Coupled neutronic thermo-hydraulic analysis of full PWR core with Monte-Carlo based BGCore system

BGCore reactor analysis system was recently developed at Ben-Gurion University for calculating in-core fuel composition and spent fuel emissions following discharge. It couples the Monte Carlo transport code MCNP with an independently developed burnup and decay module SARAF. Most of the existing MCNP based depletion codes (e.g. MOCUP, Monteburns, MCODE) tally directly the one-group fluxes and reaction rates in order to prepare one-group cross sections necessary for the fuel depletion analysis. BGCore, on the other hand, uses a multi-group (MG) approach for generation of one group cross-sections. This coupling approach significantly reduces the code execution time without compromising the accuracy of the results. Substantial reduction in the BGCore code execution time allows consideration of problems with much higher degree of complexity, such as introduction of thermal hydraulic (TH) feedback into the calculation scheme. Recently, a simplified TH feedback module, THERMO, was developed and integrated into the BGCore system. To demonstrate the capabilities of the upgraded BGCore system, a coupled neutronic TH analysis of a full PWR core was performed. The BGCore results were compared with those of the state of the art 3D deterministic nodal diffusion code DYN3D (Grundmann et al.; 2000). Very good agreement in major core operational parameters including k-eff eigenvalue, axial and radial power profiles, and temperature distributions between the BGCore and DYN3D results was observed. This agreement confirms the consistency of the implementation of the TH feedback module. Although the upgraded BGCore system is capable of performing both, depletion and TH analyses, the calculations in this study were performed for the beginning of cycle state with pre-generated fuel compositions. © 2011 Published by Elsevier B.V.

Implementation of multi-group cross-section methodology in BGCore MC-depletion code

BGCore is a software package for comprehensive computer simulation of nuclear reactor systems and their fuel cycles. The BGCore interfaces Monte Carlo particles transport code MCNP4C with a SARAF module - an independently developed code for calculating in-core fuel composition and spent fuel emissions following discharge. In BGCore system, depletion coupling methodology is based on the multi-group approach that significantly reduces computation time and allows tracking of large number of nuclides during calculations. In this study, burnup calculation capabilities of BGCore system were validated against well established and verified, computer codes for thermal and fast spectrum lattices. Very good agreement in k eigenvalue and nuclide densities prediction was observed for all cases under consideration. In addition, decay heat prediction capabilities of the BGCore system were benchmarked against the most recent edition of ANS Standard methodology for UO2 fuel decay power prediction in LWRs. It was found that the difference between ANS standard data and that predicted by the BGCore does not exceed 5%.

Investigating vibration dyanmics of cross-coupled MEMS resonators for reduced motional resistance

This paper investigates the vibration dynamics of a closed-chain, cross-coupled architecture of MEMS resonators. The system presented here is electrostatically transduced and operates at 1.04 MHz. Curve veering of the eigenvalue loci is used to experimentally quantify the coupling spring constants. Numerical simulations of the motional resistance variation against induced perturbation are used to assess the robustness of the cross-coupled system as opposed to equivalent traditional open-ended linear one-dimensional coupling scheme. Results show improvements of as much as 32% in the motional resistance between the cross-coupled system and its one-dimensional counterpart. © 2013 IEEE.

Wave propagation in a slowly-varying duct with mean vortical swirling flow

The propagation of unsteady disturbances in a slowlyvarying cylindrical duct carrying mean swirling flow is investigated using a multiple-scales technique. This is applicable to turbomachinery flow behind a rotor stage when the swirl and axial velocities are of the same order. The presence of mean vorticity couples acoustic and vorticity equations which produces an eigenvalue problem that is not self-adjoint unlike that for irrotational mean flow. In order to determine the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down where a mode changes from cut on to cut off. In this region the amplitude is governed by a form of Airy's equation, and the effect of swirl is to introduce a small shift in the origin of the Airy function away from the turning-point location. The variation of axial wavenumber and amplitude along the duct is calculated. In hard-walled ducts mean swirl is shown to produce much larger amplitude variation along the duct compared with a nonswirling flow. Mean swirl also has a large effect in ducts with finite-impedance walls which differs depending on whether modes are co-rotating with the swirl or counter rotating. © 2001 by A.J. Cooper, Published by the American Institute of Aeronautics and Astronautics, Inc.

Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

Optical analysis of AlGaInP laser diodes with real refractive index guided self-aligned structure

Optical modes of AlGaInP laser diodes with real refractive index guided self-aligned (RISA) structure were analyzed theoretically on the basis of two-dimension semivectorial finite-difference methods (SV-FDMs) and the computed simulation results were presented. The eigenvalue and eigenfunction of this two-dimension waveguide were obtained and the dependence of the confinement factor and beam divergence angles in the direction of parallel and perpendicular to the pn junction on the structure parameters such as the number of quantum wells, the Al composition of the cladding layers, the ridge width, the waveguide thickness and the residual thickness of the upper P-cladding layer were investigated. The results can provide optimized structure parameters and help us design and fabricate high performance AlGaInP laser diodes with a low beam aspect ratio required for optical storage applications.

