On the second order characterization of ultrashort pulses

Abstract

The spectral properties of almost-Gaussian functions are considered and applied to the characterization of the second-order approximation in the expansion of the coefficients of almost-perfect optical pulses. Specifically, adding small amounts of odd-order Hermite-Gaussians to a Gaussian induces a second-order increase in the time-bandwidth product, while the increase in the time-bandwidth product from adding even-order Hermite-Gaussians is higher-order and hence smaller. We indicate the class of small perturbations of Gaussian functions which change neither the temporal profile of the intensity nor the intensity of the spectral profile.     

Threshold up-crossing by second order methods

The up-crossing of a scalar Gaussian process through various types of time-dependent thresholds is studied. Some approximate, analytical formulas yielding the expected number of up-crossings during a time interval [0, T] is derived. An intercomparison study is performed, in which the Laplace asymptotic method, the parametric sensitivity factor method with FORM/SORM and the suggested approximate formulas, are compared.     

On the decomposition of symmetric tensors into traceless symmetric tensors

The procedure of the decomposition of symmetric tensors defined in E_n into traceless symmetric tensors is given. Then this procedure is applied to symmetric tensors of 2-7 order.     

Isotropic tensor-valued polynomial function of second and third-order tensors

Third-order tensor-valued functions appear in the theory of turbulence as the stropholysis tensor that parametrizes the breaking of reflectional symmetry in the spectrum of turbulence and as the correlations of triple fluctuating velocity components whose spatial gradients represent the rate of transport of turbulence by random fluctuations. The formulation of rational models for these quantities involves, in the first instance, the correct representation of a third-order tensor-valued isotropic function as a function of tensors of order two and three. In this paper, we present the derivation of an appropriate representation formula and discuss its potential applications.     

Distorted yield surfaces – modelling by higher order anisotropic hardening tensors

Most of the constitutive models for metallic materials assume yield functions of von Mises or generalized Tsai–Wu type. Isotropic and/or kinematic evolutions are developed for hardening, which correspond to affin expansions or simple shifting of original yield surfaces, whereas experimental results show a distinctive change of the shape of yield surfaces (rotated or dented) depending on loading conditions and load paths. To cover the material behaviour with distorted yield surfaces a hierarchical expansion of yield functions to hardening tensors of the fourth and the sixth order is proposed. Parameters of corresponding evolutionary equations are determined by model parameter optimization. The extended model is investigated comparing numerical results to cyclic experimental data in biaxial σ–τ space.     

On a nonautonomous semilinear second order evolution equation in a hilbert space

An existence and uniqueness theorem is shown for a semilinear nonautonomous evolution equation in a Hilbert space which is the abstract model for several partial differential equations of mathematical physics. Further, asymptotic behavior of solutions is studied by means of compact process theory.     

Deviations of the equilibrium order parameter from mean field theory in superconducting aluminum films

Superconducting aluminum films show deviations from the mean field theory prediction of the temperature dependence of the equilibrium order parameter close toT _c . We show that these deviations can be explained by intrinsic variations inT _c from grain to grain. When the coherence length is larger than the grain size, the deviations will occur over a much smaller temperature interval than the intrinsic variations because of the proximity effect.Work performed under the auspices of the U.S. Energy Research and Development Administration.     

On the representation of constitutive relations using structure tensors

The purpose of this paper is to present a general formulation of the representation of constitutive relations for a material with a given (material) symmetry group in terms of functionals that depend on one or more so-called structure tensors. The principal result in this work takes the form of a relation between the symmetry groups of (1), the material constitutive relation, (2), the corresponding structure tensor(s), and (3), the functional depending on these tensors. In particular, this result contains that of the Rychlewski-Zhang representation theorem (e.g. Zhang and Rychlewski [1]) for anisotropic solids as a special case, and as such clarifies, simplifies and generalizes their formulation.     

Dynamics of the order parameter of superconducting aluminum films

The imaginary part of the pair-field susceptibility of dirty-limit, superconducting, aluminum films has been obtained both above and below the transition temperature by analyzing the I–V characteristic of asymmetric superconducting tunneling junctions. Results obtained above the transition temperature have been found to be consistent with a diffusive time-dependent Ginzburg-Landau equation. Below the transition temperature two modes have been found, one propagating and the other diffusing. The resonant frequency and damping constant of the propagating mode have been compared with the predictions of a phenomenological two-fluid hydrodynamic theory given by Bray and Schmidt. A somewhat more detailed comparison has been made with a microscopic theory given by Schön and Schmid in which the propagating and diffusing modes, respectively, are associated with transverse and longitudinal fluctuations of the order parameter. In both the microscopic and macroscopic theories the propagating mode is a high-frequency superconducting analog of second sound in that it consists of a counter motion of the normal and superfluid.Supported in part by the U.S. Energy Research and Development Administration under contract E(11-1) 1569 and by the Graduate School of the University of Minnesota.     

