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Related Concept Videos

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.
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Law of Independent Assortment02:03

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While Mendel’s Law of Segregation states that the two alleles for one gene are separated into different gametes, a different question of how different genes are inherited remains. For example, is the gene for tall plants inherited with the gene for green peas? Mendel asked this question by experimenting with a dihybrid cross; a cross in which both parents are homozygous for two distinct traits resulting in an F1 generation that are heterozygous for both traits.
Law of Independent Assortment02:03

Law of Independent Assortment

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The randomization process involves assigning study participants randomly to experimental or control groups based on their probability of being equally assigned. Randomization is meant to eliminate selection bias and balance known and unknown confounding factors so that the control group is similar to the treatment group as much as possible. A computer program and a random number generator can be used to assign participants to groups in a way that minimizes bias.
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Simple In-House Ultra-High Performance Capillary Column Manufacturing with the FlashPack Approach
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Simple In-House Ultra-High Performance Capillary Column Manufacturing with the FlashPack Approach

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Random very loose packings.

Massimo Pica Ciamarra1, Antonio Coniglio

  • 1CNISM and Department of Information Engineering, Second University of Naples, 81031 Aversa (CE), Italy. picaciam@na.infn.it

Physical Review Letters
|October 15, 2008
PubMed
Summary
This summary is machine-generated.

Researchers measured the number of stable states in granular materials, defining a new "random very loose pack" volume fraction. This provides a fundamental understanding of granular compaction and states with negative temperatures.

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Area of Science:

  • Physics
  • Materials Science
  • Statistical Mechanics

Background:

  • Granular materials exhibit complex behaviors under stress.
  • Understanding the mechanics of granular assemblies is crucial for various applications.
  • Existing models struggle to define critical packing densities.

Purpose of the Study:

  • To quantify the number of mechanically stable states in granular assemblies.
  • To define and identify the random very loose pack (RVLP) volume fraction.
  • To provide a first-principle explanation for granular compaction phenomena.

Main Methods:

  • Measurement of the number of mechanically stable states, Omega(phi), as a function of volume fraction, phi.
  • Analysis of granular entropy, S(phi) = logOmega(phi).
  • Identification of critical volume fractions, including the random close pack (RCP) and the newly defined RVLP.

Main Results:

  • Granular entropy vanishes at both high density (phi approx equal to phi_rcp) and low density (phi approx equal to phi_rvlp).
  • The maximal entropy occurs at a specific volume fraction, phi_rlp.
  • A first-principle definition for the random loose volume fraction (phi_rvlp) is established.

Conclusions:

  • The study provides a clear explanation for compaction experiments in granular materials.
  • States with phi < phi_rlp are characterized by negative temperatures within a statistical mechanics framework.
  • The findings offer a new perspective on the statistical mechanics of static granular systems.