Lagrangian symmetries are found for hydrodynamics and magnetohydrodynamics, which result in conservation of potential vorticity and of cross helicity, respectively. These symmetries, which persist in the reduction from Lagrangian to Eulerian variables, directly give rise to Casimir invariants of the Hamiltonian formalism. The mechanism of spontaneous symmetry breaking in a fluid is also presented.

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Charge independence and symmetry are approximate symmetries of nature. The observations of the small symmetry breaking effects and the consequences of those effects are reviewed. The effects of the mass difference between up and down quarks and the off shell dependence q 2 of ρ 0-ω mixing are stressed. In particular, I argue that models which predict a strong q 2 dependence of ρ 0-ω mixing seem...

FIG. 4. Dependence of the lifetime on the ratio, R, of yields in the two exposures. Curve a is computed with the use of a spectrum of E 's derived from an energy-dependent matrix element of the form y2 —1, Gaussian momentum distribution in the target nucleus, and isotropic angular distribution in the center-of-mass system. Curve b has isotropic and energy-independent matrix element, and Fermi m...

We consider linear operator equations Lf = g in the context of boundary element methods, where the operator L is equivariant i.e., commutes with the actions of a given finite symmetry group. By introducing a generalization of Reynolds projectors, we construct a decomposition of the identity operator, which in turn allows us to decompose the problem Lf = g into a finite number of symmetric subpr...

Many linear operator equations are defined on regions which are invariant under a group Γ of symmetry transformations. If in addition, the linear operator is equivariant with respect to Γ and if a discretization is made which respects the equivariance, the original discretized problem can be decomposed into a collection of much smaller problems, and a significant reduction of computational cost...

The present work is a detailed study of the connections between microstructural instabilities and their macroscopic manifestations — as captured through the effective properties — in finitely strained fiber-reinforced elastomers, subjected to finite, planestrain deformations normal to the fiber direction. The work, which is a complement to a previous and analogous investigation by the same auth...