Eigenmode confinement in semiconductor microcavity lasers with an equilateral triangle resonator

We analyze the mode behaviors for semiconductor lasers with an equilateral triangle resonator by deriving the mode field distribution and the eigenvalue equation. The eigenvalue equation shows that the longitudinal mode wavelength interval is equivalent to that of a Fabry-Perot cavity with the cavity length of 1.5a, where a is the side length of the equilateral triangle resonator. The transverse waveguiding is equivalent to as a strip waveguide with the width of root 3a/ 2, and the number of transverse modes supported by the resonator is limited by the total reflection condition on the sides of the equilateral triangle. Semiconductor microcavity laser with an equilateral triangle resonator is suitable to realize single mode operation, and the mode wavelength can be adjusted by changing the side length.

Study on tapered crossed subwavelength gratings by Fourier modal method

Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are presented, and their convergences are compared through numerical calculation. One of them is found to be suitable in modeling the diffraction efficiency of the circular tapered crossed subwavelength gratings without high absorption, and staircase approximation is further proven valid for non-highly-absorption tapered gratings. This approach is used to simulate the "moth-eye" antireflection surface on silicon, and the numerical result agrees well with the experimental one.

Non-modal instabilities of two-dimensional disturbances in plane Couette flow of a power-law fluid

Instabilities of fluid flows have traditionally been investigated by normal mode analysis, i.e. by linearizing the equations of flow and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In this paper we study the instabilities of two-dimensional Couette flow of a polymeric fluid in the framework of non-modal stability theory rather than normal mode analysis. A power-law model is used to describe the polymeric liquid. We focus on the response to external excitations and initial conditions by examining the pseudospectra structures and the transient energy growths. For both Newtonian and non-Newtonian flows, the results show that there can be a rather large transient growth even though the linear operator of Couette flow has no unstable eigenvalue. The effects of non-Newtonian viscosity on the transient behaviors are examined in this study. The results show that the "shear-thinning/shear-thickening" effect increases/decreases the amplitude of responses to external excitations and initial conditions. (C) 2010 Elsevier B.V. All rights reserved.

Instabilities and transient behaviors of a liquid film flowing down a porous inclined plane

The nonmodal linear stability of a falling film over a porous inclined plane has been investigated. The base flow is driven by gravity. We use Darcy's law to describe the flow in the porous medium. A simplified one-sided model is used to describe the fluid flow. In this model, the influence of the porous layer on the flow in the film can be identified by a parameter beta. The instabilities of a falling film have traditionally been investigated by linearizing the governing equations and testing for unstable eigenvalues of the linearized problem. However, the results of eigenvalue analysis agree poorly in many cases with experiments, especially for shear flows. In the present paper, we have studied the linear stability of three-dimensional disturbances using the nonmodal stability theory. Particular attentions are paid to the transient behavior rather than the long time behavior of eigenmodes predicted by traditional normal mode analysis. The transient behaviors of the response to external excitations and the response to initial conditions are studied by examining the pseudospectral structures and the energy growth function G(t) Before we study the nonmodal stability of the system, we extend the results of long-wave analysis in previous works by examining the linear stabilities for streamwise and spanwise disturbances. Results show that the critical conditions of both the surface mode and the shear mode instabilities are dependent on beta for streamwise disturbances. However, the spanwise disturbances have no unstable eigenvalue. 2010 American Institute of Physics. [doi:10.1063/1.3455503]

Inner structure of Spin(c)(4) gauge potential on 4-dimensional manifolds

The decomposition of Spin(c)(4) gauge potential in terms of the Dirac 4-spinor is investigated, where an important characterizing equation Delta A(mu) = -lambda A(mu) has been discovered. Here, lambda is the vacuum expectation value of the spinor field, lambda = parallel to Phi parallel to(2), and A(mu) the twisting U(1) potential. It is found that when), takes constant values, the characterizing equation becomes an eigenvalue problem of the Laplacian operator. It provides a revenue to determine the modulus of the spinor field by using the Laplacian spectral theory. The above study could be useful in determining the spinor field and twisting potential in the Seiberg-Witten equations. Moreover, topological characteristic numbers of instantons in the self-dual sub-space are also discussed.

CALCULATIONS OF THE EIGENVALUES OF PURE QUADRUPOLE INTERACTION IN MOSSBAUER-EFFECT STUDIES

Two approximate formulae to calculate the eigenvalues of pure quadrupole interaction in Mossbauer effect studies have been proposed and the eigenvalue coefficients in the formulae have been given for various excited states and ground states of the nucleus with different spin. All the eigenvalues of pure quadrupole interaction between both excited state and ground state of nucleus with spin I = 3/2 divided-by 9/2 and the electric-field gradient with different asymmetry parameter (eta = 0 divided-by 1.0) have been calculated by these formulae. The results show that the accuracies in all the calculations are more satisfactory or same in comparison with those obtained by the formula of Shenoy and Dunlap, especially when the asymmetry parameter of electric-field gradient is larger than 0.8 for the nucleus with spin I = 5/2.

