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Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Predicting Reaction Outcomes02:24

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
Multi-Step Reactions02:31

Multi-Step Reactions

Chemical reactions often occur in a stepwise fashion involving two or more distinct reactions taking place in a sequence. A balanced equation indicates the reacting species and the product species, but it reveals no details about how the reaction occurs at the molecular level. The reaction mechanism (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs. Each of the steps in a reaction mechanism is called an elementary reaction. These...
Measuring Reaction Rates03:09

Measuring Reaction Rates

Polarimetry finds application in chemical kinetics to measure the concentration and reaction kinetics of optically active substances during a chemical reaction. Optically active substances have the capability of rotating the plane of polarization of linearly polarized light passing through them—a feature called optical rotation. Optical activity is attributed to the molecular structure of substances. Normal monochromatic light is unpolarized and possesses oscillations of the electrical field in...
Reaction Rate02:53

Reaction Rate

The rate of reaction is the change in the amount of a reactant or product per unit time. Reaction rates are therefore determined by measuring the time dependence of some property that can be related to reactant or product amounts. Rates of reactions that consume or produce gaseous substances, for example, are conveniently determined by measuring changes in volume or pressure.
The mathematical representation of the change in the concentration of reactants and products, over time, is the rate...

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Rapid in-silico Battery Electrolyte Electrochemical Reaction Generation using 3T-VASP Multi-Scale Energy Minimization
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Efficient statistical inference for stochastic reaction processes.

Andreas Ruttor1, Manfred Opper

  • 1Artificial Intelligence Group, TU Berlin, Berlin, Germany.

Physical Review Letters
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

This study presents an efficient approximation for estimating parameters and states in stochastic reaction processes with limited, noisy data. The method is validated and extended to scenarios with unobserved state variables.

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Ligand-Mediated Nucleation and Growth of Palladium Metal Nanoparticles
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Area of Science:

  • Biophysics
  • Chemical Kinetics
  • Stochastic Processes

Background:

  • Stochastic reaction processes are fundamental in biological and chemical systems.
  • Estimating model parameters and state variables is crucial for understanding these systems.
  • Sparse and noisy measurements pose significant challenges for accurate estimation.

Purpose of the Study:

  • To develop an efficient approximation for parameter and state estimation in stochastic reaction processes.
  • To address the challenges posed by sparse and noisy measurements.
  • To generalize the estimation method for cases with unobserved state variables.

Main Methods:

  • Utilizing an asymptotic system size expansion for the backward equation.
  • Deriving an efficient approximation for the estimation problem.
  • Validating the approach on established model systems.

Main Results:

  • An efficient approximation for parameter and state estimation was successfully derived.
  • The method demonstrated validity on various model systems.
  • The approach was generalized to accommodate unobserved state variables.

Conclusions:

  • The developed approximation provides an effective solution for parameter and state estimation in challenging data conditions.
  • The method's generalizability enhances its applicability to a wider range of stochastic reaction systems.
  • This work contributes to improved modeling and analysis of complex reaction dynamics.