A clearer approach for defining unit systems

Quincey, Paul; Brown, Richard

doi:10.1088/1681-7575/aa7160

Cited by 8 publications

(7 citation statements)

References 12 publications

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“…At the apex, R θ = 0 by symmetry, which yields equation (3) of § 2. Note that θ is dimensionless and should be measured in radians (Mohr & Phillips 2015;Quincey & Brown 2017).…”

Section: Summary and Discussionmentioning

confidence: 99%

True versus apparent shapes of bow shocks

Tarango-Yong

Henney

2018

Monthly Notices of the Royal Astronomical Society

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Astrophysical bow shocks are a common result of the interaction between two supersonic plasma flows, such as winds or jets from stars or active galaxies, or streams due to the relative motion between a star and the interstellar medium. For cylindrically symmetric bow shocks, we develop a general theory for the effects of inclination angle on the apparent shape. We propose a new two-dimensional classification scheme for bow shapes, which is based on dimensionless geometric ratios that can be estimated from observational images. The two ratios are related to the flatness of the bow's apex, which we term planitude and the openness of its wings, which we term alatude. We calculate the expected distribution in the planitude-alatude plane for a variety of simple geometrical and physical models: quadrics of revolution, wilkinoids, cantoids, and ancantoids. We further test our methods against numerical magnetohydrodynamical simulations of stellar bow shocks and find that the apparent planitude and alatude measured from infrared dust continuum maps serve as accurate diagnostics of the shape of the contact discontinuity, which can be used to discriminate between different physical models. We present an algorithm that can determine the planitude and alatude from observed bow shock emission maps with a precision of 10 to 20%.

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“…At the apex, R θ = 0 by symmetry, which yields equation (3) of § 2. Note that θ is dimensionless and should be measured in radians (Mohr & Phillips 2015;Quincey & Brown 2017).…”

Section: Summary and Discussionmentioning

confidence: 99%

True versus apparent shapes of bow shocks

Tarango-Yong

Henney

2018

Monthly Notices of the Royal Astronomical Society

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“…As described in more detail in [4], there is a natural tendency for theoreticians to simplify equations, removing dimensional constants from them by assigning new dimensions to some quantities and then setting the constants equal to 1.…”

Section: The Urge To Reduce This Numbermentioning

confidence: 99%

“…The current situation in the SI and elsewhere is simply that, by convention, θN is set equal to 1, in exactly the same way that 1/4πε0 is set equal to 1 in some versions of CGS units, making the commonly-used equations involving angles unit-specific. This is discussed more fully in [4]. We call this the Radian Convention.…”

Section: The Radian Convention: Setting θN Equal Tomentioning

confidence: 99%

“…An earlier paper [4] described how it is useful to consider unit systems such as SI, Gaussian and "natural unit" systems as being simplifications of a more general system with five independent, or base, units. It did not attempt to justify that number on physical grounds.…”

Section: The Case For Five Independent Physical Quantities Including ...mentioning

confidence: 99%

“…Units for other quantities are derived from the base units in the usual way. The SI is an example of such a system, because it gives all five of these quantities independently defined units, even though angle is not treated as a base quantity within the system 4 .…”

Section: The Case For Five Independent Physical Quantities Including ...mentioning

confidence: 99%

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The role of unit systems in expressing and testing the laws of nature

Quincey

Burrows

2019

Metrologia

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The paper firstly argues from conservation principles that, when dealing with physics aside from elementary particle interactions, the number of naturally independent quantities, and hence the minimum number of base quantities within a unit system, is five. These can be, for example, mass, charge, length, time, and angle. It also highlights the benefits of expressing the laws of physics using equations that are invariant when the size of the chosen unit for any of these base quantities is changed. Following the pioneering work in this area by Buckingham, these are termed "complete" equations, in contrast with equations that require a specific unit to be used. Using complete equations is shown to remove much ambiguity and confusion, especially where angles are involved. As an example, some quantities relating to atomic frequencies are clarified. Also, the reduced Planck constant ħ, as commonly used, is shown to represent two distinct quantities, one an action (energy x time), and the other an angular momentum (action / angle). There would be benefits in giving these two quantities different symbols. Lastly, the freedom to choose how base units are defined is shown to allow, in principle, measurements of changes over time to dimensional fundamental constants like c.

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Units for Magnetic Quantities

Goldfarb

2021

Magnetic Measurement Techniques for Materials Characterization

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A clearer approach for defining unit systems

Cited by 8 publications

References 12 publications

True versus apparent shapes of bow shocks

True versus apparent shapes of bow shocks

The role of unit systems in expressing and testing the laws of nature

Units for Magnetic Quantities

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