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Green's Function (green + function)
Kinds of Green's Function Terms modified by Green's Function Selected AbstractsDependence of s -waves on continuous dimension: The quantum oscillator and free systemsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006K.B. Wolf Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source] Three-dimensional models of elastostatic deformation in heterogeneous media, with applications to the Eastern California Shear ZoneGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2009Sylvain Barbot SUMMARY We present a semi-analytic iterative procedure for evaluating the 3-D deformation due to faults in an arbitrarily heterogeneous elastic half-space. Spatially variable elastic properties are modelled with equivalent body forces and equivalent surface traction in a ,homogenized' elastic medium. The displacement field is obtained in the Fourier domain using a semi-analytic Green function. We apply this model to investigate the response of 3-D compliant zones (CZ) around major crustal faults to coseismic stressing by nearby earthquakes. We constrain the two elastic moduli, as well as the geometry of the fault zones by comparing the model predictions to Synthetic Aperture Radar inferferometric (InSAR) data. Our results confirm that the CZ models for the Rodman, Calico and Pinto Mountain faults in the Eastern California Shear Zone (ECSZ) can explain the coseismic InSAR data from both the Landers and the Hector Mine earthquakes. For the Pinto Mountain fault zone, InSAR data suggest a 50 per cent reduction in effective shear modulus and no significant change in Poisson's ratio compared to the ambient crust. The large wavelength of coseismic line-of-sight displacements around the Pinto Mountain fault requires a fairly wide (,1.9 km) CZ extending to a depth of at least 9 km. Best fit for the Calico CZ, north of Galway Dry Lake, is obtained for a 4 km deep structure, with a 60 per cent reduction in shear modulus, with no change in Poisson's ratio. We find that the required effective rigidity of the Calico fault zone south of Galway Dry Lake is not as low as that of the northern segment, suggesting along-strike variations of effective elastic moduli within the same fault zone. The ECSZ InSAR data is best explained by CZ models with reduction in both shear and bulk moduli. These observations suggest pervasive and widespread damage around active crustal faults. [source] A numerical method to solve the m -terms of a submerged body with forward speedINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2002W.-Y. Duan Abstract To model mathematically the problem of a rigid body moving below the free surface, a control surface surrounding the body is introduced. The linear free surface condition of the steady waves created by the moving body is satisfied. To describe the fluid flow outside this surface a potential integral equation is constructed using the Kelvin wave Green function whereas inside the surface, a source integral equation is developed adopting a simple Green function. Source strengths are determined by matching the two integral equations through continuity conditions applied to velocity potential and its normal derivatives along the control surface. After solving for the induced fluid velocity on the body surface and the control surface, an integral equation is derived involving a mixed distribution of sources and dipoles using a simple Green function and one component of the fluid velocity. The normal derivatives of the fluid velocity on the body surface, namely the m -terms, are then solved by this matching integral equation method (MIEM). Numerical results are presented for two elliptical sections moving at a prescribed Froude number and submerged depth and a sensitivity analysis undertaken to assess the influence of these parameters. Furthermore, comparisons are performed to analyse the impact of different assumptions adopted in the derivation of the m -terms. It is found that the present method is easy to use in a panel method with satisfactory numerical precision. Copyright © 2002 John Wiley & Sons, Ltd. [source] Correlation studies in weakly confining quantum dot potentialsINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 15 2008Peter Kimani Abstract We investigate the electron correlation in few-electron closed-shell atomic systems and similarly in few-electron quantum dots under weak confinement. As usual we start with restricted Hartree,Fock (HF) calculations and add electron correlation in steps in a series of approximations based on the single particle Green's function approach: (i) second-order Green function (GF); (ii) 2ph -Tamm-Dancoff approximation (TDA); and (iii) an extended version thereof which introduces ground-state correlation into the TDA. Our studies exhibit similarities and differences between weakly confined quantum dots and standard atomic systems. The calculations support the application of HF, GF, and TDA techniques in the modeling of three-dimensional quantum dot systems. The observed differences emphasize the significance of confinement and electronic features unique to quantum dots, such as the increased binding of electrons with higher angular momentum and thus,compared to atomic systems,modified shell-filling sequences. