Viewpoint Of Symmetry Research Articles

Nontrivial magnetic order: Localized versus itinerant systems (invited) (abstract)

Recently the interest in non-Neel ground states for antiferromagnetically interacting localized spin systems has been revived. We discuss to what extent the generalization of such states is possible for itinerant electrons. Multiple spin correlation functions can be used to enumerate nontrivial order parameters for localized spins. This approach can be applied to itinerant systems without any modification. However, for the transition which breaks translational symmetry, electronic states far away from the Fermi surface are important and, hence, there is no distinct energetic mechanism for the nontrivial magnetic ordering. The only exception is the Fermi surface with the nesting property. As it is shown, among all phases known for localized spins only p-type spin nematic and chiral spin states can appear as a result of a Fermi liquid breakdown with respect to the electron-hole condensation near the Fermi surface. All other phases with zero local average spin known for localized systems, either are accompanied by the charge density wave or persistent orbital currents creating orbital magnetic moments, or can not appear as a result of a phase transition driven by such mechanism. Although two aforementioned phases are equivalent to their counterparts for localized spins from the symmetry viewpoint, the driving order parameter in an itinerant case is not a multiple spin average, but a wave function of the electron-hole condensate.

Conceptual Design of Deployable Space Structures from the Viewpoint of Symmetry

The concept of symmetry is applied to the design of some existing as well as some new deployable space structures. Through the use of axis or plane symmetry, including anti-symmetry, a bay of a deployable structure may be reduced to an equivalent simple kinematic linkage. This axis of symmetry may be in the direction of deployment of the structure so that by providing a fictitious sliding joint along this axis, the problem of the design and analysis of such deployable structures can be simplified to the study of a plane or a face of the given structure. Such axis or plane of symmetry can also be used for the synthesis of new concepts. As an aid to synthesis, platonic solids can also be used for determining the orientation of these symmetric planes. Several examples are considered. A brief discussion on structural symmetry observed in graphs and dual graphs of some deployable structures will also be presented.

ANOVA models with random effects: an approach via symmetry

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

ANOVA models with random effects: an approach via symmetry

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.