Time-dependent superconductivity: Relaxation oscillations of the order parameter

The dynamics of a one-dimensional weak-link superconductor connecting two stronger superconductors is investigated by means of the time-dependent Ginzburg-Landau theory. It is shown that the singularities along the length of the weak link where the order parameter tends to zero, otherwise called phase-slip centers, are at the zeros of a theta function and the points where the total current is made up entirely of the supercurrent are at the zeros of another theta function. From the properties of these theta functions the step structure of the pair electrochemical potential is analytically derived.     

On the cross-spectral tensors for black-body emission into space

Abstract

The cross-spectral tensors for black-body emission into space are derived, and the results expressed in terms of Debye integrals which have recently been found to be important in the scalar theory of partial coherence. For the case of an infinite black-body surface, closed-form expressions can be obtained for the cross-spectral tensors which are exact within the constraints of the local thermodynamic equilibrium assumption and the idealization of a perfectly absorbing surface. The trace of the electric cross-spectral tensor agrees with the recent results in the scalar theory of emission from uniform planar Lambertian sources.     

Experimental determination of the symmetry of the order parameter in YBCO

At present, the symmetry of the order parameter in the high temperature superconductor YBCO is quite controversial. Recent experiments using SQUIDs and Josephson junctions appear to support competing theories, with some experiments supporting a d_x2_–y2 pairing symmetry for the order parameter and others a s-wave pairing symmetry. We note that a number of factors such as trapped flux, magnetic field gradients and SQUID asymmetries could lead such measurements astray. We use a Scanning SQUID Microscope and a time-reversal invariance test to resolve these experimental problems. We find the order parameter in YBCO has a time-reversal invariant d_x2–_y2 symmetric component. We estimate the amplitude of anyimaginary s-wave symmetric component to be less than 4% and anyreal s-wave component to be less than 82%.     

Contact resistance as a measure of the superconducting order parameter

We have shown experimentally that the electrical contact resistance between a thin copper wire and a bulk superconductor contains a small contribution that varies with temperature below T _c . The observed temperature dependence is always close to that of the energy gap in the superconductor.     

Structure of the order parameter in iron pnictide-based superconducting materials

Using data on the crystal symmetry of iron pnictides, we have calculated possible symmetries of singlet two-electron states corresponding to the superconducting order parameter. It has been shown that the octet line node structure observed in photoemission spectra is due to interaction between pairs of the same symmetry and that the presence of an odd component of a superconducting state in NMR spectra is associated with states on the Brillouin zone boundary.     

Determining the order parameter for the morphological analysis of two-dimensional structures

Problems encountered in determining the order parameter for two-dimensional structures are considered. The task is solved using two approaches, which are based on the spectral transformations (Fourier and Walsh) and the information entropy concept. The results of calculations for particular structures are used for a comparative analysis, showing both advantages and drawbacks of these methods.     

Equivalent surface sources using the second order vector potentialformulation

The method outlined is especially advantageous with eddy current problems, because it allows the interfaces of all conducting regions to be replaced with equivalent magnetic surface charge and surface current. These equivalent sources are an immediate result of the field computation, and require virtually no additional computation. In terms of these equivalent sources, external fields are found quite accurately from surface integrations. With boundary element method techniques, this ability is especially valuable in terms of its accuracy and speed in finding global quantities such as force. The equivalent sources are directly related to the second-order vector potential, which has separability advantages in a number of coordinate systems     

Beyond the second order system in track following servos

Voice coil linear actuators are typically characterized as a basic second order system. However, component mechanical resonant frequencies often result in design degradations in the basic second order system. These conditions manifest themselves as possible servo loop instabilities in the frequency domain. This leads to poor static positioning, stiffness and dynamic positioning inaccuracies. This paper details the procedure used in the CDC Storage Module Drive family which, by the use of electronic compensation networks, provide track following improvement as well as minimizing the effect of mechanical resonant frequencies.