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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
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State Space to Transfer Function01:21

State Space to Transfer Function

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
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A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at equilibrium. A special double arrow is used to emphasize the reversible nature of the reaction. The relative concentrations of reactants and products in equilibrium systems vary greatly;...
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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space Representation01:27

State Space Representation

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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.
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Sampling Distribution01:12

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Given simple random samples of size n from a given population with a measured characteristic such as mean, proportion, or standard deviation for each sample, the probability distribution of all the measured characteristics is called a sampling distribution. How much the statistic varies from one sample to another is known as the sampling variability of a statistic. You typically measure the sampling variability of a statistic by its standard error. The standard error of the mean is an example...
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Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
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Dynamics Sampling in Transition Pathway Space.

Hongyu Zhou1, Peng Tao1

  • 1Department of Chemistry, Center for Drug Discovery, Design, and Delivery (CD4), Center for Scientific Computation, Southern Methodist University , Dallas, Texas 75275, United States of America.

Journal of Chemical Theory and Computation
|December 2, 2017
PubMed
Summary
This summary is machine-generated.

The direct pathway dynamics sampling (DPDS) method efficiently explores multiple transition pathways on potential energy surfaces. This enhanced sampling technique aids in understanding complex chemical reactions and molecular transitions.

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Area of Science:

  • Computational Chemistry
  • Chemical Physics
  • Materials Science

Background:

  • Minimum energy pathways (MEPs) are crucial for understanding transitions between molecular states on potential energy surfaces (PES).
  • Existing chain-of-states methods efficiently calculate single MEPs but may miss alternative pathways.
  • Identifying multiple pathways is essential for a comprehensive understanding of chemical processes.

Purpose of the Study:

  • To develop an enhanced sampling method for exploring multiple transition pathways on a PES.
  • To facilitate the discovery of additional minima and their associated transition pathways.
  • To improve the exploration of high-energy regions, including transition states, on a PES.

Main Methods:

  • Developed the direct pathway dynamics sampling (DPDS) method, integrating molecular dynamics simulations within a chain-of-states framework.
  • DPDS directly samples transition pathway space on the PES without requiring predefined reaction coordinates.
  • Simulations are regulated by parameters controlling inter-state distance and pathway smoothness.

Main Results:

  • DPDS effectively samples multiple pathways connecting stable states and identifies additional minima.
  • The method efficiently explores high-energy regions of the PES, crucial for reaction dynamics.
  • Demonstrated the efficiency of DPDS through three illustrative examples.

Conclusions:

  • DPDS is a powerful tool for comprehensive exploration of transition pathway space on PES.
  • The method overcomes limitations of previous approaches by enabling the discovery of multiple pathways and minima.
  • DPDS significantly enhances the understanding of complex molecular transitions and reaction mechanisms.