On the geometry of Hamiltonian chaos

We show that Gutzwiller's characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian can be extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model when a transition is made to the dual manifold, and the geodesics in the dual space coincide with the orbits of the Hamiltonian potential model. We therefore find a direct geometrical description of the time development of a Hamiltonian potential model. The second covariant derivative of the geodesic deviation in this dual manifold generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We discuss some examples of unstable Hamiltonian systems in two dimensions giving, in particular, detailed results for a potential obtained from a fifth order expansion of a Toda lattice Hamiltonian.Comment: 7 pages TeX, Figure captions, 4 figures (eps). Some clarifications, added reference

Controlling Effect of Geometrically Defined Local Structural Changes on Chaotic Hamiltonian Systems

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a new and minimal method for achieving control of a chaotic system

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

The pop music scene in Australia in the 1960s

This thesis examines the circumstances under which the pop music scene existed in Australia during the 1960s. It is not concerned specifically with intepreting the music of the period itself. Instead the more central issues are, on the one hand, to chronicle the developnent of the pop scene (a term explained in the introduction), and, secondly, to interpret the context of involvement with pop music in Australia during this period. In the attempt to realise these aims there is a broader if less explicit agenda. This is to question some of the more conventional approaches ani assurrptions frequently invoked in the study of "culture" in Australia, both in the sense of "culture" as a ''way of life", and in the context of "culture" as artistic and intellectual pursuits. The introductory chapter is concerned with explainirq how best to examine the pop music scene in Australia, and includes a brief historiographical discussion of both general approaches to studying pop music and about the development of cultural studies in Australia. The argument developed here is that questions about "the text" and "effects" of pop music cannot be properly addressed without first attempting to understand the particular circumstances under which pop music is produced, both socially ani econanically. Chapter two is also introductory - but in a more chronological sense - focussing on the emergence of rock' n' roll in Australia in the period from 1955 to 1963. The three chapters that follow dicuss the both the economic and social conditions within the pop music scene of the mid-1960s developed. They begin with an analysis of the context of involvement in the pop music scene by members of the post-war generation, not just as performers but also in a broad spectrum of areas within the nascent music industry. This is followed in the fifth and sixth chapters by a discussion of the circumstances within which pop musicians careers developed. It is argued that beneath the surface of an apparent pop boom in which many perfonrers found it possible to earn a living outside of the conventional career paths that their parents may have hoped they would follow, success was frequently a precarious and transitory phenomenon. Explaining this involves discussinq the impact of tourirq overseas acts on local acts, the often inflexible attitudes of record ccanpanies and the musicians' union, as well as attacks on the pop scene made from police and "respectable" society, which were mostly directed at dance venues. Many of difficulties faced by pop performers intensified in the late 1960s, when, amidst the rhetoric of counterculture and the emergence of the idea of perfonner as "artist", the pop music industry more discernibly consolidated, and the conflicting interests of ''musician" and "industry" became nore apparent. The final chapter examines the endeavours of Australian pop performers overseas, and aims to locate the expectations and strategies of local pop performers within a broader trajectory encompassirq the aspirations of a Australian artists and performers from a wide range of pursuits. Included here is a discussion about the Battle of the Sounds ccompetition, a contest whose major prize was a trip overseas for the victorious pop group. Connexions are suggested between the failure of Battle of the Sounds winners, and many other Australan acts, to succeed overseas, and the conditions in which their careers developed in Australi

'A Divided Soul'? the Cold War odyssey of O. John Rogge

In 1948 O. John Rogge, a prominent American liberal, was a contender for the Progressive Party's vice-presidential nomination. He was then a man of the Left: an activist in the international peace movement, a champion of radical causes and a defender of organizations deemed subversive by the Department of Justice. In 1951 he persuaded his\ud client to turn government witness in the Rosenberg espionage trial and was converted into 'Rogge the Rat' by his former allies. In tracing this transformation, this paper will argue that Rogge was neither a typical Cold War apostate nor a typical anti-Stalinist intellectual. Instead, his political trajectory was the outcome of a failed attempt to steer global politics away from Cold War dichotomies. The paper will therefore throw new light\ud both on the movement to find a 'third way' between East and West, and on the phenomenon of non-communist Left activism during the early Cold War