The two-semester sequence, Internal Processes 1 and 2, provides an introduction to the "Physics of Astrophysics" for first-year graduate students in APS. In the second semester, we cover aspects of radiative transfer and astrophysical fluid dynamics, with applications to accretion flows, accretion disks, sound waves, shock waves, compressible fluids, MHD, and classical instabilities (Jeans, Rayleigh-Taylor, Kelvin-Helmholtz). The course will include numerous homework sets, which will be returned with solutions. The course grade will be based on: homework (50%), final exam (30%), term paper/presentation (10%), and the quality and effectiveness of class participation (10%). A fourth weekly meeting will be devoted especially to broader implications of physical processes from the course to recent scientific papers, order-of-magnitude estimation, and oral discussion. The material for the second semester will include aspects of the following topics:

- Random walk, Binomial distributions, and diffusion
- Transport coefficients, mean-free-paths, collision times
- Scattering and absorption, line escape formalism
- Langevin and Fokker-Planck equations; applications
- Definitions (specific intensity, mean intensity, flux moments)
- Equation of transfer limits (pure emission, absorption)
- Source function and formal solution
- Gaussian quadratures, Eddington & two-stream approx.
- Grey atmosphere (Milne solution) and emergent intensity
- Radiative equilibrium; effects of absorption and scattering
- Line formation; redistribution function; escape probability, diffusion approximation
- Mean opacities (flux-weighted, Rosseland, Planck, Absorption means)
- Boltzmann Equation and Intro to Kinetic Theory
- Boltzmann H-Theorem, Entropy, Collision Integral
- Applications of the Boltzmann Equation
- Conservation Laws (moments of Boltzmann Equation)
- The continuum model and requirements for a fluid
- Conservation laws, fluid kinematics (Eulerian, Lagrangian)
- Advective Derivative, Vector Fields, Vector Calculus
- Mass and Momentum Equations (Euler and Bernoulli)
- Vorticity, Vorticity Freezing, Vorticity Equation
- Bernoulli Theorem, Kelvin Circulation Theorem, applications
- Kinematics of Fluid Motion (strain, stress, relative motion)
- Stress-Strain Relations (Stress Tensor and Strain-Rate Tensors)
- Newtonian fluids (compressibility, viscosity coefficients, pressure)
- Derivation of Navier-Stokes Equation
- Reynolds Number and non-dimensional equations of motion
- Mechanical Viscosity (Classic Shear flows, Couette flow, pipe flow)
- Energy Equations (First Law, Reynolds transport theorem, dissipation)
- Heat Equation (conduction, diffusion, entropy, Bernoulli function)
- Spherical Accretion, Outflows, Gravitational Collapse
- Wind Equation (de Laval Nozzle, sonic point, topology)
- Bondi-Hoyle Accretion, Solar Wind critical solutions
- Accretion Disk Theory (Keplerian disks, viscous couples)
- Conservation laws (mass, angular momentum flux)
- Accretion rates, angular momentum distribution, viscosity
- Basic assumptions for magnetized fluid
- Conservation laws, Ideal MHD equations
- Magnetic diffusion equation (finite conductivity)
- Hydromagnetic equilibria (pressure, tension)
- Examples (force-free fields, magnetic flux tubes, etc)
- Waves (Alfven waves, Magnetosonic waves)
- Sound Waves and "signal speeds"
- Steepening to shock waves (PDEs and characteristics)
- Adiabatic (Rankine-Hugoniot) Jump Conditions
- Post-shock conditions, entropy generation
- Oblique shocks
- Similarity solutions (Sedov-Taylor, Wind-driven bubbles)
- Surface and Interface waves
- Role of surface and dynamic boundary conditions
- Gravity waves (shallow and deep-water limits)
- Dispersion relations, Stability and instability
- Rayleigh-Taylor and Kelvin-Helmholtz Inatbilities
- Gravitational (Jeans) Instability (perturbation analysis)
- Convective Instability (Schwarzschild criterion, entropy)
- Stable atmospheres (Brunt-Vaisala frequency, buoyancy)
- Characteristics of turbulent flows
- Chaotic, nonlinear, diffusivity, vorticity cascades. dissipation
- Kolmogoroff spectrum, eddy cascade, scaling relations
- Molecular vs Eddy Viscosities
- Taylor and Kolmogorov microscales
- Introduction to numerical simulations of turbulence

Introduction to Transport Phenomena

Introduction to Radiative Transfer

Boltzmann Equation and Applications

Introduction to Fluid Dynamics

Strain Rate and Viscous Stresses

Applications to Accretion Flows

Magnetohydrodynamics (MHD)

Shock Waves

Fluid Waves and Instabilities

Intro to Turbulence