Highest weight representations of Euclidean Kac-Moody algebras spanned by the principal subalgebra action

The aim of this Letter is to characterize the representations of Euclidean Ka-Moody with highest weight, spanned by the principal subalgebra action on a highest-weight vector.We conjecture that, modulo the Dynkin diagram automorphisms, only the basic representations have this property. This is proved for A _infn ^sup(1) , D _inf4 ^sup(1) , and A _inf2 ^sup(2) .     

Extended super-Kač-Moody algebras and their super-derivation algebras

We study theN-extended super-Ka-Moody algebras, i.e. extensions of the Lie algebra of the loop group over the super-circleA _N . The extensions are characterized by 2-cocycles which are computed in terms of the cyclic cohomology of the Grassmann algebra withN generators. The graded algebra of super-derivations compatible with each extension is determined. The casesN=1,2,3 are examined in detail and their relation with the Ademollo et al. superconformal algebras is discussed. We examine the possibility of defining new superconformal algebras which, forN>1, generalize theN=1 Ramond-Neveu-Schwarz algebra.     

(T * G) t : A toy model for conformal field theory

We study a chiral operator algebra of conformal field theory and quantum deformation of the finite-dimensional Lie group to obtain the definition of (T ^* G) _t and its representation.The closeness of the Ka-Moody algebras, constituting the chiral operator algebra of a typical (and generic) conformal field theory model, namely the WZNW model, and quantum deformation of corresponding finite-dimensional Lie groupG has become more and more evident in recent years [1–5]. This in particular prompts further investigation of the differential geometry of such deformations. The notion of tangent and cotangent bundles is basic in classical differential geometry. It is only natural that the quantum deformations ofTG andT ^* G are to be introduced alongside those forG itself. Physical ideas could be useful for this goal.Indeed, theT ^* G can be interpreted as a phase space for a kind of a top, generalizing the usual top associated withG=SO(3). The classical mechanics is a natural language to describe differential geometry, whereas the usual quantization is nothing but the representation theory.In this paper we put corresponding formulas in such a fashion that their deformation becomes almost evident, given the experience in this domain. As a result we get the definition of (T ^* G) _t and its representation (t is the deformation parameter).To make the exposition most simple and formulas transparent we shall work on an example ofG=sl(2) and present results in such a way that the generalizations become evident. We shall stick to generic complex versions, real and especially compact forms requiring some additional consideration, not all of which are self-evident.This work was supported in part by a grant provided by the Academy of Finland, and the U.S. Department of Energy (DOE) under contract DE-AC02-76ER03069     

Monte Carlo methods for yrast spectroscopy

We discuss the details of the recently proposed Monte Carlo method to evaluate the exact energies of yrast levels. Energy levels are evaluated up to J = 18 with small statistical errors using the Metropolis method for the case of ¹⁶⁶Er using the pairing plus quadrupole model within one major shell. We also discuss the evaluation of the probabilities of the Hartree-Fock-Bogoliubov wave functions in the corresponding yrast eigenstates and they are found to be large. The model displays a too strong backbending behaviour not seen experimentally.Received: 29 September 2003, Published online: 24 August 2004PACS: 21.60.-n Nuclear-structure models and methods - 02.70.Ss Quantum Monte Carlo methods - 21.60.Ka Monte Carlo models - 21.10.Re Collective levels     

A priori analysis of sub-grid variance of a reactive scalar using DNS data of high Ka flames

Direct numerical simulations (DNS) of low and high Karlovitz number (Ka) flames are analysed to investigate the behaviour of the reactive scalar sub-grid scale (SGS) variance in premixed combustion under a wide range of combustion conditions (regimes). An order of magnitude analysis is performed to assess the importance of various terms in the variance evolution equation and the analysis is validated using the DNS results. This analysis sheds light on the relative behaviour among turbulent transport and production, scalar dissipation and chemical processes involved in the evolution of the SGS variance at different Ka. The common expectation is that the variance equation shifts from a reaction-dissipation balance at low Ka to a production–dissipation balance at high Ka with diminishing reaction contribution. However, in large eddy simulation (LES), a high Ka alone does not make the reaction term negligible, as the relative importance of the reaction term has a concurrent increase with filter size. The filter size can be relatively large compared with the Kolmogorov length scale in practical LES of high Ka flames, and as a consequence a reaction–production–dissipation balance may prevail in the variance equation even in a high Ka configuration, and this possibility is quantified using the DNS analysis in this work. This has implications from modelling perspectives, and therefore two commonly used closures in LES for the SGS scalar dissipation rate are investigated a priori to estimate the importance of the above balance in LES modelling. The results are explained to highlight the interplay among turbulence, chemistry and dissipation processes as a function of Ka.     

