Dynamic responses of orthotropic plates under moving masses

Summary The problem considered is that of heavy masses moving on lightweight rectangular plates of orthotropic materials, slated for use in space structures. The dynamic equation of motion for orthotropic plates which contains singularities in both space and time variables is first presented. The response is expressed as a summation of double series of eigenfunctions. The equation of motion is transformed into an integro-differential equation for modal amplitudes using the Green's function. The Green's function is chosen to satisfy the initial conditions, the boundary conditions, and the transient conditions due to the moving masses. The solution series exhibits a good convergence. The effect of orthotropicity on natural frequencies and dynamic responses is demonstrated.

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Dynamische Antwort orthotroper Platten auf bewegte Massenpunkte

übersicht Behandelt wird die Bewegung von Massenpunkten auf rechteckigen Leichtbau-Platten aus orthotropem Werkstoff, die für Raumfahrtkonstruktionen vorgesehen sind. ZunÄchst wird die Bewegungsgleichung orthotroper Platten mit singulÄren Ausdrücken in den Raum- und Zeitkoordinaten angegeben. Die Antwort wird als Doppelsumme einer zweifachen Reihenentwicklung dargestellt und die Bewegungsgleichung mit Hilfe der Greenschen Funktion in eine Integro-Differentialgleichung für die Modalamplituden transformiert. Die Greensche Funktion ist so gewÄhlt, da\ sie die Anfangs- und Randbedingungen sowie die übergangsbedingungen unter der bewegten Masse erfüllt. Die Lösung durch Reihenentwicklung zeigt gute Konvergenz. Der Einflu\ der Orthotropie auf die Eigenfrequenzen und die dynamischen Antworten wird veranschaulicht.

     

Colour intransparency and the cross sections for colour-singlet and colour-octet hadrons in the Low-Nussinov model

The dependence of cross sections on the colour state of the colliding hadrons is investigated within the Low-Nussinov model of two-gluon exchange. The total cross sections for colour-octet hadrons are practically constant as functions of the hadronic radii, while they tend to zero when the radii of the colour-singlet hadrons approach zero. The slope parameter of the differential clastic cross sections for small momentum transfers is rather insensitive to the colour structure of the colliding hadrons. The integrated colour exchange cross section is calculated.     

Advection of a passive vector field by the Gaussian velocity field with finite correlations in time

Using the field theoretic renormalization group technique the model of a passive vector field advected by an incompressible turbulent flow is investigated up to the second order of the perturbation theory (two-loop approximation). The turbulent environment is given by statistical fluctuations of the velocity field that has a Gaussian distribution with zero mean and defined noise with finite correlations in time. Two-loop analysis of all possible scaling regimes in general d-dimensional space is done in the plane of exponents ? ? η, where ? characterizes the energy spectrum of the velocity field in the inertial range E ∝ k ^{1 ? 2ε}, and η is related to the correlation time at the wave number k which is scaled as k ^{?2 + η}. It is shown that the scaling regimes of the present model of vector advection have essentially different properties than the scaling regimes of the corresponding model of passively advected scalar quantity. The results demonstrate the fact that within the present model of passively advected vector field the internal tensor structure of the advected field can have nontrivial impact on the diffusion processes deep inside in the inertial interval of given turbulent flow.     

Mass Power Spectrum in a Universe Dominated by the Chaplygin Gas

The mass power spectrum for a Universe dominated by the Chaplygin gas is evaluated numerically from scales of the order of the Hubble horizon to 100 Mpc. The results are compared with a pure baryonic Universe and a cosmological constant model. In all three cases, the spectrum increases with k, the wavenumber of the perturbations. The slope of the spectrum is higher for the baryonic model and smaller for the cosmological constant model, the Chaplygin gas interpolating these two models. The results are analyzed in terms of the sound velocity of the Chaplygin gas and the moment the Universe begins to accelerate.     

Localized proton spectroscopy without water suppression: removal of gradient induced frequency modulations by modulus signal selection

Most Magnetic Resonance Spectroscopy (MRS) localization methods can generate gradient vibrations at acoustic frequencies and/or magnetic field oscillation, which can cause a time-varying magnetic field superimposed onto the static one. This effect can produce frequency modulations of the spectral resonances. When localized MRS data are acquired without water suppression, the associated frequency modulations are manifested as a manifold of spurious peaks, called sidebands, which occur symmetrically around the water resonance. These sidebands can be larger than the small metabolite resonances and can present a problem for the quantitation of the spectra, especially at short echo times. Furthermore, the resonance lineshapes may be distorted if any low frequency modulations are present. A simple solution is presented which consists of selecting the modulus of the acquired Free Induction Decay (FID) signal. Since the frequency modulations affect only the phase of the FID signal, the obtained real spectrum of the modulus is free from the spurious peaks where quantitative results may be directly obtained. Using this method, the distortions caused by the sidebands are removed. This is demonstrated by processing proton MRS spectra acquired without water suppression collected from a phantom containing metabolites at concentrations comparable to those in human brain and from a human subject using two different localization methods (PRESS and Chemical Shift Imaging PRESS-(CSI)). The results obtained illustrate the ability of this approach to remove the spurious peaks. The corrected spectra can then be fit accurately. This is confirmed by the results obtained from both the relative and the absolute metabolites concentrations in phantoms and in vivo.     

Mössbauer study of Brazilian soapstone

Steatite mineral rocks, soapstone, have been studied by X-ray diffraction, optical microscopic analysis (modal analysis), electron probe micro analysis and Mössbauer spectroscopy for characterization, mineral percentages and chemical composition. Mössbauer spectra show both, magnetic interactions corresponding to magnetite and doublets corresponding to talc. chlorite, dolomite and tremolite. The temperature dependence of the quadrupole splitting in dolomite has been explained in terms of crystal field interaction.