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

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。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|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|A Highly Absorptive Surface Whose Reflectivity is Strongly Specular

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

ρn′′=一个n12圆周率σn和−(ϑ在−ϑ一世)2/2σn2+○n,n=1,2,3,4

σn=12圆周率bnϑ一世

## 有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。