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Related Concept Videos

Time and frequency -Domain Interpretation of Phase-lead Control01:24

Time and frequency -Domain Interpretation of Phase-lead Control

Phase-lead controllers are commonly used in various control systems to enhance response speed and stability. Adjusting the brightness on a television screen offers a practical example of phase-lead control. When contrast is enhanced, a phase-lead controller is employed. Mathematically, phase-lead control is identified when the first parameter is smaller than the second.
The design of phase-lead control involves the strategic placement of poles and zeros to balance steady-state error and system...
The Phase Rule01:20

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
Phase Transitions02:31

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
Phase Transitions01:21

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
Phase Changes01:19

Phase Changes

Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
Time and frequency -Domain Interpretation of Phase-lag Control01:21

Time and frequency -Domain Interpretation of Phase-lag Control

Phase-lag controllers are widely used in control systems to improve stability and reduce steady-state errors. A dimmer switch controlling the brightness of a light bulb serves as a practical example of phase-lag control, gradually adjusting the bulb's brightness. Mathematically, phase-lag control or low-pass filtering is represented when the factor 'a' is less than 1.
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Updated: May 31, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
08:39

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator

Published on: January 28, 2019

Phase-corrected surface hopping: correcting the phase evolution of the electronic wavefunction.

Neil Shenvi1, Joseph E Subotnik, Weitao Yang

  • 1Department of Chemistry, Duke University, Durham, North California 27708, USA. neil.shenvi@duke.edu

The Journal of Chemical Physics
|July 20, 2011
PubMed
Summary
This summary is machine-generated.

A simple correction to the electronic equation of motion significantly improves scattering probabilities in the fewest-switches surface hopping algorithm for large systems. This enhancement offers greater accuracy without increasing computational cost.

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Last Updated: May 31, 2026

Shaping the Amplitude and Phase of Laser Beams by Using a Phase-only Spatial Light Modulator
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Published on: January 28, 2019

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Chemical Dynamics

Background:

  • The fewest-switches surface hopping algorithm is crucial for simulating nonadiabatic dynamics.
  • Accurate calculation of electronic wavefunction evolution is essential for understanding chemical reactions.
  • Existing methods face challenges in large, complex systems.

Purpose of the Study:

  • To introduce a simple correction to the electronic equation of motion within the fewest-switches surface hopping algorithm.
  • To enhance the accuracy of calculating nonadiabatic effects in large molecular systems.
  • To demonstrate the improved performance of the corrected algorithm.

Main Methods:

  • Modified the electronic equation of motion in the fewest-switches surface hopping algorithm.
  • Applied the corrected algorithm to one-dimensional and two-dimensional model problems.
  • Compared the accuracy of the corrected approach against traditional methods.

Main Results:

  • The simple correction leads to a dramatic improvement in scattering probabilities.
  • The corrected algorithm yields substantially greater accuracy compared to the traditional approach.
  • The enhancement is achieved without any additional computational cost.

Conclusions:

  • The corrected electronic equation of motion offers a computationally inexpensive yet highly effective way to improve surface hopping simulations.
  • This method significantly enhances the accuracy of calculating nonadiabatic effects, particularly for large systems.
  • The approach is broadly applicable to various surface hopping methodologies and model systems.