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Real Part (real + part)
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] Consistency of the spatial autocorrelation method with seismic interferometry and its consequenceGEOPHYSICAL PROSPECTING, Issue 3 2008Toshiaki Yokoi ABSTRACT We have cross-checked the conventional theory of the spatial autocorrelation method and the consequence of seismic interferometry: the retrieval of the elastodynamic Green's function. Their mutual consistency is almost complete. The basic formulas of the conventional spatial autocorrelation theory can be derived by an alternative approach based on the retrieval of the elastodynamic Green's function. The only discrepancy is found with the average of the complex coherence function over azimuth in a wavefield dependent on azimuth. It is hypothesized, in discussion, that this discrepancy is due to the way of representing the wavefield in the background theory of seismic interferometry that can produce only wavefields moderately dependent on azimuth and that the mentioned consequence of seismic interferometry can also only make sense in a wavefield moderately dependent on azimuth. Our field experiment with a wavefield dependent on azimuth showed that the consequence of seismic interferometry in the logical framework of the conventional spatial autocorrelation theory is appropriate under such degrees of approximation as the measure proposed in this study, i.e., the deviation of the total dispersion curves is between about 10 and 16 per cent at the maximum from those averaged over azimuth. The acceptance of the retrieval of Green's function gives a proper physical meaning to the complex coherence function: the real part of the elastodynamic Green's function normalized by its zero-offset version. This makes it possible to take a deterministic approach rather than the statistical one on which the conventional spatial autocorrelation method is based and gives fruitful new aspects and perspectives. For example, the formula for the multi-mode case is given and the possibility of exploration of two or three dimensional velocity structures is suggested. [source] A field test of imaging properties of rotational invariants of the magnetotelluric impedance tensorGEOPHYSICAL PROSPECTING, Issue 3 2005László Szarka ABSTRACT A part of the Békés Basin (an extensional sub-basin of the Pannonian Basin, where the basement under thick Pannonian sediments is well known from deep boreholes and from seismic measurements, and where many magnetotelluric (MT) soundings have been carried out for frequencies ranging from 1 to 10,3 Hz) was selected as a test area to assess the imaging performances of various apparent-resistivity definitions computed with rotational invariants of either the real part of the complex impedance tensor, or its imaginary part, or both. A comparison (based on earlier 3D numerical studies) has been made between the magnetotelluric images obtained in this way and the depths to the high-resistivity basement, as known from boreholes and seismic investigations. The correlation coefficient between the series of basement depth values at 39 MT sites and the apparent-resistivity values was found to be stronger and high correlation appeared at a shorter period when it was computed with apparent resistivities based on the real tensor rather than with apparent resistivities based on the imaginary tensor. In the light of our studies, ,ReZ and the impedance phase seem to be more informative than any other combination of magnetotelluric interpretation parameters. [source] Modelling of GPR waves for lossy media obeying a complex power law of frequency for dielectric permittivityGEOPHYSICAL PROSPECTING, Issue 1 2004Maksim Bano ABSTRACT The attenuation of ground-penetrating radar (GPR) energy in the subsurface decreases and shifts the amplitude spectrum of the radar pulse to lower frequencies (absorption) with increasing traveltime and causes also a distortion of wavelet phase (dispersion). The attenuation is often expressed by the quality factor Q. For GPR studies, Q can be estimated from the ratio of the real part to the imaginary part of the dielectric permittivity. We consider a complex power function of frequency for the dielectric permittivity, and show that this dielectric response corresponds to a frequency-independent- Q or simply a constant- Q model. The phase velocity (dispersion relationship) and the absorption coefficient of electromagnetic waves also obey a frequency power law. This approach is easy to use in the frequency domain and the wave propagation can be described by two parameters only, for example Q and the phase velocity at an arbitrary reference frequency. This simplicity makes it practical for any inversion technique. Furthermore, by using the Hilbert transform relating the velocity and the absorption coefficient (which obeys a frequency power law), we find the same dispersion relationship for the phase velocity. Both approaches are valid for a constant value of Q over a restricted frequency-bandwidth, and are applicable in a material that is assumed to have no instantaneous dielectric response. Many GPR profiles acquired in a dry aeolian environment have shown a strong reflectivity inside dunes. Changes in water content are believed to be the origin of this reflectivity. We model the radar reflections from the bottom of a dry aeolian dune using the 1D wavelet modelling method. We discuss the choice of the reference wavelet in this modelling approach. A trial-and-error match of modelled and observed data was performed to estimate the optimum set of parameters characterizing the materials composing the site. Additionally, by combining the complex refractive index method (CRIM) and/or Topp equations for the bulk permittivity (dielectric constant) of moist sandy soils with a frequency power law for the dielectric response, we introduce them into the expression for the reflection coefficient. Using this method, we can estimate the water content and explain its effect on the reflection coefficient and on wavelet modelling. [source] Photonic Crystal Formed by the Imaginary Part of the Refractive IndexADVANCED MATERIALS, Issue 24 2010Juntao Li A periodic array of dye-doped disks that form a 2D photonic lattice is fabricated and characterized. The array was generated by interference lithography, and the voids of the template were filled by SU8 without doping. This creates a photonic lattice with a uniform real part of the refractive index, but a periodically modulated imaginary part. The structure is characterized by diffraction measurements; the structure only diffracts light in the spectral range where the dye absorbs, hence acts like a truly imaginary index photonic crystal. [source] Passive rational fitting of a network transfer function from its real partINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2008Anne Y. Woo Abstract A methodology is presented for the rational function approximation of a passive network function from sampled values of its real part over the bandwidth of interest. The accuracy and validity of the proposed methodology are demonstrated through its application to the fitting of several broadband, multiport transfer functions. