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Using a previously developed semiclassical theory of electronic excitations, the cross sections that result from potential-curve crossings are calculated for a model system. The phenomena appearing in the differential cross sections are displayed and discussed.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photoelectron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The study of charge changing cross sections of fast ions colliding with matter provides the fundamental basis for the analysis of the charge states produced in such interactions. Given the high degree of complexity of the phenomena, there is no theoretical treatment able to give a comprehensive description. In fact, the involved processes are very dependent on the basic parameters of the projectile, such as velocity charge state, and atomic number, and on the target parameters, the physical state (molecular, atomic or ionized matter) and density. The target velocity, may have also incidence on the process, through the temperature of the traversed medium. In addition, multiple electron transfer in single collisions intrincates more the phenomena. Though, in simplified cases, such as protons moving through atomic hydrogen, considerable agreement has been obtained between theory and experiments However, in general the available theoretical approaches have only limited validity in restricted regions of the basic parameters. Since most measurements of charge changing cross sections are performed in atomic matter at ambient temperature, models are commonly based on the assumption of targets at rest, however at Astrophysical scales, temperature displays a wide range in atomic and ionized matter. Therefore, due to the lack of experimental data , an attempt is made here to quantify temperature dependent cross sections on basis to somewhat arbitrary, but physically reasonable assumptions.
We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.
The prediction of rotordynamic coefficients for gas seals is achieved with the aid of a two-volume bulk flow model based on turbulent rotationally symmetric 3D flow calculations including swirl flow. Comparison of cross-coupling and damping coefficients with measurements confirm this approach. In particular the theoretically predicted phenomenon that labyrinth damping is retained without inlet swirl is confirmed. This is important for the design of high pressure compressors, where labyrinth damping is a major contribution improving rotor stability. Discrepancies are found when comparing theory with measured direct stiffness and the cross-coupling damping coefficients. First measurements of labyrinth seals on a recently installed test rig operated with water are presented. Since forces are larger than on test stands operated with air and since individual chamber forces are obtained phenomena like inlet effects may be studied.
The theory of acoustic plane wave normally incident on a clamped panel in a rectangular duct is developed. The coupling theory between the elastic vibrations of the panel (plate) and the acoustic wave propagation in infinite space and in the rectangular duct is considered. The partial differential equation which governs the vibration of the panel (plate) is modified by adding to its stiffness (spring) forces and damping forces, and the fundamental resonance frequency and the attenuation factor are discussed. The noise reduction expression based on the theory is found to agree well with the corresponding experimental data of a sample aluminum panel in the mass controlled region, the damping controlled region, and the stiffness controlled region. All the frequency positions of the upward and downward resonance spikes in the sample experimental data are identified theoretically as resulting from four cross interacting major resonance phenomena: the cavity resonance, the acoustic resonance, the plate resonance, and the wooden back panel resonance.
Linear stability theory results are presented for flight and low-disturbance wind tunnels, at low and high speeds, and for T-S, Gortler, and cross-flow modes. Results show that, in the absence of Morkovin 'bypasses', transition at low background disturbance levels corresponds to N-factors of the order of 9 to 11, provided that phenomena such as curvature effects are included. The results point to a wider range of applicability for the e exp N method than previously conjectured, and suggest that the e exp N method can be used to parametrize transition predictions as a function of parameters which affect the mean flow profiles for such purposes as LFC and minimum drag design.
The concept of how magnetosheath plasma can cross the magnetopause is one of the key elements for a global view of the magnetosphere. According to this view, viscous interaction is the main process to produce convection of plasma in the magnetotail, resulting in auroral phenomena, and other related processes. The mechanism is illustrated herein. The key element is that the electric field is not constant, as assumed in reconnection theories, but reverse within the magnetopause current sheet. Particles, representing magnetosheath ions were traced as they impinge upon the magnetopause.
The behaviors of the near- and far-field two-lobe radiation patterns from a circular-core two-mode fiber are studied by using both the mode and Kirchhoff diffraction theories. The electric field outside the output endface of the fiber is derived from the electric field distribution of the LP sub 01 and LP sub 11 modes at the fiber endface using the Kirchhoff diffraction formula. Different phenomena are studied by solving this expression numerically at near-and far-fields. The Gouy phase shifts are quantitatively evaluated at cross-sections of the near field. The results reveal the distortion and dislocation of the far-field two-lobe pattern induced by an inclination angle of the fiber endface.
Closed-form expressions and tables composed from these expressions are presented for complete and partial conic and spheric bodies at combined angles of attack and sideslip in Newtonian flow. Aerodynamic coefficients of these bodies are tabulated for various body segments over a range of angles of attack from 1 deg to 85 deg and angles of sideslip from 0 deg to 15 deg. Some comparisons between Newtonian predictions and hypersonic experimental aerodynamic characteristics were made for conic bodies hawing various surface slopes, nose bluntnesses, and body cross sections to indicate the range of validity of the theory. In general, the theory is shown to agree quite well with experimental results for sharp-nose complete cones and for configurations hawing large blunted noses and steep surface slopes. However, agreement between theory and experiment generally is poor for the more slender, slightly blunted complete or half conic bodies and also for sharp-nose half conic bodies where real-flow phenomena such as forebody interference, viscous forces, leeward surface contributions, or leading-edge pressure reductions may have significant effect. The agreement between theory and experiment for the bodies considered can be improved by using the stagnation pressure coefficient behind a normal shock rather than 2 as the Newtonian coefficient, although for the sharp-nose half conic bodies there i s no theoretical justification for this modification.
