Three-dimensional Dipole Research Articles

Three-dimensional localization of interictal epileptiform activity with dipole analysis: Comparison with intracranial recordings and SPECT findings

Seventeen patients with therapy-resistant partial epilepsy were studied in order to compare the localization of the epileptic focus provided by three-dimensional dipole analysis of scalp interictal epilepriform EEG activity to the localization of the ictal pacemaker zone obtained by intracranial recordings. The results were also compared with regional abnormalities in interictal 99mTc-hexamethylpropy-lenenamine oxime single-photon emission computed tomography (SPECT). Dipole analysis was performed using a well-known commercial computer program based on a three-shell model. For 12 of the 17 patients, the dipoles for all the individual spikes were located in the same area, in two cases, two separate locations were found, and in three cases the dipoles were scattered over a large area. In 8 of the 12 patients with a single dipole location, intracranial ictal recordings revealed a seizure initiation zone corresponding to the dipole location. In another two cases, intraoperative corticography confirmed the dipole findings. In the two remaining patients, the intracranial recordings revealed a different pattern of seizure initiation than had been anticipated from the dipole analysis. In one of the two patients with two dipole locations, intracranial recordings revealed a seizure initiation zone corresponding to one of the two dipole location sites, whereas in the other patient the seizure onset pattern was more complex. In two of the three patients with widely scattered dipole areas, seizure onset was complex, whereas in the third patient a localized seizure onset was found. In 10 of the 12 patients with a single dipole location site, there was good correlation between this site and regions of low flow in the interictal SPECT measurements. In both patients with two dipole areas, there was a low flow area corresponding to at least one of the dipole localizations. In two of the three patients with widespread dipoles, there were major SPECT low-flow areas, whereas in the third patient interictal SPECT was normal. Although our investigations so far are tentative, we think the results indicate that dipole analysis of interictal epileptiform EEG activity may become a useful supplementary method for the localization of the epileptogenic region in patients who are under consideration for surgical therapy, especially if combined with SPECT or other independent localizing techniques.

Theoretical rotational—vibrational spectrum of SiH 2 (X 1A 1 and a 3B 1)

The three-dimensional potential energy and electric dipole moment functions of the X 1A 1 and a 3B 1 states of SiH 2 have been calculated from highly correlated CEPA electronic wavefunctions. The analytic representations of these functions have been used in perturbational and variational calculations of the rotationally resolved absorption spectrum of X 1A 1 SiH 2. In the variational calculations all anharmonicity effects and vibration—rotation couplings have been considered. The equilibrium spectroscopic constants for SiH 2, SiD 2, and SiHD (X 1A 1 and a 3B 1) isotopomers and absolute integrated band intensities are given. The calculated vibrational band origins agree to within 10–40 cm −1 with available gas phase experimental values. It has been shown that due to strong Fermi resonances the 1ν 1 and 2ν 2 bands have almost equal integrated band intensities in the absorption spectrum and overlap with the 1ν 3 band between 1800 and 2300 cm −1. For the most intense transitions absolute line intensities are given. In the electronic ground state of SiH 2 the vibrational band intensities of the fundamental absorption transitions are found to be more intense than the pure rotational transition in the vibrational ground state.

Spectrum and dynamics of the CH chromophore in CD 2HF. II. Ab initio calculations of the potential and dipole moment functions

We report ab initio (SCF-MP2 and CI) calculations on the three-dimensional anharmonic potential and dipole functions of the coupled vibrational modes of the CH chromopore in CD 2HF. Predictions of fundamental and overtone spectra are obtained from 3D solutions of the vibrational Schrödinger equation and are compared with experiment. The dominant Fermi and Darling-Dennison coupling constants in the effective Hamiltonian representation of experiment and theory agree well. Predicted overtone band strengths are satisfactory and very sensitive to the dipole function used.

