From conformal embeddings to quantum symmetries: an exceptional SU(4) example

We briefly discuss several algebraic tools that are used to describe the quantum symmetries of Boundary Conformal Field Theories on a torus. The starting point is a fusion category, together with an action on another category described by a quantum graph. For known examples, the corresponding modular invariant partition function, which is sometimes associated with a conformal embedding, provides enough information to recover the whole structure. We illustrate these notions with the example of the conformal embedding of SU(4) at level 4 into Spin(15) at level 1, leading to the exceptional quantum graph E4(SU(4)).Comment: 22 pages, 3 color figures. Version 2: We changed the color of figures (ps files) in such a way that they are still understood when converted to gray levels. Version 3: Several references have been adde

Orders and dimensions for sl(2) or sl(3) module categories and Boundary Conformal Field Theories on a torus

After giving a short description, in terms of action of categories, of some of the structures associated with sl(2) and sl(3) boundary conformal field theories on a torus, we provide tables of dimensions describing the semisimple and co-semisimple blocks of the corresponding weak bialgebras (quantum groupoids), tables of quantum dimensions and orders, and tables describing induction - restriction. For reasons of size, the sl(3) tables of induction are only given for theories with self-fusion (existence of a monoidal structure).Comment: 25 pages, 5 tables, 9 figures. Version 2: updated references. Typos corrected. Several proofs added. Examples of ADE and generalized ADE trigonometric identities have been removed to shorten the pape

From modular invariants to graphs: the modular splitting method

We start with a given modular invariant M of a two dimensional su(n)_k conformal field theory (CFT) and present a general method for solving the Ocneanu modular splitting equation and then determine, in a step-by-step explicit construction, 1) the generalized partition functions corresponding to the introduction of boundary conditions and defect lines; 2) the quantum symmetries of the higher ADE graph G associated to the initial modular invariant M. Notice that one does not suppose here that the graph G is already known, since it appears as a by-product of the calculations. We analyze several su(3)_k exceptional cases at levels 5 and 9.Comment: 28 pages, 7 figures. Version 2: updated references. Typos corrected. su(2) example has been removed to shorten the paper. Dual annular matrices for the rejected exceptional su(3) diagram are determine

Design and characterization of all-cryogenic low phase-noise sapphire K-band oscillator for sattelite communication

An all-cryogenic oscillator consisting of a frequency-tunable sapphire resonator, a high-temperature superconducting filter and a pseudomorphic high electron-mobility transistor amplifier was designed for the K-band frequency range and investigated. Due to the high quality factor of the resonator above 1000 000 and the low amplifier phase noise of approximately -133 dBc/Hz at a frequency offset of 1kHz from the carrier, we have achieved oscillator phase-noise values superior to quartz-stabilized oscillators at the same carrier frequency for offset frequencies higher than 100 Hz. In addition to, low phase noise, our prototype oscillator possesses mechanical and electrical frequency tunability. We have implemented a two-step electrical tuning arrangement consisting of a varactor phase shifter integrated within the amplifier circuit (fine tuning by 5'kHz) and a dielectric plunger moved by a piezomechanical transducer inside the resonator housing (course tuning by 50 kHz). This tuning range is sufficient for phase locking and for electronic compensation of temperature drifts occurring during operation of the device employing a miniaturized closed-cycle Stirling-type cryocooler

Polymer transport in random flow

The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and large arguments compared to the equilibrium length. The characteristic relaxation time is computed as a function of the Weissenberg number. In the stretched state the pdf is unstationary and exhibits multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow confirm the relevance of theoretical results obtained for the delta-correlated model.Comment: 28 pages, 6 figure

A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Mesoscale properties of clay aggregates from potential of mean force representation of interactions between nanoplatelets

