The falling chain of Hopkins, Tait, Steele and Cayley

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higher-dimensional versions of it. A home camcorder is used to measure the fall of a three-dimensional version called an $xyz$-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.Comment: 17 pages, 5 figure

Reaching across continents : engaging students through virtual collaborations

Business schools have the responsibility of preparing students for work in multicultural organizations and global markets. This paper examines a situated learning experience for undergraduates through a virtual collaboration between a UK university and a Brazilian university. This facilitated remote communication using social media and smart devices, allowing students from both institutions to enhance their cross-cultural management competencies. A qualitative approach was used for the research, drawing on the reflections of the tutors from both institutions, and feedback received from students in the UK and Brazil. This paper provides empirical observations regarding the use of this innovative pedagogic approach, generating discussion of the implications for teaching, thus contributing to the literature on international collaborations in cross-cultural management education

Science Development

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68479/2/10.1177_107554708500600404.pd

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Colloquium: Statistical mechanics of money, wealth, and income

This Colloquium reviews statistical models for money, wealth, and income distributions developed in the econophysics literature since the late 1990s. By analogy with the Boltzmann-Gibbs distribution of energy in physics, it is shown that the probability distribution of money is exponential for certain classes of models with interacting economic agents. Alternative scenarios are also reviewed. Data analysis of the empirical distributions of wealth and income reveals a two-class distribution. The majority of the population belongs to the lower class, characterized by the exponential ("thermal") distribution, whereas a small fraction of the population in the upper class is characterized by the power-law ("superthermal") distribution. The lower part is very stable, stationary in time, whereas the upper part is highly dynamical and out of equilibrium.Comment: 24 pages, 13 figures; v.2 - minor stylistic changes and updates of references corresponding to the published versio

Excavation of an early 17th-century glassmaking site at Glasshouse, Shinrone, Co. Offaly, Ireland

An archaeological research excavation was conducted in the area immediately surrounding an upstanding glassmaking furnace near Shinrone, Co. Offaly, Ireland. It dates to the early to mid 17th century and was built and operated by French Huguenots, probably de Hennezells (de Hennezel/Henzeys/Hensie) who had settled in this region as part of the Crown plantation of King’s County (now Co. Offaly). This furnace, which employed wood rather than coal as a fuel, is a very rare survival, with no other upstanding examples known in Ireland, Britain or the Lorraine region of France where the form probably originated

Multifunctional P-Doped TiO 2

Multifunctional P-doped TiO2 thin films were synthesized by atmospheric pressure chemical vapor deposition (APCVD). This is the first example of P-doped TiO2 films with both P5+ and P3– states, with the relative proportion being determined by synthesis conditions. This technique to control the oxidation state of the impurities presents a new approach to achieve films with both self-cleaning and TCO properties. The origin of electrical conductivity in these materials was correlated to the incorporation of P5+ species, as suggested by Hall Effect probe measurements. The photocatalytic performance of the films was investigated using the model organic pollutant, stearic acid, with films containing predominately P3– states found to be vastly inferior photocatalysts compared to undoped TiO2 films. Transient absorption spectroscopy studies also showed that charge carrier concentrations increased by several orders of magnitude in films containing P5+ species only, whereas photogenerated carrier lifetimes—and thus photocatalytic activity—were severely reduced upon incorporation of P3– species. The results presented here provide important insights on the influence of dopant nature and location within a semiconductor structure. These new P-doped TiO2 films are a breakthrough in the development of multifunctional advanced materials with tuned properties for a wide range of applications