蒙特卡罗等效哈密顿量的1+1维检验

用最近发展起来的蒙特卡罗等效哈密顿量新方法,研究了与量子场论中Φ4模型相似的1+1维量子力学系统V(x)=μ²x²+λx⁴(其中μ²<0,λ>0)的低能物理特性.计算了能谱、波函数以及热力学可观察量.获得良好的结果,表明这种新方法有希望推广到多自由度系统和格点规范场论.     

用蒙特卡罗哈密顿量方法研究非S态

以氢原子为例，验证了Monte Carlo Hamiltonian(MCH)方法推广应用到量子力学系统中在原点发散的势的非S态的有效性，给出估计误差的新思路，得到和解析解相符的能谱和约化径向波函数.     

X射线能谱测量的蒙特卡罗成像模拟

针对高能强流电子束轰击高Z靶产生的X射线的能谱测量问题,采用蒙特卡罗方法进行成像模拟研究。高能X射线能谱通常由对X射线经过衰减体的直穿透射率曲线进行解谱获得。设计了带多准直孔的截锥体模型,在单次模拟成像中获得完整的衰减透射率曲线,有效避免了散射光子对透射率曲线以及X射线能谱重建的影响。成像面采用非均匀划分网格计数,将大部分探测计数点集中于各准直孔出口处,保证关注区域模拟成像的精细度,同时减少总体计算时间。     

一个描述轴对称、过渡核yrast带的新公式及核γ形变的一个特征量

详细地分析了一个特殊有效势的解析极限解.指出对应于yrast线的能谱,无论是轴对称、三轴形变还是γ不稳,均可用统一的公式描述.并可通过此公式来鉴定核的γ形变.作为例子,拟合了很多实际核的yrast带,并鉴定了各带的γ形变程度.     

蒙特卡罗模拟中三维介质辐射对称性检验

蒙特卡罗方法是数值模拟中一个很常用的计算方法,应用范围很广泛,并常常作为数值仿真算法的基准.概率模型和伪随机数发生器是蒙特卡罗法中两个很重要的组成部分,它们决定了蒙特卡罗法的正确性和计算精度.本文提出了一种比较充分的检验方法-三维介质辐射对称性检验法,它可在不同条件下对各种伪随机数程序进行无限制的检验,在更精细的层次上区分伪随机数发生器的优劣,同时还可检验概率模型的正确性.     

D-T中子源n-γ密度测井规律的蒙特卡罗模拟

根据D-T反应中子的能谱和角分布数据,建立了中子源模型;根据石灰岩地层标准刻度井群数据,建立了井模型。采用MCNP程序模拟了井中中子和射线的输运,得到了不同地层密度、不同源距处NaI探测器中的混合能谱和非弹能谱。在混合能谱2.5~4.5 MeV能区开窗,混合射线相对计数随源距的变化曲线显示,源距应选择在20~80 cm,密度与混合射线计数之间呈现非线性关系。在非弹能谱1.0~8.0 MeV能区开窗,非弹射线相对计数随源距的变化数据显示,源距应选择在20~40 cm或80 cm附近,密度与非弹射线计数之间成近似线性关系。     

空间辐射环境及人体剂量蒙特卡罗模拟

针对空间辐射环境进行了理论分析,并使用蒙特卡罗方法,对银河宇宙射线及典型太阳质子事件进行了模拟。通过分析常规屏蔽对空间辐射场及人体剂量的影响、屏蔽下的次级粒子产额等,验证了蒙特卡罗工具包Geant4应用于空间辐射防护研究的准确性。模拟发现：在常规屏蔽厚度的情况下,对于太阳质子事件,由于其能量主要分布在低能量段(100 MeV以下),屏蔽效果随屏蔽厚度的增加明显增大,1 g/cm2 Al等效厚度屏蔽皮肤剂量可降低至其初始剂量值的8%左右,10 g/cm2 Al等效厚度的屏蔽可降低至初始剂量值的048%左右;而对于银河宇宙射线,由于其平均能量较高,屏蔽层的屏蔽作用并不明显,在浅层组织剂量甚至有所增加。     

D-T中子源n-γ密度测井规律的蒙特卡罗模拟

根据D-T反应中子的能谱和角分布数据,建立了中子源模型;根据石灰岩地层标准刻度井群数据,建立了井模型。采用MCNP程序模拟了井中中子和射线的输运,得到了不同地层密度、不同源距处NaI探测器中的混合能谱和非弹能谱。在混合能谱2.5~4.5 MeV能区开窗,混合射线相对计数随源距的变化曲线显示,源距应选择在20~80 cm,密度与混合射线计数之间呈现非线性关系。在非弹能谱1.0~8.0 MeV能区开窗,非弹射线相对计数随源距的变化数据显示,源距应选择在20~40 cm或80 cm附近,密度与非弹射线计数之间成近似线性关系。     

钚体源样品γ能谱计算的蒙特卡罗方法

提出了钚体源样品γ能谱分步计算的蒙特卡罗模型和方法.采用分步和直接计算两种方法对球壳形钚体源样品的γ能谱进行了模拟计算.用实验测量的γ能谱验证了计算结果的可靠性，计算结果与实验测量值在10%的误差范围符合.通过对Steve Fetter模型的模拟计算表明：对于外面包有若干屏蔽层的钚体源样品大系统，采用分步方法进行能谱计算，可以使结果快速收敛.     

