Chaos and Complexity Physics

Blogs on Nonlinear Dynamics and Chaos Theory

Physics of the Flipping iPhone and the Fate of the Earth

Explore the stability of rigid body rotation

Spontaneous Symmetry Breaking: A Mechanical Model

See how a simple mechanical model captures some of the physics of the Big Bang as well as solid-state phase transitions.

Surfing on a Black Hole: Accretion Disk Death Spiral

Find out where does the energy of astrophysical jets come from?

Random Walks with Paul Langevin: Stochastic Dynamics

Adding stochastic forces to deterministic chaos.

A Random Walk in 10 Dimensions

A look at wandering about in a 10-dimensional landscape.

The Transverse Doppler Effect and Relativistic Time dilation

The Doppler effect viewed at right angles to the motion.

Locking Clocks in Strong Gravity

Synchronizing clocks near neutron stars and black holes.

The Physics of Stein’s Gate

A fun look at the mathematics of the divergence meter from the Japanese animé “Stein’s Gate”.

A Short History of Fractal Dimension

Fractal mathematics

Edward Lorenz’ Chaotic Butterfly

The beginning of chaos theory.

The Physics of U. S. Presidential Elections

Why are so many elections so close?)

The Ups and Downs of the Compound Double Pendulum

Lagrangian mechanics of the double pendulum

Up-side-down Physics:

Dynamic Equilibrium and the Inverted Pendulum

Henri Poincaré and his Homoclinic Tangle

The beginning of chaos theory

Looking Under the Hood of the Generalized Stokes Theorem

Stoke’s theorem is central to high-dimensional vector calculus

George Stoke’s Law of Drag

The law of viscous drag

Hermann Grassmann’s Nimble Wedge Product

The utility of the wedge product in multi-dimensional vector calculus

Vladimir Arnold’s Cat Map

The Cat Map and Hamiltonian physics

How Number Theory Protects You from the Chaos of the Cosmos

KAM theory and chaos of the solar system

The Fast and the Slow of Grandfather Clocks

Limit-Cycle Oscillators

George Duffing’s Equation

Nonlinear spring equation and chaos

How to Weave a Tapestry from Hamiltonian Chaos

Periodic Hamiltonian chaos

Biased Double-well Potential

Bistability, Bifurcation and Hysteresis

Orbiting Photons around a Black Hole

Optical approximation of the gravitational deflection of light

Getting Armstrong, Aldrin and Collins Home from the Moon

Apollo 11 and the Three-Body Problem

Introduction to Modern Dynamics

Chaos, Networks, Space and Time (Oxford, 2019)

The physics of nonlinear dynamics and complex systems.