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Related Concept Videos

Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

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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Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
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Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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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...
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Transition path sampling for discrete master equations with absorbing states.

Nathan Eidelson1, Baron Peters

  • 1Santa Barbara High School, Santa Barbara, California 93103, USA.

The Journal of Chemical Physics
|September 11, 2012
PubMed
Summary
This summary is machine-generated.

A new hybrid kinetic Monte Carlo-Transition Path Sampling (kMC-TPS) algorithm was developed for analyzing rare transitions. This method, validated on a trp-cage folding model, ensures detailed balance and yields results consistent with brute force simulations.

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Area of Science:

  • Computational Chemistry
  • Statistical Mechanics
  • Biophysics

Background:

  • Transition Path Sampling (TPS) algorithms are crucial for studying rare events in molecular dynamics.
  • Existing TPS implementations lack integration with kinetic Monte Carlo (kMC) dynamics, which are based on discrete master equations.

Purpose of the Study:

  • To introduce a novel hybrid kMC-TPS algorithm.
  • To demonstrate that the new algorithm satisfies detailed balance within the transition path ensemble.
  • To provide a method for analyzing rare transitions in complex systems where exact enumeration of states is infeasible.

Main Methods:

  • Development of a hybrid algorithm combining kMC and TPS.
  • Proof of detailed balance satisfaction for the kMC-TPS algorithm.
  • Application and validation of the algorithm using a simplified Markov State Model of trp-cage folding.

Main Results:

  • The kMC-TPS algorithm successfully satisfies detailed balance.
  • Transition path ensembles generated by kMC-TPS are consistent with brute force kMC simulations.
  • Committor probabilities and local fluxes from kMC-TPS align with exact solutions for simple master equations.

Conclusions:

  • The new kMC-TPS method offers a viable approach for rare transition analysis in complex systems.
  • This algorithm extends the applicability of TPS to systems governed by discrete master equations.
  • It provides a powerful tool for systems where exact solutions are computationally prohibitive due to the large number of states.