- Phase diagram of a pure pVT system
- Phase diagram of a "normal" substance [tsl3]
- Phase diagram of H
_{2}O [tsl4] - Phase diagram of carbon [tsl6]
- Ferrimagnetic phases [tsl49]
- Liquid crystal phases [tsl51]
- Ordering of surfactant molecules [tsl50]
- Phase coexistence: Gibbs phase rule [tln27]

- Classification of phase transitions [tln28]

- Gibbs free energy and derivatives at discontinuous transition [tsl7]
- Gibbs free energy and derivatives at continuous transition [tsl8]
- Clausius-Clapeyron equation [tln29]

- Entropy of a supercooled liquid [tex30]
- Coexistence line of continuous phase transition [tex37]
- Heat capacity of vapor in equilibrium with liquid phase [tex41]
- Discontinuous transition: change in internal energy [tex123]
- Latent heat and response functions [tex124]
- Dry ice [tex125]
- Abnormal phase behavior [tex54]

- Law of corresponding states [tln30]
- Guggenheim plot [tsl9]

- Van der Waals equation of state with coexistence curve [tsl10]
- Maxwell construction [tln31]
- Gibbs and Helmholtz free energies of the van der Waals
fluid
at T<T
_{c}[tsl11] - Condensation and evaporation [tln32]
- Dieterici equation of state [tex34]
- Melting or freezing [tex51]
- Triple point phase changes [tex52]

- Helium liquids [tln33]
- Phase diagram of
^{4}He [tsl13] - Phase diagram of
^{3}He [tsl14] - Exotic properties of helium II [tln34]
- Thermodynamics of a superconductor
- Superconducting transition [tln35]
- Thermodynamics of a ferromagnet [tsl5]
- Structural transitions of iron [tex53]
- Phase coexistence of ammonia [tex55]
- Latent heat and heat capacities at superconducting transition [tex44]

- Mean-field model of ferromagnet (from equations of state)

- Ginzburg-Landau theory of continuous transition
- Ginzburg-Landau theory of discontinuous transition
- Van der Waals gas as mean-field model

- Critical-point singularities
- Critical exponents of magnetic system
- Critical exponents of fluid system
- Mean-field values of critical exponents
- Exponent inequalities

- Lattice versus continuum
- Role of dimensionality
- Ising model

- Potts model
- Vertex model

- XYZ model

- n-vector model

- Ordering and fluctuations

- Universality in critical behavior

- Application to magnetism
- Application to metallic alloy
- Application to lattice gas
- T=0 phase diagrams of Ising spin chains
- Mean-field approximation
- Bragg-Williams approximation
- Bethe approximation
- Equivalent-neighbor coupling

- Ising chains
- Further neighbor coupling
- Alternating coupling
- Correlation functions
- n-vector chains
- Ising model in two dimensions
- Ising lattice gas

Renormalization group theory

- Cybernetics
- Synergetics
- Systems theory
- Science of complexity

- Adaptivity
- Emergent attributes (functions)

- Self-organisation
- Network structures (hierarchy, hubs, scale-free, fractal)

- Self-replication
- Global decisions from local information
- Random explorations and focused processes (chance and necessity)
- Edge of chaos

- Genetic algorithms [psl1] [psl3]

- Cellular automata [psl2]

- One degree of freedom [mln71]

- Phase portraits [msl5] [msl7] [msl18] [msl19]

- Solution by quadrature [mln4]

- Solution by separation of variables [mln72]
- A drop of fluid disappearing [mex101]

- Modeling attenuation [mex230]

- Balancing the water level in a cone [mex112]

- Growth of falling raindrop [mex229]

- Classification of fixed points in plane [mln73]
[msl10]

- Isoclines [mln31]

- Bifurcations
- Limit cycles [mln74]

- Hopf bifurcation [mex19]

- Feedback control [mln33] [mex110]

- Integrability as a universal or contingent property [mln98] [mln99]
[msl15]

- Poincaré surface of section [mln100]
- Toda system (integrable) [msl12]
- Hénon-Heiles system (nonintegrable) [msl13]

- Dissipative dynamical systems [mln101]

- Fixed points in 3D phase flow [msl16]
- Limit cycles in 3D phase flow [msl17]
- Toroidal attractor in 3D phase flow [msl18]
- Strange attractor in 3D phase flow [msl19]
- Rössler band
- Lorenz attractor

- Iterated maps

- Logistic model (continuous time) [mln32]
[mex107]

- Logistic map (discrete time) [mln34]

- Period-doubling route to chaos [msl35] [msl41]

- Universal features

Anharmonicities in vibrations (in part from PHY520)

- Linearly damped harmonic oscillator [mln6]

- Harmonic oscillator with attenuation [pmex12]

- Driven harmonic oscillator [mln28]
[mln29] [pmln1]

- Amplitude resonance [msl48]

- Lattice vibrations and normal modes [mln43]
[mln30] [mln48]

- Molecular vibrations [pmln2]

- Parametric resonance
- Anharmonic vibrations
- Effects of anharmonicity on resonance

Self-organization

Interactions -> structures -> functions

Do you have a question about any of the problems [_ex]?

Do you need a hint?

Do you wish to suggest additional problems?

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Last updated 06/10/16