New compact forms of the trigonometric Ruijsenaars-Schneider system

The reduction of the quasi-Hamiltonian double of ${\mathrm{SU}}(n)$ that has been shown to underlie Ruijsenaars' compactified trigonometric $n$-body system is studied in its natural generality. The constraints contain a parameter $y$, restricted in previous works to $0<y < \pi/n$ because Ruijsenaars' original compactification relies on an equivalent condition. It is found that allowing generic $0<y<\pi/2$ results in the appearance of new self-dual compact forms, of two qualitatively different types depending on the value of $y$. The type (i) cases are similar to the standard case in that the reduced phase space comes equipped with globally smooth action and position variables, and turns out to be symplectomorphic to ${\mathbb{C}P^{n-1}}$ as a Hamiltonian toric manifold. In the type (ii) cases both the position variables and the action variables develop singularities on a nowhere dense subset. A full classification is derived for the parameter $y$ according to the type (i) versus type (ii) dichotomy. The simplest new type (i) systems, for which $\pi/n < y < \pi/(n-1)$, are described in some detail as an illustration.Comment: 31 page

On the Chiral WZNW Phase Space, Exchange r-Matrices and Poisson-Lie Groupoids

This is a review of recent work on the chiral extensions of the WZNW phase space describing both the extensions based on fields with generic monodromy as well as those using Bloch waves with diagonal monodromy. The symplectic form on the extended phase space is inverted in both cases and the chiral WZNW fields are found to satisfy quadratic Poisson bracket relations characterized by monodromy dependent exchange r-matrices. Explicit expressions for the exchange r-matrices in terms of the arbitrary monodromy dependent 2-form appearing in the chiral WZNW symplectic form are given. The exchange r-matrices in the general case are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group $G$, exchange r-matrices are exhibited that are in one-to-one correspondence with the possible PL structures on $G$ and admit them as PL symmetries.Comment: Based on a lecture by L.F. at the Seminaire de Mathematiques Superieures, Montreal, 1999; LaTeX, 21 page

The Mullins effect in the wrinkling behavior of highly stretched thin films

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure

Undirectional calcium and nucleotide fluxes in cardiac sarcoplasmic reticulum. II. Experimental results

Unidirectional calcium influx and efflux were evaluated in cardiac sarcoplasmic reticulum (SR) by 45Ca- 0Ca exchange at steady state calcium uptake in the absence of calcium precipitating anions. Calcium efflux was partitioned into a pump-mediated efflux and a parallel passive efflux by separately measuring passive efflux referable to the steady state. Unidirectional and net ATP-ADP fluxes were measured using [3H]-ATP -- ADP and [3H]- ADP -- ATP exchanges. Methods are presented that take into account changing specific activities and sizes of the nucleotide pools during the measurement of nucleotide fluxes. The contribution of competent and incompetent vesicles to the unidirectional and net nucleotide fluxes was evaluated from the specific activity of these fluxes in incompetent vesicles and from the fraction of vesicles that were incompetent. The results indicate that, in cardiac SR, unidirectional calcium fluxes are larger than the unidirectional nucleotide fluxes contributed by competent vesicles. Because the net ATPase rate of competent vesicles is similar to the parallel passive efflux, it appears that cardiac SR Ca-ATPase tightly couples ATP hydrolysis to calcium transport even at static head, with a coupling ratio near 1.0

Requirements for regional short-haul air service and the definition of a flight program to determine neighborhood reactions to small transport aircraft

An evaluation of the current status and future requirements of an intraregional short haul air service is given. A brief definition of the different types of short haul air service is given. This is followed by a historical review of previous attempts to develop short haul air service in high density urban areas and an assessment of the current status. The requirements for intraregional air service, the need for economic and environmental viability and the need for a flight research program are defined. A detailed outline of a research program that would determine urban community reaction to frequent operations of small transport aircraft is also given. Both the operation of such an experiment in a specific region (San Francisco Bay area) and the necessary design modifications of an existing fixed wing aircraft which could be used in the experiment are established. An estimate is made of overall program costs