有限元结构动力分析的广义特征值的神经计算

广义特征值问题是结构动力分析计算的关键之一.应用Reyle igh极小值原理,将神经网络的能量函数的极小点对应于广义特征值问题的最小特征值所对应的特征向量,在神经网络朝着能量函数极小点运动的同时得到了最小特征值所对应的特征向量的精确解答.从特征值的变分特性出发,给出了基于罚函数法的其他特征值的神经网络求解方案,从而在理论上给出了广义特征值问题的所有特征值的神经网络求解方法.仿真计算表明,该方法正确、有效可行.

中低纬度变化磁场的暴时特征研究

Magnetic storm is a kind of severe disturbances in the whole solar-earth electromagnetic space. It has significant effects on communication, electric power, oil transport pipe and human activities in space. Therefore, magnetic storms are worth for applications systems, not only being a favorable issue for scientists. In this paper, the spatial and temporal distributions of the magnetic fields produced by the magnetosphere-ionosphere current systems during storms are studied. Four parts are included in this paper decomposion of different disturbances with different origins, topological structure of the ring current, the asymmetric characteristics of the ring current, and the statistic peculiarities of the day-to-day variability (DTD) of Sq. 1 The decomposition of magnetic disturbances at mid-low latitudes and its evolutions during storms Transient variations in the geomagnetic field recorded at mid-low latitudes mainly include the storm-time variation (Dst), solar quiet daily variation (Sq) and disturbance daily variation (SD). With the data of the geomagnetic meridian chain observatories in China, 25 storms during the period of 1997 to 1999 have been analyzed. According to the features of different variations, a method of “three-steps decomposition” is developed by using the method of Natural Orthogonal Components (NOC), Correlation Analysis and Fourier Analysis to separate those three components in turn. The results show that, the first eigenmode by the MNOC clearly describing the special distribution and temporal evolution of storm-time variation, in addition, Correlation Analysis and Fourier Analysis offer a useful method to extract the Sq and SD variations. The latitudinal shift of the Sq current focus seems to be the principal reason of the day-to-day variaitons in the daily range of Sq. The magnitude of SD reaches a maximum during the main phase, and then gradually decreases. 2 The topology structure of the ring current during storms Both the mechanism of the ring current and the geomagnetic data suggest that the central plane of the ring current is declining to the geomagnetic equator plane with a tilt angle δ. Using the H and Z component data at two stations in a meridian chain, we deduce a new parameter describing the invariable peculiarity of different storms. Then the δ angle is calculated by using the data from a meridian chain and tested with the ERC model. Finally the deduced tilt angles are used to modify Dst index. 3 The asymmetric characteristics of the ring current during storms The variations of the geomagnetic field at mid-low latitudes show a significant dawn-dusk asymmetry, resulting from the superposition of the fields from the symmetric ring current and the partial ring current. On the basis of the data from the 20°E, 30°E meridian chains and 30°N latitudinal chain, the dawn-dusk asymmetry is investigated by using three methods, namely, statistic analysis, ring current model calculation and typical event analysis. This characteristic implies the asymmetry of the spatial distribution of the ring current. In addition, during the main phase after the sudden commencement (SC), H field increases and reaches maximum around noontime, implying the effect of the Chapman-Ferraro current. 4 The statistic characteristics of the day-to-day variability and its mechanism The day-to-day variability of the geomagnetic Sq field is studied by using the magnetic data from a meridian chain of magnetometers along 120° E longitude. The method of NOC is applied to separate the Sq variation from complicated disturbances. The first eigenmode with the largest eigenvalue represents fairly well the Sq variation with a conspicuous day-to-day variability in the daily range. For the stations on the same north- or south-side of the Sq current system focus, the day-to-day variations show a positive correlation. In contrast, for the stations on the different sides of the Sq focus, they show a negative correlation, suggesting an important role of latitudinal shift of the Sq current system focus to the day-to-day variability of the Sq daily range. The Sq daily range is correlated with the magnetic indices Ap and Dst in a peculiar way: on some severe disturbed days, noticeably enhancements of the Sq are observed, implying increases of the ionospheric conductivities and/or tidal wind velocities; on other severe disturbed days, however, dramatically reduced Sq variations occur, suggesting dominant effects of the ‘disturbance dynamo’ process.

Three-dimensional dispersive metallic photonic crystals with a bandgap and a high cutoff frequency.

The goal of this work is to analyze three-dimensional dispersive metallic photonic crystals (PCs) and to find a structure that can provide a bandgap and a high cutoff frequency. The determination of the band structure of a PC with dispersive materials is an expensive nonlinear eigenvalue problem; in this work we propose a rational-polynomial method to convert such a nonlinear eigenvalue problem into a linear eigenvalue problem. The spectral element method is extended to rapidly calculate the band structure of three-dimensional PCs consisting of realistic dispersive materials modeled by Drude and Drude-Lorentz models. Exponential convergence is observed in the numerical experiments. Numerical results show that, at the low frequency limit, metallic materials are similar to a perfect electric conductor, where the simulation results tend to be the same as perfect electric conductor PCs. Band structures of the scaffold structure and semi-woodpile structure metallic PCs are investigated. It is found that band structures of semi-woodpile PCs have a very high cutoff frequency as well as a bandgap between the lowest two bands and the higher bands.