Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

Adaptive sequential Monte Carlo approach for real-time applications

This paper presents an adaptive Sequential Monte Carlo approach for real-time applications. Sequential Monte Carlo method is employed to estimate the states of dynamic systems using weighted particles. The proposed approach reduces the run-time computation complexity by adapting the size of the particle set. Multiple processing elements on FPGAs are dynamically allocated for improved energy efficiency without violating real-time constraints. A robot localisation application is developed based on the proposed approach. Compared to a non-adaptive implementation, the dynamic energy consumption is reduced by up to 70% without affecting the quality of solutions. © 2012 IEEE.

On the use of predictor-corrector method for coupled Monte Carlo burnup codes

This paper investigates the effect of the burnup coupling scheme on the numerical stability and accuracy of coupled Monte-Carlo depletion calculations. We show that in some cases, even the Predictor Corrector method with relatively short time steps can be numerically unstable. In addition, we present two possible extensions to the Euler predictor-corrector (PC) method, which is typically used in coupled burnup calculations. These modifications allow using longer time steps, while maintaining numerical stability and accuracy. © 2013 Elsevier Ltd. All rights reserved.

Numerical stability of the predictor-corrector method in Monte Carlo burnup calculations of critical reactors

Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the simplest methods, such as the beginning-of-step and middle-of-step constant flux approximations, are numerically unstable in fuel cycle calculations of critical reactors. Here we show that even the predictor-corrector methods that are implemented in established Monte Carlo burnup codes can be numerically unstable in cycle calculations of large systems. © 2013 Elsevier Ltd. All rights reserved.

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.

Efficient generation of one-group cross sections for coupled Monte Carlo depletion calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The onegroup cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term "universal" means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code. Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential. An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

The stochastic implicit Euler method - A stable coupling scheme for Monte Carlo burnup calculations

Existing Monte Carlo burnup codes use various schemes to solve the coupled criticality and burnup equations. Previous studies have shown that the coupling schemes of the existing Monte Carlo burnup codes can be numerically unstable. Here we develop the Stochastic Implicit Euler method - a stable and efficient new coupling scheme. The implicit solution is obtained by the stochastic approximation at each time step. Our test calculations demonstrate that the Stochastic Implicit Euler method can provide an accurate solution to problems where the methods in the existing Monte Carlo burnup codes fail. © 2013 Elsevier Ltd. All rights reserved.

Communication: energy benchmarking with quantum Monte Carlo for water nano-droplets and bulk liquid water.

We show the feasibility of using quantum Monte Carlo (QMC) to compute benchmark energies for configuration samples of thermal-equilibrium water clusters and the bulk liquid containing up to 64 molecules. Evidence that the accuracy of these benchmarks approaches that of basis-set converged coupled-cluster calculations is noted. We illustrate the usefulness of the benchmarks by using them to analyze the errors of the popular BLYP approximation of density functional theory (DFT). The results indicate the possibility of using QMC as a routine tool for analyzing DFT errors for non-covalent bonding in many types of condensed-phase molecular system.

Numerically stable Monte Carlo-burnup-thermal hydraulic coupling schemes

This paper presents stochastic implicit coupling method intended for use in Monte-Carlo (MC) based reactor analysis systems that include burnup and thermal hydraulic (TH) feedbacks. Both feedbacks are essential for accurate modeling of advanced reactor designs and analyses of associated fuel cycles. In particular, we investigate the effect of different burnup-TH coupling schemes on the numerical stability and accuracy of coupled MC calculations. First, we present the beginning of time step method which is the most commonly used. The accuracy of this method depends on the time step length and it is only conditionally stable. This work demonstrates that even for relatively short time steps, this method can be numerically unstable. Namely, the spatial distribution of neutronic and thermal hydraulic parameters, such as nuclide densities and temperatures, exhibit oscillatory behavior. To address the numerical stability issue, new implicit stochastic methods are proposed. The methods solve the depletion and TH problems simultaneously and use under-relaxation to speed up convergence. These methods are numerically stable and accurate even for relatively large time steps and require less computation time than the existing methods. © 2013 Elsevier Ltd. All rights reserved.

Generation of SFR few-group constants using the Monte Carlo code serpent

In this study, the Serpent Monte Carlo code was used as a tool for preparation of homogenized few-group cross sections for the nodal diffusion analysis of Sodium cooled Fast Reactor (SFR) cores. Few-group constants for two reference SFR cores were generated by Serpent and then employed by nodal diffusion code DYN3D in 2D full core calculations. The DYN3D results were verified against the references full core Serpent Monte Carlo solutions. A good agreement between the reference Monte Carlo and nodal diffusion results was observed demonstrating the feasibility of using Serpent for generation of few-group constants for the deterministic SFR analysis.

Control of aircraft in the terminal manoeuvring area using parallelised sequential Monte Carlo

This paper reports on the use of a parallelised Model Predictive Control, Sequential Monte Carlo algorithm for solving the problem of conflict resolution and aircraft trajectory control in air traffic management specifically around the terminal manoeuvring area of an airport. The target problem is nonlinear, highly constrained, non-convex and uses a single decision-maker with multiple aircraft. The implementation includes a spatio-temporal wind model and rolling window simulations for realistic ongoing scenarios. The method is capable of handling arriving and departing aircraft simultaneously including some with very low fuel remaining. A novel flow field is proposed to smooth the approach trajectories for arriving aircraft and all trajectories are planned in three dimensions. Massive parallelisation of the algorithm allows solution speeds to approach those required for real-time use.

