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Related Concept Videos

Conservation of Mass in Finite Cotrol Volume01:16

Conservation of Mass in Finite Cotrol Volume

The principle of conservation of mass is a fundamental law in fluid mechanics and is applied using the continuity equation. We apply the concept to a finite control volume to derive the continuity equation.
A system is defined as a collection of unchanging contents, and the conservation of mass states that a system's mass is constant.
Energy Associated With a Charge Distribution01:21

Energy Associated With a Charge Distribution

The work done to bring a charge through a distance r is given by the potential difference between the initial and the final position. To assemble a collection of point charges, the total work done can be expressed in terms of the product of each pair of charges divided by their separation distance, defined with respect to a suitable origin. Solving this expression gives the energy stored in a point charge distribution.
Continuous Charge Distributions01:17

Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
The electric charge can also be subjected to an analogical...
Coulomb's Law01:30

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude of the force is linearly proportional to the net charge on each object and inversely proportional to the square of the distance between them. The direction of the force vector is along the imaginary line joining the two objects and is dictated by the signs of the charges involved.
Newton's third law applies to the Coulomb force — the force on...
Conservation of Mass in Fixed, Nondeforming Control Volume01:07

Conservation of Mass in Fixed, Nondeforming Control Volume

The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...
Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.

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Related Experiment Video

Updated: Jun 21, 2026

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

Dense QCD in a finite volume.

Naoki Yamamoto1, Takuya Kanazawa

  • 1Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan.

Physical Review Letters
|August 8, 2009
PubMed
Summary

We found that the Dirac spectrum reveals the color superconducting gap in Quantum Chromodynamics (QCD) at high baryon density. Partition function zeros show a characteristic X-shape, indicating diquark pairing and Z(2)LxZ(2)R symmetry.

Area of Science:

  • High-energy physics
  • Quantum Chromodynamics (QCD)
  • Condensed matter physics

Background:

  • QCD properties at high baryon density are crucial for understanding dense matter.
  • Color superconductivity is a predicted phase in such conditions.
  • Finite volume effects can alter phase structures.

Purpose of the Study:

  • Investigate QCD properties in a finite volume at high baryon density.
  • Explore the occurrence and signatures of color superconductivity.
  • Relate Dirac operator eigenvalues to the color superconducting gap.

Main Methods:

  • Derivation of exact sum rules for Dirac operator eigenvalues.
  • Analysis of partition function zeros in the complex quark mass plane.
  • Study within a finite volume with high baryon density.

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Finite Element Modelling of a Cellular Electric Microenvironment

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Last Updated: Jun 21, 2026

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
05:39

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Finite Element Modelling of a Cellular Electric Microenvironment
08:23

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Main Results:

  • The Dirac spectrum is directly linked to the color superconducting gap (Delta).
  • An X-shaped spectrum of partition function zeros near the origin is identified.
  • This spectral signature reflects the Z(2)LxZ(2)R symmetry of diquark pairing.

Conclusions:

  • The derived sum rules provide a tool to probe the superconducting gap.
  • The X-shaped zero spectrum is a universal signature of color superconductivity.
  • Results are valid in the domain Delta(-1)<