Theoretical potential energy function and rovibronic spectrum of CO+2(X 2Πg)

For the electronic ground state of CO+2 the three-dimensional potential energy, electric dipole, and transition moment functions have been calculated from highly correlated multireference configuration interaction electronic wave functions. Along the antisymmetric stretching displacements the shape of the potential energy functions is found to be very sensitive to the electron correlation effect. Using a modified theoretical potential energy function rovibronic energy levels have been calculated variationally by the method of Carter and Handy. In this approach, anharmonicity, rotation–vibration, electronic angular momenta, and electron spin coupling effects have been accounted for. The vibronic band origins agree to within about 10 to 20 cm−1 with the available experimental data, and the rotational levels agree to within 0.01 cm−1 for low J values. Additional vibrational band origins have been predicted for energies up to 3200 cm−1. The anomalously low frequency of the antisymmetric stretching mode and its inverse anharmonicity in the X 2Πg state of CO+2 have been reproduced with the potential energy functions for the adiabatic states. Previously, it has been assumed that this effect is due to the vibronic coupling. The molecular parameters of one-dimensional effective Hamiltonians obtained from fits of the spectral data are compared with those derived from the theoretical potential.

Accurate Matching of electromagnetic dipole data with CT and MR images

Interpretation of EEG (electroencephalography) or MEG (magnetoencephalography) derived three-dimensional dipole localizations is hampered by poor visualization. This paper describes a method for combining dipole data with structural image data of the same patient. To ensure high precision this method utilizes external markers that are easy to apply. These markers can achieve subslice accuracy and can even be used to pinpoint reference points outside the scanned volume. Accurate matching is thus provided even in standard imaging protocols employing thick slices and/or large interslice gaps. The results of the matching method are presented in 2D and 3D visualizations. The hybrid images facilitate the interpretation of dipole localizations with respect to the patient's anatomy.

Complete active space self-consistent field potential energy surfaces, dipole moment functions, and spectroscopic properties of O3, CF2, NO−2, and NF+2

Three-dimensional potential energy and dipole moment surfaces have been calculated for the 24 electron triatomics O3, CF2, NO−2, and NF+2 using complete active space self-consistent field wave functions (CASSCF) and a basis set of 87 (99 for NO−2) contracted Gaussian-type orbitals (cGTOs). The analytical potential energy functions (PEFs) have been used in perturbation and variational calculations of anharmonic spectroscopic constants and vibrational energy levels. The results for O3 and CF2 are compared to the available experimental data, and predictions of the rotational and vibrational spectra of NO−2 and NF+2 have been made by comparison to these species. The equilibrium geometries of NO−2 and NF+2 are predicted to be re=1.260 Å, θe=116.5° and re=1.242 Å, θe=108.0°, respectively. The fundamental vibrational frequencies (ν1,ν2,ν3) and absolute band intensities (at 300 K) of these two ions are predicted to be 1286 cm−1/31 cm−2 atm−1, 782 cm−1/13 cm−2 atm−1, 1232 cm−1/2900 cm−2 atm−1 (NO−2) and 1272 cm−1/181 cm−2 atm−1, 711 cm−1/25 cm−2 atm−1, 1210 cm−1/1230 cm−2 atm−1 (NF+2). Band intensities for several low-lying vibrational transitions have been calculated for all four species from the CASSCF dipole moment functions, and comparisons to experiment have been made for O3 and CF2.

Discrete complex images of a three-dimensional dipole above and within a lossy ground

The paper introduces a new method of discrete complex images, to evaluate the Sommerfeld integrals arising in the problem of a three-dimensional dipole above and within a lossy ground. The spectral domain quantity, which is independent of spatial co-ordinates, is accurately approximated by a short series of exponential functions. By use of the Prony method and nonlinear optimisation technique, and through the Sommerfeld equality, the Sommerfeld integrals can be analytically evaluated into simple closed forms of spatial complex images. Various dipoles (HED, VED, HMD and VMD) above and within the lossy ground are studied. Numerical results show that for any parameters of the lossy ground, the closed-form Green function approaches the precision of the ‘nearly exact’ results of Sommerfeld integrals.