The Bacterial Photosynthetic Reaction Center as a Model for Membrane Proteins

Membrane proteins participate in many fundamental cellular processes. Until recently, an understanding of the function and properties of membrane proteins was hampered by an absence of structural information at the atomic level. A landmark achievement toward understanding the structure of membrane proteins was the crystallization (1) and structure determination (2-5) the photosynthetic reaction center (RC) from the purple bacteria Rhodopseudomonas viridis, followed by that of the RC from Rhodobacter sphaeroides (6-17). The RC is an integral membrane protein-pigment complex, which carries out the initial steps of photosynthesis (reviewed in 18). RCs from the purple bacteria Rps. viridis and Rb. sphaeroides are composed of three membrane-associated protein subunits (designated L, M, and H), and the following cofactors: four bacteriochlorophylls (Bchl or B), two bacteriopheophytins (Bphe or [phi]), two quinones, and a nonheme iron. The cofactors are organized into two symmetrical branches that are approximately related by a twofold rotation axis (2, 8). A central feature of the structural organization of the RC is the presence of 11 hydrophobic [alpha]-helixes, approximately 20-30 residues long, which are believed to represent the membrane-spanning portion of the RC (3, 9). Five membrane-spanning helixes are present in both the L and M subunits, while a single helix is in the H subunit. The folding of the L and M subunits is similar, consistent with significant sequence similarity between the two chains (19-25). The L and M subunits are approximately related by the same twofold rotation axis that relates the two cofactor branches. RCs are the first membrane proteins to be described at atomic resolution; consequently they provide an important model for discussing the folding of membrane proteins. The structure demonstrates that [alpha]-helical structures may be adopted by integral membrane proteins, and provides confirmation of the utility of hydropathy plots in identifying nonpolar membrane-spanning regions from sequence data. An important distinction between the folding environments of water-soluble proteins and membrane proteins is the large difference in water concentration surrounding the proteins. As a result, hydrophobic interactions (26) play very different roles in stabilizing the tertiary structures of these two classes of proteins; this has important structural consequences. There is a striking difference in surface polarity of membrane and water-soluble proteins. However, the characteristic atomic packing and surface area appear quite similar. A computational method is described for defining the position of the RC in the membrane (10). After localization of the RC structure in the membrane, surface residues in contact with the lipid bilayer were identified. As has been found for soluble globular proteins, surface residues are less well conserved in homologous membrane proteins than the buried, interior residues. Methods based on the variability of residues between homologous proteins are described (13); they are useful (a) in defining surface helical regions of membrane and water-soluble proteins and (b) in assigning the side of these helixes that are exposed to the solvent. A unifying view of protein structure suggests that water-soluble proteins may be considered as modified membrane proteins with covalently attached polar groups that solubilize the proteins in aqueous solution

A generalized approach for measuring the dielectric properties of lossy composite materials

A generalized technique is presented to measure the dielectric properties of lossy composite materials. The overall method is based on measuring the spectral domain reflection and transmission coefficients of the material-under-test (MUT) using a Vector Network Analyzer (VNA), and then finding the dielectric properties of MUT from the measured scattering data using a proposed reconstruction algorithm. The effect of noise on the reconstruction is examined, and it is observed that even with 5% relative error in the scattering data, the proposed algorithm produces a stable inversion

Interplay between mesoscopic phase separation and bulk magnetism in the layered NaxCoO2

Specific heat of the layered NaxCoO2 (x=0.65, 0.70 and 0.75) oxides has been measured in the temperature range of 3-360 K and magnetic field of 0 and 9 T. The analysis of data, assuming the combined effect of inter-layer superexchange and the phase separation into mesoscopic magnetic domains with localized spins embedded in a matrix with itinerant electronic character, suggests that the dominant contribution to the specific heat in the region of short-range ordering is mediated by quasi-2D antiferromagnetic clusters, perpendicular to the CoO2 layers

Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.Comment: 23 page

Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing

We study the error rate of CNOT operations in the Kane solid state quantum computer architecture. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off diagonal elements of the system's density matrix. Using available spin echo decay data, the CNOT error rate is estimated at approsimately 10^{-3}.Comment: New version includes substantial additional data and merges two old figures into one. (12 pages, 6 figures