Open theoretical problems in the physics of aperiodic systems

Quasicrystals have intrigued and stimulated research in a large number of disciplines. Mathematicians, physicists, chemists, metallurgists and materials scientists have found in them a fertile ground for new insights and discoveries. In the quarter century that has ensued since the publication of the experimental observation of a quasiperiodic Al-Mn alloy \cite{shecht}, many different kinds of quasiperiodic alloys have been manufactured and studied. The physical properties of quasicrystals are no less interesting than the unusual structural properties that led to their discovery in 1984. In this review, I present some of the properties that characterize quasicrystals, briefly discuss several types of theories that have been put forward, and describe some new behaviors that might be investigated by experiment.Comment: 6 pages, 5 figures, plenary lecture for CMAC (Complex metallic alloys) workshop (Zagreb, 2009

Quasiperiodic Heisenberg antiferromagnets in two dimensions

This is a review of the properties of 2d quantum quasiperiodic antiferromagnets as reported in studies that have been carried out in the last decade. Many results have been obtained for perfectly ordered as well as for disordered two dimensional bipartite quasiperiodic tilings. The theoretical methods used include spin wave theory, and renormalization group along with Quantum Monte Carlo simulations. These methods all show that the ground state of these unfrustrated antiferromagnets have N\'eel type order but with a highly complex spatial distribution of local staggered magnetization. The ground state properties, excitation energies and spatial dependence, structure factor, and local susceptibilities are presented. The effects of introducing geometrical disorder on the magnetic properties are discussed.Comment: 21 pages, 29 figure

From \u27Break Out\u27 to \u27Breakthrough\u27: Successful Market Strategies of Immigrant Entrepreneurs in the UK

This paper explores the strategies that enable ethnic minority immigrant entrepreneurs to \u27break out\u27 of local ethnic markets and \u27break through\u27 into more promising markets with greater opportunities. It analyzes the contextual and personal characteristics of the entrepreneurs that implement those strategies, based on a primary survey of South Asian entrepreneurs in the UK. The analysis suggests that breaking out of co-ethnic customer markets is neither necessary nor sufficient for entrepreneurial expansion. The critical factor is the entrepreneur\u27s ability to break through into customer markets that are larger, by geographical reach or profit margins and value added. Many successful immigrant entrepreneurs leverage market knowledge of their home countries. At the same time, the more successful entrepreneurs break out of ethnic labor markets by hiring non-ethnic employees. The capacity to \u27break out\u27 and \u27break through\u27 into larger, global markets, is strengthened by the entrepreneur\u27s education, experience, access and ability to leverage international business networks, and agility to move into more promising markets

Linear Models for Multivariate Repeated Measures Data

We study the general linear model (GLM) with doubly exchangeable distributed error for m observed random variables. The doubly exchangeable linear model (DEGLM) arises when the m¡dimensional error vectors are \doubly exchangeable" (de¯ned later), jointly normally distributed, which is much weaker assumption than the independent and identically distributed error vectors as in the case of GLM or classical GLM (CGLM). We estimate the parameters in the model and also ¯nd their distributions.Multivariate repeated measures; Linear model; Replicated observations.

The eight-fold way for optical quasicrystals

In a recent Letter we proposed a means to realize a quasicrystal with eight-fold symmetry by trapping particles in an optical potential created by four lasers. The quasicrystals obtained in this way, which are closely related to the well-known octagonal tiling, offer unique possibilities to study the effects of quasiperiodicity on physical properties. This method allows to transform the structures, to inflate or deflate them, include interactions or disorder and thus realize a large variety of theoretical models, both classical and quantum. In this paper we derive a number of interesting geometrical properties of the optical quasicrystals, and present some results obtained by numerical calculations.Comment: Paper following short report published in Europhys.Lett. vol.104 p. 66003 (2013