统计代写|蒙特卡洛方法代写Monte Carlo method代考|STAT4063

如果你也在 怎样代写蒙特卡洛方法Monte Carlo method这个学科遇到相关的难题,请随时右上角联系我们的24/7代写客服。

蒙特卡洛方法,或称蒙特卡洛实验,是一类广泛的计算算法,依靠重复随机抽样来获得数值结果。其基本概念是利用随机性来解决原则上可能是确定性的问题。

statistics-lab™ 为您的留学生涯保驾护航 在代写蒙特卡洛方法Monte Carlo method方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写蒙特卡洛方法Monte Carlo method代写方面经验极为丰富,各种代写蒙特卡洛方法Monte Carlo method相关的作业也就用不着说。

我们提供的蒙特卡洛方法Monte Carlo method及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
统计代写|蒙特卡洛方法代写Monte Carlo method代考|STAT4063

统计代写|蒙特卡洛方法代写Monte Carlo method代考|A Highly Absorptive Surface Whose Reflectivity is Strongly Specular

Aeroglaze ${ }^{\circledR} \mathrm{Z} 302[2]$ is a polyurethane-based paint whose absorptivity typically exceeds $90 \%$ in the visible part of the spectrum, depending on the coating thickness. It is unique in that the reflected component of radiation is mostly specular. Its special properties make it the coating of choice for many aerospace and optical applications where a surface must be an exceptionally efficient absorber but where diffuse reflection is undesirable. A typical application is the interior surface of a blackbody cavity used as a calibration target. In this case the cavity geometry would be such that several specular reflections would occur before an incident ray could escape, and any diffuse component of reflectivity present would diminish the effectiveness of the design because it would allow some power to escape the cavity with each reflection. Such diffuse “leaks” can

be significant when the effective emissivity of the cavity must be unity to better than three nines.

Prokhorov and Prokhorova [3] describe a three-component semiempirical model based on their own measurements of the BRDF of Z302 at a wavelength of $\lambda=10.6 \mu \mathrm{m}$. We have used the same data, represented by the symbols in Figure $4.4$, to derive a purely empirical four-component model, represented by the curves in the figure. Both the Prokhorov and Prokhorova model and our model are in excellent agreement with the measurements. Our four-component model [4] has the form
$$
B R D F=\rho_{1}^{\prime \prime}+\rho_{2}^{\prime \prime}+\rho_{3}^{\prime \prime}+\rho_{4}^{\prime \prime},
$$
where
$$
\rho_{n}^{\prime \prime}=A_{n} \frac{1}{\sqrt{2 \pi} \sigma_{n}} e^{-\left(\vartheta_{v}-\vartheta_{i}\right)^{2} / 2 \sigma_{n}^{2}}+O_{n}, \quad n=1,2,3,4
$$
In Eq. (4.11), $\vartheta_{i}$ and $\vartheta_{v}$ are the incidence and viewing angles shown in the inset in Figure $4.4$, and $A_{n}, \sigma_{n}$, and $O_{n}$ are empirical curve-fitling parameters. The form of Eq. (4.11) is recognizable as the normal probability distribution function multiplied by a scaling factor $A_{n}$ and shifted

in amplitude by an offset $O_{n}$. In practice the additive offsets for the four values of $n$ are gathered into a single constant. The fit illustrated in Figure $4.4$ was obtained by defining the standard deviation
$$
\sigma_{n}=\frac{1}{\sqrt{2 \pi} b_{n} \vartheta_{i}}
$$
and the multiplicative constant
$$
A_{n}=\frac{B_{n}}{b_{n} \vartheta_{i}},
$$

统计代写|蒙特卡洛方法代写Monte Carlo method代考|A Highly Reflective Surface Whose Reflectivity is Strongly Diffuse

We next consider a practical application whose accurate simulation requires a bidirectional spectral reflection model. The integrating sphere [5] often plays a central role in radiometric instrument calibration, surface optical behavior measurement, and radiant source characterization $[6,7]$. The purpose of an integrating sphere is to convert a collimated beam of monochromatic light, such as might be provided by a laser source, into a larger, weaker source of diffuse light at the same wavelength. The essential property of the integrating sphere is its ability to produce a Lambertian source of monochromatic radiation due to multiple scattering from its interior walls. This requirement will be satisfied exactly for a completely enclosed spherical cavity, even when the wall coating is not itself a perfectly diffuse reflector. However, a practical integrating sphere must be fitted with ports that allow the illuminating beam to enter and the instrument under calibration to

view the interior wall. The ports inevitably allow some of the entering radiation to escape before being completely diffused by reflections, thereby compromising the desired effect. In practice the ports are made as small as possible compared to the diameter of the sphere, and the interior walls are treated with a highly reflective, highly diffuse coating.
The author and his coworkers [8] have investigated the departure from ideal behavior of a practical integrating sphere, with emphasis on the influence of directionality. The results of that investigation are offered here as an example of an application in which the diffuse gray assumption may be inadequate. We consider an application in which a relatively small integrating sphere is to be used on-orbit to calibrate a radiometer against a reference radiometer by having both instruments observe the same sector of the interior wall through two separate ports. Because the calibrations will be repeated over a period of up to several years, it is important to know how the calibration factor might be expected to vary with aging of the wall coating. It is further interesting to know how the degree of directionality of reflections from the walls might influence its performance.

