fluid%20dynamics
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1: 11.12 Physical Applications
§11.12 Physical Applications
►Applications of Struve functions occur in water-wave and surface-wave problems (Hirata (1975) and Ahmadi and Widnall (1985)), unsteady aerodynamics (Shaw (1985) and Wehausen and Laitone (1960)), distribution of fluid pressure over a vibrating disk (McLachlan (1934)), resistive MHD instability theory (Paris and Sy (1983)), and optical diffraction (Levine and Schwinger (1948)). More recently Struve functions have appeared in many particle quantum dynamical studies of spin decoherence (Shao and Hänggi (1998)) and nanotubes (Pedersen (2003)). …2: 19.35 Other Applications
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§19.35(ii) Physical
►Elliptic integrals appear in lattice models of critical phenomena (Guttmann and Prellberg (1993)); theories of layered materials (Parkinson (1969)); fluid dynamics (Kida (1981)); string theory (Arutyunov and Staudacher (2004)); astrophysics (Dexter and Agol (2009)). …3: 9.16 Physical Applications
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►Within classical physics, they appear prominently in physical optics, electromagnetism, radiative transfer, fluid mechanics, and nonlinear wave propagation.
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►In fluid dynamics, Airy functions enter several topics.
In the study of the stability of a two-dimensional viscous fluid, the flow is governed by the Orr–Sommerfeld equation (a fourth-order differential equation).
…Other applications appear in the study of instability of Couette flow of an inviscid fluid.
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►The KdV equation and solitons have applications in many branches of physics, including plasma physics lattice dynamics, and quantum mechanics.
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4: 21.9 Integrable Equations
§21.9 Integrable Equations
►Riemann theta functions arise in the study of integrable differential equations that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). …5: Sidebar 21.SB1: Periodic Surface Waves
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►Fluid Mech.
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6: William P. Reinhardt
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►He has recently carried out research on non-linear dynamics of Bose–Einstein condensates that served to motivate his interest in elliptic functions.
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►This is closely connected with his interests in classical dynamical “chaos,” an area where he coauthored a book, Chaos in atomic physics with Reinhold Blümel.
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►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.
7: 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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A First Course in Fluid Dynamics.
Cambridge University Press, Cambridge.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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8: Sidebar 5.SB1: Gamma & Digamma Phase Plots
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►This pattern is analogous to one that would be seen in fluid flow generated by a semi-infinite line of vortices.
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►The fluid flow analogy in this case involves a line of vortices of alternating sign of circulation, resulting in a near cancellation of flow far from the real axis.
9: 28.33 Physical Applications
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McLachlan (1947, Chapters XVI–XIX) for applications of the wave equation to vibrational systems, electrical and thermal diffusion, electromagnetic wave guides, elliptical cylinders in viscous fluids, and diffraction of sound and electromagnetic waves.
McLachlan (1947, Chapter XV) for amplitude distortion in moving-coil loud-speakers, frequency modulation, dynamical systems, and vibration of stretched strings.