Potential energy and dipole moment functions of the HCS radical

The three-dimensional MCSCF CI potential energy, electric dipole and electronic transition moment functions have been calculated for the X 2A′ and A 2A″ electronic states of the HCS radical. These states adiabatically correlate with the two components of a 2Π electronic state for linear configurations and their ro-vibronic spectra exhibit the Renner-Teller effect. Such spectra have been evaluated from variational ro-vibronic wavefunctions, which take into account both anharmonicity effects and rotation-vibration coupling. The nuclear and electronic angular momentum couplings have also been considered. Spectroscopic constants for the X 2A′ and A 2A″ states calculated by perturbation theory are given. The calculated equilibrium geometries are: R e CH: 1.083 Å (X), 1.063 Å (A), R e CS: 1.573 Å (X), 1.557 Å (A) and α e HCS: 131.8° (X), 180° (A), respectively. The electronic barrier to linearity in the electronic ground state is calculated to be 3063 ± 200 cm −1. The fundamental vibrational band origins and intensities (at 300 K) in the electronic ground state of HCS are predicted to be: 3104 cm −1/6 cm −2 atm −1 (CH stretch), 1165 cm −1/43cm −2 atm −1 (CS stretch) and 871 cm −1/54 cm −2 atm −1 (bend). The fundamental frequencies are expected to be accurate to within about 30 cm −1, the vibrational intensities to within about 10 to 20%. The electric dipole moment μ 0 (X) is calculated to be 0.85 ± 0.05 D. The K-reordering due to the electronic angular momentum coupling is discussed. Absolute line intensities (up to J″ = 9) have been calculated and are given for a few intense lines.

The potential energy and dipole moment surfaces of NF2 and O−3 by complete active space self-consistent field

Three-dimensional potential energy and dipole moment surfaces have been calculated for the 25 electron radicals NF2 and O−3 in their 2B1 ground electronic states by the complete active space self-consistent field (CASSCF) method with basis sets of 87 (NF2) and 99 (O−3) contracted Gaussian-type orbitals. Spectroscopic constants have been calculated from the analytical potential energy functions for each species, and the results for NF2 are compared to the available experimental data. Predictions of the rotational and rotational–vibrational spectra of O−3 have been made by comparison to the NF2 results. Vibrational band origins have been calculated by perturbation theory and also variationally in a basis of distributed Gaussian functions. Rotationless dipole moment matrix elements and vibrational band intensities have been determined from the CASSCF dipole moment functions. The fundamental vibrational band origins and intensities of O−3 are predicted to be 979 cm−1/0.87 cm−2 atm−1 (ν1), 565 cm−1/17.8 cm−2 atm−1 (ν2), and 739 cm−1/2620 cm−2 atm−1 (ν3). Smaller basis set calculations of the first three excited electronic states of O−3 have also been carried out, and the results are compared to previous photodissociation experiments.

Past, present and future of topographic mapping

Traditional EEG and EP analysis is trace-oriented. When mapping became popular, results of waveform analysis were mapped. Increased exposure to brain field maps has begun to orient analysis to the spatial aspects. Different maps must be generated by different neuronal populations; this offers direct key to the analysis of higher brain function. Space-oriented data reduction selects maps with optimal signal/noise ratio using Global Dissimilarity index. Classification and statistics of map landscapes uses extracted descriptors (locations of extrema or centroids) or three-dimensional dipole models. Map classification leads to adaptive segmentation of evoked or spontaneous map series into functional micro-states, the putative building blocks of perception and cognition.

A theoretical rotationally resolved infrared spectrum for H2O+ (X 2B1)

Three-dimensional potential energy and electric dipole moment functions for the electronic ground state of H2O+ have been calculated from highly correlated multiconfiguration reference configuration interaction (MRCI) electronic wave functions. The analytic representations of these functions have been used in vibrational and perturbational calculations of the rovibrational absorption spectrum of H2O+. The quartic force fields in normal coordinates have been employed in the evaluation of the equilibrium spectroscopic constants in H2O+, D2O+, and HDO+ by perturbation theory. The equilibrium structure, vibrational band origins, centrifugal distortion constants and rotational energy levels agree very well with the available experimental data. Absolute vibrational band intensities have been calculated from the dipole moment functions and are compared with theoretical integrated band intensities. The radiative lifetimes of excited vibrational states exhibit mode specific variations. The rotationally resolved room temperature absorption spectra have been evaluated ab initio for the pure rotational and the ν2, 2ν2, ν1, ν3, and 3ν2 transitions. The rovibrational electric dipole transition matrix elements and absolute line intensities are given for the most intense transitions. These data take full account of anharmonicity effects and vibration–rotation coupling.

