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相关概念视频

Second Order systems II01:18

Second Order systems II

113
In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
113
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

83
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
83
State Space Representation01:27

State Space Representation

209
The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
209
Second Order systems I01:20

Second Order systems I

161
A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
161
Second-order Op Amp Circuits01:19

Second-order Op Amp Circuits

350
Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.
The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means...
350
Second Derivatives and Laplace Operator01:22

Second Derivatives and Laplace Operator

1.3K
The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or vector function yield second order expressions. Second-order expressions play a very important role in mathematics and physics. Some second order expressions include the divergence and curl of a gradient function, the divergence and curl of a curl function, and the gradient of a divergence function.
Consider a scalar function. The curl of its...
1.3K

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相关实验视频

Updated: Jul 6, 2025

Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests
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Accurate Determination of the Equilibrium Surface Tension Values with Area Perturbation Tests

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走向一个随机的完整的活跃空间第二阶段扰动理论.

Arta A Safari1, Robert J Anderson1, Giovanni Li Manni1

  • 1Max-Planck-Institute for Solid State Research, 70569 Stuttgart, Germany.

The journal of physical chemistry. A
|December 28, 2023
PubMed
概括

引入了一种用于计算电子结构的新随机方法,即随机-完全活动空间二次扰动理论 (随机-CASPT2). 这种方法克服了精确量子化学计算的数值挑战,在二元体上证明了这一点.

科学领域:

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

背景情况:

  • 精确的电子结构计算对于理解化学反应和材料特性至关重要.
  • 随机方法为传统的高精度量子化学技术提供了一个计算效率高的替代方案.
  • 在准确计算高阶减少密度矩阵 (RDMs) 对于随机量子化学方法存在挑战.

研究的目的:

  • 开发和验证一个内部合约的随机完全活跃空间二次扰动理论 (随机-CASPT2) 方法.
  • 在完整的配置交互量子蒙特卡洛 (FCIQMC) 框架内引入一种用于计算更高阶RDM的新协议.
  • 解决和克服在随机量子化学计算中的数值条件问题.

主要方法:

  • 减少密度矩阵 (RDM) 的随机抽样,直到排名四.
  • 开发一种新的FCIQMC协议,包括限制激发采样,RDM平均和正半确预测.
  • 应用随机-CASPT2方法与一般化的福克矩阵收缩.
  • 使用CASSCF ((12,12) /CASPT2.2) 计算二元结合曲线.

主要成果:

  • 随机-CASPT2的成功实施,使得随机采样RDMs的计算成为可能.
  • 在FCIQMC中用于高阶RDM计算的强大的协议,减轻数值不稳定性.

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  • 通过准确计算二聚合物结合曲线来证明该方法的能力.
  • 避免了以前与扰乱器重叠矩阵正交关系的数值调节问题.

    • 结论:

    • 开发的随机-CASPT2方法为电子结构计算提供了稳定和高效的方法.
    • 基于FCIQMC的新RDM计算协议提高了随机量子化学的可靠性.
    • 这项工作为将先进的随机量子化学方法应用于更大,更复杂的系统铺平了道路.