Decomposition of splitting invariants in split real groups

To a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad construct a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group.Comment: 22 page

The development and application of time resolved PIV at the University of Strathclyde

This paper describes the development of time resolved particle image velocimetry (PIV) within the Department of Mechanical Engineering at the University of Strathclyde. The Department's first PIV systems were developed on a limited budget and used existing and second hand equipment. The original technique which, employed 16mm high speed cinematography, is described. The introduction and development of low cost systems employing high speed digital video (HSDV) is discussed and, finally, the Department's new time resolved PIV system, supplied by Dantec Dynamics, is introduced. For each of the PIV systems that have been developed a critical analysis of their functionality is given and samples of the data that they have been produced are shown. Data are presented from systems such as de-rotated centrifugal impellers, air bubbles growing in columns of water, pulsatile jets and vortex shedding

A crossing probability for critical percolation in two dimensions

Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pi_h by treating it as a correlation function of boundary operators in the Q goes to 1 limit of the Q state Potts model. We extend his results to find an analogous formula for pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo changed

Fractional chemotaxis diffusion equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macromolecular crowding or other obstacles

Pliny’s “Role models of both sexes”: gender and exemplarity in the Letters

PublishedArticleThe Letters of Pliny the Younger are notable both for their portraits of outstanding women and for their thoughtful treatment of exemplarity. This article explores Pliny’s innovative portrayal in his Letters of women as moral exempla within his new framework of exemplarity, and the challenge he poses to traditional Roman gender stereotyping. Among the contemporaries whom Pliny and his friends admire and emulate there are many female exempla as well as male, and in his letters he systematically plays down the difference between the sexes at the level of abstract virtue (if not at the level of social role). Exemplary men and women are represented as sharing the same moral qualities and as having the same rhetorical force. Indeed Pliny deliberately subverts the traditional gender tropes found in earlier authors in order to draw attention to his new emphasis on the moral equivalence of the sexes. Pliny’s treatment of female exempla substantially develops possibilities already evident in earlier epistolary works, sets him apart from his friend Tacitus and his teacher Quintilian, and may have been influential on subsequent authors, and even perhaps in the lives of Roman men and women

Anomalous subdiffusion with multispecies linear reaction dynamics

We have introduced a set of coupled fractional reaction-diffusion equations to model a multispecies system undergoing anomalous subdiffusion with linear reaction dynamics. The model equations are derived from a mesoscopic continuous time random walk formulation of anomalously diffusing species with linear mean field reaction kinetics. The effect of reactions is manifest in reaction modified spatiotemporal diffusion operators as well as in additive mean field reaction terms. One consequence of the nonseparability of reaction and subdiffusion terms is that the governing evolution equation for the concentration of one particular species may include both reactive and diffusive contributions from other species. The general solution is derived for the multispecies system and some particular special cases involving both irreversible and reversible reaction dynamics are analyzed in detail. We have carried out Monte Carlo simulations corresponding to these special cases and we find excellent agreement with theory

Exemplary Influences and Augustus' pernicious moral legacy

This is a final draft of the book chapter. The final version will appear in the Oxford book in 2014. OUP has kindly given permission for us to pre-publish the chapter on this site.No abstract available

Signature Characters for the Virasoro Algebra

The number of ghost states at each energy level in a non-unitary conformal field theory is encoded in the signature characters of the relevant Virasoro algebra highest weight representations. We give expressions for these signature characters. These results complete Friedan-Qiu-Shenker's analysis of the Virasoro algebra's highest weight representations.Comment: 9 pp. (Tex instructions corrected.