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Community-contributed installable additions to the Wolfram Language

PeterBurbery/DimensionalAnalysis

(1.18.0) current version: 1.30.0 »

A paclet for dimensional analysis

Contributed by: Peter Cullen Burbery

This paclet contains functions for dimensional analysis.

Installation Instructions

To install this paclet in your Wolfram Language environment, evaluate this code:
PacletInstall["PeterBurbery/DimensionalAnalysis"]


To load the code after installation, evaluate this code:
Needs["PeterBurbery`DimensionalAnalysis`"]

Details

I chose an image of James Clerk Maxwell for my paclet. Maxwell unified electricity and magnetism into electromagnetism.

Paclet Guide

Examples

Basic Examples (15) 

The QED Euler-Heisenberg Lagrangian factor is measured with the SI derived unit

Out[0]=
. Express this as a combination of the Rydberg constant for time, the speed of light for length, the reduced Planck constant for mass, and the Josephson constant or the Von Klitzing constant for electric current:

In[1]:=
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Out[1]=

Transform the quantity

Out[1]=
into a natural unit system form:

In[2]:=
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Out[2]=

Specify the basis of the unit system as the speed of light, the Josephson constant, the reduced Planck constant, the Rydberg constant, and the Boltzmann constant:

In[3]:=
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Out[3]=

The quartic Cauchy coefficients are measured in

Out[3]=
. Transform this to the Planck unit system:

In[4]:=
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Out[4]=
In[5]:=
Entity["PhysicalQuantity", "QuarticCasimirOperatorPoincareGroup"]["SIUnit"]
Out[5]=

The quartic Casimir operator of the Poincare group is measured in

Out[5]=
. Express this as a product of the SI defining constants:

In[6]:=
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Out[6]=

Compute an approximate answer:

In[7]:=
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Out[7]=

Find the canonical dimensional product for the QED Euler-Heisenberg Lagrangian factor:

In[8]:=
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Out[8]=

FInd the dimensions for the weber unit:

In[9]:=
CanonicalDimensions[Quantity["Webers"]]
Out[9]=

Find the definitions with the canonical ordering time, length, mass, electric current, temperature, amount of substance, luminous intensity:

In[10]:=
CanonicalDimensionsVector[Quantity["Webers"]]
Out[10]=

Find the canonical dimensional form of a unit with symbols for dimensions:

In[11]:=
CanonicalDimensionalForm[Quantity["Webers"]]
Out[11]=

Find the form in scientific notation:

In[12]:=
CanonicalDimensionalScientificNotationForm[Quantity["Webers"]]
Out[12]=

Find the idealized SI constant's definition of the weber:

In[13]:=
IdealizedSIConstantsDefinition[Quantity[1, "Webers"]]
Out[13]=

Find the Planck form of a unit:

In[14]:=
PlanckUnitConversion[Quantity["Webers"]]
Out[14]=

Find the Stoney form of a unit:

In[15]:=
StoneyUnitConversion[Quantity["Webers"]]
Out[15]=

Find information for a physical observation:

In[16]:=
PhysicalObservationInformation[ Quantity[129, "Webers" "Candelas" "Amperes"]]
Out[16]=

Publisher

Peter Burbery

Compatibility

Wolfram Language Version 13.1

Version History

  • 1.30.0 – 19 November 2022
  • 1.29.0 – 19 November 2022
  • 1.28.0 – 19 November 2022
  • 1.27.0 – 19 November 2022
  • 1.26.0 – 19 November 2022
  • 1.25.0 – 19 November 2022
  • 1.24.0 – 19 November 2022
  • 1.23.0 – 18 November 2022
  • 1.22.0 – 18 November 2022
  • 1.21.0 – 18 November 2022
  • 1.20.0 – 05 November 2022
  • 1.19.0 – 05 November 2022
  • 1.18.0 – 05 November 2022
  • 1.17.0 – 05 November 2022
  • 1.16.0 – 17 September 2022
  • 1.15.0 – 17 September 2022
  • 1.14.0 – 17 September 2022
  • 1.13.0 – 17 September 2022
  • 1.12.0 – 17 September 2022
  • 1.10.0 – 17 September 2022
  • 1.9.0 – 17 September 2022
  • 1.8.0 – 17 September 2022
  • 1.7.0 – 17 September 2022
  • 1.6.0 – 17 September 2022
  • 1.5.0 – 17 September 2022
  • 1.4.0 – 17 September 2022
  • 1.3.0 – 17 September 2022
  • 1.2.0 – 17 September 2022
  • 1.1.0 – 17 September 2022
  • 1.0.0 – 17 September 2022

License Information

MIT License

Paclet Source

Source Metadata

  • Citation: Source, reference or citation information

See Also