We use the MCRT method to simulate illumination of the interior by a quasi-monochromatic light source at a wavelength, $0.9 \mu \mathrm{m}$, for which the $B R F$ model developed below may be considered valid. For purposes of the current investigation the diameter of the port through which the narrow light beam is admitted may be considered sufficiently small compared to the diameters of the two viewing ports to neglect its presence in the ray trace. The hypothetical experimental arrangement is illustrated in Figure 4.12.

统计代写|蒙特卡洛方法代写Monte Carlo method代考|The Band-Averaged Spectral Radiation

The case studies presented in Sections $4.3$ and $4.4$ exemplify direct application of the MCRT method without recourse to radiation distribution factors, which were not needed to accomplish the stated goals. Furthermore, they involve situations for which the wavelength interval of interest is sufficiently narrow that the surface models used are, to an acceptable approximation, independent of wavelength. However, in some cases radiation distribution factors are required, as explained in Chapter 3. The radiation distribution factor introduced and used in Chapter 3 for gray surfaces had two subscripts, $i$ and $j$, the indices of the emitting and absorbing surface. For the case of spectral radiation it is necessary to add a third subscript, $k$, representing the wavelength interval $\Delta \lambda_{k}$ in which the distribution factor applies. We define the band-averaged spectral radiation distribution factor $D_{i j k}$ as the fraction of power emitted in wavelength

interval $\Delta \lambda_{k}$ by surface element $i$ that is absorbed by surface element $j$, both directly and due to all possible reflections within the enclosure.
Estimation of the band-averaged spectral radiation distribution factor matrix assumes the availability of a dense data set ultimately based on extensive laboratory measurements. Imagine a bookshelf in a virtual thermophysical properties library bearing the label “Bidirectional Spectral Reflectivity.” Upon perusal of this bookshelf we might find books with titles “Z302,” “Spectralon,” “Gold Black,” and other optical coatings. When we take down one of these books and open to its table of contents; we find chapter titles such as “Wavelength Interval Between $0.01$ and $0.10 \mu \mathrm{m}$,” and “Wavelength Interval Between $0.10$ and $1.00 \mu \mathrm{m}$,” and so forth. Then when we flip through Chapter 1 we notice page headings “Angle of Incidence $=5^{\circ}$,” “Angle of Incidence $=10^{\circ}$,” and, on the last page, “Angle of Incidence $=85^{\circ}$.” Finally, when we scan one of these pages from top to bottom we find on the first line “Angle of Reflectance $=5^{\circ}$, $B R D F=44.21$,” and on the second line “Angle of Reflectance $=10^{\circ}$, $B R D F 38.45$,” and so forth. Upon plotting the data found in one of these books, we recognize that the spacing between successive wavelengths, angles of incidence, and angles of reflectance is sufficiently small to allow accurate linear interpolation between tabulated values.

统计代写|蒙特卡洛方法代写Monte Carlo method代考|STAT4063

蒙特卡洛方法代考

统计代写|蒙特卡洛方法代写Monte Carlo method代考|A Highly Absorptive Surface Whose Reflectivity is Strongly Specular

气釉®从302[2]是一种基于聚氨酯的涂料,其吸收率通常超过90%在光谱的可见部分,取决于涂层厚度。它的独特之处在于辐射的反射分量大部分是镜面反射的。它的特殊性能使其成为许多航空航天和光学应用的首选涂层,在这些应用中,表面必须是非常有效的吸收体,但不希望出现漫反射。一个典型的应用是用作校准目标的黑体腔的内表面。在这种情况下,腔的几何形状将使得在入射光线能够逸出之前会发生几次镜面反射,并且存在的反射率的任何漫反射分量都会降低设计的有效性,因为它会允许一些功率随着每次反射而逸出腔。这种弥散的“泄漏”可以

当空腔的有效发射率必须是一致的,优于三个九时,这一点非常重要。

Prokhorov 和 Prokhorova [3] 描述了一个三分量半经验模型,该模型基于他们自己对 Z302 在波长为λ=10.6μ米. 我们使用了相同的数据,由图中的符号表示4.4,推导出一个纯经验的四分量模型,由图中的曲线表示。Prokhorov 和 Prokhorova 模型以及我们的模型都与测量结果非常吻合。我们的四分量模型 [4] 具有以下形式

