Higher Coxeter graphs associated to affine su(3) modular invariants

The affine $su(3)$ modular invariant partition functions in 2d RCFT are associated with a set of generalized Coxeter graphs. These partition functions fall into two classes, the block-diagonal (Type I) and the non block-diagonal (Type II) cases, associated, from spectral properties, to the subsets of subgroup and module graphs respectively. We introduce a modular operator $\hat{T}$ taking values on the set of vertices of the subgroup graphs. It allows us to obtain easily the associated Type I partition functions. We also show that all Type II partition functions are obtained by the action of suitable twists $\vartheta$ on the set of vertices of the subgroup graphs. These twists have to preserve the values of the modular operator $\hat{T}$.Comment: Version 2. Abstract, introduction and conclusion rewritten, references added. 36 page

Motor Control: Basic Units of Cortical Output?

AbstractObserving movement evoked by stimulating a single cortical neuron has proven technically impossible – until now. A new study using intracellular stimulation has revealed that the basic unit of cortical output is not necessarily basic

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

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

Rouse Chains with Excluded Volume Interactions: Linear Viscoelasticity

Linear viscoelastic properties for a dilute polymer solution are predicted by modeling the solution as a suspension of non-interacting bead-spring chains. The present model, unlike the Rouse model, can describe the solution's rheological behavior even when the solvent quality is good, since excluded volume effects are explicitly taken into account through a narrow Gaussian repulsive potential between pairs of beads in a bead-spring chain. The use of the narrow Gaussian potential, which tends to the more commonly used delta-function repulsive potential in the limit of a width parameter "d" going to zero, enables the performance of Brownian dynamics simulations. The simulations results, which describe the exact behavior of the model, indicate that for chains of arbitrary but finite length, a delta-function potential leads to equilibrium and zero shear rate properties which are identical to the predictions of the Rouse model. On the other hand, a non-zero value of "d" gives rise to a prediction of swelling at equilibrium, and an increase in zero shear rate properties relative to their Rouse model values. The use of a delta-function potential appears to be justified in the limit of infinite chain length. The exact simulation results are compared with those obtained with an approximate solution which is based on the assumption that the non-equilibrium configurational distribution function is Gaussian. The Gaussian approximation is shown to be exact to first order in the strength of excluded volume interaction, and is found to be accurate above a threshold value of "d", for given values of chain length and strength of excluded volume interaction.Comment: Revised version. Long chain limit analysis has been deleted. An improved and corrected examination of the long chain limit will appear as a separate posting. 32 pages, 9 postscript figures, LaTe

Tension Distribution of Single Motor Units in Multitendoned Muscles: Comparison of a Homologous Digit Muscle in Cats and Monkeys

To determine whether single motor units (MUs) in multitendoned muscles distribute tension to multiple tendons or instead focus tension selectively on a single tendon, we examined the distribution of tension generated by single MUs in the cat extensor digitorum lateralis (EDLat), and in its macaque homolog, the extensor digiti quarti et quinti (ED45). General properties of MUs (maximal tetanic tension, axonal conduction velocity, and twitch rise time) were similar in these muscles to those reported for other limb muscles in cats and monkeys. Most cat EDLat MUs were found to exert tension rather selectively on one of the three tendons of the muscle. Fast fatigable MUs were slightly but significantly more selective than fast fatigue-resistant and slow MUs. In contrast, and contrary to expectation, the macaque ED45 contained a lower proportion of MUs that exerted tension selectively on one of the two tendons of the muscle, and a higher proportion of relatively nonselective MUs. These findings suggest that the cat EDLat may consist of three functional subdivisions, each acting preferentially on a different tendon, whereas the macaque ED45 is more likely to function as a single multitendoned muscle

Crystal Perfection Of HgI2 Studied By Neutron And Gamma-ray Diffraction

The crystalline perfection of wire sawn pieces of vapor grown single crystals of mercuric iodide was compared with the perfection of (00l) cleaved sections of the same crystal from which nuclear radiation detectors have been fabricated. The crystalline perfection was studied using neutron and gamma-ray diffraction rocking curves. Most of the gamma-ray data were obtained using a high intensity source of 153Sm gamma rays with a wavelength of λ = 0.12 Å. Some of the data were obtained using highly penetrating 198Au gamma rays with a shorter wavelength of λ = 0.03 Å. The neutrons had a wavelength of λ = 1.07 Å. It was found that, in terms of the mosaic spread of the crystals, the cleaved detector plates have a much lower crystalline perfection than the thicker uncleaved detector plates. At the same time, the results show that for detectors cut from the same crystal, the one with the lower spectral resolution for radiation detection will also have a lower perfection and larger width of the gamma-ray rocking curve. These results suggest consideration should be given to alternative fabrication procedures for HgI2 nuclear radiation detectors

Mechanisms governing fine particulate emissions from coal flames

The primary objective of this program was to provide a basic understanding of the principal processes that govern the formation of particulate matter in the 0.5--10 {mu}m size range in pulverized coal flames. The mechanism that produces ash particles in this size range is not clear. Particle sizes smaller than the 0.5--10 {mu}m size range are generally accepted to result from a vaporization/condensation mechanism while particles larger than this size result from the coalescence of ash in coal particles which may breakup as they burn. This program combined experimental and theoretical studies to understand the mechanisms which control the production of ash in the 0.5--10 {mu}m size range. (VC

Mechanisms governing fine particulate emissions from coal flames. Final report

The primary objective of this program was to provide a basic understanding of the principal processes that govern the formation of particulate matter in the 0.5--10 {mu}m size range in pulverized coal flames. The mechanism that produces ash particles in this size range is not clear. Particle sizes smaller than the 0.5--10 {mu}m size range are generally accepted to result from a vaporization/condensation mechanism while particles larger than this size result from the coalescence of ash in coal particles which may breakup as they burn. This program combined experimental and theoretical studies to understand the mechanisms which control the production of ash in the 0.5--10 {mu}m size range. (VC