Three-dimensional Green Function Research Articles

Description of magnetic force microscopy by three-dimensional tip Green's function for sample magnetic charges

The three-dimensional Green's function of magnetic force microscopy for a point magnetic dipole tip was analytically obtained in spatial and frequency domains. The influence of MFM measuring conditions, such as the tip magnetization direction and the tip–sample spacing on the Green's function was clarified. The application of the Green's function to the interpretation of the MFM images with different measuring conditions was demonstrated.

An analytical model for time-dependent deformation of a circular plate illuminated by a laser pulse

An analytical model is developed which describes the deformation process in a moderately thick plate following the absorption of a laser pulse. The model is based on the temperature gradient mechanism of the three-dimensional Green function of temperature in the plate which is heated with a Gaussian source at its surface. Therefore, the results of the presented model are valid for times longer than the laser pulse.

Wave radiation by a three-dimensional body in a narrow tank

An integral equation approach is utilized to investigate the influence of tank walls on the hydrodynamics of an arbitrary three-dimensional body undergoing prescribed oscillatory motions in a narrow tank. The solution uses an appropriate three-dimensional Green's function which satisfies the tank-wall boundary conditions. Numerical results are presented for truncated cylinders of circular and elliptic cross-section which illustrate the influence of the tank walls on the added mass and radiation damping. The results indicate that the hydrodynamics of an oscillating body in a narrow tank may be quite different from those of the same body in the open sea.

Hydrodynamic Loads on a Three-Dimensional Body in a Narrow Tank

Abstract An integral equation approach is utilized to investigate the influence of tank walls on the hydrodynamic forces experienced by an arbitrary three-dimensional body situated in a narrow wave tank. An appropriate three-dimensional Green function which satisfies the tank-wall boundary conditions is developed to facilitate the solution. Numerical results are presented for truncated cylinders of circular and elliptic cross section which illustrate the effect of the tank walls on the wave-induced forces. The numerical results indicate that the hydrodynamic loads on a three-dimensional body in a narrow tank may be quite different from those on the same body in the open sea.

Prediction of periodic loadings on single rotation propfan with off-axis inflow

A three-dimensional Green's function potential paneling method is used to predict the propfan unsteady load in a yawed flow condition when the axis of blade rotation is inclined to the freest ream. Unsteady response is predicted in a frequency domain with proper predetermined interblade phase angle. The method is shown to be accurate and efficient in computation comparing to a time-domain calculation. Single-rotation propfan blade SR2 is used to demonstrate the capability. The effects of shaft angle of attack, advance ratio, number of blades, and Mach number on the response due to the off-axis inflow are studied. The results indicate that the shaft angle of attack has a major effect on the unsteady blade loading.

Radiation and canonical sources in uniaxial dielectric media

The three-dimensional electric Green function for uniaxial dielectric media has been given by Chen (1973, 1983) Here we give the magnetic Green's function, whose form suggests that magnetic field formulations may be more tractable than electric field formulations. Using the electric and the magnetic Green's functions, canonical sources for the independent generation of the ordinary and the extraordinary fields are also obtaned.

Closed formula for the static three-dimensional Green function in microstrip structures

As an alternative to the previously available infinite-series representation, a simple closed formula is determined to calculate the potential created by a point unit charge placed on the air-dielectric interface of a microstrip structure.

A Two- or Three-Dimensional Green's Function Which can be Applied to Hyperfrequency Microelectronic Transmission Lines (Letters)

Knowing Green's function and the charge density found on different conductors, the diverse capacities can eventually be calculated by solving an integral equation. This has been dealt with only for simple dielectric-conductor configurations. In Coen's article, the integral representation of log (Z) is employed in calculating Green's function for microstrips (with or without an upper ground plane). Electrostatically speaking, the boundary conditions along conductors or dielectric interfaces are represented by means of infinite charge series.

Slicing procedure for approximate three-dimensional Green's functions for cracks in plates of finite thickness

Exact results for the stress intensity factor are presented for an external circular crack with oppositely directed concentrated loads applied to the crack surfaces. This result is specialized to the case of a semi-infinite crack in an infinite body with concentrated loads on the crack. A procedure is then suggested by which one can obtain from the corresponding plane result the approximate three-dimensional Green's function (concentrated load result) for any straight crack in an infinite elastic body. This procedure is used to determine the Green's functions for a finite-length crack in an infinite body, and is then used in conjunction with a suggested “slicing” procedure to obtain approximate three-dimensional Green's function for plates of finite thickness and infinite extent, containing finite length cracks. Previously existing solutions for crack problems are compared with results obtained by application to plate tension and bending problems of the three-dimensional Green's functions. The results indicate that the procedure yields satisfactory results when stress gradients through the plate thickness are not excessive. However, an accurate assessment of the validity of the slicing procedure awaits further progress in three-dimensional crack analysis.

General transport theory of noise in pn junction-like devices—I. Three-dimensional Green's function formulation

A general collective treatment of noise in three-dimensional junction devices of arbitrary geometry is presented, using Green's functions as in recent transport noise theories. The low-injection theory is extended to open-circuited devices. The density spectra are given in a form in which the volume part is linear in the Green's function and the covariance function, while the surface part is quadratic in the Green's function. The density covariance function for the short-circuited junction is Poissonian for low injection, except for a surface singularity. The noise input e.m.f and output current generator, as well as their cross correlation, are found directly for the hybrid transistor model and are expressed in the h′ parameters, without the usual network transformation. The exact results indicate distributed effects; in particular, the current gain in the noise expressions (α noise) is not equal to the small signal current gain α. The one-dimensional standard results are recovered in a lumped model approximation. For high injection, only the case of quasi band-band recombination (the Shockley-Read levels have equal capture probabilities for electrons and holes) is considered in this paper. The covariance function is then as for low injection but of half strength. The terminal noise depends, besides on the admittance or impedance and the current, on the emitter efficiency γ, the mobility ratio b, and the ratio of the junction admittance and the bulk admittance resulting from modulation effects. As a byproduct of this study, all pertinent network parameters are expressed in Green's functions.