### 物理代写|流体力学代写Fluid Mechanics代考|AMME2261

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• 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

## 物理代写|流体力学代写Fluid Mechanics代考|The concept of an interface

The general concept of an interface assumes contact or separation between material objects. While the concept of an interface in physics may refer to situations of a very different nature, there are also commonalities between these. Among these commonalities, we will study surface quantities and balance laws in particular, i.e. equations with partial derivatives that connect these quantities, in interaction with those in the media in contact.

Under certain conditions, using simplifying hypotheses, it is possible to establish balance laws for interfaces using physico-chemical quantities constituent mass, total mass, momentum, energy, entropy – in a unique form, as is done for continuous 3D media (whether fluid or solid). We will see that this requires a small-scale internal exploration of the interface throughout its thickness, and an integration of the results obtained in the normal direction.

## 物理代写|流体力学代写Fluid Mechanics代考|Interface in physics and geometric surfaces

The term “interface” refers to a separation surface. However, while the term “surface” has a precise meaning in mathematics, being a 2D manifold endowed with geometric properties, the definition of discontinuity surfaces must be refined by mechanics, more generally, in physics or chemistry.

Thus, as soon as this interface presents internal physical properties such as surface tension, or when it modifies the exchanges between the media that it separates, or again, when it is the site of production of different natures, it is no longer a simple separation surface.

On the contrary, there is the question of the scale of observation. The interface appears as a discontinuity surface on a macroscopic scale, but may become a continuous medium on a smaller scale. Moreover, if we observe it on an even smaller scale, the continuity gives way to atomic and molecular discontinuities and their constituents, the elementary particles (Rocard 1933; Roussel 2016).

For a mechanical physicist, the macroscopic description is required to model a problem. However, the mechanical physicist must sometimes go down to a very small scale within the objects to understand their behavior.
This is true for both interfaces and bulks. The mechanical physicist and thermodynamician willingly explore the molecular level to understand the behavior of gases, liquids or solids. The application of the laws of mechanics to objects at a molecular level makes it possible to establish macroscopic constitutive laws of mechanics for continuous media through the statistical theories that use approximations. These scientists commonly use Boltzmann’s equation, Fermi’s theory and the BBGKY hierarchy. The experimental measurements provide the data that allows them to use the modeling techniques developed from these laws.

It is the same for interfaces. These interfaces can be considered as surfaces with physical properties on a macroscopic scale, but if we examine them on a smaller scale, using powerful microscopes, we will see many differences. Whether or not we go as far as the molecular level, there is indeed a thickness to what appears to be a simple geometric surface. Thus, it is useful to talk about interfacial thickness and an interfacial zone – or an interfacial layer – when we study the interior of an interface in detail (Gatignol and Prud’homme 2001). This exploration will be carried out on a single scale, that of thickness, i.e. in the direction normal to the surface. Thus, the scales in the other directions that are tangential to the surface are left unchanged.

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## MATLAB代写

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