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Related Concept Videos

Symmetry in Maxwell's Equations01:28

Symmetry in Maxwell's Equations

Once the fields have been calculated using Maxwell's four equations, the Lorentz force equation gives the force that the fields exert on a charged particle moving with a certain velocity. The Lorentz force equation combines the force of the electric field and of the magnetic field on the moving charge. Maxwell's equations and the Lorentz force law together encompass all the laws of electricity and magnetism. The symmetry that Maxwell introduced into his mathematical framework may not be...
Differential Form of Maxwell's Equations01:17

Differential Form of Maxwell's Equations

James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and Faraday.
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Gauss's Law: Spherical Symmetry01:26

Gauss's Law: Spherical Symmetry

A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a uniform...
Resultant Moment: Scalar Formulation01:31

Resultant Moment: Scalar Formulation

When multiple forces act on an object in two-dimensional space, the concept of the net moment can be used to understand the tendency of these forces to induce rotational motion about a fixed point. The scalar formulation of the resultant moment is a helpful tool in analyzing the equilibrium of structures subjected to multiple forces.
To determine the resultant moment, the moments caused by all the forces in a system in the x-y plane are considered. Positive moments are typically...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...

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Related Experiment Video

Updated: Jun 18, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Correct virial formulation in the isotropic periodic sum method.

Iordan H Hristov1, Reginald Paul, Stephen J Paddison

  • 1Department of Chemistry, University of Calgary, 2500 University Dr. NW, Calgary, Alberta T2N 1N4, Canada. hristov@ucalgary.ca

The Journal of Chemical Physics
|November 10, 2009
PubMed
Summary

The isotropic periodic sum (IPS) method

Area of Science:

  • Computational physics and chemistry.
  • Methodology development in molecular simulations.

Background:

  • The isotropic periodic sum (IPS) method is used for calculating the virial in simulations.
  • The original IPS formulation has limitations regarding the virial calculation due to a fixed cutoff radius.

Purpose of the Study:

  • To address the limitations in the original isotropic periodic sum (IPS) method's virial calculation.
  • To identify and correct a missing virial term in the IPS method.

Main Methods:

  • Revisiting the theoretical formulation of the virial in the IPS method.
  • Consistent calculation of virials using IPS and cutoff plus long-range correction methods.
  • Derivation of a simplified virial calculation for 1/r(n) potentials.

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Related Experiment Videos

Last Updated: Jun 18, 2026

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package
06:37

Analyzing Melts and Fluids from Ab Initio Molecular Dynamics Simulations with the UMD Package

Published on: September 17, 2021

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

Main Results:

  • A previously neglected virial term in the IPS method was identified.
  • Consistent calculation significantly reduces the difference between IPS and cutoff plus long-range correction virials.
  • The corrected IPS virial is simpler to compute.

Conclusions:

  • The original IPS method's virial calculation requires correction for accurate results.
  • The corrected IPS method provides a more accurate and simpler approach to virial calculation.
  • The simplified virial calculation is applicable to 1/r(n) potentials.