Noncommutative symmetric functions and Laplace operators for classical Lie algebras

New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).Comment: 25 page

L-branes

The superembedding approach to $p$-branes is used to study a class of $p$-branes which have linear multiplets on the worldvolume. We refer to these branes as L-branes. Although linear multiplets are related to scalar multiplets (with 4 or 8 supersymmetries) by dualising one of the scalars of the latter to a $p$-form field strength, in many geometrical situations it is the linear multiplet version which arises naturally. Furthermore, in the case of 8 supersymmetries, the linear multiplet is off-shell in contrast to the scalar multiplet. The dynamics of the L-branes are obtained by using a systematic procedure for constructing the Green-Schwarz action from the superembedding formalism. This action has a Dirac-Born-Infeld type structure for the $p$-form. In addition, a set of equations of motion is postulated directly in superspace, and is shown to agree with the Green-Schwarz equations of motion.Comment: revised version, minor changes, references added, 22 pages, no figures, LaTe

Multiplicity, Invariants and Tensor Product Decomposition of Tame Representations of U(\infty)

The structure of r-fold tensor products of irreducible tame representations of the inductive limit U(\infty) of unitary groups U(n) are are described, versions of contragredient representations and invariants are realized on Bargmann-Segal-Fock spaces.Comment: 48 pages, LaTeX file, to appear in J. Math. Phy

The Schwinger SU(3) construction - I: Multiplicity problem and relation to induced representations

The Schwinger oscillator operator representation of SU(3) is analysed with particular reference to the problem of multiplicity of irreducible representations. It is shown that with the use of an $Sp(2,R)$ unitary representation commuting with the SU(3) representation, the infinity of occurrences of each SU(3) irreducible representation can be handled in complete detail. A natural `generating representation' for SU(3), containing each irreducible representation exactly once, is identified within a subspace of the Schwinger construction; and this is shown to be equivalent to an induced representation of SU(3).Comment: Latex, 25 page

Lorentz harmonics and superfield action. D=10, N=1 superstring

We propose a new version of the superfield action for a closed D=10, N=1 superstring where the Lorentz harmonics are used as auxiliary superfields. The incorporation of Lorentz harmonics into the superfield action makes possible to obtain superfield constraints of the induced worldsheet supergravity as equations of motion. Moreover, it becomes evident that a so-called 'Wess-Zumino part' of the superfield action is basically a Lagrangian form of the generalized action principle. We propose to use the second Noether theorem to handle the essential terms in the transformation lows of hidden gauge symmetries, which remove dynamical degrees of freedom from the Lagrange multiplier superfield.Comment: 23 pages, latex, no figures. V.2, minor corrections, a reference adde

Energy efficient engine high-pressure turbine detailed design report

The energy efficient engine high-pressure turbine is a single stage system based on technology advancements in the areas of aerodynamics, structures and materials to achieve high performance, low operating economics and durability commensurate with commercial service requirements. Low loss performance features combined with a low through-flow velocity approach results in a predicted efficiency of 88.8 for a flight propulsion system. Turbine airfoil durability goals are achieved through the use of advanced high-strength and high-temperature capability single crystal materials and effective cooling management. Overall, this design reflects a considerable extension in turbine technology that is applicable to future, energy efficient gas-turbine engines

Gauge symmetry in phase space with spin, a basis for conformal symmetry and duality among many interactions

