Point Dipole Source Research Articles

Negative refraction and sub-wavelength imaging through surface waves on structured perfect conductor surfaces

We report that the negative refraction can be achieved through surface waves on a metal surface with the array of drilled holes. Using a rigid full-vectorial three-dimensional finite-difference time-domain method, we also demonstrate the sub-wavelength imaging of a point dipole source by a slab of such a structure.

Representation of bioelectric current sources using Whitney elements in the finite element method

Bioelectric current sources of magneto- and electroencephalograms (MEG, EEG) are usually modelled with discrete delta-function type current dipoles, despite the fact that the currents in the brain are naturally continuous throughout the neuronal tissue. In this study, we represent bioelectric current sources in terms of Whitney-type elements in the finite element method (FEM) using a tetrahedral mesh. The aim is to study how well the Whitney elements can reproduce the potential and magnetic field patterns generated by a point current dipole in a homogeneous conducting sphere. The electric potential is solved for a unit sphere model with isotropic conductivity and magnetic fields are calculated for points located on a cap outside the sphere. The computed potential and magnetic field are compared with analytical solutions for a current dipole. Relative difference measures between the FEM and analytical solutions are less than 1%, suggesting that Whitney elements as bioelectric current sources are able to produce the same potential and magnetic field patterns as the point dipole sources.

Assessment criteria for MEG/EEG cortical patch tests

To validate newly developed methods or implemented software for magnetoencephalography/electroencephalography (MEG/EEG) source localization problems, many researchers have used human skull phantom experiments or artificially constructed forward data sets. Between the two methods, the use of an artificial data set constructed with forward calculation attains superiority over the use of a human skull phantom in that it is simple to implement, adjust and control various conditions. Nowadays, for the forward calculation, especially for the cortically distributed source models, generating artificial activation patches on a brain cortical surface has been popularized instead of activating some point dipole sources. However, no well-established assessment criterion to validate the reconstructed results quantitatively has yet been introduced. In this paper, we suggest some assessment criteria to compare and validate the various MEG/EEG source localization techniques or implemented software applied to the cortically distributed source model. Four different criteria can be used to measure accuracy, degrees of focalization, noise-robustness, existence of spurious sources and so on. To verify the usefulness of the proposed criteria, four different results from two different noise conditions and two different reconstruction techniques were compared for several patches. The simulated results show that the new criteria can provide us with a reliable index to validate the MEG/EEG source localization techniques.

Arbitrary source and receiver positioning in finite‐difference schemes using Kaiser windowed sinc functions

In finite‐difference methods a seismic source can be implemented using either initial wavefield values or body forces. However, body forces can only be specified at finite‐difference nodes, and, if using initial values, a source cannot be located close to a reflecting boundary or interface in the model. Hence, difficulties can exist with these schemes when the region surrounding a source is heterogeneous or when a source either is positioned between nodes or is arbitrarily close to a free surface. A completely general solution to these problems can be obtained by using Kaiser windowed sinc functions to define a small region around the true source location that contains several nodal body forces. Both monopole and dipole point sources can be defined, enabling many source types to be implemented in either acoustic or elastic media. Such a function can also be used to arbitrarily locate receivers. If the number of finite‐difference nodes per wavelength is four or more (and with a source region half‐width of only four nodes) this scheme results in insignificant phase errors and in amplitude errors of no more than 0.1%. Numerical examples for sources located less than one node from either a free surface or an image source demonstrate that the scheme can be used successfully for any surface‐source or multisource configuration.

Radiation patterns of novel one- and three-tine tuning forks

Inspired by recent results [D. A. Russell, Am. J. Phys. 68, 1139–1145 (2000)] showing that the traditional two-tine tuning fork behaves as a linear quadrupole source, novel one-tine and three-tined tuning forks were constructed. The three identical tines on the three-tined fork were equally spaced around a circle and oriented so that each tine oscillated radially when exciting the fundamental mode. The angular dependence of the radiated sound from these forks was investigated as a function of distance from the symmetry axis of each fork. In the near field, the three-tined fork has three major maxima, one adjacent to each tine, and three minor maxima, one opposite each tine. The minor maxima disappear in the far-field measurements. These results were compared to a simple model wherein each tine behaves as an independent point dipole source [P. M. Morse and K. U. Ingard, Theoretical Acoustics, 2nd ed. (Princeton U.P., Princeton, NJ, 1986), p. 313]. The simple model shows good, but not perfect, agreement with the measured radiation patterns.

