### 物理代写|统计物理代写Statistical Physics of Matter代考|FY828

statistics-lab™ 为您的留学生涯保驾护航 在代写统计物理Statistical Physics of Matter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。我们的专家在代写统计物理Statistical Physics of Matter代写方面经验极为丰富，各种代写统计物理Statistical Physics of Matter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

## 物理代写|统计物理代写Statistical Physics of Matter代考|Phenomenological Methods of Coarse-Graining

A task of modelling biological systems thus starts with identifying the primary degrees of freedom $\mathcal{Q}$ and the associated effective Hamiltonian or free energy function $\mathcal{F}(\mathcal{Q})$. For a solution of many solute particles with nontrivial interactions $\Phi_{e f f}{\mathcal{Q}}$ (4.82), $\mathcal{Q}$ is $\left{\boldsymbol{r}{U}\right}$, the configurations of all the solute particles. The evaluation of the free energy using (5.2) with $\mathcal{F}{\mathcal{Q}}=\Phi{e f f}{\mathcal{Q}}$, however, is very difficult analytically and quite costly numerically. As introduced earlier, a further simplification of the coarse-grained description is possible by adopting the lattice model. In the model the volume of the solution is divided into cells or sites, each of which contains a solute particle or none. As was shown in Chap. 4, the mesoscopic state is then represented by the occupation number in each site, $\mathcal{Q}=\left{n_{i}\right}(i=1,2 \ldots)$, where $n_{i}$ is either 0 or 1 . With the interactions between two particles in the nearest neighborhood included as contact attraction and hard-core exclusion, the lattice model can deal with a great variety of problems with relative simplicity.

For analysis of a long-chain polymer, we may use a lattice model in which particles in the cells are interconnected (Fig. 5.1a). We may conduct further coarse-graining, and regard the polymer as a semi-flexible, curved rod, called a worm-like chain (Fig. 5.1b). Instead of a configuration of particles, $\mathcal{Q}$ is now a continuous function ${\boldsymbol{r}(s)}$, which represents the position of the chain along the contour distance $s$. In this case of a semi-flexible chain there is an orientational correlation between neighboring chain segments. If the polymer chain is very long, it can be represented as a flexible string of beads, each of which comprises sufficient number of monomers such that there is no correlation between the beads; this process gives rise to a flexible chain with a new coarse-grained continuous curve $\left{\boldsymbol{r}_{f}(s)\right}$. The relevant level of the description is often guided by measurement. An example is the end-to-end distance of the polymer to describe its conformation $\mathcal{Q}=\boldsymbol{R}$ (Fig. 5.1c).

## 物理代写|统计物理代写Statistical Physics of Matter代考|Water and Biologically-Relevant

Water is abundant and ubiquitous in our body and on earth. Despite its critical importance in life, and compared with the spectacular development of modern physics, fundamental understanding of its physics is surprisingly poor. In principle statistical mechanics is expected to explain its physical properties in a quantitative detail, but is quite difficult to implement due to the relative complexity of water molecules and the non-isotropic interactions among them. The statistical mechanics study for water is rare and limited (Dill et al. 2005; Stanley et al. 2002). Instead of the statistical mechanics we give a semi-quantitative sketch of basic thermal properties of water and the hydrogen bonding that underlies the unique characteristics of water.

We also introduce the biologically relevant interactions between objects in water. They are hydrophilic and hydrophobic interactions, the electrostatic interaction among charges and dipoles, and Van der Waals interactions. In many cases, the electrostatic interactions turn out to he weak with the strength comparable to the thermal energy $k_{B} T$ and much less upon thermalization, due to the screening effects of water’s high dielectric constant and the ion concentration. These weak interactions facilitate conformational changes of biological soft matter such as polymers and membranes at body temperature.

## 物理代写|统计物理代写Statistical Physics of Matter代考|Phenomenological Methods of Coarse-Graining

(5.2) 评估自由能 $\mathcal{F} \mathcal{Q}=\Phi e f f \mathcal{Q}$ 然而，在分析上非常困难并且在数值上非常昂贵。如前所述，通过采用格模型 可以进一步简化粗粒度描述。在模型中，溶液的体积被划分为细胞或位点，每个细胞或位点都包含一个溶质颗粒或 哪里 $n_{i}$ 是 0 或 1 。由于最近邻域中两个粒子之间的相互作用包括接触吸引和硬核排斥，晶格模型可以相对简单地处 理各种各样的问题。

## 有限元方法代写

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## 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。