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008 [source] Role of resonances in building cross sections: Comparison between the Mittag,Leffler and the T-matrix Green function expansion approachesINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 6 2007Ksenia Shilyaeva Abstract Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S-matrix and the associated Green function. The performance of the Mittag,Leffler expansion and T-matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s -wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag,Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S-matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] Effects of dilution and disorder on magnetism in diluted spin systemsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2007Guixin Tang Abstract The influence of configurational disorder on the magnetic properties of diluted Heisenberg spin systems is studied with regard to the ferromagnetic stability of diluted magnetic semiconductors. The equation of motion of the magnon Green's function is decoupled by Tyablikov approximation. With supercell approach, the concentrations of magnetic ions are determined by the size of the supercell in which there is only one magnetic ion per supercell in our method. In order to distinguish the influence of dilution and disorder, there are two kinds of supercells being used: the diluted and ordered case and the diluted and disordered case. The configurational averaging of magnon Green function due to disorder is treated in the augmented space formalism. The random exchange integrals between two supercells are treated as a matrix. The obtained magnon spectral densities are used to calculate the temperature dependence of magnetization and Curie temperature. The results are shown as following: (i) dilution leads to increasing the averaged distance of two magnetic ions, further decreases the effective exchange integrals and is main reason to reduce Curie temperature; (ii) spatial position disorder of magnetic ions results in the dispersions of the exchange integrals between two supercells and slightly changes ferromagnetic transition temperature; (iii) the exponential damping of distance dependence obviously reduces Curie temperature and should be set carefully in any phenomenological model. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Lattice Green function for electrons in magnetic fieldPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 2 2003Maciej M. Ma Abstract The energy spectrum of electrons on a square lattice in an applied magnetic field composes the famous Hofstadter butterfly with a recursive internal subband structure. An effective method for calculating the Green function for such a system is proposed. The standard approach requires an explicit knowledge of the eigenstates and eigenenergies of the system; here we derive a Harper-like equation, that allows us to calculate the Green function for the lattice electrons in the field directly. The method is particularly useful in the weak-field regime, where the standard calculations are cumbersome. [source] Diffusion-Influenced Reversible Trapping Problem in the Presence,of,an,External FieldCHEMISTRY - AN ASIAN JOURNAL, Issue 1-2 2006Soohyung Park Abstract We investigate the field effect on the diffusion-influenced reversible trapping problem in one dimension. The exact Green function for a particle undergoing diffusive motion between two static reversible traps with a constant external field is obtained. From the Green function, we derive the various survival probabilities. Two types of trap distribution for the many-body problem are considered, the periodic and random distributions. The mean survival probability is obtained for the crossing-forbidden case for the two types of trap distribution. For the periodic distribution it decays exponentially. For the random trap distribution, similar to the irreversible case, there exists a critical field strength at which the long time asymptotic behavior undergoes a kinetic transition from the power law to exponential behaviors. The difference between equilibrium concentrations for the two types of trap distribution due to the fluctuation effect of trap concentration vanishes as the field strength increases. [source] Wigner ensemble Monte-Carlo simulation of nano-MOSFETs in degenerate conditionsPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2008D. Querlioz Abstract Wigner quasi-distribution function is an appropriate quantum mechanics formulation to study the transition from semi-classical to quantum transport in nano-devices since it can accurately describe quantum transport including the decoherence due to scatterings. We have recently developed an efficient approach to solving the Wigner transport equation using a Monte Carlo (MC) algorithm that has been applied to Resonant Tunnelling Diodes and nano-MOSFET simulation. The approach is here extended to incorporate degeneracy effects that are important in highly doped MOSFETs. The calculation is compared with Non Equilibrium Green's Function and the semi-classical Boltzmann equation. Relative importance of quantum transport and decoherent scattering is discussed at low and room temperatures. