Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

4.0K
The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
4.0K
Poisson's Ratio01:23

Poisson's Ratio

2.3K
Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
2.3K
Sampling Distribution01:12

Sampling Distribution

17.6K
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...
17.6K
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

4.5K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
4.5K
Polymers: Molecular Weight Distribution01:10

Polymers: Molecular Weight Distribution

4.0K
For any given polymer, the weight average molecular weight (Mw) is higher than, if not equal to, the number average molecular weight (Mn). The only situation in which the weight average molecular weight and the number average molecular weight are equal is when a polymer consists only of chains with equal molecular weight. However, this never happens in a synthetic polymer, since it is difficult to control the polymerization process up to a molecular level with accuracy to a hundred percent.
4.0K
Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.3K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.3K

You might also read

Related Articles

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

Sort by
Same author

Heisenberg spin chain with random-sign couplings.

Proceedings of the National Academy of Sciences of the United States of America·2024
Same author

Coarse-Grained Entanglement and Operator Growth in Anomalous Dynamics.

Physical review letters·2022
Same author

Overactivated transport in the localized phase of the superconductor-insulator transition.

Nature communications·2021
Same author

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid.

Physical review letters·2021
Same author

Many-Body Delocalization as Symmetry Breaking.

Physical review letters·2021
Same author

Quantum Hall Network Models as Floquet Topological Insulators.

Physical review letters·2020
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

Related Experiment Video

Updated: Apr 25, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.8K

Length distributions in loop soups.

Adam Nahum1, J T Chalker1, P Serna2

  • 1Theoretical Physics, Oxford University, 1 Keble Road, Oxford OX1 3NP, United Kingdom.

Physical Review Letters
|August 29, 2014
PubMed
Summary
This summary is machine-generated.

Researchers analyzed loop length distributions in statistical lattice models. They found macroscopic loop distributions follow a Poisson-Dirichlet pattern, influenced by system parameters and symmetries.

More Related Videos

Analysis and Specification of Starch Granule Size Distributions
08:46

Analysis and Specification of Starch Granule Size Distributions

Published on: March 4, 2021

4.7K
Author Spotlight: Technologies and Challenges in Elemental Analysis of Food Samples
06:53

Author Spotlight: Technologies and Challenges in Elemental Analysis of Food Samples

Published on: December 22, 2023

3.9K

Related Experiment Videos

Last Updated: Apr 25, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

9.8K
Analysis and Specification of Starch Granule Size Distributions
08:46

Analysis and Specification of Starch Granule Size Distributions

Published on: March 4, 2021

4.7K
Author Spotlight: Technologies and Challenges in Elemental Analysis of Food Samples
06:53

Author Spotlight: Technologies and Challenges in Elemental Analysis of Food Samples

Published on: December 22, 2023

3.9K

Area of Science:

  • Statistical mechanics
  • Lattice field theory
  • Probability distributions

Background:

  • Statistical lattice ensembles in 3+ dimensions exhibit phases where longest loops occupy a significant system fraction.
  • Understanding loop length distributions is crucial in these phases.

Purpose of the Study:

  • To develop methods for calculating moments of loop length distributions in statistical lattice models.
  • To characterize the joint length distribution of macroscopic loops.

Main Methods:

  • Utilized complex projective (CP(n-1)) and real projective (RP(n-1)) sigma models.
  • Employed replica techniques for calculating distribution moments.
  • Investigated loop fugacity and ensemble symmetries.

Main Results:

  • Derived the joint length distribution for macroscopic loops, identifying it as Poisson-Dirichlet.
  • Determined the parameter θ of the Poisson-Dirichlet distribution is fixed by loop fugacity and ensemble symmetries.
  • Characterized length distributions for shorter loops.

Conclusions:

  • The Poisson-Dirichlet distribution accurately describes macroscopic loop lengths in these statistical models.
  • The derived methods and findings are validated by numerical simulations.