Weis said it will not be a one-dimensional system.

When going from one to more space dimensions, a number of statements from one-dimensional systems can still be applied.

However, it was shown by Tomonaga in 1950 that this principle is only valid in one-dimensional systems.

This result is interesting because rule 110 is an extremely simple one-dimensional system, and one which is difficult to engineer to perform specific behavior.

The simplest form of the particle in a box model considers a one-dimensional system.

More generally, a typical energy function of a one-dimensional system has a Taylor expansion in the extension q:

Emphasis is placed on one-dimensional systems, but flat plate problems are also discussed.

Consider first a one-dimensional system with short range interactions.

This in turn allows to define the "thermodynamic state" of a one-dimensional mechanical system.

Of course in one-dimensional systems, resonances are shape resonances.