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Impact of strain on scaling of Double Gate nanoMOSFETs using NEGF approachPHYSICA STATUS SOLIDI (C) - CURRENT TOPICS IN SOLID STATE PHYSICS, Issue 1 2008A. Martinez Abstract The effect of biaxial strain on double gate (DG) nanoscaled MOSFET with channel lengths in the nanometre range is investigated using Non-Equilibrium Green's Functions (NEGF) simulations. The NEGF simulations are fully 2D in order to accurately evaluate the effects of strain in strongly confined channels. Starting with a 14 nm gate length DG MOSFET with a corresponding body thickness of 9 nm we scale the transistors to gate lengths of 10, 6 and 4 nm and body thicknesses of 6.1, 2.6 and 1.3 nm, respectively. The simulated ID-VG characteristics show 11% improvement in the oncurrent for the 14 nm gate length transistor due to the , valley splitting. This improvement in the on-current is due to separate contributions from the 2 fold and 4 fold valleys to the carrier transport. However, in the device with an extreme body thickness of 1.3 nm the strain has no impact on its performance because the strong confinement itself produces a large valley splitting. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A unified continuum representation of post-seismic relaxation mechanisms: semi-analytic models of afterslip, poroelastic rebound and viscoelastic flowGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2010Sylvain Barbot SUMMARY We present a unified continuum mechanics representation of the mechanisms believed to be commonly involved in post-seismic transients such as viscoelasticity, fault creep and poroelasticity. The time-dependent relaxation that follows an earthquake, or any other static stress perturbation, is considered in a framework of a generalized viscoelastoplastic rheology whereby some inelastic strain relaxes a physical quantity in the material. The relaxed quantity is the deviatoric stress in case of viscoelastic relaxation, the shear stress in case of creep on a fault plane and the trace of the stress tensor in case of poroelastic rebound. In this framework, the instantaneous velocity field satisfies the linear inhomogeneous Navier's equation with sources parametrized as equivalent body forces and surface tractions. We evaluate the velocity field using the Fourier-domain Green's function for an elastic half-space with surface buoyancy boundary condition. The accuracy of the proposed method is demonstrated by comparisons with finite-element simulations of viscoelastic relaxation following strike-slip and dip-slip ruptures for linear and power-law rheologies. We also present comparisons with analytic solutions for afterslip driven by coseismic stress changes. Finally, we demonstrate that the proposed method can be used to model time-dependent poroelastic rebound by adopting a viscoelastic rheology with bulk viscosity and work hardening. The proposed method allows one to model post-seismic transients that involve multiple mechanisms (afterslip, poroelastic rebound, ductile flow) with an account for the effects of gravity, non-linear rheologies and arbitrary spatial variations in inelastic properties of rocks (e.g. the effective viscosity, rate-and-state frictional parameters and poroelastic properties). [source] Required source distribution for interferometry of waves and diffusive fieldsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2009Yuanzhong Fan SUMMARY The Green's function that describes wave propagation between two receivers can be reconstructed by cross-correlation provided that the receivers are surrounded by sources on a closed surface. This technique is referred to as ,interferometry' in exploration seismology. The same technique for Green's function extraction can be applied to the solution of the diffusion equation if there are sources throughout in the volume. In practice, we have only a finite number of active sources. The issues of the required source distribution is investigated, as is the feasibility of reconstructing the Green's function of the diffusion equation using a limited number of sources within a finite volume. We study these questions for homogeneous and heterogeneous media for wave propagation and homogeneous media for diffusion using numerical simulations. These simulations show that for the used model, the angular distribution of sources is critical in wave problems in homogeneous media. In heterogeneous media, the position and size of the heterogeneous area with respect to the sources determine the required source distribution. For diffusion, the sensitivity to the sources decays from the midpoint between the two receivers. The required width of the source distribution decreases with frequency, with the result that the required source distribution for early- and late-time reconstruction is different. The