Separatrix Separation. A pendulum in motion can either swing from side to side or turn in a continuous circle. ... Navier–Stokes. The Navier-Stokes equations, developed in 1822, are used to describe the motion of viscous fluid. ...
Exponents and dimensions. ...
Impossibility theorems. ...
Spin glass.

Explanation:

Discovered in 1879 by the physicist Edwin Hall, it occurs when an electrical current is passed through a sheet of metal while a magnetic field is applied at right angles. Hall noticed that a small amount of current was deflected off to the side.

The Navier-Stokes equations were derived by Navier, Poisson, Saint-Venant, and Stokes between 1827 and 1845. These equations are always solved together with the continuity equation: The Navier-Stokes equations represent the conservation of momentum, while the continuity equation represents the conservation of mass.

Exponents and Dimensions. Contributed by: M. Aizenman (Princeton Univ.), Jan. 28, 1999. Abstract Various systems of statistical mechanics are approachable in two dimensions by exactand by rigorousmethods.

Among the most important advances in the social sciences of the 20 th century is Kenneth Arrow ’s Impossibility Theorem. The full explanation of this theorem first appeared in Arrow’s 1951 book, Social Choice and Individual Values.

An important, exactly solvable model of a spin glass was introduced by David Sherrington and Scott Kirkpatrick in 1975. It is an Ising model with long range frustrated ferro- as well as antiferromagnetic couplings.

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