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Related Concept Videos

Crossing Over01:30

Crossing Over

Crossing over is the exchange of genetic information between homologous chromosomes during prophase I of meiosis I. Genetic recombination gives rise to allelic diversity in the newly formed daughter cells. In humans, crossing over produces genetically distinct haploid egg and sperm cells that undergo fertilization to produce unique offspring. Before cell division starts, the germ cell’s chromosome(s) undergo duplication in the S phase of the cell cycle. As the cells enter prophase I, duplicated...
Crossing Over01:34

Crossing Over

Unlike mitosis, meiosis aims for genetic diversity in its creation of haploid gametes. Dividing germ cells first begin this process in prophase I, where each chromosome—replicated in S phase—is now composed of two sister chromatids (identical copies) joined centrally.
The homologous pairs of sister chromosomes—one from the maternal and one from the paternal genome—then begin to align alongside each other lengthwise, matching corresponding DNA positions in a process called synapsis.
In order to...
Crossing over01:34

Crossing over

Unlike mitosis, meiosis aims for genetic diversity in its creation of haploid gametes. Dividing germ cells first begin this process in prophase I, where each chromosome—replicated in S phase—is now composed of two sister chromatids (identical copies) joined centrally.
The homologous pairs of sister chromosomes—one from the maternal and one from the paternal genome—then begin to align alongside each other lengthwise, matching corresponding DNA positions in a process called synapsis.
In order to...
Cluster Sampling Method01:20

Cluster Sampling Method

Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
To choose a cluster sample, divide the population into clusters (groups) and then randomly select some of the clusters. All the members from these clusters are in the cluster sample. For example, if you randomly sample four departments from your...
Random Variables01:09

Random Variables

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...
¹H NMR: Long-Range Coupling01:27

¹H NMR: Long-Range Coupling

The coupling interactions of nuclei across four or more bonds are usually weak, with J values less than 1 Hz. While these are usually not observed in spectra, the presence of multiple bonds along the coupling pathway can result in observable long-range coupling.
In alkenes, spin information is communicated via σ–π overlap, as seen in allylic (four-bond) and homoallylic (five-bond) couplings. These coupling interactions are stronger when the σ bond is parallel to the alkene π orbitals.

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Related Experiment Video

Updated: Jun 21, 2026

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
06:18

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR

Published on: July 11, 2025

Crossing bonds in the random-cluster model.

Wenan Guo1, Youjin Deng, Henk W J Blöte

  • 1Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

We studied crossing bonds in the two-dimensional Potts model using a Coulomb gas mapping. Crossing bonds were found to be irrelevant, contrasting with other models and explained by a novel analysis.

Related Experiment Videos

Last Updated: Jun 21, 2026

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR
06:18

Frequency and Distribution of Crossovers in Caenorhabditis elegans Meiosis by SNP Genotyping using Real-time PCR

Published on: July 11, 2025

Area of Science:

  • Statistical mechanics
  • Condensed matter physics
  • Quantum field theory

Background:

  • The random-cluster representation is a powerful tool for studying statistical models.
  • Understanding critical phenomena and phase transitions is crucial in physics.

Purpose of the Study:

  • To determine the scaling dimension of crossing bonds in the 2D Potts model.
  • To investigate the relevance of crossing bonds in critical and tricritical regimes.
  • To reconcile discrepancies between the Potts model and O(n) models.

Main Methods:

  • Mapping the random-cluster model to a Coulomb gas.
  • Analyzing the scaling field associated with crossing bonds.
  • Performing finite-size-scaling analysis using transfer-matrix calculations.

Main Results:

  • The scaling field for crossing bonds is found to be irrelevant in both critical and tricritical regimes.
  • This finding contrasts with the relevance of crossing bonds in the tricritical O(n) model.
  • An explanation is provided for the differing exponents between the O(1) and q=2 random-cluster models.

Conclusions:

  • The irrelevance of crossing bonds in the 2D Potts model is confirmed.
  • The study clarifies the relationship between different models and their critical behaviors.
  • Numerical transfer-matrix calculations provide independent validation of the theoretical findings.