derived source distribution criterion for diffusion suggests that the cross-correlation-based interferometry is difficult to apply in field condition. [source] On establishing the accuracy of noise tomography travel-time measurements in a realistic mediumGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2009Victor C. Tsai SUMMARY It has previously been shown that the Green's function between two receivers can be retrieved by cross-correlating time series of noise recorded at the two receivers. This property has been derived assuming that the energy in normal modes is uncorrelated and perfectly equipartitioned, or that the distribution of noise sources is uniform in space and the waves measured satisfy a high frequency approximation. Although a number of authors have successfully extracted travel-time information from seismic surface-wave noise, the reason for this success of noise tomography remains unclear since the assumptions inherent in previous derivations do not hold for dispersive surface waves on the Earth. Here, we present a simple ray-theory derivation that facilitates an understanding of how cross correlations of seismic noise can be used to make direct travel-time measurements, even if the conditions assumed by previous derivations do not hold. Our new framework allows us to verify that cross-correlation measurements of isotropic surface-wave noise give results in accord with ray-theory expectations, but that if noise sources have an anisotropic distribution or if the velocity structure is non-uniform then significant differences can sometimes exist. We quantify the degree to which the sensitivity kernel is different from the geometric ray and find, for example, that the kernel width is period-dependent and that the kernel generally has non-zero sensitivity away from the geometric ray, even within our ray theoretical framework. These differences lead to usually small (but sometimes large) biases in models of seismic-wave speed and we show how our theoretical framework can be used to calculate the appropriate corrections. Even when these corrections are small, calculating the errors within a theoretical framework would alleviate fears traditional seismologists may have regarding the robustness of seismic noise tomography. [source] Measuring finite-frequency body-wave amplitudes and traveltimesGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 1 2006Karin Sigloch SUMMARY We have developed a method to measure finite-frequency amplitude and traveltime anomalies of teleseismic P waves. We use a matched filtering approach that models the first 25 s of a seismogram after the P arrival, which includes the depth phases pP and sP. Given a set of broad-band seismograms from a teleseismic event, we compute synthetic Green's functions using published moment tensor solutions. We jointly deconvolve global or regional sets of seismograms with their Green's functions to obtain the broad-band source time function. The matched filter of a seismogram is the convolution of the Green's function with the source time function. Traveltimes are computed by cross-correlating each seismogram with its matched filter. Amplitude anomalies are defined as the multiplicative factors that minimize the RMS misfit between matched filters and data. The procedure is implemented in an iterative fashion, which allows for joint inversion for the source time function, amplitudes, and a correction to the moment tensor. Cluster analysis is used to identify azimuthally distinct groups of seismograms when source effects with azimuthal dependence are prominent. We then invert for one source time function per group. We implement this inversion for a range of source depths to determine the most likely depth, as indicated by the overall RMS misfit, and by the non-negativity and compactness of the source time function. Finite-frequency measurements are obtained by filtering broad-band data and matched filters through a bank of passband filters. The method is validated on a set of 15 events of magnitude 5.8 to 6.9. Our focus is on the densely instrumented Western US. Quasi-duplet events (,quplets') are used to estimate measurement uncertainty on real data. Robust results are achieved for wave periods between 24 and 2 s. Traveltime dispersion is on the order of 0.5 s. Amplitude anomalies are on the order of 1 db in the lowest bands and 3 db in the highest bands, corresponding to amplification factors of 1.2 and 2.0, respectively. Measurement uncertainties for amplitudes and traveltimes depend mostly on station coverage, accuracy of the moment tensor estimate, and frequency band. We investigate the influence of those parameters in tests on synthetic data. Along the RISTRA array in the Western US, we observe amplitude and traveltime patterns that are coherent on scales of hundreds of kilometres. Below two sections of the array, we observe a combination of frequency-dependent amplitude and traveltime patterns that strongly suggest wavefront healing effects. [source] Search for direct empirical spatial correlation signatures of the critical triggering earthquake modelGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 3 2004G. Ouillon SUMMARY We propose a new test of the critical earthquake model based on the hypothesis that precursory earthquakes are ,actors' that create fluctuations in the stress field which exhibit an increasing correlation length as the critical large event becomes imminent. Our approach constitutes an attempt to build a more physically based time-dependent indicator (cumulative scalar stress function), in the spirit of, but improving on, the cumulative Benioff strain used in previous works documenting the phenomenon of accelerating seismicity. Using a simplified scalar space and time-dependent viscoelastic Green's function in a two-layer model of the Earth's lithosphere, we compute spatiotemporal pseudo-stress fluctuations induced by a series of events before four of the largest recent shocks in southern California. Through an appropriate spatial wavelet transform, we then estimate the contribution of each event in the series to the correlation properties of the simplified pseudo-stress field around the location of the mainshock at different scales. This allows us to define a cumulative scalar pseudo-stress function which reveals neither an acceleration of stress storage at the epicentre of the mainshock nor an increase of the spatial stress,stress correlation length similar to those observed previously for the cumulative Benioff strain. The earthquakes we studied are thus either simple ,witnesses' of a large-scale tectonic organization, or are simply unrelated, and/or the Green's function describing interactions between earthquakes has a significantly longer range than predicted for standard viscoelastic media used here. [source] A comparison of two spectral approaches for computing the Earth response to surface loadsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2000E. Le Meur Summary When predicting the deformation of the Earth under surface loads, most models follow the same methodology, consisting of producing a unit response that is then con-volved with the appropriate surface forcing. These models take into account the whole Earth, and are generally spherical, computing a unit response in terms of its spherical harmonic representation through the use of load Love numbers. From these Love numbers, the spatial pattern of the bedrock response to any particular scenario can be obtained. Two different methods are discussed here. The first, which is related to the convolution in the classical sense, appears to be very sensitive to the total number of degrees used when summing these Love numbers in the harmonic series in order to obtain the corresponding Green's function. We will see from the spectral properties of these Love numbers how to compute these series correctly and how consequently to eliminate in practice the sensitivity to the number of degrees (Gibbs Phenomena). The second method relies on a preliminary harmonic decomposition of the load, which reduces the convolution to a simple product within Fourier space. The convergence properties of the resulting Fourier series make this approach less sensitive to any harmonic cut-off. However, this method can be more or less computationally expensive depending on the loading characteristics. This paper describes these two methods, how to eliminate Gibbs phenomena in the Green's function method, and shows how the load characteristics as well as the available computational resources can be determining factors in selecting one approach. [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] Green's function interpolations for prestack imagingGEOPHYSICAL PROSPECTING, Issue 1 2000Manuela Mendes A new interpolation method is presented to estimate the Green's function values, taking into account the migration/inversion accuracy requirements and the trade-off between resolution and computing costs. The fundamental tool used for this technique is the Dix hyperbolic equation (DHE). The procedure, when applied to evaluate the Green's function for a real source position, uses the DHE to derive the root-mean-square velocity, vRMS, from the precomputed traveltimes for the nearest virtual sources, and by linear interpolation generates vRMS for the real source. Then, by applying the DHE again, the required traveltimes and geometrical spreading can be estimated. The inversion of synthetic data demonstrates that the new interpolation yields excellent results which give a better qualitative and quantitative resolution of the imaging sections, compared with those carried out by conventional linear interpolation. Furthermore, the application to synthetic and real data demonstrates the ability of the technique to interpolate Green's functions from widely spaced virtual sources. Thus the proposed interpolation, besides improving the imaging results, also reduces the overall CPU time and the hard disk space required, hence decreasing the computational effort of the imaging algorithms. [source] An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rockINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2003A. Ghassemi Abstract In the numerical simulation of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one-dimensional and perpendicular to the fracture in order to avoid the discretization of the three-dimensional reservoir geometry. In this paper we demonstrate that by utilizing the integral equation formulation with a Green's function, the three-dimensional heat flow in the reservoir can be modelled without the need of discretizing the reservoir. Numerical results show that the three-dimensional heat conduction effect can significantly alter the prediction of heat extraction temperature and the reservoir life as compared to its one-dimensional simplification. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical simulation grounding system buried within horizontal multilayer earth in frequency domainINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2007Zhong-Xin Li Abstract A novel mathematical model for accurately calculating the currents flowing along the conductors of grounding system below high voltage a.c. substations and nearby floating metallic structure buried in horizontal multilayer earth model has been developed in this paper. Not only the mutual conductive and capacitive coupling influences of leakage currents, but also mutual inductive coupling influence of network currents flowing along the conductors of grounding system and nearby floating metallic structure in the horizontal multilayer earth model have been considered in this model, and only propagation effect of electromagnetic wave within limited area of the substation has been neglected. The quasi-static complex image method and closed form of Green's function are introduced into this model to accelerate the calculation. The model is then implemented in a computer program, which can be used to calculate currents distribution along the conductors of any configuration of grounding system, and with or without floating metallic structure under some hundreds of kHz frequency harmonic wave. Copyright © 2006 John Wiley & Sons, Ltd. [source] Vector Hankel transform analysis of a tunable circular microstrip patchINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2005T. Fortaki Abstract In this paper, a rigorous analysis of the tunable circular microstrip patch is performed using a dyadic Green's function formulation. To make the theoretical formulation more general and hence valid for various antennas structures (not only limited to tunable microstrip patch); the dyadic Green's function is derived when the patch is assumed to be embedded in a multilayered dielectric substrate. A very efficient technique to derive the dyadic Green's function in the vector Hankel transform domain is proposed. Using the vector Hankel transform, the mixed boundary value problem is reduced to a set of vector dual integral equations. Galerkin's method is then applied to solve the integral equation where two sets of disk current expansions are used. One set is based on the complete set of orthogonal modes of the magnetic cavity, and the other consists of combinations of Chebyshev polynomials with weighting factors to incorporate the edge condition. Convergent results for these two sets of disk current expansions are obtained with a small number of basis functions. The calculated resonant frequencies and quality factors are compared with experimental data and shown to be in good agreement. Finally, numerical results for the air gap tuning effect on the resonant frequency and half-power bandwidth are also presented. Copyright © 2005 John Wiley & Sons, Ltd. [source] On the residue calculus evaluation of the 3-D anisotropic elastic green's functionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 5 2004A.-V. Phan Abstract An algorithm based upon the residue calculus for computing three-dimensional anisotropic elastic Green's function and its derivatives has been presented in Sales and Gray (Comput. Structures 1998; 69:247,254). It has been shown that the algorithm runs three to four times faster than the standard Wilson,Cruse interpolation scheme. However, the main concern of the Sales,Gray algorithm is its numerical instability that could lead to significant errors due to the existence of multiple poles of the residue. This paper proposes a remedy for the problem by adding the capability to evaluate the Green's function in case of multiple poles of the residue. Further, an improved numerical implementation based on the use of double-subscript-notation elastic constants in determining the Christoffel tensor is also at issue. Copyright © 2004 John Wiley & Sons, Ltd. [source] Local discretization error bounds using interval boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009B. F. Zalewski Abstract In this paper, a method to account for the point-wise discretization error in the solution for boundary element method is developed. Interval methods are used to enclose the boundary integral equation and a sharp parametric solver for the interval linear system of equations is presented. The developed method does not assume any special properties besides the Laplace equation being a linear elliptic partial differential equation whose Green's function for an isotropic media