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相关概念视频

Sound as Pressure Waves01:17

Sound as Pressure Waves

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Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...
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Intensity and Pressure of Sound Waves01:05

Intensity and Pressure of Sound Waves

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The intensity of sound waves can be related to displacement and pressure amplitudes by using their wave expressions and the definition of intensity. The critical step to achieve this is to write the power delivered by the particles on the wave as the product of force and velocity and simplify the force per unit area as the pressure. The velocity of the medium's particles can be derived from the displacement.
Unlike the time average of a sinusoidal term, which is zero since it is positive...
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Kinetic and Potential Energy of a Wave01:10

Kinetic and Potential Energy of a Wave

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All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge concrete buildings, causing them to fall. Loud sounds can damage nerve cells in the inner ear, causing permanent hearing loss. The waves of the oceans can erode beaches. 
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Force can be calculated from the expression for potential energy, which is a function of position. The component of a conservative force, in a particular direction, equals the negative of the derivative of the corresponding potential energy with respect to the displacement in that direction. For regions where potential energy changes rapidly with displacement, the work done and force is maximum. Also, when force is applied along the positive coordinate axis, the potential energy decreases with...
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Electrostatic Boundary Conditions01:16

Electrostatic Boundary Conditions

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Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
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Consider the wave equation for a sinusoidal wave moving in the positive x-direction. The wave equation is a function of both position and time. From the wave equation, two different graphs can be plotted.
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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密度函数理论中的耐噪力计算:基于波形的方法的表面综合方法.

Moritz Gubler1, Jonas A Finkler1,2, Stig Rune Jensen3

  • 1Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland.

The journal of physical chemistry. A
|January 27, 2025
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概括

我们介绍了一种新的方法来计算量子力学力量,使用应力张量的表面积分. 这种方法提高了密度函数理论 (DFT) 计算的准确性,特别是在波纹方法中,并增强了机器学习的潜力.

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科学领域:

  • 计算物理 计算物理
  • 量子化学 是一个量子化学.
  • 材料科学 材料科学 材料科学

背景情况:

  • 使用Hellmann-Feynman定理的密度函数理论 (DFT) 中的传统力计算可能存在不准确性,特别是在像波点这样的高级基础集表示中.
  • 精确计算力对于分子动力学模拟和预测材料特性至关重要.

研究的目的:

  • 引入和验证一个新的方法来计算量子力学力量在DFT.
  • 在特定的计算环境中解决Hellmann-Feynman定理的局限性.
  • 为训练机器学习潜力提供准确的力量数据.

主要方法:

  • 开发了一种通过量子力学应力张量的表面积积计算力的方法.
  • 将该方法应用于使用轨道的多分辨率波纹表示的系统.
  • 整合了力计算方法与机器学习技术的潜在培训.

主要成果:

  • 表面积分法产生了非常准确的力,与Hellmann-Feynman定理相比,它与潜在能量表面具有更高的一致性.
  • 该方法表现出稳健性和可靠性,特别是在不连续的基础集和波纹方法的DFT中.
  • 使用表面积分计算的力足以准确地训练机器学习的潜能,与赫尔曼-费曼定理的不同.

结论:

  • 在应力张量上的表面积分为DFT中的力计算提供了更准确和可靠的替代方案,特别是在基于波纹的方法中.
  • 这种方法克服了Hellmann-Feynman定理对特定基础集合的关键限制.
  • 表面积积的高精度使其能够有效地用于开发先进的机器学习潜力.