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01:10Van der Waals Equation
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The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
4.1K
01:07Gauss's Law
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If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
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04:01Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation
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Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
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02:35Clausius-Clapeyron Equation
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The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
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01:22Generalized Hooke's Law
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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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01:26Thermodynamic Potentials
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Thermodynamic potentials are state functions that are extremely useful in analyzing a thermodynamic system. They have dimensions of energy. The four important thermodynamic potentials are internal energy, enthalpy, Helmholtz free energy, and Gibbs free energy. These thermodynamic potentials can be expressed using two of the following variables: pressure, volume, temperature, and entropy. These two variables are expressed as the rate of change of the thermodynamic potential with respect to other...
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从一开始就概括了朗格温方程.
Pinchen Xie1, Roberto Car1,2,3, Weinan E4,5
1Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544.
概括
我们开发了ab initio通用朗格温方程 (AIGLE) 以使用机器学习来建模缓慢的材料和分子动态. 这种方法可以实现高效的多尺度建模,准确捕捉低频动态和远红外吸收.
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科学领域:
- 计算材料科学科学 计算材料科学
- 理论化学 理论化学
- 统计力学 统计力学
背景情况:
- 在材料和分子中建模慢集体变量 (CVs) 是具有计算挑战性的.
- 现有的方法往往难以捕捉跨多个尺度的动态.
- 基于量子力学的原子模拟是准确的,但在计算上昂贵.
研究的目的:
- 为了引入一种基于机器学习的新方法,ab initio泛化朗格文方程 (AIGLE),用于建模缓慢的CV动态.
- 通过从高准确度量子力学模拟中学习参数来实现高效的多尺度建模.
- 为了证明AIGLE在研究晶体酸中中等尺度过程的能力.
主要方法:
- 使用莫里-兹万齐格形式主义开发了AIGLE,结合了由波动-散流定理所限制的力场,内存内核和噪声发生器.
- 集成的老与深潜力的分子动力学和电子密度的功能理论.
- 应用AIGLE研究场驱动的铁电域墙壁动力学和酸中的粗粒电二极管的格子.
主要成果:
- 成功地模拟了晶体酸中中等尺度动态,包括场驱动的域壁运动和二极管格子动态.
- 该方法将ab initio模拟扩展到传统分子动力学无法访问的基于噪声的系统.
- 证明了比分子动力学更大的数量级的计算效率,同时准确地复制低频动力学和远红外吸收.
结论:
- 为材料和分子中缓慢动态的多尺度建模提供了强大而高效的框架.
- 该方法准确地捕捉了低频率的微观动态,这对于理解远红外吸收等现象至关重要.
- AIGLE为模拟复杂系统开辟了新的途径,传统方法在计算上是不可避免的.