Thermodynamics for Fractional Exclusion Statistics

We discuss the thermodynamics of a gas of free particles obeying Haldane's exclusion statistics, deriving low temperature and low density expansions. For gases with a constant density of states, we derive an exact equation of state and find that temperature-dependent quantities are independent of the statistics parameter.Comment: 9 pages, Revtex, no figures. References correcte

Correspondence between conformal field theory and Calogero-Sutherland model

We use the Jack symmetric functions as a basis of the Fock space, and study the action of the Virasoro generators $L_n$. We calculate explicitly the matrix elements of $L_n$ with respect to the Jack-basis. A combinatorial procedure which produces these matrix elements is conjectured. As a limiting case of the formula, we obtain a Pieri-type formula which represents a product of a power sum and a Jack symmetric function as a sum of Jack symmetric functions. Also, a similar expansion was found for the case when we differentiate the Jack symmetric functions with respect to power sums. As an application of our Jack-basis representation, a new diagrammatic interpretation is presented, why the singular vectors of the Virasoro algebra are proportional to the Jack symmetric functions with rectangular diagrams. We also propose a natural normalization of the singular vectors in the Verma module, and determine the coefficients which appear after bosonization in front of the Jack symmetric functions.Comment: 23 pages, references adde

Alternating Spin and Orbital Dimerization in Strong-coupling Two-band Models

We study a one-dimensional Hamiltonian consisting of coupled SU(2) spin and orbital degrees of freedom. Using the density matrix renormalization group, we calculate the phase-diagram and the ground state correlation functions for this model. We find that, in addition to the ferromagnetic and power-law antiferromagnetic phases for spin and orbital degrees of freedom, this model has a gapless line extending from the ferromagnetic phase to the Bethe ansatz solvable SU(4) critical point, and a gapped phase with doubly degenerate ground states which form alternating spin and orbital singlets. The spin-gap and the order parameters are evaluated and the relevance to several recently discovered spin-gap materials is discussed.Comment: 4 pages REVTEX and 4 Postscript figure

Development of gold-catalysed reactions and C-H functionalisations

This thesis is comprised of an introductory chapter, followed by four chapters outlining the research undertaken by the author throughout the duration of study. Chapter 1 provides an introduction to homogeneous gold(I) catalysis, focusing on the selective hydrofunctionalisation of 1,3-disubstituted allenes and in particular axial-to point chirality transfer. Chapter 2 describes the development of the first gold-catalysed intermolecular hydroalkoxylation of 1,3-disubstituted allenes to occur with excellent chirality transfer. The substrate scope and limitations of the reaction were investigated. A wide range of allenes and alcohols were shown to be suited to the reaction, with excellent chirality transfer achieved through prevention of the competing allene racemisation. Chapter 3 outlines the successful development of gold-catalysed hydroarylations of 1,3-disubstituted allenes. Excellent chirality transfer for the hydroarylation of allenes was achieved for the first time and the scope was extended to nucleophiles previously reported to be unsuited to the hydrofunctionalisation of 1,3-disubstituted allenes. Chapter 4 presents the first dual gold and photoredox catalysed aryl-aryl cross coupling which occurs through C-H activation. This work also constitutes the first gold-catalysed C(sp2)-H activation reaction which does not require stoichiometric oxidant. Chapter 5 details the development of a metal-, light- and photocatalyst free Minisci type alkylation procedure which is suitable for the late-stage C-H functionalisation of N-heteroarene and 1,4-quinone moieties, and uses cheap and readily available carboxylic acids

Fabrication of natural and magnetic slippery surfaces

2019 Summer.Includes bibliographical references.Liquid-infused porous surfaces (LIPS) are a type of low adhesion surfaces. They allow most common solids and liquids to slide off the surface easily. Because of this they are able to reduce the adhesion of food, ice, and even blood platelets to surfaces. As a result, LIPS have applications in reducing food waste, aircraft and powerlines deicing, and hemocompatable implants. However, most LIPS are made of toxic fluorocarbon materials. In this work, in order to eschew toxic fluorocarbon materials, we designed several LIPS made from natural hemp products. The first is an all-natural LIPS made from hemp fibers, which could help reduce or eliminate liquid food waste. The second is an aluminum LIPS that shows excellent anti-icing and de-icing properties. The third is a titanium nanotube LIPS that allows blood to slide off without impinging or clotting. This surface also shows excellent platelet reduction. Finally, we demonstrated a simple way of replicating this LIPS system on multiple metals including copper and steel. Further, we demonstrated a simple fabrication of LIPS on top of the fabricated texture atop a magnetic tape. Magnetic tapes are no longer widely used and they are extremely difficult to dispose of. In this magnetic tape-based LIPS, we were able to use an external magnet to manipulate droplets on the surface of the magnetic tape. This can lead to a microfluidic system with a repurposed substrate and precise manipulation of droplets using a magnetic field

Class Warfare: Did Socioeconomic Divisions Undermine The South?

There is no mistaking the theme of this passionate book: the Confederacy lost the Civil War because of the arrogance and avarice of the planter class. The planters started a conflict that they alone wanted, contends David Williams, and they did nothing during the course of the rebellion to win the ...

Fields of Blood: The Prairie Grove Campaign

Revitalizing the Importance of the Prairie Grove Campaign If further proof were needed of William L. Shea’s mastery of the Civil War campaign history, this is it. A professor of history at the University of Arkansas at Monticello, Shea has previously coauthored splendid studies of the ...