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Related Concept Videos

Second Order systems II01:18

Second Order systems II

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.
If  ζ...
Second Order systems I01:20

Second Order systems I

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...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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, the...
Introduction to Differential Equations01:20

Introduction to Differential Equations

A differential equation is a mathematical expression that establishes a relationship between a function and its derivatives. These equations are fundamental in modeling dynamic systems across various fields of science and engineering. The order of a differential equation is defined by the highest order derivative present in the equation. A first-order differential equation includes only the first derivative, while a second-order differential equation includes up to the second derivative of the...
State Space Representation01:27

State Space Representation

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...
Multimachine Stability01:25

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:

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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
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Published on: December 4, 2017

Ab initio multiple spawning dynamics using multi-state second-order perturbation theory.

Hongli Tao1, Benjamin G Levine, Todd J Martínez

  • 1Department of Chemistry, Stanford University, Stanford, California 94305, USA.

The Journal of Physical Chemistry. A
|November 6, 2009
PubMed
Summary
This summary is machine-generated.

We developed an advanced computational method, ab initio multiple spawning with multi-state second-order perturbation theory (AIMS-MSPT2), to simulate molecular dynamics with nonadiabatic effects. This method reveals how dynamic correlation influences excited-state decay pathways in ethylene.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Molecular Dynamics

Background:

  • Nonadiabatic effects are crucial in excited-state molecular dynamics.
  • Accurate simulation of these effects requires sophisticated theoretical methods.

Purpose of the Study:

  • To implement and apply the multi-state second-order perturbation theory (MS-CASPT2) within the ab initio multiple spawning (AIMS) framework.
  • To investigate the excited-state dynamics of ethylene, focusing on nonadiabatic decay pathways.

Main Methods:

  • Development and implementation of the AIMS-MSPT2 method for first-principles molecular dynamics.
  • Efficient numerical calculation of nonadiabatic couplings requiring minimal extra energy computations.
  • Application to simulate the excited-state dynamics of ethylene.

Main Results:

  • Identified two primary conical intersection pathways (twisted-pyramidalized and ethylidene) responsible for ultrafast excited-state to ground-state population transfer in ethylene.
  • Demonstrated that dynamic correlation significantly impacts the branching ratio between these decay pathways.
  • Showed that the twisted-pyramidalized intersection pathway is favored over the ethylidene-like pathway under AIMS-MSPT2 description.

Conclusions:

  • The AIMS-MSPT2 method provides a robust framework for studying nonadiabatic molecular dynamics.
  • Dynamic correlation plays a critical role in determining the outcome of excited-state decay processes.
  • The findings offer detailed insights into the photodynamics of ethylene, with implications for understanding similar processes in other molecules.