Approximating the maximum ergodic average via periodic orbits

Let sigma: Sigma(A) -> Sigma(A) be a subshift of finite type, let M-sigma be the set of all sigma-invariant Borel probability measures on Sigma(A), and let f : Sigma(A) -> R be a Holder continuous observable. There exists at least one or-invariant measure A which maximizes integral f d mu. The following question was asked by B. R. Hunt, E. Ott and G. Yuan: how quickly can the maximum of the integrals integral f d mu be approximated by averages along periodic orbits of period less than p? We give an example of a Holder observable f for which this rate of approximation is slower than stretched-exponential in p

The local potential approximation in the background field formalism

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.Comment: 40 pages, version accepted by JHE

The accelerated characterization of viscoelastic composite materials

Necessary fundamentals relative to composite materials and viscoelasticity are reviewed. The accelerated characterization techniques of time temperature superposition and time temperature stress superposition are described. An experimental procedure for applying the latter to composites is given along with results obtained on a particular T300/934 graphite/epoxy. The accelerated characterization predictions are found in good agreement with actual long term tests. A postcuring phenomenon is discussed that necessitates thermal conditioning of the specimen prior to testing. A closely related phenomenon of physical aging is described as well as the effect of each on the glass transition temperature and strength. Creep rupture results are provided for a variety of geometries and temperatures for T300/934 graphite/epoxy. The results are found to compare reasonably with a modified kinetic rate theory

In Defense of Security, Liberty and Property: The English Origins of an Individual Right to Bear Arms

Does the Second Amendment to the U.S. Constitution provide for an individual or collective right to bear arms? My thesis addresses this question by examining the development of seventeenth and eighteenth-century English common law and political and legal philosophy to support an individual right to bear arms and demonstrates how the founding fathers were greatly influenced by this English precedent. As the records of the Boston Massacre trials demonstrate, the English common law and natural rights theory firmly established a fundamental right of self-preservation, which under the exigencies of the situation might be exercised through the use of firearms. During the seventeenth century, the evolution of natural rights theory contributed to the transformation of a duty to bear arms into a right. Both Thomas Hobbes and John Locke stressed that the right of self-preservation was possessed by the individual, the residue of those ceded to society in the state of nature. The English Whig political theorists, including James Harrington, Algerdon Sydney, John Trenchard and Thomas Gordon, all emphasized that it was incumbent upon each individual citizen to possess arms as a bulwark against the threat to liberties posed by a tyrannical government. The evolution of an individual right to bear arms culminated in the drafting of Article VII of the English Bill of Rights, providing that all protestants had the right to bear arms. The natural right of self-defense can also be seen in the works of the English jurists during the seventeenth and eighteenth centuries and in the development of the English common law. Edward Coke, William Hawkins, Matthew Hale, Michael Foster and William Blackstone all wrote extensively of the natural right of self-defense and this right was repeatedly acknowledged in numerous court cases during the eighteenth century. The English legal and radical Whig writers had a profound influence upon American legal and political thought during the eighteenth century. Their works were widely read and frequently cited by both the political elite and the ordinary person in colonial America. This is repeatedly demonstrated by the multiple references in pre-revolutionary political literature and commentary surrounding the drafting of the constitution. The language of the Second Amendment is opaque and its legislative history sparse. Yet the drafters of the constitution lived in a society where gun ownership was common, where a firearm was used as readily for hunting and defending oneself as for service in a militia. They contemplated an individual right to bear arms