is known. Numerical results are presented showing the guarantee of the bounds on the solution as well as the convergence of the discretization error. Copyright © 2008 John Wiley & Sons, Ltd. [source] Full-wave analysis of single cylindrical striplines and microstriplines with multilayer dielectricsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2006Farid Bouttout Abstract In this paper, the spectral-domain method is used to calculate the propagation characteristics of cylindrical microstrip transmission lines. The problem is formulated using an electric field integral equation and the spectral-domain Green's function. The solutions of the field components are obtained in matrix forms, which facilitate the calculations of the Green's function and the power flowing over the lines. The Green's functions are obtained in terms of transition matrices over the dielectric layers. The obtained integral equation is solved by moment method using four kinds of basis functions. The convergence of the method is proven. Based on the power,current definition, a stationary expression for the characteristic impedance has been derived analytically. Numerical results of the effective dielectric constant and the characteristic impedance for various line parameters are calculated and analysed. The computed data are found to be in good agreement with results obtained using other methods. The formulation is then applied to covered microstripline, microstripline and stripline with air gaps, for which data are not found in the literature to date. The presented method is used to guide design of microstrip coil for magnetic resonance imaging. This method is also suitable for investigation of multiconductor strip lines. Copyright © 2006 John Wiley & Sons, Ltd. [source] Indirect boundary element method for unsteady linearized flow over prolate and oblate spheroids and hemispheroidal protuberancesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 2 2004Lisa F. Shatz Abstract The indirect boundary element method was used to study the hydrodynamics of oscillatory viscous flow over prolate and oblate spheroids, and over hemispheroidal bodies hinged to a plate. Analytic techniques, such as spheroidal coordinates, method of images, and series representations, were used to make the numerical methods more efficient. A novel method for computing the hydrodynamic torque was used, since for oscillatory flow the torque cannot be computed directly from the weightings. Instead, a Green's function for torque was derived to compute the torque indirectly from the weightings. For full spheroids, the method was checked by comparing the results to exact solutions at low and high frequencies, and to results computed using the singularity method. For hemispheroids hinged to a plate, the method for low frequencies was checked by comparing the results to previous results, and to exact solutions at high frequencies. Copyright © 2004 John Wiley & Sons, Ltd. [source] Disordered lattice networks: general theory and simulationsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 6 2005Stefano GiordanoArticle first published online: 16 NOV 200 Abstract In this work we develop a theory for describing random networks of resistors of the most general topology. This approach generalizes and unifies several statistical theories available in literature. We consider an n-dimensional anisotropic random lattice where each node of the network is connected to a reference node through a given random resistor. This topology includes many structures of great interest both for theoretical and practical applications. For example, the one-dimensional systems correspond to random ladder networks, two-dimensional structures model films deposited on substrates and three-dimensional lattices describe random heterogeneous materials. Moreover, the theory is able to take into account the anisotropic percolation problem for two- and three-dimensional structures. The analytical results allow us to obtain the average behaviour of such networks, i.e. the electrical characterization of the corresponding physical systems. This effective medium theory is developed starting from the properties of the lattice Green's function of the network and from an ad hoc mean field procedure. An accurate analytical study of the related lattice Green's functions has been conducted obtaining many closed form results expressed in terms of elliptic integrals. All the theoretical results have been verified by means of numerical Monte-Carlo simulations obtaining a remarkably good agreement between numerical and theoretical values. Copyright © 2005 John Wiley & Sons, Ltd. [source] Advanced models for transient analysis of lossy and dispersive anisotropic planar layersINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1 2010Giulio Antonini Abstract A new model is proposed for the transient analysis of the electromagnetic field propagation through anisotropic lossy and dispersive layers. The propagation equations of the electromagnetic fields are solved as a Sturm,Liouville problem leading to identify its dyadic Green's function in a series rational