Rare and Forbidden Decays of D Mesons

We summarize the results of two recent searches for flavor-changing neutral current, lepton-flavor violating, and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. Using data from Fermilab charm hadroproduction experiment E791, we examined D+ and Ds pi,l,l and K,l,l decay modes and the D0 dilepton decay modes containing either l+,l-, a rho0, K*0, or phi vector meson, or a non-resonant pi,pi, K,pi, or K,K pair of pseudoscalar mesons. No evidence for any of these decays was found. Therefore, we presented branching-fraction upper limits at 90% confidence level for the 51 decay modes examined. Twenty-six of these modes had no previously reported limits, and eighteen of the remainder were reported with significant improvements over previously published results.Comment: To be published in the proceedings of the XXXVI Rencontre de Moriond, Electroweak Interactions and Unified Theories conference, Les Arcs, France (10--17 March 2001). (On behalf of the Fermilab E791 Collaboration) Uses moriond.sty, two figures + picture, 5 pages total. Should fit both A4 and US letter format

Fine structure of distributions and central limit theorem in diffusive billiards

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean square displacement, but changes the limiting shape of the distributions to a non-gaussian one. Using the same methods, we give numerical evidence that a non-chaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E. Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander

Plasma etching a ceramic composite

Plasma etching is found to be a superior metallographic technique for evaluating the microstructure of a ceramic matrix composite. The ceramic composite studied is composed of silicon carbide whiskers (SiC(sub W)) in a matrix of silicon nitride (Si3N4), glass, and pores. All four constituents are important in evaluating the microstructure of the composite. Conventionally prepared samples, both as-polished or polished and etched with molten salt, do not allow all four constituents to be observed in one specimen. As-polished specimens allow examination of the glass phase and porosity, while molten salt etching reveals the Si3N4 grain size by removing the glass phase. However, the latter obscures the porosity. Neither technique allows the SiC(sub W) to be distinguished from the Si3N4. Plasma etching with CF4 + 4 percent O2 selectively attacks the Si3N4 grains, leaving SiC(sub W) and glass in relief, while not disturbing the pores. An artifact of the plasma etching reaction is the deposition of a thin layer of carbon on Si3N4, allowing Si3N4 grains to be distinguished from SiC(sub W) by back scattered electron imaging

Chaos in cylindrical stadium billiards via a generic nonlinear mechanism

We describe conditions under which higher-dimensional billiard models in bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium to dimensions above two. An example is a three-dimensional stadium bounded by a cylinder and several planes; the combination of these elements may give rise to defocusing, allowing large chaotic regions in phase space. By studying families of marginally-stable periodic orbits that populate the residual part of phase space, we identify conditions under which a nonlinear instability mechanism arises in their vicinity. For particular geometries, this mechanism rather induces stable nonlinear oscillations, including in the form of whispering-gallery modes.Comment: 4 pages, 4 figure

Structure and evolution of strange attractors in non-elastic triangular billiards

We study pinball billiard dynamics in an equilateral triangular table. In such dynamics, collisions with the walls are non-elastic: the outgoing angle with the normal vector to the boundary is a uniform factor $\lambda < 1$ smaller than the incoming angle. This leads to contraction in phase space for the discrete-time dynamics between consecutive collisions, and hence to attractors of zero Lebesgue measure, which are almost always fractal strange attractors with chaotic dynamics, due to the presence of an expansion mechanism. We study the structure of these strange attractors and their evolution as the contraction parameter $\lambda$ is varied. For $\lambda$ in the interval (0, 1/3), we prove rigorously that the attractor has the structure of a Cantor set times an interval, whereas for larger values of $\lambda$ the billiard dynamics gives rise to nonaccessible regions in phase space. For $\lambda$ close to 1, the attractor splits into three transitive components, the basins of attraction of which have fractal basin boundaries.Comment: 12 pages, 10 figures; submitted for publication. One video file available at http://sistemas.fciencias.unam.mx/~dsanders

Review of Recent Searches for Rare and Forbidden Dilepton Decays of Charmed Mesons

I briefly review the results of recent searches for flavor-changing neutral current and lepton-flavor and lepton-number violating decays of D+, Ds, and D0 mesons (and their antiparticles) into modes containing muons and electrons. The primary focus is the results from Fermilab charm hadroproduction experiment E791. E791 examined 24 pi,l,l and K,l,l decay modes of D+ and Ds and l+l- decay modes of D0. Limits presented by E791 for 22 rare and forbidden dilepton decays of D mesons were more stringent than those obtained from previous searches, or else were the first reported.Comment: 8 pages, 1 figure, uses psfig.sty and RevTeX, submitted to Modern Physics Letters A, based on a Fermilab "Joint Theoretical and Experimental" tal

Sumptuary Synergy: British Imperialism Through the Tartan and Slave Trades

Sumptuary laws have been a useful tool for various national powers in regulating subjects and to promote class differentiation and business interests. The genesis of this study was one such law, entitled the South Carolina Negro Act of 1735, stipulating that slave garments could only be made of low-quality textiles. These fabrics were reflective of slaves living in chattel environments, thus also representing a slave’s status in society. This law forbade slaves from wearing “any sort of garment or apparel whatsoever, finer, other or of greater value than Negro cloth, duffels, coarse kerseys, osnabrigs, blue linen, check linen, or coarse garlix, or calicoes, checked cottons or Scottish plaids.” As most of the textiles listed in the law were somewhat generic and manufactured in several places, it was interesting to the authors that those who crafted the law were more specific to incorporate “Scottish plaids” as one of the acceptable textiles for slave clothing. Textiles were one of the pillars of England and colonial America’s slave trading economy. In fact, the American Colonies had become one of England’s greatest customers, as they represented a distinct piece of what has been termed the “Triangular Trade.” Gold bullion and manufactured goods left England bound for India’s textile manufacturing centers and also to Western Africa’s slave trading centers. These economic inputs provided the fuel necessary to procure goods, such as, inexpensive Indian Madras textiles and humans/slaves, which would then leave India and Africa bound for the plantations of the United States and Caribbean islands. Ships returning from the Americas to England would then supply raw materials, such as sugar and cotton, to fuel English industries, thus completing the cycle. By 1773, America would consume approximately one quarter of products that were made in England