241Am-Be中子参考辐射的蒙特卡罗模拟研究

研究用于校准场所中子剂量监测仪表的241Am-Be中子参考辐射场计量特性。采用蒙特卡罗方法模拟了空气自由中子参考辐射(FRNR),GB/T 14055规定的最小尺寸中子参考辐射(SRNR)和实际中子参考辐射(ARNR)中不同检验点处中子周围剂量当量率、散射中子占比和能谱分布特征。研究结果表明,空气对FRNR中的剂量率和能谱分布影响小,近似为理想中子参考辐射;采用5%含硼聚乙烯作屏蔽的最小尺寸SRNR可减少热中子,降低散射中子占比,影锥法不适用于小尺寸中子参考辐射中对散射中子的修正;ARNR中的散射中子更少、占比更低,影锥法所得散射中子占比与理论值基本一致。     

The Convergence of Markov Chain Monte Carlo Methods: From the Metropolis Method to Hamiltonian Monte Carlo

From its inception in the 1950s to the modern frontiers of applied statistics, Markov chain Monte Carlo has been one of the most ubiquitous and successful methods in statistical computing. The development of the method in that time has been fueled by not only increasingly difficult problems but also novel techniques adopted from physics. Here, the history of Markov chain Monte Carlo is reviewed from its inception with the Metropolis method to the contemporary state‐of‐the‐art in Hamiltonian Monte Carlo, focusing on the evolving interplay between the statistical and physical perspectives of the method.     

Monte Carlo Hamiltonian: Linear Potentials

We further study the validity of the Monte Carlo Hamiltonian method. The advantage of the method,in comparison with the standard Monte Carlo Lagrangian approach, is its capability to study the excited states. Weconsider two quantum mechanical models: a symmetric one V(x) = |x|/2; and an asymmetric one V(x) = ∞, forx ＜ 0 and V(x) = x, for x ≥ 0. The results for the spectrum, wave functions and thermodynamical observables are inagreement with the analytical or Runge-Kutta calculations.     

Monte Carlo Hamiltonian:Inverse Potential

The Monte Carlo Hamiltonian method developed recently allows to investigate the ground state and low-lying excited states of a quantum system, using Monte Carlo (MC) algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applied to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.     

Hamilt onian Monte Carlo Application to (2+1)-Dimensional Quant um Mechanics

Using a recently developed Hamiltonian Monte Carlo method, we compute the lowlying energy spectrum and wavefunctions as well as thermodynamical observables in (2+1)-dimensional quantum mechanics, and give an estimate of the statistical errors. Our numerical results are in good agreement with the exact ones.     

Monte Carlo calculations of the magnetocaloric effect in gadolinium

In this work we discuss the magnetocaloric effect in metallic gadolinium. We use a model Hamiltonian of interacting 4f spins and treat the 4f spin–spin interaction both in the mean field approximation and in the Monte Carlo simulation. The calculations show that the mean field approximation yields reasonable results for the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but it fails in explaining the experimental data of specific heat at the magnetic ordering temperature. On the other hand, our theoretical results show that the Monte Carlo calculation describes well not only the magnetocaloric potentials ΔS$\mathrm{\Delta }S$ and Δ_Tad$\mathrm{\Delta }{T}_{\mathrm{ad}}$ but also the specific heat capacity.     

用MCH方法研究库仑屏蔽势的高角动量能谱

以库仑屏蔽势为模型,用蒙特卡罗哈密顿方法对库仑屏蔽势束缚态进行研究,并把结果和传统的数值解一维薛定谔方程的方法相比较,在基态或激发态,都得出相一致的结果.     

Monte Carlo simulation of indoor external exposure due to gamma-emitting radionuclides in building materials

The use of building materials containing naturally occurring radionuclides,such as ⁴⁰K, ²³⁸U, ²³²Th and their progeny, could lead to external exposures to the residents of such buildings. In this paper, a set of models are constructed to calculate the specific effective dose rates (the effective dose rate per Bq/kg of ⁴⁰K, the ²³⁸U series, and the ²³²Th series) imposed on residents by building materials with the MCNPX code. The effect of chemical composition, position concerned in the room and thickness as well as density of material is analyzed. In order to facilitate more precise assessment of indoor external dose due to gamma-emitting radionuclides in building materials, three regressive expressions are proposed and validated by measured data to calculate specific effective rates for ⁴⁰K, the ²³⁸U series and the ²³²Th series, respectively.     

Monte Carlo simulation of indoor external exposure due to gamma-emitting radionuclides in building materials

The use of building materials containing naturally occurring radionuclides such as^40K,^238U,^232Th and their progeny, could lead to external exposures to the residents of such buildings. In this paper, a set of models are constructed to calculate the specific effective dose rates（the effective dose rate per Bq/kg of ^40K, the ^238U series,and the ^232Th series） imposed on residents by building materials with the MCNPX code. The effect of chemical composition, position concerned in the room and thickness as well as density of material is analyzed. In order to facilitate more precise assessment of indoor external dose due to gamma-emitting radionuclides in building materials,three regressive expressions are proposed and validated by measured data to calculate specific effective rates for40 K,the238U series and the232 Th series, respectively.