THE INFLUENCE OF UNEVEN BLADE SPACING ON THE SPL AND NOISE SPECTRA RADIATED FROM RADIAL FANS

The influence of irregular blade spacing of car alternator radial fans on the total sound pressure level (SPL) and the noise spectrum has been investigated. For this purpose, theSPLand spectra were computed theoretically and the values were compared to measured results for several types of fans with various blade spacing. As theoretical background, the theory describing discrete frequency sound radiated by axial fans in open space was adopted. This was done in order to model theSPLand the spectra of alternator radial fans, placed inside a casing. Furthermore, due to the low blade tip Mach number, blades were modelled as dipole point sources. It was found, in accordance with previous results from known literature, that alterations in blade spacing do not significantly alter the totalSPLnor the cooling capacity of the alternator radial fan. However, significant dispersion of the sound power over several harmonics was found with irregular fan blade spacing, thus allowing for a reduction of the siren effect. This phenomenon was predicted theoretically and confirmed experimentally.

Human evoked potentials to long duration vibratory stimuli: role of muscle afferents

Tonic vibratory stimuli of 1000 ms duration and different frequencies were delivered to muscles of the forearms of young human subjects. Evoked potentials (EPs) were recorded from 29 scalp channels and revealed phasic highly lateralised and focally distributed EPs during the first 100 ms of the recording epoch that could be adequately modelled with a single point dipole source located in the vicinity of the central sulcus contralateral to the stimulated arm. A later negativity with an onset of about 400 ms and a duration of about 800 ms was found to be symmetrically distributed over fronto-central regions. This negativity is interpreted in terms of cortical activation beyond the primary sensory fields and could be related to the kinaesthetic phenomena experienced during muscle vibration.

Human evoked potentials to long duration vibratory stimuli: role of muscle afferents

Tonic vibratory stimuli of 1000 ms duration and different frequencies were delivered to muscles of the forearms of young human subjects. Evoked potentials (EPs) were recorded from 29 scalp channels and revealed phasic highly lateralised and focally distributed EPs during the first 100 ms of the recording epoch that could be adequately modelled with a single point dipole source located in the vicinity of the central sulcus contralateral to the stimulated arm. A later negativity with an onset of about 400 ms and a duration of about 800 ms was found to be symmetrically distributed over fronto-central regions. This negativity is interpreted in terms of cortical activation beyond the primary sensory fields and could be related to the kinaesthetic phenomena experienced during muscle vibration.

Electromagnetic Inverse Problems and Generalized Sommerfeld Potentials

In this article we study the inverse boundary value problem for Maxwell’s equation; that is, we determine the scalar permeability, permissibility, and conductivity of a body from electromagnetic field measurements outside the body. In this paper, the problem is approached by using certain generalized Sommerfeld potentials that are shown to satisfy a vector-valued Schrodinger equation. By using these potentials, the inverse boundary value problem is reduced to the problem of determining the potential of this second-order operator. Further, it is shown that the electromagnetic material parameters can be determined by using electric or magnetic dipole point sources only.

Polarization properties of near-field waves in homogeneous isotropic and anisotropic media: numerical modelling

SUMMARY The paper deals with the polarization properties of complete body waves propagating in elastic, homogeneous, unbounded, isotropic and anisotropic media. The waves excited by a point dipole source and by a line dipole source in an isotropic medium are computed by the numerical integration of Green's function. The waves excited by a line dipole source in an anisotropic medium are modelled by the finite-difference method. It is shown that complete radiation patterns of P- and S-waves of the dipole source in isotropic as well as anisotropic media do not generally have nodal lines, and that P- and S-waves are not generally polarized linearly, but quasi-elliptically. The degree of ellipticity decreases with increasing ratio r/λ and depends on the azimuth. A significant value of ellipticity was observed in the vicinity of the far-field nodal lines even for ratios r/λ≅ 10 and more. For an anisotropic medium in the vicinity of the source a difference was detected between the predominant polarization direction of complete waves and the far-field polarization direction.

Two-microphone finite difference approximation errors in the interference fields of point dipole sources

The two-microphone sound intensity measurement technique has been used extensively over the last 10 years for the determination of sound power of noise sources, the determination and ranking of noise sources, and the sound transmission loss of structures. In this paper, theoretical expressions have been developed for the finite difference approximation errors that occur in estimating sound intensity in the interference fields of point harmonic and random dipole sources. Here, expressions have also been developed for the finite difference approximation error analysis of a simple harmonic point dipole located over a reflecting plane using the method of images. Sample calculations have been included to show the effects of the microphone separation distance, the distance of the measurement location from the source, the geometrical arrangement of the sources, the phase difference between the two point sources, and their relative strengths. These calculations suggest that increasing the microphone spacing increases the magnitude of the error level and also that the geometrical arrangement of the sources has a considerable effect on that level.