Design and Implementation of a Millimeter Wave Monolithic Integrated Mixer

This paper discusses design and implementation of a millimeterwave monolithic integrated balanced mixer, the measured performance compared with the predicted one is also reported. By designing this MMIC mixer, various mathematical methods are used, in which the Method of Conversion Matrix has been extended by the author to meet the requirement of inter-modulation analysis. The mixer is realized in a 2×3mm ² GaAs chip, working in Ka band with bandwidth of 5GHz with a noise figure less than 10 dB.     

A note on Killing vectors in algebraically special vacuum space-times

A study is made on the connection between the existence of a Killing vector whose associated bivector (Ka;b) is null and the Petrov type. A theorem of Debney is refined. Also considered is a particular case (omitted in Debney's papers) in which the bivector is nonnull.     

Raising and Lowering Operators for Orbital Angular Momentum Quantum Numbers

Two vector operators aimed at shifting orbital angular momentum quantum number l successfully constructed based on the primary form proposed by Prof. X.L. Ka in 2001. The lowering operators can give the lowest angular momentum quantum numbers l for a given magnetic quantum number m in spherical harmonics |lm〉; and the state with minimum angular momentum quantum number in whole set of the spherical harmonics turns out to be |0,0〉. How to use the raising and lowering operators as acting on the state |0,0〉. to generate whole set of spherical harmonics is illustrated.     

Simulations and experiments on the ignition probability in turbulent premixed bluff-body flames

The ignition characteristics of a premixed bluff-body burner under lean conditions were investigated experimentally and numerically with a physical model focusing on ignition probability. Visualisation of the flame with a 5 kHz OH* chemiluminescence camera confirmed that successful ignitions were those associated with the movement of the kernel upstream, consistent with previous work on non-premixed systems. Performing many separate ignition trials at the same spark position and flow conditions resulted in a quantification of the ignition probability P_ign, which was found to decrease with increasing distance downstream of the bluff body and a decrease in equivalence ratio. Flows corresponding to flames close to the blow-off limit could not be ignited, although such flames were stable if reached from a richer already ignited condition. A detailed comparison with the local Karlovitz number and the mean velocity showed that regions of high P_ign are associated with low Ka and negative bulk velocity (i.e. towards the bluff body), although a direct correlation was not possible. A modelling effort that takes convection and localised flame quenching into account by tracking stochastic virtual flame particles, previously validated for non-premixed and spray ignition, was used to estimate the ignition probability. The applicability of this approach to premixed flows was first evaluated by investigating the model's flame propagation mechanism in a uniform turbulence field, which showed that the model reproduces the bending behaviour of the S_T-versus-u′ curve. Then ignition simulations of the bluff-body burner were carried out. The ignition probability map was computed and it was found that the model reproduces all main trends found in the experimental study.     

Short pulse Z -scan investigations of optical nonlinearities of a novel organometallic complex: [(C2H5)4N]2[Cu(dmit)2] at 532 and 1064?nm

A novel dmit organometallic complex: [(C₂H₅)₄N]₂[Cu(dmit)₂] (dmit^2-=1,3-dithiole-2-thione-4,5-dithiolate), abbreviated as EtCu, was synthesized. Afterwards its optical nonlinearities in acetone solution at 532 nm and 1064 nm were studied by the Z-scan technique with laser pulses of picosecond duration. The two-photon absorption at 1064 nm and the saturable absorption at 532 nm were observed. The Z-scan curves also revealed that EtCu sample solutions exhibited self-defocusing effects at both wavelengths. The origins were analyzed for the differences between the results. All the outcomes suggest that this material is potential for nonlinear optical device applications. PACS 42.65.An; 42.65.Hw; 42.65.Jx; 81.20.Ka; 78.30.Jw     

