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Related Concept Videos

Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
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Woodward–Hoffmann Selection Rules and Microscopic Reversibility01:34

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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
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Subnanometer-Resolution Structural Determination of Hemagglutinin from Cryo-Electron Tomography of Influenza Viruses
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Subnanometer-Resolution Structural Determination of Hemagglutinin from Cryo-Electron Tomography of Influenza Viruses

Published on: November 7, 2025

Parametric Rietveld refinement.

Graham W Stinton1, John S O Evans

  • 1Department of Chemistry, University of Durham, UK.

Journal of Applied Crystallography
|May 23, 2009
PubMed
Summary
This summary is machine-generated.

Parametric Rietveld refinement analyzes multiple diffraction datasets using a single evolving model. This advanced method improves parameter precision and allows direct refinement of physical quantities from data.

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Area of Science:

  • Crystallography
  • Materials Science
  • Data Analysis

Background:

  • Traditional Rietveld refinement analyzes diffraction data sets independently.
  • Sequential or independent analysis can lead to loss of precision and potential errors.
  • A unified approach is needed to leverage time- or variable-dependent diffraction data effectively.

Purpose of the Study:

  • To introduce and describe the method of parametric Rietveld refinement.
  • To highlight the advantages of parametric refinement over independent or sequential analyses.
  • To demonstrate its capability in refining structural models from variable-dependent diffraction data.

Main Methods:

  • Fitting an ensemble of diffraction data (collected over time, temperature, pressure, etc.) to a single, evolving structural model.
  • Utilizing physically realistic models during the data analysis process.
  • Directly refining non-crystallographic quantities (e.g., temperature, rate constants) from diffraction data.

Main Results:

  • Achieves higher precision in refined structural parameters.
  • Enables the application of physically constrained models.
  • Facilitates direct extraction of kinetic and thermodynamic information.
  • Helps to mitigate the occurrence of false minima in refinement.

Conclusions:

  • Parametric Rietveld refinement offers a powerful, integrated approach for analyzing variable-dependent diffraction data.
  • This method enhances accuracy, incorporates physical realism, and extracts more information compared to traditional techniques.
  • It represents a significant advancement in structural analysis using diffraction methods.