Monitoring and preventing numerical oscillations in 3D simulations with coupled Monte Carlo codes

Previous studies have reported that different schemes for coupling Monte Carlo (MC) neutron transport with burnup and thermal hydraulic feedbacks may potentially be numerically unstable. This issue can be resolved by application of implicit methods, such as the stochastic implicit mid-point (SIMP) methods. In order to assure numerical stability, the new methods do require additional computational effort. The instability issue however, is problem-dependent and does not necessarily occur in all cases. Therefore, blind application of the unconditionally stable coupling schemes, and thus incurring extra computational costs, may not always be necessary. In this paper, we attempt to develop an intelligent diagnostic mechanism, which will monitor numerical stability of the calculations and, if necessary, switch from simple and fast coupling scheme to more computationally expensive but unconditionally stable one. To illustrate this diagnostic mechanism, we performed a coupled burnup and TH analysis of a single BWR fuel assembly. The results indicate that the developed algorithm can be easily implemented in any MC based code for monitoring of numerical instabilities. The proposed monitoring method has negligible impact on the calculation time even for realistic 3D multi-region full core calculations. © 2014 Elsevier Ltd. All rights reserved.

聚烯烃官能化及其反应共混的Monte Carlo

针对马来酸酐(MAH)接枝聚丙烯(PP)和聚乙烯(PE)、不相容共混物的反应增容、聚丙烯共混物在剪切流动过程中形态结构演化等聚烯烃反应加工中典型的化学和物理问题开展了计算机模拟和实验研究。 首先，我们建立和完成了适用于Monte Carlo计算机模拟的MAH接枝PP和PE的反应动力学模型及模拟程序的编写与运行。对于MAH接枝PP，模拟结果表明接枝产物所占比例与MAH初始浓度有关。当MAH浓度较低时(小于2.5 wt%)，MAH主要接枝在由β裂解所产生PP链末端上；而在MAH浓度较大时(大于2.5 wt%)，大部分MAH接枝在PP链上的三级碳上。这一结论很好地解决了多年来存在的关于MAH接枝PP位置的争议。为了进一步验证模拟结果，在实验上我们制备了不同MAH(13C标记)初始浓度下接枝PP的系列样品。核磁共振(NMR)研究结果表明MAH的初始浓度明显影响不同接枝产物所占比例，具体表现为MAH接枝到PP三级碳的MAH的NMR共振峰（δ= 32.0 ppm）随MAH的初始浓度的增加而明显增强，而接枝到由β裂解所产生PP链末端的MAH的NMR共振峰（δ=30.3 ppm）随MAH的初始浓度的增加而明显减弱。这与模拟结果一致。对于MAH接枝线性PE，模拟结果表明MAH接在PE主链上形成枝状结构所占比例随MAH初始浓度的增加而增加，而接在两PE主链中间形成桥状结构所占比例随MAH初始浓度的增加而下降。当MAH浓度非常低的时候，两种结构所占比例相当接近。这一结果改变了人们对这一问题的传统认识，即在任何条件下桥状结构所占比例都远远低于枝状结构。以上结果为MAH接枝聚乙烯、聚丙烯分子结构的调控提供了科学依据。 其次，我们开展了伴有化学反应的不相容共混聚合物的增容，即反应增容的Monte Carlo模拟研究。模拟结果表明官能化聚合物A的加入有效改善了聚合物A与极性聚合物B的相容性。当聚合物A为分散相时，A-B和A-B-A嵌段共聚物的增容效果比B-A-B嵌段共聚物好。我们发现原位生成的A-B、A-B-A和B-A-B三种嵌段共聚物在共混体系中微观结构各不相同。所生成的A-B两嵌段共聚物分布在A/B两相界面上，其A、B嵌段分别嵌入A、B相区里；所生成的A-B-A三嵌段共聚物则通过“桥状结构”连接两个被分散的A相区；所生成的B-A-B三嵌段共聚物则以“折叠结构”存在于A/B两相界面。此外，我们还研究了接枝共聚物在A/B/接枝共聚物三元共混体系中的增容效果及其微观结构。模拟结果表明，接枝共聚物的结构和支链长度对其在共混物中的微观结构和分散相粒径影响很大。当添加A-g-B接枝共聚物作为增容剂时，如果其支链较短，部分接枝共聚物将会在连续相中形成胶束；当其支链较长时，它们会通过“桥状结构”连接分散相形成网络结构。当选择B-g-A接枝共聚物作为增容剂，如果其支链长度较短，部分共聚物会在分散相里形成胶束；如果其支链较长，大部分共聚物将存在于A/B两相界面上连接A、B两相。 最后，我们在线跟踪研究了聚丙烯共混物在剪切流动过程中形态结构演化过程，观察到了剪切流动下尼龙6(PA6)液滴在PP连续相中的破裂过程。结果表明PA6液滴同时存在fracture 和tip streaming 两种破裂模式。在该共混体中添加少量的SEBS或SEBS-g-MAH，发现在适当的剪切条件下PA6液滴可通过SEBS粘结形成非常有序的规则结构，即平行排列的线条结构。有趣的是这种平行排列的线条结构垂直于剪切流动方向。进一步研究结果表明该结构是一亚稳态，其最终要聚集成球状结构。有意义的是该亚稳态结构可以保持数十分钟以上，这使得人们有足够的时间降温将该结构“冻结”住。这一结果为通用高分子共混物有序结构的外场调控提供了成功范例。