Theoretical rotational–vibrational spectrum of H2S

The high resolution rovibrational spectrum of H2S has been evaluated from three-dimensional ab initio potential energy and electric dipole moment functions and variational rovibrational eigenfunctions, which took full account of anharmonicity effects and rotation–vibration coupling. The quality of the near equilibrium theoretical potential energy function has been checked by comparisons with experimental equilibrium structure, empirical quartic force fields, vibrational band origins, centrifugal distortion constants, and rotational energy levels. All parameters agree well with the available experimental data. Vibrational band intensities for the ν2, 2ν2, ν1, and ν3 bands have been calculated from empirical and ab initio dipole moment functions and compared with experimental and theoretical integrated band intensities. The difficulties arising by the derivation of such data from the experimental intensities of H2S are discussed. The theoretical results strongly suggest that higher than first derivatives are needed for a proper description of the dipole moment function. The room temperature absorption spectra have been evaluated ab initio for the pure rotational and the ν2, 2ν2, ν1, and ν3 transitions. The unusual intensity pattern of the P, Q, and R branches attributed to the rotational–vibrational coupling has been well reproduced. Absolute line intensities calculated previously by perturbation theory are compared with variational results. The purely theoretical line intensities agree satisfactorily with experiment for the bending transitions, however, the extremely flat regions of the dipole moment functions along the bond stretching displacements make the transition intensities very sensitive to the values of the dipole moment derivatives.

Theoretical calculations of the vibrational transition probabilities in hydrogen selenide

Three-dimensional ab initio dipole and potential energy functions for H 2Se have been calculated from highly correlated SCEP CEPA wavefunctions. First-order relativistic corrections according to the Cowan-Griffin approach, which retains only the mass velocity and one-electron Darwin terms, have been applied. These data have been used in perturbation and variational calculations of anharmonic vibration-rotation term values and wavefunctions. Radiative transition probabilities between vibrational levels up to about 10000 cm −1 have been calculated from electric dipole transition matrix elements. It is found that the radiative lifetimes vary in a mode-specific way.

Two-dimensional chiral dipolar systems: a theoretical investigation

The authors study the ground-state properties of a planar assembly of molecules carrying a permanent three-dimensional dipole moment and subject to a short-range intermolecular spontaneous twist. This twist is modelled by a chiral Dzyaloshinskii-Moriya term (1963) for the inplane components of the dipoles and affects the ordering structure of the molecules through the dipole-lattice coupling. This model should be of relevance in explaining the (quasi-) equilibrium spiral shapes of two-dimensional chiral crystals observed by Weis and McConnell (1984, 1985). Two limits are considered in the paper. (a) For a weak surface tension chain-like structure are favoured. They show, using an analytical approach as well as numerical simulations, that spiral structures are indeed obtained. (b) For a strong enough surface tension more compact geometries are expected. The authors argue that the 'surface' instabilities will occur if the coupling between the 'surface' and the bulk is sufficiently weakened by defects.

Vibrational radiative lifetimes in H 2Se and HCS −

Vibrational dipole matrix elements and radiative transition probabilities for H 2Se and HCS − have been evaluated from theoretical three-dimensional electric dipole moment and potential energy functions. The radiative lifetimes of the ( v=1, J=0) levels of HCS − have been calculated to be 3.5 ms (CH stretch), 172 ms (HCS bend) and 785 ms (CS stretch), and in H 2Se to be 122 ms (symmetric stretch), 1045 ms (bend) and 101 ms (asymmetric stretch). The lifetimes of higher vibrational states with no extensive mode-mixing decrease with increasing vibrational quantum number and vary in a mode-specific way.