乙RDF=ρ1′′+ρ2′′+ρ3′′+ρ4′′,
在哪里

ρn′′=一个n12圆周率σn和−(ϑ在−ϑ一世)2/2σn2+○n,n=1,2,3,4
在等式。(4.11),ϑ一世和ϑ在是图中插图所示的入射角和视角4.4, 和一个n,σn, 和○n是经验曲线拟合参数。方程的形式。(4.11) 可识别为正态概率分布函数乘以比例因子一个n并转移

幅度偏移○n. 在实践中,四个值的附加偏移量n聚集成一个常数。如图所示的配合4.4通过定义标准偏差获得

σn=12圆周率bnϑ一世
和乘法常数

一个n=乙nbnϑ一世,

统计代写|蒙特卡洛方法代写Monte Carlo method代考|A Highly Reflective Surface Whose Reflectivity is Strongly Diffuse

我们接下来考虑一个实际应用,其精确模拟需要双向光谱反射模型。积分球 [5] 通常在辐射测量仪器校准、表面光学行为测量和辐射源表征中发挥核心作用[6,7]. 积分球的目的是将准直的单色光束(例如可能由激光源提供)转换成更大、更弱的相同波长的漫射光源。积分球的基本特性是由于其内壁的多次散射,它能够产生单色辐射的朗伯源。对于完全封闭的球形空腔,即使壁涂层本身不是完美的漫反射器,该要求也将完全满足。然而,一个实用的积分球必须配备允许照明光束进入的端口,并且被校准的仪器可以

查看内墙。这些端口不可避免地允许一些进入的辐射在被反射完全漫射之前逸出,从而损害所需的效果。实际上,与球体的直径相比,这些端口尽可能地小,并且内壁采用高反射、高漫射涂层处理。
作者和他的同事 [8] 研究了实际积分球与理想行为的偏离,重点是方向性的影响。该调查的结果在此作为一个应用示例提供,其中漫反射灰色假设可能不充分。我们考虑一个应用,其中一个相对较小的积分球将在轨道上用于校准辐射计与参考辐射计,方法是让两个仪器通过两个单独的端口观察内壁的同一扇区。由于校准将在长达数年的时间内重复进行,因此了解校准因子如何随着墙壁涂层的老化而变化非常重要。

我们使用 MCRT 方法来模拟一个波长的准单色光源对内部的照明,0.9μ米, 为此乙RF下面开发的模型可能被认为是有效的。出于当前研究的目的,可以认为窄光束通过的端口的直径与两个观察端口的直径相比足够小,以忽略它在光线轨迹中的存在。假设的实验安排如图 4.12 所示。

统计代写|蒙特卡洛方法代写Monte Carlo method代考|The Band-Averaged Spectral Radiation

章节中介绍的案例研究4.3和4.4举例说明 MCRT 方法的直接应用,无需借助辐射分布因子,而实现既定目标则不需要这些辐射分布因子。此外,它们涉及感兴趣的波长间隔足够窄的情况,以至于所使用的表面模型在可接受的近似值上与波长无关。但是,在某些情况下,需要辐射分布因子,如第 3 章所述。第 3 章介绍和使用的灰色表面的辐射分布因子有两个下标,一世和j,发射和吸收表面的指数。对于光谱辐射的情况,需要添加第三个下标,ķ,代表波长间隔Δλķ其中分布因子适用。我们定义频带平均光谱辐射分布因子D一世jķ作为以波长发射的功率的一部分

间隔Δλķ按面元一世被表面元素吸收j,直接和由于外壳内所有可能的反射。
频带平均光谱辐射分布因子矩阵的估计假设密集数据集的可用性最终基于广泛的实验室测量。想象一下虚拟热物理属性库中的一个书架,上面贴有“双向光谱反射率”标签。仔细阅读这个书架,我们可能会发现标题为“Z302”、“Spectralon”、“Gold Black”和其他光学涂层的书籍。当我们取下其中一本书并打开其目录时;我们找到章节标题,例如“Wavelength Interval Between0.01和0.10μ米,”和“波长间隔0.10和1.00μ米,”等等。然后,当我们翻阅第 1 章时,我们注意到页面标题“入射角=5∘,“ “入射角=10∘,”以及最后一页的“入射角=85∘。” 最后,当我们从上到下扫描其中一个页面时,我们在第一行发现“反射角=5∘, 乙RDF=44.21,”和第二行的“反射角=10∘,乙RDF38.45,”等等。在绘制其中一本书中的数据后,我们认识到连续波长、入射角和反射角之间的间距足够小,可以在表格值之间进行准确的线性插值。

统计代写|蒙特卡洛方法代写Monte Carlo method代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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