Numerical calculation of the runaway electron distribution function and associated synchrotron emission

Synchrotron emission from runaway electrons may be used to diagnose plasma conditions during a tokamak disruption, but solving this inverse problem requires rapid simulation of the electron distribution function and associated synchrotron emission as a function of plasma parameters. Here we detail a framework for this forward calculation, beginning with an efficient numerical method for solving the Fokker–Planck equation in the presence of an electric field of arbitrary strength. The approach is continuum (Eulerian), and we employ a relativistic collision operator, valid for arbitrary energies. Both primary and secondary runaway electron generation are included. For cases in which primary generation dominates, a time-independent formulation of the problem is described, requiring only the solution of a single sparse linear system. In the limit of dominant secondary generation, we present the first numerical verification of an analytic model for the distribution function. The numerical electron distribution function in the presence of both primary and secondary generation is then used for calculating the synchrotron emission spectrum of the runaways. It is found that the average synchrotron spectra emitted from realistic distribution functions are not well approximated by the emission of a single electron at the maximum energy.     

基于MATLAB的球谐函数M函数库

以MATLAB为设计语言,开发了系列用于原子轨道球谐函数Y_(1m)(θ,φ)如s、p、d、f原子轨道及sp~3和d~2sp~3杂化轨道角度函数可视化的精确、快速、简便的m函数库。根据球坐标的自变量定义域:φ∈[0,2π]、θ∈[0,π],设定离散的自变量值T,P,对球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的解析式进行计算机程序化,根据解析式计算对应的R值,然后由MATLAB矩阵变换命令[X,Y,Z]=sph2cart(T,P,R)和绘图命令mesh(X,Y,Z)实现球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的可视化。详细介绍了程序设计思路、编写方法,给出了球谐函数Y_(1m)(θ,φ)及杂化轨道角度函数的解析式数组算法表达式、m-file绘图程序和运行结果。     

Search for the upper bound of Bayesian estimates of the parameter in an exponential failure model with two known quantiles of an a priori distribution function

A fast exact algorithm of searching for the upper bound of Bayesian estimates for the parameter of the exponential distribution under the condition that an a priori distribution belongs to the class of all distribution functions with two equal quantiles. This problem arises in analyzing the sensitivity of Bayesian estimates to the choice of an a priori distribution in an exponential failure model. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 1, pp. 90–102, January–February 2007.     

An efficient energy-conserving numerical model for the electron energy distribution function in the presence of electron-electron collisions

An efficient algorithm to calculate the contribution of electron-electron collisions in the Boltzmann equation for free electrons, in the two-term approximation is presented. The electron-electron collision term must be energy-conserving, while, due to non-linearity, commonly used algorithms do not satisfy this requirement. The efficiency of the algorithm make feasible the use of a non-linear iterative solver to conserve electron energy in electron-electron collisions.The performance of the proposed algorithm has been compared with standard numerical schemes obtaining: 1) considerable gain in computational time; 2) the conservation of the total electron energy density in e-e collisions under the required tolerance.     

EIQNK curve analysis for the design of distribution center and warehouse with spline function

This paper discussed the EIQ and EIQNK curve metohd for the selection of machine and equipments in the design of distribution center or warehouse.This curve are expressed with orthogonal polynominals and spline functions and how the function applied of this problems.The shape of EIQNK curves are split into differents classes and discussed the characteristic of warehouse or distribution. Fuzzy EIQNK curve analysis also discussed.     

A new algorithm for importance analysis of the inputs with distribution parameter uncertainty

Importance analysis is aimed at finding the contributions by the inputs to the uncertainty in a model output. For structural systems involving inputs with distribution parameter uncertainty, the contributions by the inputs to the output uncertainty are governed by both the variability and parameter uncertainty in their probability distributions. A natural and consistent way to arrive at importance analysis results in such cases would be a three-loop nested Monte Carlo (MC) sampling strategy, in which the parameters are sampled in the outer loop and the inputs are sampled in the inner nested double-loop. However, the computational effort of this procedure is often prohibitive for engineering problem. This paper, therefore, proposes a newly efficient algorithm for importance analysis of the inputs in the presence of parameter uncertainty. By introducing a ‘surrogate sampling probability density function (SS-PDF)’ and incorporating the single-loop MC theory into the computation, the proposed algorithm can reduce the original three-loop nested MC computation into a single-loop one in terms of model evaluation, which requires substantially less computational effort. Methods for choosing proper SS-PDF are also discussed in the paper. The efficiency and robustness of the proposed algorithm have been demonstrated by results of several examples.     

