Physics of Waves| Physics of Waves |
General Concepts on Waves
> s.a. Coherence; green functions [propagator];
partial differential equations.
* Radiation vs waves: Those two concepts can
usually be identified, physically, but conceptually radiation involves energy transport.
* Frequency: Measured by an
observer with 4-velocity ua,
ω = −ka
ua.
* Wave number / vector:
The spatial wave vector k and spacetime wave vector
ka are the variables on
which the Fourier transforms of waves depend; The vector k
is perpendicular to each wave front and points in the direction in which
the wave moves; For a pure-frequency wave, its magnitude k
= 2π/λ.
* Power: If I
= p u is the intensity vector, the power is P
= ∫S
I · dA.
@ General references on waves: Georgi 93;
Jonsson & Yngvason 95 [math];
AJP(01)aug [book reviews];
Nettel 08 [including solitons and chaos];
Freegarde 12
[r CP(13)];
Fitzpatrick 13;
in Thorne & Blandford 15;
Fleisch & Kinnaman 15 [II, student guide];
Franklin 20.
@ Related topics:
Abraham-Shrauner et al JPA(06) [type-II hidden symmetries];
Orefice et al PE(15)-a1506 [exact, trajectory-based approach].
> Online resources:
see MathWorld page.
> Related topics:
see types of wave equations and solutions;
wave phenomena [including tails in curved
spacetimes, negative frequencies].
Special Techniques and Concepts for Wave Equations
> s.a. green functions; velocity.
@ Initial / boundary value problem: Beyer a1211 [inequivalent formulations];
Baer & Wafo MPAG(15)-a1408 [initial-value problems on manifolds].
@ Characteristic problem: Frittelli JPA(04) [first-order reduction];
Babiuc et al CQG(14) [well-posedness].
@ Related topics: Gundlach et al CQG-a1010 [spherical harmonics decomposition in arbitrary dimensions];
> s.a. decomposition of
functions; hamiltonian systems.
Types of Waves and Backgrounds > s.a. dissipative media;
huygens principle; magnetism [plasmas].
* In a fluid: Acoustic waves;
Surface waves; Buoyancy waves; Lamb waves (acoustic in nature, different propagation).
@ Dispersive media:
Havelock 14;
Kuzelev & Rukhadze 09;
> s.a. dispersion.
@ Random / disordered medium:
Kogan & Kaveh cm/94/PRB,
FP(96);
Brzezniak & Haba JPA(01)qp/00;
Ramm PLA(03) [many small bodies];
Miniatura et al PRA(07)-a0704 [which-path information];
Sahlmann PRD(10)-a0911 [random lattice, dispersion relation];
Popoff et al PRL(10)
+ van Putten & Mosk Phy(10)
+ letter [transmission matrix];
Ramm a1105 [many small particles];
Willis PRS(11) [effective fields];
Godin et al WRCM(11)-a1110 [1D];
> s.a. Anderson
Localization; velocity [speedup].
@ In black hole spacetimes: Dafermos & Rodnianski a0811-ln [black-hole exteriors];
Shlapentokh-Rothman AHP(15)-a1302 [Kerr spacetime, mode stability];
> s.a. kerr-ads spacetime; reissner-nordström
solution; schwarzschild solution.
@ In cosmological spacetimes: Galstian et al JMP(10)-a0908 [Einstein and de Sitter spacetimes];
Battista et al IJGMP(15)-a1410 [Kasner spacetime];
Alho et al a1805 [near cosmological singularities];
> s.a. fields in FLRW backgrounds.
@ Other curved spacetimes:
Pol'shin gq/98,
gq/98,
gq/98 [and group theory];
Grant et al CMP(09)-a0710 [singular spacetimes];
Ionescu & Klainerman CMP(09) [ill-posed problems, uniqueness results];
Falciano & Goulart CQG(12)-a1112 [new symmetry];
Harte & Drivas PRD(12)-a1202 [effects of light cone caustics];
Waldmann a1208-ln [Green functions, Cauchy problem];
> s.a. gödel solution;
perturbations in general relativity.
@ Random metric fluctuations: Hu & Shiokawa PRD(98)gq/97,
Shiokawa PRD(00)ht [stochastic spacetime];
Dettmann et al JPA(04) [trajectory stabilization].
@ Other backgrounds: D'Ancona & Fanelli m.AP/05 [with electromagnetic potential, dispersion];
Popov & Kovalchuk MMAS(12)-a1112 [non-uniform media];
Ingremeau a1512 [manifolds of non-positive curvature, distorted plane waves];
Dappiaggi et al LMP(19)-a1804 [static, with timelike boundary].
> Other types of waves and backgrounds:
see electromagnetism; gravitational
phenomena; gravitational waves;
Lamb Waves; sound.
Generalizations > s.a. graph
theory in physics; non-commutative theories;
partial differential equations.
@ More general backgrounds: Vickers & Wilson CQG(00)gq/99 [conical spacetimes].
@ Discrete: Das CJP(10)-a0811 [covariant phase space];
Comech & Komech RJMP(11)-a1008 [well-posedness, etc];
Osharovich & Ayzenberg-Stepanenko a1108 [periodic lattices, resonant waves];
Kutsenko a1305 [on periodic lattice/graphs with defects];
> s.a. fractals in physics.
main page
– abbreviations
– journals – comments
– other sites – acknowledgements
send feedback and suggestions to bombelli at olemiss.edu – modified 3 jan 2021