Jordan cells in logarithmic limits of conformal field theory

It is discussed how a limiting procedure of conformal field theories may result in logarithmic conformal field theories with Jordan cells of arbitrary rank. This extends our work on rank-two Jordan cells. We also consider the limits of certain three-point functions and find that they are compatible with known results. The general construction is illustrated by logarithmic limits of (unitary) minimal models in conformal field theory. Characters of quasi-rational representations are found to emerge as the limits of the associated irreducible Virasoro characters.Comment: 16 pages, v2: discussion of three-point functions and characters included; ref. added, v3: version to be publishe

Transparent switchboard

A tin oxide coating is formed on a plate of glass and the coating is then etched away from the glass in thin lines to form separate electrical conductors which extend to one end of the plate and connect to either a vertical (column) or horizontal (row) position sensing SCR circuit. A thin transparent insulating coating is formed over the oxide layer except at selected touch points which are positioned in a matrix pattern of vertical columns and horizontal rows. Touching one of these points with a finger bridges the thin line between adjacent conductors to activate trigger circuits in the particular row and column sensing circuits associated with the point touched. The row and column sensing circuits are similar and are powered with a low frequency, ac voltage source. The source for the row circuits is 180 out of phase with the source for the column circuits so that one circuit acts as ground for the other during half of the supply voltage cycle. The signals from the sensing circuits are input to a logic circuit which determines the presence of a valid touch, stores a binary matrix number associated with the touched point, signals a computer of the presence of a stored number and prevents storage of a new number before receiving an enable signal from the computer

Polynomial Fusion Rings of Logarithmic Minimal Models

We identify quotient polynomial rings isomorphic to the recently found fundamental fusion algebras of logarithmic minimal models.Comment: 18 page

Solvable Critical Dense Polymers on the Cylinder

A lattice model of critical dense polymers is solved exactly on a cylinder with finite circumference. The model is the first member LM(1,2) of the Yang-Baxter integrable series of logarithmic minimal models. The cylinder topology allows for non-contractible loops with fugacity alpha that wind around the cylinder or for an arbitrary number ell of defects that propagate along the full length of the cylinder. Using an enlarged periodic Temperley-Lieb algebra, we set up commuting transfer matrices acting on states whose links are considered distinct with respect to connectivity around the front or back of the cylinder. These transfer matrices satisfy a functional equation in the form of an inversion identity. For even N, this involves a non-diagonalizable braid operator J and an involution R=-(J^3-12J)/16=(-1)^{F} with eigenvalues R=(-1)^{ell/2}. The number of defects ell separates the theory into sectors. For the case of loop fugacity alpha=2, the inversion identity is solved exactly for the eigenvalues in finite geometry. The eigenvalues are classified by the physical combinatorics of the patterns of zeros in the complex spectral-parameter plane yielding selection rules. The finite-size corrections are obtained from Euler-Maclaurin formulas. In the scaling limit, we obtain the conformal partition functions and confirm the central charge c=-2 and conformal weights Delta_t=(t^2-1)/8. Here t=ell/2 and t=2r-s in the ell even sectors with Kac labels r=1,2,3,...; s=1,2 while t is half-integer in the ell odd sectors. Strikingly, the ell/2 odd sectors exhibit a W-extended symmetry but the ell/2 even sectors do not. Moreover, the naive trace summing over all ell even sectors does not yield a modular invariant.Comment: 44 pages, v3: minor correction

A wind tunnel investigation of the shape of uncharged raindrops in the presence of an external, electric field

Results of a wind tunnel experiment in which electrically uncharged water drops of 500 to 3000 microns equivalent radius are freely suspended in the vertical air stream of the UCLA cloud tunnel are presented. During this suspension the drops were exposed to external vertical electric fields of 500 to 8,000 volts/cm. The change in drop shape with drop size and electric field strength was noted and is discussed in the light of theoretical work cited in the literature which unfortunately does not take into account the effects of air flow past the drop. The wind tunnel study is documented by stills from a 16 mm film record that demonstrates the shape of water drops in response to both hydrodynamic and electric forces

On the Putative Detection of z>0 X-ray Absorption Features in the Spectrum of Markarian 421

In a series of papers, Nicastro et al. have reported the detection of z>0 OVII absorption features in the spectrum of Mrk421 obtained with the Chandra Low Energy Transmission Grating Spectrometer (LETGS). We evaluate this result in the context of a high quality spectrum of the same source obtained with the Reflection Grating Spectrometer (RGS) on XMM-Newton. The data comprise over 955ks of usable exposure time and more than 26000 counts per 50 milliAngstrom at 21.6 Angstroms. We concentrate on the spectrally clean region (21.3 < lambda < 22.5 Angstroms) where sharp features due to the astrophysically abundant OVII may reveal an intervening, warm--hot intergalactic medium (WHIM). We do not confirm detection of any of the intervening systems claimed to date. Rather, we detect only three unsurprising, astrophysically expected features down to the Log(N_i)~14.6 (3 sigma) sensitivity level. Each of the two purported WHIM features is rejected with a statistical confidence that exceeds that reported for its initial detection. While we can not rule out the existence of fainter, WHIM related features in these spectra, we suggest that previous discovery claims were premature. A more recent paper by Williams et al. claims to have demonstrated that the RGS data we analyze here do not have the resolution or statistical quality required to confirm or deny the LETGS detections. We show that our careful analysis resolves the issues encountered by Williams et al. and recovers the full resolution and statistical quality of the RGS data. We highlight the differences between our analysis and those published by Williams et al. as this may explain our disparate conclusions.Comment: 19 pages/7 figures/4 tables. 060424 submitted to ApJ 060522 re-submitted following ApJ reques

Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath

We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice initialized such that a very long transitory period of time in which standard Boltzmann statistics is insufficient is reached. Our study of the nonlinear system locked in this {\em non-Gibbsian} state focuses on the dynamics of discrete breathers (also called intrinsic localized modes). It is found that part of the energy spontaneously condenses into several discrete breathers. Although these discrete breathers are extremely long lived, their total number is found to decrease as the evolution progresses. Even though the total number of discrete breathers decreases we report the surprising observation that the energy content in the discrete breather population increases. We interpret these observations in the perspective of discrete breather creation and annihilation and find that the death of a discrete breather cause effective energy transfer to a spatially nearby discrete breather. It is found that the concepts of a multi-frequency discrete breather and of internal modes is crucial for this process. Finally, we find that the existence of a discrete breather tends to soften the lattice in its immediate neighborhood, resulting in high amplitude thermal fluctuation close to an existing discrete breather. This in turn nucleates discrete breather creation close to a already existing discrete breather