Rigorous Analysis of the Disk-Loaded Waveguide Slow-Wave Structures

Recently disk-loaded waveguide has been widely used in high-power traveling wave tubes (HPTWT). Although TM ₀₁ mode is it's main mode, the asymmetry mode may be excited by slight asymmetry of the structure, misalignment of the beam, or the asymmetry associated with the input or output structure. So research about asymmetry mode of disk-loaded waveguide is necessary. The general dispersion equation and interaction impedance expression of disk-loaded waveguide is obtained with accurate field theory for the first time. Based on these results, a broadband and a narrowband disk-loaded waveguides are designed which can be used in the Ka band HPTWT. Moreover, the theoretical calculated results are compared with the simulated results from the HFSS (High Frequency Structure Simulator) code using finite element method. It is found that frequency domain overlapped by these two modes of the narrowband structure is very narrow, so the HEM ₁₁ mode may be ignored when calculating Beam-wave interaction. In the other hand, the interaction impedance of HEM ₁₁ mode is very low generally.     

Effect of adsorption of alkali metal atoms on the work function of rutile

Calculation of the change of work function Δφ at the surface of TiO₂ due to the adsorption of Na, Ka, and Cs atoms has been carried out in the framework of a model taking into account the repulsion of adatoms and metallization of the adsorbed layer. The calculation results are in good agreement with experiment.     

A Compact Monopulse Radial Line Slot Array Antenna at Millimeter Wavelengths

This paper describes the design and performance of a radial line slot array antenna (RLSA) which generates sum or difference far field patterns. The antenna consists of rectangular waveguide to radial line transition, radial line and slot arrays etched on the upper plate of the radial line. A novel rectangular waveguide to radial line transition is designed to build up the dominate TEM mode in radial line to excite the slot arrays which are arranged in concentric rings on the upper plate of the radial line. The antenna radiates linear polarization at Ka band. Monopulse operation is obtained by a sum and difference network which is a compact eight-port comparator consisting of coplanar magic tees. The sum and difference network is waveguide structure whose loss is less than that of microstrip structure at millimeter wave lengths. The monopulse performances can be used in monopulse tracking and anti-collision application etc. Genetic algorithm (GA) is applied to optimize the parameters of the transition and antenna to obtain good performances. Note: Part of this paper has been presented in the oral session ThuA5 on Transmission Lines and Antennas in IRMMW-THz2006 Conference, pages: 535.Number: 376636Title: Radial line slot array antenna at millimeter wave lengths     

A symmetry of the string background field equations

We investigate the effect of duality transformations on the geometries of a subclass of two-dimensional non-linear sigma-models. We identify the torsion which appears on dualizing such a model, initially without Wess-Zumino-Witten term, as the field strength of the gauge connection appearing in a Kałuza-Klein interpretation of the initial geometry. We show that duality preserves quantum conformal invariance at order [α′]⁰, where α′ is the string tension parameter, provided the change induced in the geometry by duality is accompanied by a shift in the dilaton field. We interpret these combined transformations as a symmetry of the order [α′]⁰ string background field equations.     

Hydrothermal synthesis and microstructure investigation of nanostructured bismuth telluride powder

Nanostructured thermoelectric Bi₂Te₃ powders with various morphologies were hydrothermally synthesized using different precursors and routes to give an experimental comprehension on the formation of the nanopowders. It was found that the polyhedral Bi₂Te₃ particles are formed by surface nucleation in a continuous nucleation process, the hexagonal Bi₂Te₃ thin sheets are formed in a nucleus saturation process due to the anisotropic growth of the crystals, and the mono-atom reaction model leads to irregular bent thin Bi₂Te₃ sheets. Some quasi one-dimensional nanorods and nanotubes were also found in the synthesized Bi₂Te₃ powders. PACS 81.05.Hd; 81.20.Ka; 61.46.+w     

Studies on the Formation of β-Cyclodextrin/Alkylcobaloxime Inclusion Complexes by Using NMR Methods

Abstract

It has been established that alkylcobaloxime(R=i-C₄H₉, n-C₄H₉, n-C_sH₁₁, c-C₆H₁₁, PhCH₂) and β-cyclodextrin form a kind of 1: 1 inclusion complexes in aqueous solution by ¹H NMR spectroscopy. Ka and ?ΔG^θ were calculated according to chemical shift changes of different probe protons. The stability constant(Ka) has been found increasing in the order: PhCH₂ > n-C₅H₁₁ > c-C₆H₁₁ > i-C₄H₉ > n-C₄H₉.     

