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1: 8.24 Physical Applications

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§8.24(iii) Generalized Exponential Integral

►The function $E_p\left(x\right)$, with $p>0$, appears in theories of transport and radiative equilibrium (Hopf (1934), Kourganoff (1952), Altaç (1996)). …

2: 6.17 Physical Applications

… ►Geller and Ng (1969) cites work with applications from diffusion theory, transport problems, the study of the radiative equilibrium of stellar atmospheres, and the evaluation of exchange integrals occurring in quantum mechanics. …

3: 18.39 Applications in the Physical Sciences

… ►Shizgal (2015) gives a broad overview of techniques and applications of spectral and pseudo-spectral methods to problems arising in theoretical chemistry, chemical kinetics, transport theory, and astrophysics. … ►

Table 18.39.1: Typical Non-Classical Weight Functions Of Use In DVR Applications^a

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Name of OP System	$w(x)$	$[a,b]$	Notation	Applications
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Half-Freud Druvesteyn	$\exp \left(-x^4\right)$	$[0,\mathrm{\infty })$	$D_n(x)$	Electron Transport in Plasmasd
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… ►For interpretations of zeros of classical OP’s as equilibrium positions of charges in electrostatic problems (assuming logarithmic interaction), see Ismail (2000a, b).

4: 22.19 Physical Applications

… ► $\theta$ being the angular displacement from the point of stable equilibrium, $\theta =0$. … ►for the initial conditions $\theta (0)=0$, the point of stable equilibrium for $E=0$, and $d\theta (t)/dt=\sqrt{2E}$. … ►

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Figure 22.19.1: Jacobi’s amplitude function $\mathrm{am}(x,k)$ for $0\le x\le 10\pi$ and $k=0.5,0.9999,1.0001,2$. …This corresponds to the pendulum being “upside down” at a point of unstable equilibrium. … Magnify

… ►As $a\to \sqrt{1/\beta }$ from below the period diverges since $a=\pm \sqrt{1/\beta }$ are points of unstable equilibrium. … ►For an initial displacement with , bounded oscillations take place near one of the two points of stable equilibrium $x=\pm \sqrt{1/\beta }$. …

5: 5.20 Physical Applications

… ►The probability density of the positions when the gas is in thermodynamic equilibrium is: …

6: Bibliography P

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Influence of equilibrium shear flow along the magnetic field on the resistive tearing instability. Phys. Fluids 26 (10), pp. 2966–2975.

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External Links:

ISSN 0031-9171, Document, MathReview, ZentralBlatt

Referenced by:

§11.12, §11.7(ii).

Encodings:

BibTeX

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7: Bibliography H

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Mathematical Problems of Radiative Equilibrium. Cambridge Tracts in Mathematics and Mathematical Physics No. 31, Cambridge University Press, Cambridge.

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Notes:

Reprinted by Stechert-Hafner, Inc., New York, 1964

External Links:

MathReview, ZentralBlatt

Referenced by:

§8.19(ix), §8.24(iii).

Encodings:

BibTeX

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8: Bibliography D

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Atomic motions in a rigid sphere gas as a problem in neutron transport. Nucl. Sci. Eng. 24 (2), pp. 142–152.

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Referenced by:

§18.39(iii).

Encodings:

BibTeX

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9: 31.15 Stieltjes Polynomials

… ►The system (31.15.2) determines the $z_k$ as the points of equilibrium of $n$ movable (interacting) particles with unit charges in a field of $N$ particles with the charges ${\gamma }_j/2$ fixed at $a_j$. …

10: Bibliography G

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Error bounds in equilibrium statistical mechanics. J. Math. Phys. 9, pp. 655–663.

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External Links:

ZentralBlatt

Referenced by:

§18.39(iii), §18.40(ii).

Encodings:

BibTeX

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