Corrected Sum Rule, Generalized Virial Identity and Elementary Excitation Spectrum of Bose–Einstein Condensates at Any Trapped Atom Number

Using a corrected sum rule and a generalized virial identity, we study the analytical expression for entire modes of the collective elementary excitation spectrum in a trapped Bose–Einstein condensate at any atom number. Explicit analytical formulas for the spectrum are obtained for the harmonic traps with both spherical symmetry and axial symmetry using the gaussian approximation for the N-body ground-state wave function of the condensate. These formulas give the simple dependence of all energy levels on the atom numbers, their interaction strength and trap geometry parameters.     

Second harmonic generation from a ferroelectric film

We derive an expression for transmittivity (T_SHG) of second harmonic generation (SHG) signals from a ferroelectric (FE) film. Intensities of up and down fields in the medium are investigated in relation to T_SHG. The derivations are made based on undepletion of input fields and nonlinear wave equation derived from the Maxwell equations. We present two cases: film without mirrors and with partial mirrors. Expressions for the newly derived nonlinear susceptibility coefficients of SHG for real crystal symmetry [J. Opt. Soc. Am. B 19 (2002) 2007] are used to get more realistic results. Variations in T_SHG with respect to film thickness are illustrated.     

Synthesis of Rice Processing Plants. I. Development of Simplified Models

This article, the first of three articles on the synthesis of rice processing plants, focuses on the development of simplified mathematical models necessary for use in optimizing rice processing plants. The second concentrates on the optimal synthesis of a rice plant and the third on the sensitivity of the optimization to uncertainty in model parameters. Existing models for rice processing unit operations are not suitable for flowsheet optimization and new models need to be developed to overcome numerical difficulties that occur in optimization applications, specifically in mixed integer nonlinear programming (MINLP) applications. Simplified models of the drying, cooling, and tempering units are developed. In addition head rice yield models, used as a quality indicator, energy consumption, and economic models were also developed. Naturally, the new models exhibit some mismatch with respect to the existing models from which they were developed. However, a sensitivity analysis, presented in Part III, has shown that the optimal flowsheet structure was not sensitive to a lack of fit between the simplified and complex models. The simplified models were found adequate to be appropriate for use at the synthesis stage.     

Effect of the Distribution of Manganese Ions on the Properties of Mn-Doped (Ba,Y)TiO3 PTCR Ceramics

The electrical properties and microstructure of (Ba,Y)TiO₃ PTCR ceramics were studied. The results indicate that the Mn ions increase the intergranular barrier height and produce a high-resistance layer on the grain surface. The temperature-dependent resistances of the grain bulk, surface layer, and grain boundaries, the temperature coefficient of resistance, and the magnitude of the varistor effect were assessed as a function of Mn content.     

Moving Least-Squares Differential Quadrature Method for Free Vibration of Antisymmetric Laminates

In this paper, the moving least-squares differential quadrature (MLSDQ) method is employed for free vibration of thick antisymmetric laminates based on the first-order shear deformation theory. The generalized displacements of the laminates are independently approximated with the centered moving least-squares (MLS) technique within each domain of influence. The MLS nodal shape functions and their partial derivatives are computed quickly through back-substitutions after only one LU decomposition. Subsequently, the weighting coefficients in the MLSDQ discretization are determined with the nodal partial derivatives of the MLS shape functions. The MLSDQ method combines the merits of both the differential quadrature and meshless methods which can be conveniently applied to complex domains and irregular discretizations without loss of implementation efficiency and numerical accuracy. The natural frequencies of the laminates with various edge conditions, ply angles, and shapes are calculated and compared with the existing solutions to study the numerical accuracy and stability of the MLSDQ method. Effects of support size, order of completeness of basis functions, and node irregularity on the numerical accuracy are investigated in detail.     

Start-up and steady-state results of a full-scale UASB reactor treating malting wastewater.

