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Off-diagonal Elements (off-diagonal + element)
Selected AbstractsGauge-independent quantum dynamics on phase-space of charged scalar particlesFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 2-3 2003S. Varró On the basis of the Hamiltonian form of the Klein-Gordon equation of a charged scalar particle field introduced by Feshbach and Villars, the gauge-invariant 2×2 Wigner matrix has been constructed whose diagonal elements describe positive and negative charge densities and the off-diagonal elements correspond to cross-densities in phase-space. The system of coupled transport equations has been derived in case of interaction with an arbitrary external electromagnetic field. A gauge-independent generalization of the free particle representation due to Feshbach and Villars is given, and on the basis of it both the nonrelativistic and the classical limits of the general relativistic quantum Boltzmann-Vlasov equation(RQBVE) is discussed. In the non-relativistic limit (p/mc,0) the set of equations of motion decouple to two independent quantum transport equations describing the dynamics of oppositely charged positon and negaton densities separately. In the classical limit(,,0) two relativistic Boltzmann-Vlasov equations result for the diagonal positon and negaton densities. It is obtained that, though in the latter equations the Planck constant , is absent, the real part of the cross-density does not vanish. [source] Non-diagonal MIMO QFT controller design reformulationINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 9 2009Mario Garcia-Sanz Abstract This paper presents a reformulation of the full-matrix quantitative feedback theory (QFT) robust control methodology for multiple-input,multiple-output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non-diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off-diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop-by-loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd. [source] Non-diagonal controllers in MIMO quantitative feedback designINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 4 2002Edward Boje Abstract This paper discusses multivariable quantitative feedback design through the use of controllers with off-diagonal elements. Controller design for multivariable plants with significant uncertainty is simpler and potentially less conservative if some sort of dominance is achieved (by reducing the interaction effect of off-diagonal plant elements) before a diagonal (decentralized) controller design is attempted. Traditional approaches for achieving dominance are not applicable when plant uncertainty must be considered. This paper discusses parallel and series implementations and for the latter, a pseudo-Gauss elimination approach to the design has been developed. The interaction is measured using the Perron,Frobenius root of an interaction matrix. In some applications, it is possible to trade off individual plant cases against each other in order to reduce to the worst-case interaction over the entire plant set. Copyright © 2002 John Wiley & Sons, Ltd. [source] Topological Electronegativity Index and Its Application , I. Ionization Potentials of Alkyl Groups and Alkyl HalidesMOLECULAR INFORMATICS, Issue 9 2007Chenzhong Cao Abstract A Topological Electronegativity Index (TEI) for alkyl group was developed, based on the bond adjacency matrix of the radical atom. Taking the radical atom and the adjacency atoms (or groups) as the vertices of molecular graph of the alkyl group, the bond adjacency matrix was constructed, in which the diagonal elements were assigned the Pauling electronegativity of the atom (or group), and the off-diagonal elements were assigned values 1 or 0. The off-diagonal elements represent the bond connections: that is when the two atoms (or groups) connect with each other, it is 1; otherwise is 0. From the matrix, the eigenvalues were obtained and its geometric mean value was considered as the TEI of an alkyl. The calculated TEI has good correlation with its experimental ionization potential. Further, the TEI was applied to correlate with the ionization potentials of alkyl halides and substituted ethenes, and to correlate with the Bond Dissociation Energies (BDEs) of the CiH bonds in alkanes. [source] Changes in optical properties of MnAs thin films on GaAs(001) induced by ,- to ,-phase transitionPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 4 2008B. Gallas Abstract MnAs layers with 45 nm thickness were grown epitaxially on GaAs(001) substrates. Ellipsometry measurements were made in the spectral range 0.045 eV to 6 eV as a function of temperature (between ,10 °C and 50 °C) at 70° of incidence. In this way the transition from the hexagonal ,-phase to the orthorhombic ,-phase could be monitored. Non-zero off-diagonal elements of the Jones matrix for an azimuth of 38° off the [10] axis of the substrate indicate that the optical functions of MnAs are anisotropic in both phases. The optical conductivity exhibits low-energy interband transitions around 0.3 eV, more clearly seen in the ,-phase than in the ,-phase. Extrapolation of the optical conductivity to zero frequency confirms that the ,-phase is about two times more conducting than the ,-phase. A broad structure is observed in the visible range around 3 eV. The ,-phase is characterised by an anisotropy induced energy difference of this structure with a maximum at 2.8 eV for the extraordinary index and at 3.15 eV for the ordinary index. This difference vanishes in the ,-phase in which anisotropy mainly induces changes in amplitude of the 3 eV structure. The assignment of the structures will be discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Monitoring the ,- to ,-phase transition in MnAs/GaAs(001) thin films as function of temperaturePHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 4 2008B. Gallas Abstract MnAs layers with a 5 nm thick amorphous GaAs capping layer were grown epitaxially on GaAs(001). Generalized ellipsometric measurements were made on a 45 nm thick layer in the spectral range 1.5,4 eV at temperatures between ,10 °C and 50 °C in steps of 5 °C. By using both the diagonal and off-diagonal elements of the Jones matrix, the in-plane unixial anisotropy of MnAs was determined in terms of the ordinary and extraordinary complex dielectric functions. The measurements at each temperature could be well reproduced by modeling using the optical properties of the two limiting phases ,-MnAs and ,-MnAs determined at ,10 °C and 50 °C, respectively. The best sensitivity to the volume fractions of the two phases was obtained near 2.2 eV by monitoring the generalized ellipsometric parameter ,p for which the variations reached 30°. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||