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相关概念视频

First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

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Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If...
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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

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Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about...
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Poisson's And Laplace's Equation01:25

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The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
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Equilibrium Conditions for a Particle01:23

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving01:23

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

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Consider a wooden box and a cylinder of known masses m1 and m2, respectively,  hanging from a ceiling with the help of a massless pulley system.
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相关实验视频

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High-Resolution Neutron Spectroscopy to Study Picosecond-Nanosecond Dynamics of Proteins and Hydration Water
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使用WSINDy从粒子数据中学习平均场方程.

Daniel A Messenger1, David M Bortz1

  • 1Department of Applied Mathematics, University of Colorado Boulder, 11 Engineering Dr, Boulder, CO 80309, USA.

Physica D. Nonlinear phenomena
|July 21, 2023
PubMed
概括
此摘要是机器生成的。

我们为相互作用粒子系统 (IPS) 引入了一个弱形式稀疏识别方法. 这种方法降低了计算成本,并提高了大规模粒子模拟的噪声稳定性.

关键词:
数据驱动的建模.相互作用的粒子系统.平均场的极限值.稀疏回归是一种稀疏的回归.弱体形式 弱体形式

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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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In Situ Mapping of the Mechanical Properties of Biofilms by Particle-tracking Microrheology
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科学领域:

  • 计算物理学的计算物理.
  • 应用数学 应用数学 应用数学
  • 复杂的系统复杂的系统.

背景情况:

  • 相互作用粒子系统 (IPS) 通常涉及高计算复杂性.
  • 现有的系统识别方法在很大的粒子数量和有限的实验数据上扎.
  • 噪声强度对于物理系统的真实模拟至关重要.

研究的目的:

  • 为IPS开发一种计算效率高,噪声稳固的系统识别方法.
  • 为了使管理大规模IPS的随机微分方程的恢复.
  • 将拟议的方法与现有的强形式方法进行对比.

主要方法:

  • 使用平均场理论概念用于IPS.
  • 应用非线性动力学 (WSINDy) 算法的弱形式稀疏识别.
  • 为数以千计的粒子和不到100个实验的系统开发一个方案.

主要成果:

  • 在普通最小平方设置中根据标准规律性假设证明收率.
  • 在一个和两个空间维度中展示数值收率.
  • 成功地将该方法应用于同质化理论,群动力学和凯勒-塞格尔模型.

结论:

  • 开发的弱形稀疏识别方法为IPS提供了快速可靠的方法.
  • 该方法有效地减少了大量粒子的计算复杂性.
  • 这种技术在系统识别中为内在和外在噪声提供了稳定性.