-level first principle electronic structure calculations on doped grain boundaries (GB) in SrTiO₃. This was motivated by the electron holography experiments, which were able to quantify the electrostatic potential and the associated space charge distribution across the Mn-doped GB in this material. The embedded cluster Discrete Variational (DV)-X method was used to determine the charge and the densities of states for several idealized models of a single crystal and symmetrical tilt grain boundaries in SrTiO₃. Special attention was given to the role of Mn⁺² and Mn⁺³ acceptors substituting for Ti⁺⁴ resulting in charge segregation across the grain boundaries, which was shown in the electron holography experiments. We have found that Mn replacing Ti prefers to have valence charge around +2 and this picture agrees with the experimental observation of negative grain boundary charges in the GB core.     

Phonon Raman scattering of R2CuO4 (R = Pr, Nd, Sm, and Gd)

For Gd₂CuO₄, a new symmetry-forbidden phonon for the tetragonal T structure is observed. This implies that oxygen in the CuO₂ plane is locally distorted along the CuO₂ plane. Such distortion has never been observed for other T-type superconductors, which show superconductivity by Ce doping. The disappearance of superconductivity for Gd can be correlated with the appearance of the distortion due to oxygen in the CuO₂ plane.     

Effective Łojasiewicz inequalities in semialgebraic geometry

The main result of this paper can be stated as follows: letV ⁿ be a compact semialgebraic set given by a boolean combination of inequalities involving only polynomials whose number and degrees are bounded by someD > 1. LetF, G[X₁,, X_n] be polynomials with degF, degG D inducing onV continuous semialgebraic functionsf, g:VR. Assume that the zeros off are contained in the zeros ofg. Then the following effective ojasiewicz inequality is true: there exists an universal constantc ₁ and a positive constantc ₂ (depending onV, f,g) such that for allxV. This result is generalized to arbitrary given compact semialgebraic setsV and arbitrary continuous functionsf,g:V . An effective global ojasiewicz inequality on the minimal distance of solutions of polynomial inequalities systems and an effective Finiteness Theorem (with admissible complexity bounds) for open and closed semialgebraic sets are derived.     

Lambda-Calculus with Director Strings

We present a name free -calculus with explicit substitutions, based on a generalised notion of director strings. Terms are annotated with information – directors – that indicate how substitutions should be propagated. We first present a calculus where we can simulate arbitrary -reduction steps, and then simplify the rules to model the evaluation of functional programs (reduction to weak head normal form). We also show that we can define the closed reduction strategy. This is a weak strategy which, in contrast with standard weak strategies, allows certain reductions to take place inside -abstractions thus offering more sharing. Our experimental results confirm that, for large combinator-based terms, our weak evaluation strategies out-perform standard evaluators. Moreover, we derive two abstract machines for strong reduction which inherit the efficiency of the weak evaluators.Projet Logical, Pôle Commun de Recherche en Informatique du plateau de Saclay, CNRS, École Polytechnique, INRIA, Université Paris-Sud.     

A density-functional-based tight-binding scheme for the study of silicon- oxygen compounds

Crystalline and molecular silicon-oxygen compounds are investigated using asimplified LCAO-LDA scheme for the construction of a nonorthogonal tight-binding Hamiltonian within a two-centre approximation. The repulsive part ofthe potential is derived as a universal short-range pair potential fromfitting the difference between the band structure energy of proper molecularsystems and the corresponding SCF-LDA cohesive energy curves. The methodallows, under consideration of the electronic states, molecular dynamicssimulations of large finite as well as condensed systems. The applicabilityof this method to the important class of silicon oxides and related moleculesis demonstrated. In particular, the properties of the equilibrium structureof -quartz and several siloxane molecules are calculated and are foundto agree well with both experiment and self-consistent calculations. To obtainsuch a good agreement, it is necessary to also include the unoccupied 3dstates of Si into the LCAO basis of the wave functions.     

The influence of the polarization of the radiation on the accuracy of the transmission of the dimensions of the unit of temperature in radiation thermometry

The results of an investigation of different types of tungsten lamps in order to estimate the components of the error budget of spectrum-pyrometer apparatus are presented. Quantitative relations are considered and the results of experimental research, which enable systematic methods to be developed for eliminating the influence of polarization of the radiation of the lamps in standard radiation thermometry, are analyzed.Translated from Izmeritelnaya Tekhnika, No. 9, pp. 42–45, September, 2004.     

Sparse BEM for potential theory and Stokes flow using variable order wavelets

Wavelets for the discretization of boundary integral operators usually have fixed order and are constructed in some parameter space of the surface. Here a new approach is presented, where the order is flexible and no parameterizations are needed. The wavelets are restrictions of piecewise polynomial functions in three variables on the boundary manifold. This construction is especially suited for surfaces with complicated geometries. If the polynomial order is suitably adjusted to the level of the wavelet, then the non-standard form of a large class of boundary integral operators can be truncated to contain only O(N) non-vanishing entries while retaining the asymptotic convergence of the full Galerkin scheme. An algorithm which sets up the basis and the non-standard form in O(N) operations will be discussed. The method is applied to problems from potential theory and Stokes flow and compared with the Fast Multipole Method.     

Novel methodology to investigate superconducting dielectric resonators

An analytical method is presented for investigating the resonant behavior of a c-axis oriented YBa₂Cu₂O_7–(0) thin film on a resonator composed of LaAlO₃ (001). The concept of the negative dielectric medium for a superconductor is introduced within the framework of the two-fluid model, which permits us to treat a superconductor as any other penetrable materials so that only its electromagnetics are concerned. A conformai transformation is further suggested to map the original open boundary-value problem to a closed one. This not only makes the original problem readily solvable by using the variational technique, but is also a powerful tool for analyzing some kinds of problems such as the propagation characteristics of the superconducting microstripe and coplanar waveguide structures.     

Finite element recovery techniques for local quantities of linear problems using fundamental solutions

We show that local quantities of interest such as displacements or stresses of a FE–solution can be calculated with improved accuracy if fundamental solutions are employed. The approach is based on Bettis theorem and an integral representation of the local quantities via Greens function. The unknown Greens function is split into a regular part and a fundamental solution so that only the regular part must be approximated on the finite element ansatz space. Some numerical studies for linear elasticity will illustrate our approach.