A low temperature relation R = Ωβ/4πμ between the radius R of a compactly supported 2D vorticity (plasma density) field, the total circulation Ω (total electron charge) and the ratio μ/β (Larmor frequency), is rigorously derived from a variational Principle of Minimum Energy for 2D Euler dynamics. This relation and the predicted structure of the global minimizers or ground states are in agreeme...

A real pendulum with friction will oscillate for a while after a short push, but will eventually come to rest close to a location where is potential energy has a minimum. If the system is closed, i.e. without a source of energy, it will eventually stop moving at a location near a minimum of the potential, no matter what type of friction force acts on the pendulum. This ‘variation principle’ is ...

Pipe systems are often used to transfer moderate to medium water volumes between reservoirs or from well fields to consumers. Such systems consisting of an arbitrary number of reservoirs or other types of sources and sinks are considered here. The Lagrangean optimization principle is used for the determination of all pipe diameters giving minimum total cost of the system, when the individual di...

The spring rates of a coiled helical spring under an axial force and an axially directed torque are derived by a consistent application of Castigliano’s second theorem, and it is shown that the coupling between the two loads may not always be neglected. The spring rate of an extensional spring is derived for the first time through the use of the displacement based principle of minimum total pot...