Anisotropic fluctuation magnetoconductivity in Bi2Sr2Ca2Cu3Ox thin films

Measurements of the fluctuation magnetoconductivity as a function of both the magnetic field up to 13 T and the temperature in thin films of Bi₂Sr₂Ca₂Cu₃O_x are presented. The variation of the magnetoconductivity with the magnetic field strength is quadratic at temperatures distantly above the critical temperatureT _c and changes to an entirely negative curvature nearT _c . The latter behavior is attributed to an inhomogeneous critical temperature in the films. The results are analyzed in terms of recent theoretical models for fluctuation-enhanced magnetoconductivity in layered superconductors. The magnetoconductivity in a magnetic field oriented normal to the copper-oxide layers is dominated by the orbital contribution of the Aslamazov-Larkin effect. The magnetoconductivity in the parallel orientation is distinctly smaller and provides evidence for the corresponding Zeeman contribution. The latter measurement also indicates that the Maki-Thompson process may be insignificant in Bi₂Sr₂Ca₂Cu₃O_x.     

Angle-resolved photoemission spectroscopy of band tails and anomalous kinetics of underdoped cuprates

The electron-phonon interaction in cuprates with c-axis polarised optical phonons, which is roughly one order of magnitude stronger than superexchange, bounds holes into mobile bipolarons. Bipolarons pin the chemical potential within the charge-transfer gap of doped Mott insulators, accounting for unusual kinetics and thermodynamics of doped cuprates such as the Nernst and giant proximity effects, pseudo-gaps, and normal-state diamagnetism. We propose that “quasi-particle” peaks, “Fermi-arcs”, and high-energy “waterfalls” in the photoemission spectra of cuprates originate from the photo-ionization matrix elements of disorder-localised band-tails in the charge-transfer gap.     

RANS and LES computations of the tip-leakage vortex for different gap widths

In hydraulic turbines, the tip-leakage vortex is responsible for flow instabilities and for promoting erosion due to cavitation. To better understand the tip vortex flow, Reynolds-averaged Navier–Stokes (RANS) and large eddy simulation (LES) computations are carried out to simulate the flow around a NACA0009 blade including the gap between the tip and the wall. The main focus of the study is to understand the influence of the gap width on the development of the tip vortex, as for instance its trajectory. The RANS computations are performed using the open source solver OpenFOAM 2.1.0, two incidences and five gaps are considered. The LESs are achieved using the YALES2 solver for one incidence and two gaps.

The validation of the results is performed by comparisons with experimental data available downstream the trailing edge. The position of the vortex core, the mean velocity and the mean axial vorticity fields are compared at three different downstream locations. The results show that the mean behaviour of the tip vortex is well captured by the RANS and LES computations compared to the experiment. The LES results are also analysed to bring out the influence of the gap width on the development of the tip-leakage vortex. Finally, a law that matches the vortex trajectory from the leading edge to the mid-chord is proposed. Such a law can be helpful to determine, in case of cavitation, if the tip vortex will interact with the walls and cause erosion.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

Iterative Algorithms for Equilibrium Problems

We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms.     

Cyclic codes of length 2 m

In this paper explicit expressions ofm + 1 idempotents in the ring are given. Cyclic codes of length 2 ^m over the finite fieldF _q, of odd characteristic, are defined in terms of their generator polynomials. The exact minimum distance and the dimension of the codes are obtained.     

一个包含Euler函数及k阶Smarandache ceil函数的方程及其正整数解

设k≥2为给定的整数．对任意正整数n,k阶Smarandache ceil函数Sk（n）定义为Sk（n）=min{x：x∈N,n｜x^k}．本文的主要目的是利用初等方法研究函数方程Sk（n）=Ф（n）的可解性,并给出该方程的所有正整数解,其中Ф（n）为Euler函数．     

Supercontinuum generation and nonlinear pulse propagation in photonic crystal fiber: influence of the frequency-dependent effective mode area

Numerical simulations are used to study the effect of the frequency dependence of the effective mode area in photonic crystal fiber on supercontinuum generation. We quantify how the frequency dependence of the effective area influences the propagation characteristics through a modified optical shock term and identify the major consequence as a reduction in the extreme long-wavelength edge of the supercontinuum spectrum. Our results show that, for the parameter regimes used in many previous supercontinuum generation experiments using near-infrared femtosecond pump sources around 800 nm, this effect would be expected to be negligible. However, for pumps in the 1000–1500 nm range, the inclusion of this effect would be expected to be crucial for accurate comparison of simulations with experiment.     

Optically S-polarized surface waves in symmetrical nonlinear sensors: Thermal effects

A surface wave in a planar nonlinear waveguide is a current problem that has several applications in modern electronics and optics such as optical sensors design. The effect of thermal stress on the optical performance of a nonlinear symmetrical sensor is studied. The mathematical forms of the dispersion equation and thermal-stress sensitivity are analytically derived and plotted numerically. It is found that the thermal sensitivity of the sensor can be controlled by tuning the core size, by changing the loading materials, and by carefully selecting the materials.