Abstract
This is a collection of short articles on various aspects of continuum physics. They are intended to familiarize the reader with applications, in contrast to the more formal approach of the preceding chapters. The collection is neither complete nor systematic, we therefore simply order the articles alphabetically by their titles.
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- 1.
There is no overall accepted terminology which distinguishes between a three-dimensional manifold \(\mathcal{V}\), a volume, and its content V , likewise called volume.
- 2.
Not to be confused with a beam of light or particles.
- 3.
Up to interchanging x with y or x → − x or y → − y or both.
- 4.
Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen a rough translation of which is On the movement of particles suspended in a resting liquid as required by the molecular-kinetic theory of heat.
- 5.
The term Brownian movement is used in the literature as well.
- 6.
A diluted gas of ν moles at temperature T within a vessel of volume V exerts a pressure p = νRTV.
- 7.
True mass minus mass of displaced liquid.
- 8.
More accurately: non-negative.
- 9.
Note that t → f(t) describes a fluctuation since \({ \langle }\,f(t)\,{ \rangle } = 0\).
- 10.
The electromagnetic field of white light has a spectral density which, at least in the visible region, does not depend on ω, or color.
- 11.
We cannot rely on the statement that expectation values do not depend on time. In fact, demanding x(0) = 0 breaks time translation symmetry.
- 12.
Note that μ coincides with the shear modulus which is also denoted by G. While elasticity moduli are isothermal quantities, the Lamé parameters refer to adiabatic thermodynamic processes.
- 13.
We freely mix \(x = ({x}_{1},{x}_{2},{x}_{3}) = (x,y,z)\).
- 14.
More precisely, its Fourier transform.
- 15.
For simplicity, we assume an optically isotropic medium.
- 16.
As contrasted with waveguides.
- 17.
The principal value symbol \(\,\textrm{ Pr}\,\) specifies how to cope with the singularity at u = ω.
- 18.
\({L}_{\textrm{ TE}}\) is dimensionless which is desirable for numerical investigation.
- 19.
A is negative if \((f,Af) \leq 0\) for all f, here: \((f,{f}^{{\prime\prime}}) = -({f}^{{\prime}},{f}^{{\prime}}) \leq 0\).
- 20.
This is just one of many forms.
- 21.
Later on we drop the tilde as indicator of a Fourier component.
- 22.
Optical activity is an exception.
- 23.
We drop the arguments \((\omega ,{ k} = 0)\).
- 24.
In this context: per unit length.
- 25.
At least only indirectly, because n, Γ and Ω have to be calculated within the framework of quantum mechanics. Even for quasi-free electrons, m is the effective mass an expression which depends explicitly on \(\hslash \).
- 26.
We assume a positive Verdet constant.
- 27.
Glass fibers have minimal absorption losses at λ = 1. 50 μ{ m}.
- 28.
Measured in { m}3 { s} − 1.
- 29.
Velocity gradients.
- 30.
In this context: per unit mass.
- 31.
The word seems to be reserved for microwave and optical applications.
- 32.
Système international d’unités in French.
- 33.
DC means direct current, as contrasted with AC, alternating current.
- 34.
With respect to energy.
- 35.
c is the vacuum speed of light.
- 36.
See the article on Natural Units.
- 37.
In this context: per unit length.
- 38.
What you should not do!
- 39.
Latin dexter, right handed.
- 40.
Ten volts per micrometer correspond to hundred thousand Volts per centimeter.
- 41.
Optical activity is an exception.
- 42.
products of powers of
- 43.
For He-Ne laser light, from [5].
- 44.
Everything not forbidden is compulsory.
- 45.
Kaye and Laby [5], for He-Ne laser light.
- 46.
See Pearson [9].
- 47.
http://www.aliensaint.com/uo/java/rd/ by Jonathan Lidbeck while he was with the University of Oregon.
- 48.
Latin lamina, layer.
- 49.
In this article the tilde does not denote the Fourier transform, but a small deviation from the equilibrium value.
- 50.
M is the molar mass of air and R denotes the universal gas constant.
- 51.
A harmonic function f = f(x, y) is a solution of Δf = 0 where \(\Delta = {\partial }_{x}^{2} + {\partial }_{y}^{2}\). A biharmonic function fulfills \(\Delta \Delta f = 0\).
- 52.
The limit R → 0 is not allowed because one would leave the realm of continuum physics.
- 53.
We choose the square root of a complex number such that its real part is positive.
- 54.
We follow electrical engineering tradition and talk of frequencies f instead of angular frequencies ω = 2πf.
- 55.
Electronics is limited by μ{ m} dimensions, therefore times below \(\approx 1{0}^{-14}\) s cannot be resolved. The natural time for phonon-electron interactions is the natural atomic time unit of \(\approx 1{0}^{-17}\) s.
- 56.
It vanishes in a super-conductor where \(1/\sigma = 0\).
- 57.
\({\partial }_{x}^{2}\) is defined for twice differentiable functions vanishing at x = 0 and \(x = \mathcal{l}\).
- 58.
Also quint, Quinte (German), quinta (Italian).
- 59.
In German nomenclature B is denoted as H and H\(\flat \) as B; cf. the well-known B-A-C-H motif.
- 60.
Das wohltemperierte Clavier in German. Clavier in this context is any keyboard instrument, not just the piano or Klavier in German. The first volume was completed in 1722, the second in 1742.
- 61.
These two nuclei have rather large binding energies per nucleon, they are made up of three resp. four helium nuclei. Iron has the largest binding energy, it is the most common remnant of supernovae.
- 62.
The gravitational force of a rotationally symmetric mass distribution is the same as that of a point mass at the origin. Only mass which is closer to the origin contributes. This finding goes back to Newton.
- 63.
The distance from the star’s center is rR ∗ , and so on. All physical quantities are now dimensionless.
- 64.
The mass of a white dwarf cannot exceed 1.44 sun masses.
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Hertel, P. (2012). Examples. In: Continuum Physics. Graduate Texts in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29500-3_4
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