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

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

Bayesian Optimisation for Safe Navigation under Localisation Uncertainty

In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.Comment: To appear in the proceedings of the 18th International Symposium on Robotics Research (ISRR 2017

Study of high voltage solar array configurations with integrated power control electronics

Solar array electrical configurations for voltage regulatio

Single wall carbon nanotube double quantum dot

We report on two top-gate defined, coupled quantum dots in a semiconducting single wall carbon nanotube, constituting a tunable double quantum dot system. The single wall carbon nanotubes are contacted by titanium electrodes, and gated by three narrow top-gate electrodes as well as a back-gate. We show that a bias spectroscopy plot on just one of the two quantum dots can be used to extract the addition energy of both quantum dots. Furthermore, honeycomb charge stability diagrams are analyzed by an electrostatic capacitor model that includes cross capacitances, and we extract the coupling energy of the double quantum dot.Comment: Published in Applied Physics Letters 4 December 2006. http://link.aip.org/link/?APL/89/23211

Automated Identification and Differentiation of Spectrally Similar Hydrothermal Minerals on Mars

Early telescopic observations corroborated hydration related absorptions on Mars in the infrared. Images from the Viking missions led to speculation of hydrothermal alteration and were followed by two missions which mapped the spatial variability of the ~ 3 m hydration feature. Since then, the Compact Reconnaissance Imager for Mars (CRISM) has provided high spatial resolution (up to 18m) spectral identification of a suite of hydrothermal and diagenetic minerals which have illuminated a range of formation mechanisms. Presence/absence and spatial segregation or mixing of minerals like prehnite, epidote, chlorite amphiboles, and mixed-layer Fe/Mg smectite-chlorite provide valuable evidence for the geologic setting of deposits on Earth, and these phases are often used as temperature and aqueous chemistry indicators in terrestrial systems. Mapping the distribution of these phases will help to answer whether Mars had widespread conditions favorable for low-grade metamorphism and diagenesis, or only focused hydrothermal systems in areas of high heat flow. Further characterizing the chemistry and structure of these phases will then help to answer how most of the widespread Fe/Mg phyllosilicates formed, further defining early geochemical cycling and climate. A fully automated approach for accurate mapping of important hydrothermal mineral phases on Mars has been a challenge. Due to overlapping features in the M-OH region (~2.2-2.4 m), the strongest absorption features of chlorite, prehnite, and epidote in the short-wave infrared are difficult to distinguish from one another and from the most commonly occurring hydrated silicates on Mars, Fe/Mg smectites. Weaker absorptions are present in both prehnite and epidote which help to distinguish them from chlorite and smectites, but their relative strength in the presence of noise and spatial mixing is often too low to confidently identify them without the noise suppression and feature enhancement methods described here. The spectral signatures of mixed-layer Fe/Mg smectite-chlorite and partially chloritized Fe/Mg smectites have not yet been adequately assessed. Here we evaluate the effectiveness of two empirical and statistical methods for identifying and differentiating these phases using CRISM data