An Imhoff tank was reconstructed into a 250 m3 UASB reactor in order to treat a malting plant wastewater. The UASB was inoculated with sludge from an anaerobic lagoon used for slaughterhouse wastewater treatment. After two months of operation the reactor achieved full load with an HRT of 17 h, a COD removal higher than 80% and a biogas production of 300 m3/day (77% average methane content), with an organic loading rate of 3.6 kgCOD/m3.d (0.24 kgCOD/kgVSS.d). A yield coefficient of 0.09 gVSS/gCODrem was found from a mass balance. The fat present in the inoculated sludge (48 mg/gSSV) did not affect the start up performance. Sludge from the inoculum with high content of fat (270 mg/gSSV), was separated by flotation in the first week of operation. The COD removal efficiency was scarcely influenced by the reactor operation temperature (17-25 degrees C).     

Serially concatenated space-time codes with iterative decoding and performance limits of block-fading channels

This work considers space-time channel coding for systems with multiple-transmit and a single-receive antenna, over space uncorrelated block-fading (quasi-static) channels. Analysis of the outage probability over such channels reveals the existence of a threshold phenomenon. The outage probability can be made arbitrary small by increasing the number of transmit antennas, only if the E/sub b//N/sub 0/ is above a threshold which depends on the coding rate. Furthermore, it is shown that when the number of transmit antennas is increased, the /spl epsi/-capacity of a block-fading Rayleigh channel tends to the Shannon capacity of an additive white Gaussian noise channel. This paper also presents space-time codes constructed as a serial concatenation of component convolutional codes separated by an interleaver. These schemes provide full transmit diversity and are suitable for iterative decoding. The rate of these schemes is less than 1 bit/s/Hz, but can be made arbitrary close to 1 bit/s/Hz by the use of Wyner-Ash codes as outer components. Comparison of these schemes with structures from literature shows that performance gains can be obtained at the expense of a small decrease in rate. Computer simulation results over block-fading Rayleigh channels show that the frame-error rate of several of these schemes is within 2-3 dB from the theoretical outage probability.     

A New Measure of Misfit for Covariance Structure Models

Various fit indices exist in structural equation models. Most of these indices are related to the noncentrality parameter (NCP) of the chi-square distribution that the involved test statistic is implicitly assumed to follow. Existing literature suggests that few statistics can be well approximated by chi-square distributions. The meaning of the NCP is not clear when the behavior of the statistic cannot be described by a chi-square distribution. In this paper we define a new measure of model misfit (MMM) as the difference between the expected values of a statistic under the alternative and null hypotheses. This definition does not need to assume that the population covariance matrix is in the vicinity of the proposed model, nor does it need for the test statistic to follow any distribution of a known form. The MMM does not necessarily equal the discrepancy between the model and the population covariance matrix as has been assumed in existing literature. Bootstrap approaches to estimating the MMM and a related quantity are developed. An algorithm for obtaining bootstrap confidence intervals of the MMM is constructed. Examples with practical data sets contrast several measures of model misfit. The quantile-quantile plot is used to illustrate the unrealistic nature of chi-square distribution assumptions under either the null or an alternative hypothesis in practice.

     

Analysis of feedback for higher order polarization-mode dispersion mitigation of NRZ 40-Gb/s optical transmission

First-order polarization-mode dispersion (PMD) compensation by means of a polarization controller and a differential delay line is not sufficient to guarantee error-free transmission for 40-Gb/s channels when higher order effects severely increase signal distortion. Higher order mitigation is possible by cascading more than one first-order block. However, only two-stage or three-stage devices remain simple enough to be actually controlled. The performance of such higher order PMD compensators is evaluated by means of numerical simulations. Two different feedback signals have been used, demonstrating that first-order and higher order PMD distortion of nonreturn-to-zero (NRZ) pulses at 40 Gb/s can be strongly mitigated for instantaneous values of the differential group delay (DGD) up to the bit slot, when the compensator is properly controlled.