On attractors, spectra and bifurcations of random dynamical systems

In this thesis a number of related topics in random dynamical systems theory are studied: local attractors and attractor-repeller pairs, the exponential dichotomy spectrum and bifurcation theory. We review two existing theories in the literature on local attractors for random dynamical systems on compact metric spaces and associated attractor-repeller pairs and Morse decompositions, namely, local weak attractors and local pullback attractors. We extend the theory of past and future attractor-repeller pairs for nonautonomous systems to the setting of random dynamical systems, and define local strong attractors, which both pullback and forward attract a random neighbourhood. Some examples are given to illustrate the nature of these different attractor concepts. For linear systems considered on the projective space, it is shown that a local strong attractor that attracts a uniform neighbourhood is an object with sufficient properties to prove an analogue of Selgrade's Theorem on the existence of a unique finest Morse decomposition. We develop the dichotomy spectrum for random dynamical systems and investigate its relationship to the Lyapunov spectrum. We demonstrate the utility of the dichotomy spectrum for random bifurcation theory in the following example. Crauel and Flandoli [Journal of Dynamics and Differential Equations, 10(2):259–274, 1998] studied the stochastic differential equation formed from the deterministic pitchfork normal form with additive noise. It was shown that for all parameter values this system possesses a unique invariant measure given by a globally attracting random fixed point with negative Lyapunov exponent, and hence the deterministic bifurcation scenario is destroyed by additive noise. Here, however, we show that one may still observe qualitative changes in the dynamics at the underlying deterministic bifurcation point, in terms of: a loss of hyperbolicity of the dichotomy spectrum; a loss of uniform attractivity; a qualitative change in the distribution of finite-time Lyapunov exponents; and that whilst for small parameter values the systems are topologically equivalent, there is a loss of uniform topological equivalence.Open Acces

The Contribution of the First Stars to the Cosmic Infrared Background

We calculate the contribution to the cosmic infrared background from very massive metal-free stars at high redshift. We explore two plausible star-formation models and two limiting cases for the reprocessing of the ionizing stellar emission. We find that Population III stars may contribute significantly to the cosmic near-infrared background if the following conditions are met: (i) The first stars were massive, with M > ~100 M_sun. (ii) Molecular hydrogen can cool baryons in low-mass haloes. (iii) Pop III star formation is ongoing, and not shut off through negative feedback effects. (iv) Virialized haloes form stars at about 40 per cent efficiency up to the redshift of reionization, z~7. (v) The escape fraction of the ionizing radiation into the intergalactic medium is small. (vi) Nearly all of the stars end up in massive black holes without contributing to the metal enrichment of the Universe.Comment: 11 pages, 6 figures, expanded discussion, added mid-IR to Fig 6, MNRAS in pres

Liberalism and the Moral Significance of Individualism: A Deweyan View

A liberalism which scorns all individualism is fundamentally misguided. This is the chief thesis of this paper. To argue for it, I look closely at some key concepts. The concepts of morislity and individualism are crucial. I emphasize Dewey on the "individuality of the mind" and a Deweyan discussion of language, communication, and community. The thesis links individualism and liberalism, and since appeals to liberalism have broader appeal in the present context of discussions, I start with consideration of liberalism. The aim is to dispute overly restrictive conceptions and explore a broader perspective. To bring the argument to a close, attention turns first to Dewey on value inquiry, to Dewey's "democratic individualism" (cf. Dewey 1939, 179), and to the concept of moral community. Disputing the acquisitiveness of utilitarian influences in classical liberalism, a Deweyan argument from the nature of moral community supports re-emphasis on individualism in contemporary liberal thought

Henry Cabot Lodge, Alexander Hamilton and the Political Thought of the Gilded Age

We are currently witnessing a renewal of broad public interest in the life and career of Alexander Hamilton – justly famed as an American founder. This volume examines the possible present-day significance of the man, noting that this is not the first revival of interest in the statesman. Hamilton was a major background figure in the GOP politics of the Gilded Age, with the powerful US Senator Henry Cabot Lodge, Sr. drawing on Hamilton to inspire a new, assertive American role in the world. Hamilton was first prominent as a soldier and aide to General Washington, and believed in centralization of power in the federal government and an energetic presidency. He founded the American financial system as the first Secretary of the Treasury, and was a great moving force of America’s first nationalist-conservative party – the Federalists. As shown here, close scholarly attention to Lodge’s biography brings out the darker sides of the celebrated hero. Hamilton’s deeper conviction was the need of an elitist “aristocratic republic,” and he was an advocate of military-commercial empire. The Gilded Age Hamilton revival helped inspire the Spanish-American war of 1898 and an American overseas empire. This book will be of interest for students and professionals in political philosophy, political science, American history and American studies

Differential input preamplifier

Preamplifier chops and amplifies very low level output of thermopile infrared detectors that will be used to measure thermal energy flux of Jupiter and its departure from a blackbody spectrum. Output signal has negligible phase shift. AC signal is RC-coupled to input stage of other amplifiers

Does Language Determine Our Scientific Ideas?

SummaryThis paper argues that the influence of language on science, philosophy and other field is mediated by communicative practices. Where communications is more restrictive, established linguistic structures exercise a tighter control over innovations and scientifically motivated reforms of language. The viewpoint here centers on the thesis that argumentation is crucial in the understanding and evaluation of proposed reforms and that social practices which limit argumentation serve to erode scientific objectivity. Thus, a plea is made for a sociology of scientific belief designed to understand and insure social‐institutional conditions of the possibility of knowledge and its growth. A chief argument draws on work of Axelrod concerning the evolution of cooperation

Review of Ulrich Baltzer, "Erkenntnis als Relationengeflecht: Kategorien bei Charles S. Peirce"

This book arose from the author’s recent dissertation written under the Gerhard Schonrich at Munich. It focuses on Peirce’s theory of categories and his epistemology. According to Baltzer, what is distinctive in Peirce’s theory of knowledge is that he reconstrues objects as “knots in networks of relations.” The phrase may ring a bell. It suggests a structuralist interpretation of Peirce, influenced by the Munich environs. The study aims to shows how Peirce’s theory of categories supports his theory of knowledge and how “question concerning a priori structures of knowledge” are transformed within this relational framework. A chief critical target is David Savan’s semiotics, specifically the idea that “the multiplicity of development of the categories” is “conditioned by nothing but the indefiniteness of the categories.”1 But in contrast with this, if there is any indefiniteness in the categories, they cannot fully direct their own application, and this is to say regarding them “that our knowledge is never absolute but always swims, as it were, in a continuum...”2 If the doctrine of continuity applies to the categories, they also have a continuum to swim in

Landau, Abrikosov, Hofstadter: Magnetic Flux Penetration in a Lattice Superconductor

Magnetic flux penetration in superconductors involves a rich variety of subtle phenomena, much of which is still poorly understood. Here these complexities are studied by formulating the Ginzburg-Landau equations as a lattice gauge theory. Their solutions are compared and contrasted with the (heuristic) Landau model of type I superconductivity, and the (perturbative) Abrikosov model for type II superconductors. Novelties arise as the continuum limit is approached, related to an effect discovered by Hofstadter. Various cautionary remarks pertinent to large-scale simulations are made