Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces

We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d site animals on square and triangular lattices in non-trivial geometries. The simulations are done with the newly developed PERM algorithm which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent $\theta$ ($Z_N \sim \mu^N N^{-\theta}$). In particular, we studied animals grafted to the tips of wedges with a wide range of angles $\alpha$, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have $k$ sheets and no boundary, generalizing in this way cones to angles $\alpha > 360$ degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, $\theta \sim 1/\alpha$, only for small angles ($\alpha \ll 2\pi$), while $\theta \approx const -\alpha/2\pi$ for $\alpha \gg 2\pi$. These scalings hold both for wedges and cones. A heuristic (non-conformal) argument for the behavior at large $\alpha$ is given, and comparison is made with critical percolation.Comment: 4 pages, includes 3 figure

Experimental Studies of Low-field Landau Quantization in Two-dimensional Electron Systems in GaAs/AlGaAs Heterostructures

By applying a magnetic field perpendicular to GaAs/AlGaAs two-dimensional electron systems, we study the low-field Landau quantization when the thermal damping is reduced with decreasing the temperature. Magneto-oscillations following Shubnikov-de Haas (SdH) formula are observed even when their amplitudes are so large that the deviation to such a formula is expected. Our experimental results show the importance of the positive magneto-resistance to the extension of SdH formula under the damping induced by the disorder.Comment: 9 pages, 3 figure

Capture and inception of bubbles near line vortices

Motivated by the need to predict vortex cavitation inception, a study has been conducted to investigate bubble capture by a concentrated line vortex of core size rcrc and circulation Γ0Γ0 under noncavitating and cavitating conditions. Direct numerical simulations that solve simultaneously for the two phase flow field, as well as a simpler one-way coupled point-particle-tracking model (PTM) were used to investigate the capture process. The capture times were compared to experimental observations. It was found that the point-particle-tracking model can successfully predict the capture of noncavitating small nuclei by a line vortex released far from the vortex axis. The nucleus grows very slowly during capture until the late stages of the process, where bubble/vortex interaction and bubble deformation become important. Consequently, PTM can be used to study the capture of cavitating nuclei by dividing the process into the noncavitating capture of the nucleus, and then the growth of the nucleus in the low-pressure core region. Bubble growth and deformation act to speed up the capture process.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87832/2/022105_1.pd

Kaon photoproduction: background contributions, form factors and missing resonances

The photoproduction p(gamma, K+)Lambda process is studied within a field-theoretic approach. It is shown that the background contributions constitute an important part of the reaction dynamics. We compare predictions obtained with three plausible techniques for dealing with these background contributions. It appears that the extracted resonance parameters drastically depend on the applied technique. We investigate the implications of the corrections to the functional form of the hadronic form factor in the contact term, recently suggested by Davidson and Workman (Phys. Rev. C 63, 025210). The role of background contributions and hadronic form factors for the identification of the quantum numbers of ``missing'' resonances is discussed.Comment: 11 pages, 7 eps figures, submitted to Phys. Rev.

Szeg\"o kernel asymptotics and Morse inequalities on CR manifolds

We consider an abstract compact orientable Cauchy-Riemann manifold endowed with a Cauchy-Riemann complex line bundle. We assume that the manifold satisfies condition Y(q) everywhere. In this paper we obtain a scaling upper-bound for the Szeg\"o kernel on (0, q)-forms with values in the high tensor powers of the line bundle. This gives after integration weak Morse inequalities, analogues of the holomorphic Morse inequalities of Demailly. By a refined spectral analysis we obtain also strong Morse inequalities which we apply to the embedding of some convex-concave manifolds.Comment: 40 pages, the constants in Theorems 1.1-1.8 have been modified by a multiplicative constant 1/2 ; v.2 is a final updat

Is mindfulness Buddhist? (and why it matters).

Modern exponents of mindfulness meditation promote the therapeutic effects of "bare attention"--a sort of non-judgmental, non-discursive attending to the moment-to-moment flow of consciousness. This approach to Buddhist meditation can be traced to Burmese Buddhist reform movements of the first half of the 20th century, and is arguably at odds with more traditional Theravāda Buddhist doctrine and meditative practices. But the cultivation of present-centered awareness is not without precedent in Buddhist history; similar innovations arose in medieval Chinese Zen (Chan) and Tibetan Dzogchen. These movements have several things in common. In each case the reforms were, in part, attempts to render Buddhist practice and insight accessible to laypersons unfamiliar with Buddhist philosophy and/or unwilling to adopt a renunciatory lifestyle. In addition, these movements all promised astonishingly quick results. And finally, the innovations in practice were met with suspicion and criticism from traditional Buddhist quarters. Those interested in the therapeutic effects of mindfulness and bare attention are often not aware of the existence, much less the content, of the controversies surrounding these practices in Asian Buddhist history

A Quaternary ZnCdSeTe Nanotip Photodetector

The authors report the growth of needle-like high density quaternary Zn0.87Cd0.13Se0.98Te0.02nanotips on oxidized Si(100) substrate. It was found that average length and average diameter of the nanotips were 1.3 μm and 91 nm, respectively. It was also found that the as-grown ZnCdSeTe nanotips exhibit mixture of cubic zinc-blende and hexagonal wurtzite structures. Furthermore, it was found that the operation speeds of the fabricated ZnCdSeTe nanotip photodetector were fast with turn-on and turn-off time constants both less than 2 s

Channelling optics for high quality imaging of sensory hair

A long distance microscope (LDM) is extended by a lens and aperture array. This newly formed channelling LDM is superior in high quality, high-speed imaging of large field of views (FOV). It allows imaging the same FOV like a conventional LDM, but at improved magnification. The optical design is evaluated by calculations with the ray tracing code ZEMAX. High-speed imaging of a 2 × 2 mm(2) FOV is realized at 3.000 frames per second and 1 μm per pixel image resolution. In combination with flow sensitive hair the optics forms a wall shear stress sensor. The optics images the direct vicinity of twenty-one flow sensitive hair distributed in a quadratic array. The hair consists of identical micro-pillars that are 20 μm in diameter, 390 μm in length and made from polydimethylsiloxane (PDMS). Sensor validation is conducted in the transition region of a wall jet in air. The wall shear stress is calculated from optically measured micro-pillar tip deflections. 2D wall shear stress distributions are obtained with currently highest spatiotemporal resolution. The footprint of coherent vortical structures far away from the wall is recovered in the Fourier spectrum of wall shear stress fluctuations. High energetic patterns of 2D wall shear stress distributions are identified by proper orthogonal decomposition (POD)