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008. [source] Nonlocal stabilization via delayed relay control rejecting uncertainty in a time delayINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 1 2004L. Fridman Abstract Sufficient conditions for a robust relay delayed non-local stabilization of linear systems are found, which relate the upper bound of an uncertainty in a time delay and the maximum of the real part of system spectrum. Algorithm of delayed relay control gain adaptation for non-local stabilization is suggested. The proposed algorithm suppresses bounded uncertainties in the time delay: once this relay delayed control law for the upper bound of uncertainty in the time delay for given system is designed, we ensure non-local stabilization for all values of the time delay less than the upper bound even in the case of a variable delay. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical studies of optical switching and optical bistability phenomena of nano- or meso-size spheresJOURNAL OF MICROSCOPY, Issue 3 2003T. Okamoto Summary We propose the use of numerical calculations of the optical response of nonlinear Kerr-spheres, modifying the Mie theory. As a numerical example, we use a CuCl sphere coated with a Kerr-nonlinear sphere, taking into account the excitation of the Z3 -exciton. The results clearly show that optical bistable and/or optical switching devices can be realized on a nano- and meso-size scale when the real part of the dielectric constant of CuCl is negative. [source] Dielectric properties of (NH4)2SO4 crystals in the range of electronic excitationsJOURNAL OF SYNCHROTRON RADIATION, Issue 2 2009B. Andriyevsky Spectra of the real and imaginary parts of the pseudo-dielectric permittivity, ,,1,(E) and ,,2,(E), of ferroelectric ammonium sulfate crystals, (NH4)2SO4, have been measured in the range of electronic excitations 4.0 to 9.5,eV by ellipsometry using synchrotron radiation. Temperature dependences of the corresponding susceptibilities, ,,1,(T) and ,,2,(T), obtained for the photon energy E = 8.5,eV, related to excitations of oxygen p -electrons, reveal sharp peak-like temperature changes near the Curie point TC = 223,K. The large temperature-dependent increase of the imaginary part of the susceptibility ,2(T), together with a simultaneous decrease of the real part of the susceptibility ,1(T), take place at the phase transition. These anomalies have been ascribed mainly to the SO4 group of the crystal structure. [source] On the noise correlation matrix for multiple radio frequency coilsMAGNETIC RESONANCE IN MEDICINE, Issue 2 2007Ryan Brown Abstract Noise correlation between multiple receiver coils is discussed using principles of statistical physics. Using the general fluctuation-dissipation theorem we derive the prototypic correlation formula originally determined by Redpath (Magn Res Med 1992;24:85,89), which states that correlation of current spectral noise depends on the real part of the inverse impedance matrix at a given frequency. A distinct correlation formula is also derived using the canonical partition function, which states that correlation of total current noise over the entire frequency spectrum depends on the inverse inductance matrix. The Kramers-Kronig relation is used to equate the inverse inductance matrix to the spectral integral of the inverse impedance matrix, implying that the total noise is equal to the summation of the spectral noise over the entire frequency spectrum. Previous conflicting arguments on noise correlation may be reconciled by differentiating between spectral and total noise correlation. These theoretical derivations are verified experimentally using two-coil arrays. Magn Reson Med 58:218,224, 2007. © 2007 Wiley-Liss, Inc. [source] Microwave dielectric properties of NiFe2O4 nanoparticles ferritesMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2007C. P. L. Rubinger Abstract Nickel ferrite (NiFe2O4) was synthesized by the micelles mixing method, using lyophilized coconut oil. The method leads to the formation of ferrite nanoparticles. Nickel ferrite was prepared in coconut oil suspension and annealed during 4 h, at 400, 600, 800, 1000, and 1200°C. The X-ray diffraction (XRD) was applied to investigate the nanoparticle size dependence on the annealing temperature. Complex permittivity measurements were carried out in cavity resonators at 5.0 and 9.0 GHz, using the small perturbation theory. The main result is that the real part of the permittivity decreases with increasing annealing temperatures (3.6,2.4), while the imaginary part of the permittivity varies only for the lowest annealing temperatures, remaining low for the other samples (about 10,3). The X-ray diffractograms indicates that the nanoparticle size increase with annealing temperature, allowed the correlation between the nanoparticle size and the observed microwave dielectric response. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1341,1343, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22402 [source] Microwave dielectric properties of polybutylene terephtalate (PBT) with carbon black particlesMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 1 2005L. C. Costa Abstract The synthesis of composites based on polymers containing carbon as additives is rather relevant because it has been found that applications in several industries are increasing, particularly due to their unusual mechanical and electrical properties. By choosing the adequate doping concentrations, we can precisely control the electrical properties in the microwave frequencies, in order to tailor the desired behavior. In this study, we present the results of the complex-permittivity measurements, ,* = ,, , í ,,, at 2.7, 5, and 12.8 GHz, on polybutylene terephtalate (PBT), with different concentration of black carbon particles, using the resonant-cavity method. Measuring the shift in the resonant frequency of the cavity, ,f, caused by the insertion of the sample, we can calculate to the real part of the complex permittivity, ,,, while the measure of the change in the inverse of the quality factor of the cavity, ,(1/Q), allow us to calculate the imaginary part, ,,. Maxwell,Wagner,Sillars (MWS) and Looyenga mixture laws are applied to the obtained results. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 46: 61,63, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20901 [source] One-dimensional disordered magnetic Ising systems: A new approachPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 9 2009Vladimir Gasparian Abstract We reconsider the problem of a one-dimensional Ising model with an arbitrary nearest-neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest-neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of , -function potentials. [source] Population inversion of photoexcited electrons and holes in graphene and its negative terahertz conductivityPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2008Victor Ryzhii Abstract We demonstrate that sufficiently strong optical excitation may result in the population inversion in graphene, so that the real part of the ac conductivity can be negative in the terahertz range of frequencies. We study also how the heating of the electron-hole system influences the effect of negative ac conductivity. The effect of population inversion and negative ac conductivity might be used in graphene-based coherent sources of terahertz electromagnetic radiation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Seismic reflection coefficients of faults at low frequencies: a model studyGEOPHYSICAL PROSPECTING, Issue 3 2008Joost Van Der Neut ABSTRACT We use linear slip theory to evaluate seismic reflections at non-welded interfaces, such as faults or fractures, sandwiched between general anisotropic media and show that at low frequencies the real parts of the reflection coefficients can be approximated by the responses of equivalent welded interfaces, whereas the imaginary parts can be related directly to the interface compliances. The imaginary parts of low frequency seismic reflection coefficients at fault zones can be used to estimate the interface compliances, which can be related to fault properties upon using a fault model. At normal incidence the expressions uncouple and the complex-valued P-wave reflection coefficient can be related linearly to the normal compliance. As the normal compliance is highly sensitive to the infill of the interface, it can be used for gas/fluid identification in the fault plane. Alternatively, the tangential compliance of a fault can be estimated from the complex-valued S-wave reflection coefficient. The tangential compliance can provide information on the crack density in a fault zone. Coupling compliances can be identified and quantified by the observation of PS conversion at normal incidence, with a comparable linear relationship. [source] Asymptotic and spectral analysis of non-selfadjoint operators generated by a filament model with a critical value of a boundary parameterMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2003Marianna A. Shubov Abstract We consider a class of non-selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non-conservative boundary conditions at one end and a heavy load at the other end. The filament has a non-constant density and is subject to a viscous damping with a non-constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. In our previous paper (Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169), we have derived the asymptotic approximations for the eigenvalues and eigenfunctions of the aforementioned non-selfadjoint operators when the boundary parameters were arbitrary complex numbers except for one specific value of one of the parameters. We call this value the critical value of the boundary parameter. It has been shown (in Mathematical Methods in the Applied Sciences 2001; 24(15) : 1139,1169) that the entire set of the eigenvalues is located in a strip parallel to the real axis. The latter property is crucial for the proof of the fact that the set of the root vectors of the operator forms a Riesz basis in the state space of the system. In the present paper, we derive the asymptotics of the spectrum exactly in the case of the critical value of the boundary parameter. We show that in this case, the asymptotics of the eigenvalues is totally different, i.e. both the imaginary and real parts of eigenvalues tend to ,as the number of an eigenvalue increases. We will show in our next paper, that as an indirect consequence of such a behaviour of the eigenvalues, the set of the root vectors of the corresponding operator is not uniformly minimal (let alone the Riesz basis property). Copyright © 2003 John Wiley & Sons, Ltd. [source] Negative phase velocity in isotropic dielectric-magnetic media via homogenizationMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 4 2005Tom G. Mackay Abstract We report on a strategy for achieving negative phase velocity (NPV) in a homogenized composite medium (HCM) conceptualized using the Bruggeman formalism. The constituent material phases of the HCM do not support NPV propagation. The HCM and its constituent phases are isotropic dielectric-magnetic media; the real parts of their permittivities/permeabilities are negative-valued, whereas the real parts of their permeabilities/permittivities are positive-valued. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 313,315, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21155 [source] A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Scott A. Sarra Abstract Differentiation matrices associated with radial basis function (RBF) collocation methods often have eigenvalues with positive real parts of significant magnitude. This prevents the use of the methods for time-dependent problems, particulary if explicit time integration schemes are employed. In this work, accuracy and eigenvalue stability of symmetric and asymmetric RBF collocation methods are numerically explored for some model hyperbolic initial boundary value problems in one and two dimensions. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 [source] | |||||||||||||||||||