Analysis of Melting Particle Model and Microwave and MM-Wave Scatterings Due to a Melting Layer of Precipitation

In this paper, the water-coated snow sphere model of melting particles has been given. Based on this model, the scattering properties and albedo w₀ of melting particles have been calculated by use of the coated sphere BHCOAT method. It is shown that the albedo of melting particles may be more than the raindrops and snow spheres at 5 (C-band) and 14GHz (Ku-band). The albedo of melting particles are nearly less than the equivalent mass raindrops albedo at the Ka and mm-band of f > 20GHz. These results are in agreement with the conclusion radar observed and literature given^[1,2]. It demonstrates that the water-coated snow sphere model of melting particles is appropriate and practicable. The study is significant for the utilization of the low fade margin system in satellite communication.     

Influence of isotopic substitution on spectral and structural parameters of an isolated [F(HF)<Subscript>2</Subscript>]— complex. Substitution of a proton by a kaon and a triton

This paper continues the theoretical study (see V. P. Bulychev and M. V. Buturlimova, J. Mol. Struct. 928, 32 (2009)) of the isotopic effects in the H-bonded anionic complex [F(HF)₂]-. Isotopomers of the complex with significant differences between the masses of the light atoms are considered. The four-dimensional anharmonic vibrational problem are solved by the variational method for the symmetric complex [F(KaF)₂]-, in which both protons are substituted by a positive kaon (positive K-meson), and for the asymmetric complex [FKaFTF]-. Variables related to the changes in the lengths of molecular fragments LF (L = Ka and T) and the distances between the F^- anion and the centers of mass of LF are used as the vibra-tional coordinates. The potential energy surfaces are calculated in the MP2/6-311++G(3df,3pd) approximation taking into account the basis set superposition error. The vibrational energy levels, frequencies, and absolute intensities for spectral transitions are determined. To study the isotope effect on the geometrical parameters of the complex, the values of internuclear separations and the asymmetry parameter of the F^-…L-F bridge averaged over the ground state and several excited vibrational states are calculated, as well as their standard deviations. The calculated results are compared to the data obtained previously for the symmetric complexes [F(HF)₂]^-, [F(DF)₂]^-, and [F(TF)₂]^-.     

Constrained path calculations of the <Superscript>4</Superscript><Emphasis Type="Italic">He</Emphasis> and <Superscript>16</Superscript><Emphasis Type="Italic">O</Emphasis> nuclei

We give results for the energy of the ⁴He and ¹⁶O nuclei using the auxiliary field diffusion Monte Carlo and a path constraint. We compare the results with previous FHNC and cluster Monte Carlo calculations.Received: 1 November 2002, Published online: 15 July 2003PACS: 21.10.Dr Binding energies and masses - 21.60.Ka Monte Carlo models     

Implications for Cognitive Quantum Computation and Decoherence Limits in the Presence of Large Extra Dimensions

An interdisciplinary physical theory of emergent consciousness has previously been proposed, stemming from quantum computation-like behavior between 10⁹ or more entangled molecular qubit states (microtubulin). This model relies on the Penrose-Diósi gravity-driven wavefunction collapse framework, and thus is subject to any secondary classical and quantum gravity effects. Specifically, if large extra spatial dimensions exist in the Universe, then the resulting corrections to Newtonian gravity cause this model to suffer serious difficulties. It is shown that if the extra dimensions are larger than 100 fm in size, then this model of consciousness is unphysical. If the dimensions are on the order of 10 fm in size, then a significantly smaller number of microtubulin than originally predicted are required to satisfy experimental constraints. Some speculation on evolution of consciousness is also offered, based on the possibility that the size of these extra dimensions may have been changing over the history of the Universe. PACS numbers: 87.16.Ka, 03.67.Lx, 04.50.+h.