Study of Growth in Recent and Fossil Invertebrate Exoskeletons and Its Relationship to Tidal Cycles in the Earth-moon System Semiannual Report, May 1 - Oct. 31, 1966

Growth cycles in fossil pelecypod shells and relationship to tidal cycles in earth-moon syste

Critical random graphs: limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n,p) inside the critical window, where p = 1/n + lambda * n^{-4/3} for some lambda in R. We proved in a previous paper (arXiv:0903.4730) that considering the connected components of G(n,p) as a sequence of metric spaces with the graph distance rescaled by n^{-1/3} and letting n go to infinity yields a non-trivial sequence of limit metric spaces C = (C_1, C_2, ...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R_+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak, Pittel and Wierman by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component.Comment: 30 pages, 4 figure

Critical random graphs : limiting constructions and distributional properties

We consider the Erdos-Renyi random graph G(n, p) inside the critical window, where p = 1/n + lambda n(-4/3) for some lambda is an element of R. We proved in Addario-Berry et al. [2009+] that considering the connected components of G(n, p) as a sequence of metric spaces with the graph distance rescaled by n(-1/3) and letting n -> infinity yields a non-trivial sequence of limit metric spaces C = (C-1, C-2,...). These limit metric spaces can be constructed from certain random real trees with vertex-identifications. For a single such metric space, we give here two equivalent constructions, both of which are in terms of more standard probabilistic objects. The first is a global construction using Dirichlet random variables and Aldous' Brownian continuum random tree. The second is a recursive construction from an inhomogeneous Poisson point process on R+. These constructions allow us to characterize the distributions of the masses and lengths in the constituent parts of a limit component when it is decomposed according to its cycle structure. In particular, this strengthens results of Luczak et al. [1994] by providing precise distributional convergence for the lengths of paths between kernel vertices and the length of a shortest cycle, within any fixed limit component

Late Wenlock (middle Silurian) bio-events: Caused by volatile boloid impact/s

Late Wenlockian (late mid-Silurian) life is characterized by three significant changes or bioevents: sudden development of massive carbonate reefs after a long interval of limited reef growth; sudden mass mortality among colonial zooplankton, graptolites; and origination of land plants with vascular tissue (Cooksonia). Both marine bioevents are short in duration and occur essentially simultaneously at the end of the Wenlock without any recorded major climatic change from the general global warm climate. These three disparate biologic events may be linked to sudden environmental change that could have resulted from sudden infusion of a massive amount of ammonia into the tropical ocean. Impact of a boloid or swarm of extraterrestrial bodies containing substantial quantities of a volatile (ammonia) component could provide such an infusion. Major carbonate precipitation (formation), as seen in the reefs as well as, to a more limited extent, in certain brachiopods, would be favored by increased pH resulting from addition of a massive quantity of ammonia into the upper ocean. Because of the buffer capacity of the ocean and dilution effects, the pH would have returned soon to equilibrium. Major proliferation of massive reefs ceased at the same time. Addition of ammonia as fertilizer to terrestrial environments in the tropics would have created optimum environmental conditions for development of land plants with vascular, nutrient-conductive tissue. Fertilization of terrestrial environments thus seemingly preceded development of vascular tissue by a short time interval. Although no direct evidence of impact of a volatile boloid may be found, the bioevent evidence is suggestive that such an impact in the oceans could have taken place. Indeed, in the case of an ammonia boloid, evidence, such as that of the Late Wenlockian bioevents may be the only available data for impact of such a boloid

A simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Niels Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained because the scaling leaves invariant the position-momentum commutator. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential energy curves for the lowest singlet, triplet and excited states of H_2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.Comment: 4 pages, 5 figures, to appear in Phys. Rev. Letter

Uniform WKB approximation of Coulomb wave functions for arbitrary partial wave

Coulomb wave functions are difficult to compute numerically for extremely low energies, even with direct numerical integration. Hence, it is more convenient to use asymptotic formulas in this region. It is the object of this paper to derive analytical asymptotic formulas valid for arbitrary energies and partial waves. Moreover, it is possible to extend these formulas for complex values of parameters.Comment: 5 pages, 2 figure

Parametrically excited "Scars" in Bose-Einstein condensates

Parametric excitation of a Bose-Einstein condensate (BEC) can be realized by periodically changing the interaction strength between the atoms. Above some threshold strength, this excitation modulates the condensate density. We show that when the condensate is trapped in a potential well of irregular shape, density waves can be strongly concentrated ("scarred") along the shortest periodic orbits of a classical particle moving within the confining potential. While single-particle wave functions of systems whose classical counterpart is chaotic may exhibit rich scarring patterns, in BEC, we show that nonlinear effects select mainly those scars that are locally described by stripes. Typically, these are the scars associated with self retracing periodic orbits that do not cross themselves in real space. Dephasing enhances this behavior by reducing the nonlocal effect of interference

A Communications Manager\u27s Qualifications To Enter The Work Force: The Frequency and Distribution of Requirements

This article examines the frequency and distribution of requirements placed on communication managers within recruitment advertisements. The characteristics of recruitment advertisements seeking entry to mid-level communications managers within the Midwest region of the United States were divided into several categories including years of experience, formal education, and educational accreditation status. These categories were analyzed to identify trends and produce conclusions. The conclusions presented with the article indicate employers seek well-rounded and multi-faceted candidates, but overlook educational accreditation as a prerequisite for employment. Additionally, the article evidences both formal education and years of experience as an enhancement to a job seeker\u27s qualifications within workforce. The results of the current study prove valuable in providing information about the field of communications, the job market, general hiring processes, and the workforce. This article recommends further research in job market analysis with emphasis on educational accreditation and its impact on the workforce, job market, and economy

The Impact of Economics on Competition Law in New Zealand Some Reflections on the First Decade

The economic focus of the Commerce Act 1986 is unique in New Zealand, both in terms of its theoretical foundations and its institutional framework. The author reflects on these features of the Act and the impact that economics has had on the decision-making process. This article reviews the New Zealand landscape in terms of the goals of the Commerce Act, its institutional framework, and the manner in which the strict rules of evidence may be relaxed. It then considers, by using Justice Breyer's framework (in S J Breyer "Economics and Judging: An Afterword on Cooter and Wald" (1987) 50 Law and Contemp Probs 245), how economics has impacted upon the content of rules of law and the proof of specific economic facts. The author concludes with a brief assessment of likely and desirable future trends in New Zealand law, arguing that it was likely that economics would continue to have a major impact on the Commerce Act; aside from in the interpretation of dominance principles, the author argues that the foundations are strongly in place for the continued growth of law and economics in this field