Most stable structure for hard spheres

The hard sphere model is known to show a liquid-solid phase transition, with the solid expected to be either face centered cubic or hexagonal close packed. The difference in free energy between the two structures is very small and various attempts have been made to determine which one is the more stable. We contrast the different approaches and extend one.Comment: 5 pages, 1 embedded figure, to appear in Phys Rev

Two-point correlation properties of stochastic "cloud processes''

We study how the two-point density correlation properties of a point particle distribution are modified when each particle is divided, by a stochastic process, into an equal number of identical "daughter" particles. We consider generically that there may be non-trivial correlations in the displacement fields describing the positions of the different daughters of the same "mother" particle, and then treat separately the cases in which there are, or are not, correlations also between the displacements of daughters belonging to different mothers. For both cases exact formulae are derived relating the structure factor (power spectrum) of the daughter distribution to that of the mother. These results can be considered as a generalization of the analogous equations obtained in ref. [1] (cond-mat/0409594) for the case of stochastic displacement fields applied to particle distributions. An application of the present results is that they give explicit algorithms for generating, starting from regular lattice arrays, stochastic particle distributions with an arbitrarily high degree of large-scale uniformity.Comment: 14 pages, 3 figure

700 Families to Feed: The Challenge of Corporate Citizenship

When Howard Lutnick, CEO of Cantor Fitzgerald, was first interviewed after September 11, 2001, a tragedy that devastated his firm and stole the life of his brother, Lutnick stated that he now had “700 families to feed.” The view that he expressed was that his firm was responsible to the families of the wage earners lost in the tragedy, even though the firm was not responsible for the events that had occurred. Such assumed corporate responsibility, consistent with a stakeholder-based approach to management, is often considered to conflict with the law. The purpose of this Article is to demonstrate that stakeholder management does not inherently conflict with the law. In fact, principles of stakeholder thinking coincide with our moral intuitions, reflect many demonstrated best business practices, and promote profit-generation as envisioned and advocated by the law. This Article explores the nature of stakeholder relationships and their impact on business enterprises. The interconnected experiences of individuals and organizations in the wake of the events of September 11, while exemplary and perhaps more pronounced, are not isolated. The purpose of this Article is to draw upon such experiences in order to move beyond the traditional hub-and-spoke model of the firm, and to integrate past and present examples in a more dynamic, stakeholder-based model of corporate citizenship that bridges the gap between stakeholder thinking and the law and is both descriptive and normative.http://deepblue.lib.umich.edu/bitstream/2027.42/39919/3/wp534.pd

700 Families to Feed: The Challenge of Corporate Citizenship

When Howard Lutnick, CEO of Cantor Fitzgerald, was first interviewed after September 11, 2001, a tragedy that devastated his firm and stole the life of his brother, Lutnick stated that he now had “700 families to feed.” The view that he expressed was that his firm was responsible to the families of the wage earners lost in the tragedy, even though the firm was not responsible for the events that had occurred. Such assumed corporate responsibility, consistent with a stakeholder-based approach to management, is often considered to conflict with the law. The purpose of this Article is to demonstrate that stakeholder management does not inherently conflict with the law. In fact, principles of stakeholder thinking coincide with our moral intuitions, reflect many demonstrated best business practices, and promote profit-generation as envisioned and advocated by the law. This Article explores the nature of stakeholder relationships and their impact on business enterprises. The interconnected experiences of individuals and organizations in the wake of the events of September 11, while exemplary and perhaps more pronounced, are not isolated. The purpose of this Article is to draw upon such experiences in order to move beyond the traditional hub-and-spoke model of the firm, and to integrate past and present examples in a more dynamic, stakeholder-based model of corporate citizenship that bridges the gap between stakeholder thinking and the law and is both descriptive and normative.World Trade Center, Peace, Stakeholder thinking, Stakeholder theory, Citizenship, Corporate citizenship, Fiduciary law, Milton Friedman, Corporate social responsibilities, Social responsibilities, Stockholder theory, Stockholders, Stakeholders, Constituency statutes

The structure of the hard sphere solid

We show that near densest-packing the perturbations of the HCP structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the HCP structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than in the other structures.Comment: For related papers see: http://www.ma.utexas.edu/users/radin/papers.htm

Modelling quasicrystals at positive temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures

Tiling Spaces are Inverse Limits

Let M be an arbitrary Riemannian homogeneous space, and let Omega be a space of tilings of M, with finite local complexity (relative to some symmetry group Gamma) and closed in the natural topology. Then Omega is the inverse limit of a sequence of compact finite-dimensional branched manifolds. The branched manifolds are (finite) unions of cells, constructed from the tiles themselves and the group Gamma. This result extends previous results of Anderson and Putnam, of Ormes, Radin and Sadun, of Bellissard, Benedetti and Gambaudo, and of G\"ahler. In particular, the construction in this paper is a natural generalization of G\"ahler's.Comment: Latex, 6 pages, including one embedded figur