A response surface based optimisation algorithm for the calculation of fuzzy envelope FRFs of models with uncertain properties

This paper describes a response surface based optimisation technique for the calculation of envelope frequency response functions (FRFs) of imprecisely defined structures using the interval and fuzzy finite element method.The authors developed a hybrid - global optimisation and interval arithmetic - procedure for interval and fuzzy envelope FRF calculation. This hybrid approach reduces the computational cost of the analysis compared to a full global optimisation approach and reduces the conservatism on the envelope FRF compared to a full interval arithmetic approach.Still, the optimisation step is the computationally most expensive part of the algorithm. To handle industrially sized applications, a very efficient optimisation procedure is imperative. The response surface based procedure described in this paper decreases the computational cost of a fuzzy envelope FRF calculation with a factor 50 or more compared to the commonly used two-level full factorial design of experiments, while giving a comparable accuracy.     

A computational software tool for the minimization of costs and greenhouse gas emissions associated with water distribution systems

While evolutionary algorithms have been applied extensively to water resource problems, there remains a need to unify and consolidate computational and software approaches to solving these problems. In order to facilitate this for the minimization of costs and greenhouse gas emissions of water distribution systems, the water distribution cost-emissions nexus (WCEN) computational software framework is introduced in this paper. The software is freely available and can be easily modified in order to facilitate consistency of modeling, simulation and evaluation within different research studies. In addition, it enables consideration of the time-dependent variation of operational choices, such as emissions factors, electricity tariffs and water demands, which has not been done previously. The utility of the framework is demonstrated for a case study, the results of which show that consideration of such variations can significantly affect optimal design and operational decisions, as well as their costs and GHG emissions.     

A software framework for assessing the resilience of drinking water systems to disasters with an example earthquake case study

Water utilities are vulnerable to a wide variety of human-caused and natural disasters. The Water Network Tool for Resilience (WNTR) is a new open source Python™ package designed to help water utilities investigate resilience of water distribution systems to hazards and evaluate resilience-enhancing actions. In this paper, the WNTR modeling framework is presented and a case study is described that uses WNTR to simulate the effects of an earthquake on a water distribution system. The case study illustrates that the severity of damage is not only a function of system integrity and earthquake magnitude, but also of the available resources and repair strategies used to return the system to normal operating conditions. While earthquakes are particularly concerning since buried water distribution pipelines are highly susceptible to damage, the software framework can be applied to other types of hazards, including power outages and contamination incidents.     

A new instrument for passive remote sensing: 2. Measurement of leaf and canopy reflectance changes at 531 nm and their relationship with photosynthesis and chlorophyll fluorescence

A previously described passive remote sensing fluorimeter (see companion paper) was modified to detect changes in the reflectance of vegetation. The utility of this remote sensing technique to measure the Physiological Reflectance Index (PRI) is shown at both leaf level under laboratory conditions and at the canopy level in the field. PRI, defined as the relative changes in reflectance at 531 nm with respect to those at 570 nm (PRI=R531−R570/R531+R570), is related to xanthophyll-related, dynamic changes of non-photochemical quenching of chlorophyll fluorescence. The robustness of this relationship by simultaneous remote sensing of PRI and chlorophyll fluorescence is strengthened. At the leaf level, the existence of two kinetically distinct components of PRI is shown. A fast (within seconds) component that is partly attributed to ΔpH induced chloroplast shrinkage, and a slow (within minutes), main component that is related to xanthophyll de-epoxidation, as demonstrated by its disappearance in the presence of DTT. Overall, PRI correlated better with non-photochemical quenching of chlorophyll fluorescence (NPQ) than with any other measured parameter, including the photochemical efficiency of PSII. Finally, at the canopy level and under field conditions, it is shown that PRI can be a useful tool for remote sensing of water stress in grapevines.