The blue items below are treated in our electricity, magnetism and optics course, while the orange ones might be considered frontier applications i.e. "terra incognita where be dragons aplenty".
|
dimension:
|
n=1
|
n=2
|
n≥3
|
n>>1
|
continuum (n=∞)
|
|
linear
|
GROWTH, DECAY, OR EQUILIBRIUM
exponential growth
RC circuit
LR circuit
|
OSCILLATIONS
linear oscillator
mass and spring
LC and RLC circuits
2-body problem (Kepler, Newton)
|
civil engineering structures
electrical engineering
|
COLLECTIVE PHENOMENA
coupled harmonic oscillators
solid-state physics
molecular dynamics
equilibrium statistical mechanics
|
WAVES AND PATTERNS
elasticity
wave equations
electromagnetism (Maxwell)
quantum mechanics (Schroedinger, Heisenberg, Dirac)
heat and diffusion
acoustics
viscous fluids
|
|
nonlinear
|
fixed points
bifurcation
overdamped systems, relaxational dynamics
logistic equation for single species
|
pendulum
anharmonic oscillators
limit cycles
biological oscillators (neurons, heart cells)
predator-prey cycles
nonlinear electronics (van der Pol, Josephson)
|
CHAOS
strange attractors (Lorenz)
3-body problem (Poincare)
chemical kinetics
iterated maps (Feigenbaum)
fractals (Mandelbrot)
forced nonlinear oscillators (Levinson, Smale)
practical uses of
chaos
quantum
chaos?
|
coupled nonlinear
oscillators
lasers, nonlinear
optics
nonequilibrium statistical
mechanics
nonlinear solid-state physics
(semiconductors)
Josephson arrays
heart cell
synchronization
neural networks
immune system
ecosystems
economics
|
SPATIO-TEMPORAL
COMPLEXITY
nonlinear waves (shocks,
solitons)
plasmas
earthquakes
weather
general relativity
(Einstein)
quantum field
theory
reaction-diffusion,
biological and chemical waves
fibrillation
epilepsy
turbulent fluids (Navier-Stokes)
life
|
*This table is adapted from Steven H. Strogatz (1994) Nonlinear dynamics and chaos, with applications to physics, biology, chemistry and engineering (Perseus Books, Cambridge UK), cf. its link at Amazon.