form. Then, the corresponding poles and residues are obtained and a reduced order macromodel is generated, which can be easily embedded within existing three dimensional solvers. The model is applied to lossy and dispersive anisotropic layers with differently polarized plane,waves. Copyright © 2009 John Wiley & Sons, Ltd. [source] A Green's function-based method for the transient analysis of plane waves obliquely incident on lossy and dispersive planar layersINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 6 2008Giulio Antonini Abstract This paper presents a new methodology for the transient analysis of plane waves obliquely incident on a planar lossy and dispersive layer. The proposed model is based on the Sturm,Liouville problem associated with the propagation equations. Green's function is calculated in a series form and the open-end impedance matrix is obtained as the sum of infinite rational functions. This form permits an easy identification of poles and residues. Furthermore, the knowledge of poles leads to the development of a model order reduction technique by selecting only the dominant poles of the system. The pole,residue representation is converted into a state-space model that can be easily interfaced with ordinary differential equation solvers. The numerical results confirm the effectiveness of the proposed modeling technique. Copyright © 2008 John Wiley & Sons, Ltd. [source] Multi-region ADI DD-FDTD algorithm for the analysis of three-dimensional sparse multi-objects scattering problemINTERNATIONAL JOURNAL OF NUMERICAL MODELLING: ELECTRONIC NETWORKS, DEVICES AND FIELDS, Issue 1-2 2008Feng Xu In this paper, a multi-region domain decomposition finite-difference time-domain (DD-FDTD) algorithm is proposed and developed for the analysis of multiple-objects electromagnetic (EM) problems. A significant number of mesh nodes between objects are removed since only local meshes are generated for each object. All the separated sub-domains are interconnected by the use of a 3-D time-domain Green's function. The coupling between objects can be regarded as the equivalent spherical wave irradiations. Incident signals of the equivalent spherical waves are expressed as a spherical wave input field array according to the Huygens principle. The near-field to far-field transformation is introduced to obtain the equivalent spherical wave. Moreover, the alternating direction implicit FDTD (ADI-FDTD) scheme is applied to overcome the limit of the stability condition and increase the speed of the simulation. The new algorithm has been demonstrated and applied to solve typical 3-D multi-objects EM scattering problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] Positive width function and energy indeterminacies in ammonia moleculeINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 8 2007Theodosios G. Douvropoulos A recently published methodology based on the semiclassical path integral theory was applied in a double well structure and gave the analytic form of the system's Green's function. This type of potential can describe the ammonia molecule as far as the motion of the nitrogen atom perpendicular to the hydrogen plane is discussed. Because of the fact that a double well describes a bound system and correspondingly stationary states (constructed by the symmetric and antisymmetric superposition of the eigenstates of the two unperturbed wells), it was expected that the energy spectrum would be real, in a form of doublets due to the splitting effect that takes place. However, the result was a pair of complex poles, which had a clearly positive imaginary part for each member. The present work explains the role of the imaginary parts of the complex poles as the decay rate of quantities defined as the energy indeterminacies, which are directly related to the fact that energy is not well determined in a classically forbidden region of motion. These quantities come as a function of (d,)/dE, which is the derivative of the classical action inside the potential barrier, with respect to energy. The major contribution comes from the turning points, and then the imaginary parts are responsible, not only for the conservation of energy, but for the correct sign of time as well. In this way, a different approach for the tunneling process is adopted, in which the entry or exit of the particle from the potential barrier takes place inside a neighborhood of the turning point, as though the latter was broadened and fluctuating. The magnitude of the previously mentioned decay rate is equal to ,/,, where , is the frequency of the classical oscillations inside one well. In contrast, the inversion frequency is generated by the part of the complex pole that is unrelated to (d,)/dE and is much smaller in magnitude than the classical frequency, since it is given as ,/, exp(,,). In this way, the period of the energy fluctuations is much smaller than the internal period of the system produced by the oscillating communication of the two classically allowed regions of motion. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007 [source] | |||||||||||||||||||||||||||||||||||||