A generalized Gel'fand-Levitan-Marchenko integral equation

This study focuses on the Gel'fand-Levitan and Marchenko equations with the view of unifying them via a general integral equation formulation which is pertinent to the electromagnetic inverse scattering problem. The approach used to derive this integral equation is based on a time-domain formulation, as opposed to the traditional spectral-domain approach, which is formulated in the frequency domain. The integral equation allows the inversion of a planar stratified, lossless, and non-magnetic medium excited by a point dipole source that gives rise to either transverse-electric or transverse-magnetic polarized waves.

Efficiency of excitation of earth-ionosphere waveguide by ionospheric sources

Numerical estimates of the efficiency of excitation of the earth-ionosphere waveguide by point dipole sources located in the dayside ionosphere are obtained. A substantially inhomogeneous and anisotropic region with an upper boundary of H/sub c/ is found to exist. It is shown that horizontal sources located at heights of H > H/sub c/ are more effective than vertical sources, while orientation has no effect on the field in the waveguide. For H < H/sub c/, there exists a region where the vertical electric dipole (VED) is more effective than a horizontal electric dipole of any orientation. The efficiency of excitation of the waveguide by VED in this region increases with an increase in frequency over the range from 5-15 kHz.

Solutions of the electromagnetic wave equations for point dipole sources and spherical boundaries

Solutions of the electromagnetic wave equation are derived in systems containing spherical interfaces when the source field is that of a magnetic or electric point dipole. Piecewise constant electromagnetic parameters are assumed, but their values as well as the frequency of the source field are arbitrary. The solutions are obtained in terms of scalar and vector spherical harmonics. A sphere embedded in full space with a radial or transverse source dipole is considered explicitly.

Compression of the Hermaean magnetosphere by the solar wind

A model of the compression of the Hermaean magnetosphere by the solar wind is presented. The model considers the consequences of the finite electrical conductivity of the planetary interior on the magnetopause standoff distance under varying solar wind conditions. Although for average conditions the standoff distance is almost identical to that obtained for a point dipole source embedded in an insulating interior, for periods of above‐average solar wind dynamic pressure the compression of the planetary field between the magnetopause and the conducting interior will increase the standoff distance. From these considerations the solar wind would be expected to impact the dayside surface directly only a very small fraction of the time. Magnetic reconnection may erode the dayside magnetosphere and increase the rate of direct impact upon the surface. However, this effect is not included in the model calculations.

Diffraction of arbitrarily oriented directional sources by rigid planar screens

An analysis has been carried out to determine the diffracted fields due to directional sources located near rigid planar screens with application to the suppression of noise by acoustic barriers, especially highway barriers. Firstly, the diffracted field due to an arbitrarily oriented point dipole source is obtained by source position differentiation using the classical exact results due to McDonald. The dipole results are then combined with the monopole results to obtain the diffracted fields due to a series of combined sources having arbitrary directivity and orientation with respect to the plane of the screen. It is noted that while the diffraction problem with simple sources and planar screens exhibits reciprocity, diffraction results obtained in the present problem do not exhibit reciprocity with respect to source and observer locations. Typical computed insertion loss results are shown indicating the trends associated with source directionality, source orientation, and source location. Barrier insertion loss reductions, relative to those obtained with simple sources, are noted for vertically oriented directional sources located close to, and below, the diffracting edge.

An analysis of the acoustic power radiated by a point dipole source into a rectangular reverberation chamber

The acoustic power radiated by a point dipole source into a rectangular reverberation chamber has been calculated by consideration of the total power absorbed by the chamber surfaces. A normal mode approach has been used. The time and space averaged value of the radiated acoustic power is found to approximate closely to the free field value. An expression ion normalized standard deviation of the acoustic power radiated has been obtained as a function of source frequency, chamber volume, chamber reverberation time and dipole orientation. The radiated power has also been computed for a dipole source near one or more surfaces within the chamber and for different dipole orientations. The results make a contribution to development of the standard techniques for determination of sound power radiated by a source in reverberation chambers and complement the substantial amount of corresponding work on monopole sound sources.

The complete heart-lead relationship in the Einthoven triangle.

The relationship between the source strength and the “manifest vector” in the Einthoven Triangle is derived for a line and a point dipole source and confirmed experimentally. The result permits the interpretation of the standard ECG leads in absolute terms and corrected for body size. The manifest vector is shown to be approximately\(\sqrt 3 \) times what it would be in an otherwise similar circular slab which circumscribes the triangle.