Simulations by method · 941 simulations

Solve the quantum equations for the electrons directly, with no parameters fitted to experiment beyond the fundamental constants (density functional theory, coupled cluster).

Discretise spacetime as a four-dimensional grid and place the quantum fields on its sites.

Integrate Newton’s equations of motion for every atom in steps of about a femtosecond, using a force field for the interatomic interactions.

Repeated sampling: run the process many times with random choices and estimate the quantity of interest from the statistics.

Track many discrete bodies and the forces between them: stars, dark-matter clumps, grains of sand, plasma charges.

Treat matter as a continuous fluid or solid, express it as partial differential equations, and solve them on a mesh (finite element, finite volume, spectral).

A small number of time-dependent quantities, written as coupled equations and integrated forward (compartment models, circuits, orbits).

Events that occur at random with known rates, one reaction or one birth at a time (Gillespie, Markov chains, random walks).

Each individual has its own rules and state; the individuals interact, and collective behaviour emerges that no individual intends.

A grid of cells, each updating from its neighbours by a simple local rule.