The effects of material damage on the aeroelastic response of an anisotropic composite wing are investigated analytically. The wing is modeled as a Timoshenko beam of arbitrary cross section, applying a 24-DOF one-dimensional beam element and Cartesian coordinates. The formulations for the element stiffness matrix, the strain-displacement relations, the box-beam constitutive relations, the contributions of stringers and web, and the warping correction factor are outlined; the application of strip theory in deriving the aerodynamic model is briefly explained; and numerical results are presented in extensive graphs. It is shown that asymmetry and damage can induce bending-stretching coupling phenomena and thereby affect the stability of the aircraft either positively or negatively. The need to take such effects into account in the design of advanced composite wings is stressed.
Various aspects of radar cross-section (RCS) techniques are summarized, with emphasis placed on fundamental electromagnetic phenomena, such as plane and spherical wave formulations, and the definition of RCS is given in the far-field sense. The basic relationship between electronic countermeasures and a signature level is discussed in terms of the detectability range of a target vehicle. Fundamental radar-signature analysis techniques, such as the physical-optics and geometrical-optics approximations, are presented along with examples in terms of aircraft components. Methods of analysis based on the geometrical theory of diffraction are considered and various wave-propagation phenomena are related to local vehicle geometry. Typical vehicle components are also discussed, together with their contribution to total vehicle RCS and their individual signature sensitivities.
This review deals with the propagation of waves, especially radio waves in the ionosphere. In the macroscopic electromagnetic theory, the mathematical structure of wave propagation problems depends entirely on the properties of the dielectric operator in a magnetically nonpermeable medium. These properties can be deduced from general discussions of symmetry and considerations of physical principles. When the medium is specifically the ionosphere, various physical phenomena may occur. Because of a large number of parameters, it is desirable to define a parameter space. A point in the parameter space corresponds to a specific plasma. The parameter space is subdivided into regions whose boundaries correspond to conditions of resonance and cutoff. As the point crosses these boundaries, the refractive index surface transforms continuously.
The linear stability properties of collisionless drift instabilities are analyzed in a Harris equilibrium model of the plasma sheet boundary layer (PSBL). The strearmng ions with drift-type instabilities driven in the PSBL are considered. The fluid approximation leads to growth but predicts that the mode width approaches the gyroradius of the energetic ions. Thus an integral equation theory for the modes is developed taking into account that in the PSBL the curvature drift is weak compared with the grad-B drift. The exact wave particle resonance is kept in the nonlocal response functions. Plasma density, temperature, and magnetic gradient drift motions are taken into account. The drift modes produce an anomalous cross-field momentum transport mixing the PSBL ions on the time scale of tens of seconds. A nonlinear simulation is performed which shows the coalescence of the small scale, fast growing modes into large-scale vortices. The relation between these collective modes and plasma sheet transport phenomena is discussed including the comparison with the competing plasma mixing from single-particle stochasticity.
Testing of wind-tunnel aeroelastic models is a well established, widely used means of studying flutter trends, validating theory and investigating flutter margins of safety of new vehicle designs. The Langley Transonic Dynamics Tunnel was designed specifically for work on dynamics and aeroelastic problems of aircraft and space vehicles. A cross section of aeroelastic research and testing in the facility since it became operational more than two decades ago is presented. Examples selected from a large store of experience illustrate the nature and purpose of some major areas of work performed in the tunnel. These areas include: specialized experimental techniques; development testing of new aircraft and launch vehicle designs; evaluation of proposed "fixes" to solve aeroelastic problems uncovered during development testing; study of unexpected aeroelastic phenomena (i.e., "surprises"); control of aeroelastic effects by active and passive means; and, finally, fundamental research involving measurement of unsteady pressures on oscillating wings and control surface.
On May 15, 1969, Ogo 5 crossed the plasmapause during a major storm that produced severe geomagnetic disturbances (Kp up to 8-), large and rapid variations in ring-current intensity (as measured by Dst), intense low-latitude aurora, and persistent SAR arcs. Near the highly structured plasmasphere boundary, the electric- and magnetic-field sensors on Ogo 5 detected lower-hybrid-resonance noise bursts, whistlers, ELF hiss, and other discrete signals or emissions. Some LHR noise bursts were associated with whistlers, and these high-altitude phenomena resembled the corresponding ionospheric ones. This report contains a description of the VLF observations. We also show that intense ULF magnetic signals were present near the plasmapause, and we attempt to relate these observations to the predictions of various theories of proton ring-current decay and SAR-arc formation.
A theoretical prediction is given of the flow through thick perforated walls of low porosity resulting from the impingement of a moderately strong traveling shock wave. The model was a flat plate positioned normal to the direction of the flow. Holes bored in the plate parallel to the direction of the flow provided nominal hole length-to-diameter ratios of 10:1 and an axial porosity of 25 percent of the flow channel cross section. The flow field behind the reflected shock wave was assumed to behave as a reservoir producing a quasi-steady duct flow through the model. Rayleigh and Fanno duct flow theoretical computations for each of three possible auxiliary wave patterns that can be associated with the transmitted shock (to satisfy contact surface compatibility) were used to provide bounding solutions as an alternative to the more complex influence coefficients method. Qualitative and quantitative behavior was verified in a 1.5- by 2.0-in. helium shock tube. High speed Schlieren photography, piezoelectric pressure-time histories, and electronic-counter wave speed measurements were used to assess the extent of correlation with the theoretical flow models. Reduced data indicated the adequacy of the bounding theory approach to predict wave phenomena and quantitative response.