Face-to-face and edge-to-edge free energy interactions of Wyoming Na-montmorillonite platelets were studied by calculating potential of mean force along their center to center reaction coordinate using explicit solvent (i.e., water) molecular dynamics and free energy perturbation methods. Using a series of configurations, the Gay-Berne potential was parametrized and used to examine the meso-scale aggregation and properties of platelets that are initially random oriented under isothermal-isobaric conditions. Aggregates of clay were defined by geometrical analysis of face-to-face proximity of platelets with size distribution described by a log-normal function. The isotropy of the microstructure was assessed by computing a scalar order parameter. The number of platelets per aggregate and anisotropy of the microstructure both increases with platelet plan area. The system becomes more ordered and aggregate size increases with increasing pressure until maximum ordered state at confining pressure of 50 atm. Further increase of pressure slides platelets relative to each other leading to smaller aggregate size. The results show aggregate size of (3–8) platelets for sodium-smectite in agreement with experiments (3–10). The geometrical arrangement of aggregates affects mechanical properties of the system. The elastic properties of the meso-scale aggregate assembly are reported and compared with nanoindentation experiments. It is found that the elastic properties at this scale are close to the cubic systems. The elastic stiffness and anisotropy of the assembly increases with the size of the platelets and the level of external pressure.National Science Foundation (U.S.) (Extreme Science and Engineering Discovery Environment (XSEDE) and Texas Advanced Computing Center Grant TG-DMR100028)X-Shale Hub at MITSingapore-MIT Alliance for Research and Technolog

Determination of the Michel Parameters rho, xi, and delta in tau-Lepton Decays with tau --> rho nu Tags

Using the ARGUS detector at the $e^+ e^-$ storage ring DORIS II, we have measured the Michel parameters $\rho$, $\xi$, and $\xi\delta$ for $\tau^{\pm}\to l^{\pm} \nu\bar\nu$ decays in $\tau$-pair events produced at center of mass energies in the region of the $\Upsilon$ resonances. Using $\tau^\mp \to \rho^\mp \nu$ as spin analyzing tags, we find $\rho_{e}=0.68\pm 0.04 \pm 0.08$, $\xi_{e}= 1.12 \pm 0.20 \pm 0.09$, $\xi\delta_{e}= 0.57 \pm 0.14 \pm 0.07$, $\rho_{\mu}= 0.69 \pm 0.06 \pm 0.08$, $\xi_{\mu}= 1.25 \pm 0.27 \pm 0.14$ and $\xi\delta_{\mu}= 0.72 \pm 0.18 \pm 0.10$. In addition, we report the combined ARGUS results on $\rho$, $\xi$, and $\xi\delta$ using this work und previous measurements.Comment: 10 pages, well formatted postscript can be found at http://pktw06.phy.tu-dresden.de/iktp/pub/desy97-194.p

Role of cellular senescence and NOX4-mediated oxidative stress in systemic sclerosis pathogenesis.

Systemic sclerosis (SSc) is a systemic autoimmune disease characterized by progressive fibrosis of skin and numerous internal organs and a severe fibroproliferative vasculopathy resulting frequently in severe disability and high mortality. Although the etiology of SSc is unknown and the detailed mechanisms responsible for the fibrotic process have not been fully elucidated, one important observation from a large US population study was the demonstration of a late onset of SSc with a peak incidence between 45 and 54 years of age in African-American females and between 65 and 74 years of age in white females. Although it is not appropriate to consider SSc as a disease of aging, the possibility that senescence changes in the cellular elements involved in its pathogenesis may play a role has not been thoroughly examined. The process of cellular senescence is extremely complex, and the mechanisms, molecular events, and signaling pathways involved have not been fully elucidated; however, there is strong evidence to support the concept that oxidative stress caused by the excessive generation of reactive oxygen species may be one important mechanism involved. On the other hand, numerous studies have implicated oxidative stress in SSc pathogenesis, thus, suggesting a plausible mechanism in which excessive oxidative stress induces cellular senescence and that the molecular events associated with this complex process play an important role in the fibrotic and fibroproliferative vasculopathy characteristic of SSc. Here, recent studies examining the role of cellular senescence and of oxidative stress in SSc pathogenesis will be reviewed