Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

What is Variation?

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of any data set is its variation or spread. In some data sets, the data values are concentrated closely near the mean; in others, the data values are more widely spread out from the mean.
The range, standard deviation, standard error, and variance are the different measures of variation.
Range: The range is the difference between its maximum and...

The Uncertainty Principle

The Uncertainty Principle

Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...

Variation

Variation

An important characteristic of any set of data is the variation in the data. In some data sets, the data values are concentrated closely near the mean; in other data sets, the data values are more widely spread out from the mean. The most common measure of variation, or spread, is the standard deviation, which is the square root of variance.
When independent and dependent variables are plotted on a scatter plot, the slope of a line is a value that describes the rate of change between the two...

Hardy-Weinberg Principle

Hardy-Weinberg Principle

Diploid organisms have two alleles of each gene, one from each parent, in their somatic cells. Therefore, each individual contributes two alleles to the gene pool of the population. The gene pool of a population is the sum of every allele of all genes within that population and has some degree of variation. Genetic variation is typically expressed as a relative frequency, which is the percentage of the total population that has a given allele, genotype or phenotype.

The Pauli Exclusion Principle

The Pauli Exclusion Principle

The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:

Conservative Site-specific Recombination and Phase Variation

Conservative Site-specific Recombination and Phase Variation

Because the DNA segments are cut and reorganized in a direction-specific manner, site-specific recombination has emerged as an efficient genetic engineering technique. Flippase and Cyclization recombinases or Flp and Cre, respectively, are two members of the tyrosine recombinase family derived from bacteriophages, that are used to mediate site-specific DNA insertions, deletions, and targeted expression of proteins in mammalian cell lines.
The recognition sites for Cre recombinase called LoxP...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

External Magnetic Field Suppression of Carbon Diffusion in Iron.

Physical review letters·2026

Same author

Numerical calculation finds the revised elastic field of an edge dislocation to be incorrect.

Proceedings of the National Academy of Sciences of the United States of America·2025

Same author

Discovering melting temperature prediction models of inorganic solids by combining supervised and unsupervised learning.

The Journal of chemical physics·2024

Same author

Contributions to Diffusion in Complex Materials Quantified with Machine Learning.

Physical review letters·2024

Same author

Machine Learning Methods for Multiscale Physics and Urban Engineering Problems.

Entropy (Basel, Switzerland)·2022

Same author

Designing Optimal Perovskite Structure for High Ionic Conduction.

Advanced materials (Deerfield Beach, Fla.)·2019

Same journal

Erratum: Bacterial Turbulence at Compressible Fluid Interfaces [Phys. Rev. Lett. 136, 138301 (2026)].

Physical review letters·2026

Same journal

Unveiling Light-Quark Yukawa Flavor Structure via Dihadron Fragmentation at Lepton Colliders.

Physical review letters·2026

Same journal

Adaptable Route to Fast Coherent State Transport via Bang-Bang-Bang Protocols.

Physical review letters·2026

Same journal

Topological Transition and Emergence of Elasticity of Dislocation in Skyrmion Lattice: Beyond Kittel's Magnetic-Polar Analogy.

Physical review letters·2026

Same journal

Pound-Drever-Hall Method for Superconducting-Qubit Readout.

Physical review letters·2026

Same journal

Coupling a ^{73}Ge Nuclear Spin to an Electrostatically Defined Quantum Dot in Silicon.

Physical review letters·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jan 31, 2026

Semi-Quantitative Analysis of Peptidoglycan by Liquid Chromatography Mass Spectrometry and Bioinformatics

Semi-Quantitative Analysis of Peptidoglycan by Liquid Chromatography Mass Spectrometry and Bioinformatics

Published on: October 13, 2020

Variational Principle for Mass Transport.

Dallas R Trinkle¹

¹Department of Materials Science and Engineering, University of Illinois, Urbana-Champaign, Illinois 61801, USA.

Physical Review Letters

|December 22, 2018

Summary

This summary is machine-generated.

A new variation principle unifies mass transport calculations in solids, recasting coefficients as minima. This approach applies to all systems and enables new approximation methods with error estimation.

More Related Videos

High-throughput Screening of Recalcitrance Variations in Lignocellulosic Biomass: Total Lignin, Lignin Monomers, and Enzymatic Sugar Release

High-throughput Screening of Recalcitrance Variations in Lignocellulosic Biomass: Total Lignin, Lignin Monomers, and Enzymatic Sugar Release

Published on: September 15, 2015

Author Spotlight: Exploring Cellular Zinc Regulation Through ZnT1 Functionality

Author Spotlight: Exploring Cellular Zinc Regulation Through ZnT1 Functionality

Published on: June 2, 2023

Related Experiment Videos

Last Updated: Jan 31, 2026

Semi-Quantitative Analysis of Peptidoglycan by Liquid Chromatography Mass Spectrometry and Bioinformatics

Semi-Quantitative Analysis of Peptidoglycan by Liquid Chromatography Mass Spectrometry and Bioinformatics

Published on: October 13, 2020

High-throughput Screening of Recalcitrance Variations in Lignocellulosic Biomass: Total Lignin, Lignin Monomers, and Enzymatic Sugar Release

High-throughput Screening of Recalcitrance Variations in Lignocellulosic Biomass: Total Lignin, Lignin Monomers, and Enzymatic Sugar Release

Published on: September 15, 2015

Author Spotlight: Exploring Cellular Zinc Regulation Through ZnT1 Functionality

Author Spotlight: Exploring Cellular Zinc Regulation Through ZnT1 Functionality

Published on: June 2, 2023

Area of Science:

Solid-state physics
Materials science
Computational physics

Background:

Mass transport in solids is crucial for material properties and performance.
Existing computational methods for diffusion often lack a unifying theoretical framework.
Understanding diffusion mechanisms is key to designing new materials.

Purpose of the Study:

To derive a general variation principle for mass transport in solids.
To unify diverse computational approaches for diffusion modeling.
To provide a framework for developing new approximation methods with error estimation.

Main Methods:

Derivation of a variation principle for mass transport.
Recasting transport coefficients as minima of local thermodynamic average quantities.
Demonstration of independence from specific diffusion mechanisms.

Main Results:

A unified variational principle applicable to both amorphous and crystalline solids.
Transport coefficients are expressed as minima of local thermodynamic averages.
The principle provides a new physical interpretation of the Green function.
Quantification of the accuracy of competing diffusion approaches.

Conclusions:

The derived variational principle offers a unified and general approach to mass transport in solids.
This framework facilitates the development of novel, error-quantified approximation methods for diffusion.
The principle provides new physical insights into transport phenomena and computational methods.