Syllabus of Inactive Physics Courses
203-1-3391 Introduction to Plasma physics
- Basic definitions and parameters. Debye screening and plasma
osillations.
- Hierarchy of descriptions. Single-fluid model.
Magnetohydrodynamics.
- MHD equilibria and waves.
- MHD discontinuities. MHD in space plasmas.
- Two-fluid description. Relation to MHD.
- Waves in dispersive media - general approach.
- Waves in two-fluid hydrodynamics without and with external
magnetic field.
- Kinetic description. Landau damping.
- Microinstabilities. Beam instability.
- (Optional) Nonlinear phenomena: first concepts.
Sources:
- Introduction to Plasma Physics and Controlled Fusion, by F. Chen,
Plenum US; 2 edition (January 31, 1984).
203-2-4911 Interaction of radiation and matter 1
Light
propagation in vacuum, Polarized Light, Quantization of
the Electromagnetic field, fundamental
interaction of light with matter,
Constitutive Relations between (E,H) (D,B) and (J,E) Phenomonology of
linear absorption and emission, Refraction and dispersion, Light
Propagation in
Non-isotropic Media, External DC electric and Magnetic field effects on
absorption-emission and refraction, Nonlinear absorption, Rayleigh
scattering,
Raman scattering, Resonant line scattering, Thomson scattering,
Synchrotron
emission.
Sources:
- E.
Hecht and A. Zajac: Optics, Addison-Wesley, Reading, MA, 1979;
- A.
Yariv: Quantum Electronic, 2nd. ed.,
Wiley, N.Y., 1975;
- J.D.
Jackson: Classical Electrodynamics, 2nd. ed., Wiley, N.Y., 1975;
- B. E. A. Saleh and M. C. Teich, Fundamentals
of Photonics, (J. Wiley, N.Y., 1991)
203-2-5181 Nonlinear wave equations
- On the difference between linear and non-linear wave equations:
dissipation vs. dispersion;
- The Burgers equation in fluid dynamics and highway traffic: wave
fronts, conditions for wave-front generation, symmetries, linearization
through a Lax pair.
- The KdV (Korteweg-de Vries) equation in fluid dynamics and in
anharmonic lattice vibrations: solitons, symmetries, linearization
through a Lax pair, conserved quantities, Hamiltonian structure.
- Inverse scattering method for solving KdV equation.
- Other nonlinear wave equations related to the KdV equation.
- NLS (Nonlinear Schrödinger equation) in fluid dynamics and
nonlinear optics: solitons, symmetries, linearization through a Lax
pair, conserved quantities, Hamiltonian structure.
- Perturbed nonlinear equations: perturbative expansion of
solutions, obstacles to integrability, and how they are handled.
- Wave interactions in nonlinear wave equations.
Sources:
- G. B. Whitham – Linear and Nonlinear waves (Wiley & Sons,
1974
- V. Karpman – Nonlinear Waves in Dispersive Media (Pergamon, 1975
- A. C. Newell – Solitons in Mathematics and Physics (SIAM, 1985)
- M. J. Ablowitz & P. A. Clarkson – Solitons, Nonlinear
Evolution equations and Inverse Scattering (Cambridge, 1991)
- A. C. Newell & J. V. Moloney – Nonlinear Optics
(Addison-Wesley, 1992
- J. Billingham & C. King –Wave Motion (Cambridge, 1995)
- C. Godrèche & P. Manneville – Hydrodynamics and Nonlinear
Instabilities (Cambridge, 1998)
204-2-4741
Physics of Fluids
Ideal Fluids
(Equation of continuity, Euler's equation, Hydrostatics,
Bernouli's equation, momentum and energy fluxes, circulation, potential
flow, incompressible flow waves in fluids); Viscous fluids (Equations
of motion, energy dissipation, flow in a pipe, small Reynolds numbers,
laminar wake, damping waves); Navier-Stokes equations; Turbulence
(Steady flow, rotary flow, instabilities of flows, fully developed
turbulence); Boundary layers (Laminar layer, line of separation,
turbulent boundary layer, drag); Heat transfer in fluids; Sound waves;
Shock waves (Discontinuities, shock adiabatic, weak shocks);
One-dimensional gas flow; Nonlinear equations for waves in fluids;
basic notion if chaos in fluids.
Sources:
- L. D. Landau and E. M. Lifshitz: Fluid Mechanics, 2nd edition
(Butterworth-Henemann, Oxford, 1987) QA901.L283 1987
- D. J. Tritton, Physical Fluid Dynamics, 2nd edition (Oxford
University Press, 1988) QC151,T74 1988
- D. J. Acheson, Elementary Fluid Dynamics (Oxford University
Press, 1990) TA357.A276 1990
- V. I Karpman, Non-linear Waves in Dispersive Media (Pergamon
Press, Oxford, 1974) QA927.K27 1974
- G. Gordèche and P. Mannville, Hydrodynamics and Nonlinear
Instabilities, (Cambridge University Press, 1996) QC151.H93 1996