We show that a simple OSp(1/2) worldline gauge theory in 0-brane phase space (X,P), with spin degrees of freedom, formulated for a d+2 dimensional spacetime with two times X^0,, X^0', unifies many physical systems which ordinarily are described by a 1-time formulation. Different systems of 1-time physics emerge by choosing gauges that embed ordinary time in d+2 dimensions in different ways. The embeddings have different topology and geometry for the choice of time among the d+2 dimensions. Thus, 2-time physics unifies an infinite number of 1-time physical interacting systems, and establishes a kind of duality among them. One manifestation of the two times is that all of these physical systems have the same quantum Hilbert space in the form of a unique representation of SO(d,2) with the same Casimir eigenvalues. By changing the number n of spinning degrees of freedom the gauge group changes to OSp(n/2). Then the eigenvalue of the Casimirs of SO(d,2) depend on n and then the content of the 1-time physical systems that are unified in the same representation depend on n. The models we study raise new questions about the nature of spacetime.Comment: Latex, 42 pages. v2 improvements in AdS section. In v3 sec.6.2 is modified; the more general potential is limited to a smaller clas

On superembedding approach to type IIB 7-branes

In search for a dynamical description of Q7-branes, which were known as solutions of supergravity equations and then conjectured to be dynamical objects of type IIB string theory, we study the superembedding description of 7-branes in curved type IIB supergravity superspace. With quite minimal and natural assumptions we have found that there is no place for Q7-branes as dynamical branes in superembedding approach. Our study might give implications for the old-standing problem of the covariant and supersymmetric description of multiple Dp-brane systems.Comment: LaTeX, 40 pages, no figures. V2: 44 pages, misprints corrected, minor cosmetic changes, improvements and extensions of discussion, in particular in the parts devoted to derivation of D7-brane equations of motion (Sec. 3) and in Secs. 4.2; appendices E,F added, footnote on page 30 extended, conclusions remain the same. V3. More misprints correcte

A model study of enhanced oil recovery by flooding with aqueous surfactant solution and comparison with theory

With the aim of elucidating the details of enhanced oil recovery by surfactant solution flooding, we have determined the detailed behavior of model systems consisting of a packed column of calcium carbonate particles as the porous rock, n-decane as the trapped oil, and aqueous solutions of the anionic surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT). The AOT concentration was varied from zero to above the critical aggregation concentration (cac). The salt content of the aqueous solutions was varied to give systems of widely different, post-cac oil–water interfacial tensions. The systems were characterized in detail by measuring the permeability behavior of the packed columns, the adsorption isotherms of AOT from the water to the oil–water interface and to the water–calcium carbonate interface, and oil–water–calcium carbonate contact angles. Measurements of the percent oil recovery by pumping surfactant solutions into calcium carbonate-packed columns initially filled with oil were analyzed in terms of the characterization results. We show that the measured contact angles as a function of AOT concentration are in reasonable agreement with those calculated from values of the surface energy of the calcium carbonate–air surface plus the measured adsorption isotherms. Surfactant adsorption onto the calcium carbonate–water interface causes depletion of its aqueous-phase concentration, and we derive equations which enable the concentration of nonadsorbed surfactant within the packed column to be estimated from measured parameters. The percent oil recovery as a function of the surfactant concentration is determined solely by the oil–water–calcium carbonate contact angle for nonadsorbed surfactant concentrations less than the cac. For surfactant concentrations greater than the cac, additional oil removal occurs by a combination of solubilization and emulsification plus oil mobilization due to the low oil–water interfacial tension and a pumping pressure increase

Cyclic-averaging for high-speed analysis of resonant converters

Abstract—The paper describes the development and application of a cyclic-averaging technique for the rapid analysis of high-order resonant power converters. To provide a focus to the paper, particular emphasis is given to a 3rd-order LCC voltage output converter topology. The proposed methodology predicts steady-state voltages and currents throughout the circuit, and provides estimates of the stresses on the resonant circuit components. State-space simulations and experimental results from a 350 V-input/150 V-output converter are used to demonstrate a prediction accuracy comparable with time-domain integration-based techniques is achievable, while requiring only 1/10,000th of the computation time. In addition, a comparison with Spice simulation results shows that cyclic averaging provides commensurate predictions of voltage and current stresses on the resonant circuit components. Issues arising from the stray capacitance associated with the resonant inductor, and the corresponding sensitivity of the predicted output voltage, are also considered