Alternatives for jet engine control

Alternatives to linear quadratic regulator theory in the linear case are examined along with nonlinear modelling and optimization approaches for global control. Context for the studies has been set by the DYNGEN digital simulator and by models generated for various phases of the F100 Multivariable Control Synthesis Program. With respect to the linear alternatives, the multivariable frequency domain is stressed. Progress is reported in both the direct algebraic approach to exact model matching, by means of stimulating work on the basic computational issues, and in the indirect generalized Nyquist approach. With respect to nonlinear modelling and optimization, the emphasis is twofold: the development of analytical nonlinear models of the jet engine and the use of these models in conjunction with techniques of mathematical programming in order to study global control over nonincremental portions of the flight envelope. The possibility of using tensor methods is explored

Influence of Phase Matching on the Cooper Minimum in Ar High Harmonic Spectra

We study the influence of phase matching on interference minima in high harmonic spectra. We concentrate on structures in atoms due to interference of different angular momentum channels during recombination. We use the Cooper minimum (CM) in argon at 47 eV as a marker in the harmonic spectrum. We measure 2d harmonic spectra in argon as a function of wavelength and angular divergence. While we identify a clear CM in the spectrum when the target gas jet is placed after the laser focus, we find that the appearance of the CM varies with angular divergence and can even be completely washed out when the gas jet is placed closer to the focus. We also show that the argon CM appears at different wavelengths in harmonic and photo-absorption spectra measured under conditions independent of any wavelength calibration. We model the experiment with a simulation based on coupled solutions of the time-dependent Schr\"odinger equation and the Maxwell wave equation, including both the single atom response and macroscopic effects of propagation. The single atom calculations confirm that the ground state of argon can be represented by its field free $p$ symmetry, despite the strong laser field used in high harmonic generation. Because of this, the CM structure in the harmonic spectrum can be described as the interference of continuum $s$ and $d$ channels, whose relative phase jumps by $\pi$ at the CM energy, resulting in a minimum shifted from the photoionization result. We also show that the full calculations reproduce the dependence of the CM on the macroscopic conditions. We calculate simple phase matching factors as a function of harmonic order and explain our experimental and theoretical observation in terms of the effect of phase matching on the shape of the harmonic spectrum. Phase matching must be taken into account to fully understand spectral features related to HHG spectroscopy

Effective Gap Equation for the Inhomogeneous LOFF Superconductive Phase

We present an approximate gap equation for different crystalline structures of the LOFF phase of high density QCD at T=0. This equation is derived by using an effective condensate term obtained by averaging the inhomogeneous condensate over distances of the order of the crystal lattice size. The approximation is expected to work better far off any second order phase transition. As a function of the difference of the chemical potentials of the up and down quarks, $\delta\mu$, we get that the octahedron is energetically favored from $\delta\mu=\Delta_0/\sqrt 2$ to $0.95\Delta_0$, where $\Delta_0$ is the gap for the homogeneous phase, while in the range $0.95\Delta_0-1.32\Delta_0$ the face centered cube prevails. At $\delta\mu=1.32\Delta_0$ a first order phase transition to the normal phase occurs.Comment: 11 pages, 5 figure

Phase Measurement of Resonant Two-Photon Ionization in Helium

We study resonant two-color two-photon ionization of Helium via the 1s3p 1P1 state. The first color is the 15th harmonic of a tunable titanium sapphire laser, while the second color is the fundamental laser radiation. Our method uses phase-locked high-order harmonics to determine the {\it phase} of the two-photon process by interferometry. The measurement of the two-photon ionization phase variation as a function of detuning from the resonance and intensity of the dressing field allows us to determine the intensity dependence of the transition energy.Comment: 4 pages, 5 figures, under consideratio

The Ginzburg-Landau Free Energy Functional of Color Superconductivity at Weak Coupling

We derive the Ginzburg-Landau free energy functional of color superconductivity in terms of the thermal diagrams of QCD in its perturbative region. The zero mode of the quadratic term coefficient yields the same transition temperature, including the pre-exponential factor, as the one obtained previously from the Fredholm determinant of the two quark scattering amplitude. All coefficients of the free energy can be made identical to those of a BCS model by setting the Fermi velocity of the latter equal to the speed of light. We also calculate the induced symmetric color condensate near $T_c$ and find that it scales as the cubic power of the dominant antisymmetric color component. We show that in the presence of an inhomogeneity and a nonzero gauge potential, while the color-flavor locked condensate dominates in the bulk, the unlocked condensate, the octet, emerges as a result of a simultaneous color-flavor rotation in the core region of a vortex filament or at the junction of super and normal phases.Comment: 32 pages, Plain Tex, 3 figure

Constituent quark model for baryons with strong quark-pair correlations and non-leptonic weak transitions of hyperon

We study the roles of quark-pair correlations for baryon properties, in particular on non-leptonic weak decay of hyperons. We construct the quark wave function of baryons by solving the three body problem explicitly with confinement force and the short range attraction for a pair of quarks with their total spin being 0. We show that the existence of the strong quark-quark correlations enhances the non-leptonic transition amplitudes which is consistent with the data, while the baryon masses and radii are kept to the experiment.Comment: 4 pages, 2 figures, talk presented at KEK-Tanashi International Symposium on Physics of Hadrons and Nuclei, Tokyo, Japan, 14-17 Dec. 199

Thermodynamic properties of QCD in external magnetic fields

We consider the effect of strong external electromagnetic fields on thermodynamic observables in QCD, through lattice simulations with 1+1+1 flavors of staggered quarks at physical quark masses. Continuum extrapolated results are presented for the light quark condensates and for their tensor polarizations, as functions of the temperature and the magnetic field. We find the light condensates to undergo inverse magnetic catalysis in the transition region, in a manner that the transition temperature decreases with growing magnetic field. We also compare the results to other approaches and lattice simulations. Furthermore, we relate the tensor polarization to the spin part of the magnetic susceptibility of the QCD vacuum, and show that this contribution is diamagnetic.Comment: 13 pages, 9 figures, talks presented by FB and GE at Xth Quark Confinement and the Hadron Spectrum, 8-12 October 2012, TUM Campus Garching, Munich, German

Above threshold ionization by few-cycle spatially inhomogeneous fields

We present theoretical studies of above threshold ionization (ATI) produced by spatially inhomogeneous fields. This kind of field appears as a result of the illumination of plasmonic nanostructures and metal nanoparticles with a short laser pulse. We use the time-dependent Schr\"odinger equation (TDSE) in reduced dimensions to understand and characterize the ATI features in these fields. It is demonstrated that the inhomogeneity of the laser electric field plays an important role in the ATI process and it produces appreciable modifications to the energy-resolved photoelectron spectra. In fact, our numerical simulations reveal that high energy electrons can be generated. Specifically, using a linear approximation for the spatial dependence of the enhanced plasmonic field and with a near infrared laser with intensities in the mid- 10^{14} W/cm^{2} range, we show it is possible to drive electrons with energies in the near-keV regime. Furthermore, we study how the carrier envelope phase influences the emission of ATI photoelectrons for few-cycle pulses. Our quantum mechanical calculations are supported by their classical counterparts