A b i n i t i o calculation of spectroscopic properties for the HLiH− ion in the X 1Σ+g state

Near equilibrium three-dimensional potential energy and electric dipole moment surfaces of the bound negative ion HLiH− were calculated from highly correlated CEPA electronic wave functions. The HLiH− ion is linear with Re=1.743 Å. From the potential energy surface the anharmonic vibration–rotation term values were calculated variationally and by perturbation theory. The fundamental vibrational transitions in HLiH− are predicted to lie at ν1(J=0)=1014 cm−1, ν2(J=1)=429 cm−1, ν3(J=0)=1079 cm−1. The D0 dissociation energy relative to the LiH+H− asymptote is calculated to be 2.34 eV, the vertical electron detachment energy to be 3.10 eV. The components of the electric dipole moment surface are given analytically.

Finite element modeling of acoustic singularities with application to propeller noise

Numerical formulations and results that expand on recent developments in finite element modeling of acoustic volume sources and acoustic dipoles are presented. It is shown that with a suitable structuring of the acoustic field equations it is possible to include monopoles and dipoles within the same analysis framework as has been extensively used for interior duct acoustic and duct inlet radiation problems. This allows the extension of the finite element modeling method to include the noise sources in such applications as propellers enclosed in a duct or in free space with mean flows. The necessary structuring of the acoustic field equations is shown, and example calculations are given for the case of one-dimension al sources and body forces in the presence of mean flow, two-dimensional sources, axial body forces, and transverse body forces in the presence of uniform mean flow. Three-dimensional sources and dipoles are modeled as the Fourier sum of axially symmetric solutions without the necessity of introducing singular elements. It is further demonstrated that distributions of singularities can be readily modeled, and an example is given of the computation of the near- and far-field radiation of a propeller. Comparison of the far-field radiation directivity is made with the Gutin theory.

The calculation of perturbation and induction arrows for a three-dimensional conductivity model and dipole source fields

A numerical method is used to calculate the electromagnetic fields associated with a three-dimensional conductivity anomaly. The source field is due to horizontal magnetic dipoles placed at two different positions with respect to the conductivity anomaly. The transfer functions and related perturbation and induction arrows associated with the fields are calculated and compared with the arrows obtained from a uniform source calculation. The results show the source effect on the induction arrows and indicate that the perturbation arrows provide a method of outlining the spatial extent of the anomaly. The transfer function calculations are made for both exact and approximate normal fields. In the transfer function calculation the anomalous fields are correlated with a normal field as suggested by Schmucker (1970) and Cochrane and Hyndman (1970).

Rapid degradation phenomenon in heterojunction GaAlAs–GaAs lasers

The rapid degradation phenomenon in Ga1−xAlxAs–GaAs DH lasers has been associated with the growth of a dislocation network during the device operation. The nature of these defects has been analyzed by transmission electron microscopy in an effort to understand their origin and growth mechanism. The propagation of the dislocation network is found to take place by successive climb of a dislocation crossing the n-Ga1−xAlxAs, p-GaAs, and p-Ga1−xAlxAs layers in the stripe area. The climb process leads to the formation of a three-dimensional dislocation dipole network which extends through the three epitaxial layers and remains confined to the stripe area. A tentative model which discusses the network growth process is presented. The source of the very large vacancy concentration involved in the climb process has been attributed to the interfaces between the binary and ternary layers. The fast climb rate has been related to large drift forces acting on the vacancies during the device operation. The dominant drift forces are thought to be electrical and elastic in nature.

Particle trajectories in model current sheets: 2. Applications to auroras using a geomagnetic tail model

Individual particle trajectories are determined analytically and numerically in two possible configurations of electric and magnetic fields in the geomagnetic tail. The models are based on reconnection models incorporating a neutral point with associated neutral or current sheet and on the observed neutral sheet in the geomagnetic tail. Both models contain magnetic field lines oppositely directed on either side of a current sheet, with some field line connection through the sheet and with an electric field perpendicular to the magnetic field and parallel to the sheet. The models differ in the rate of variation of a magnetic field component perpendicular to the neutral sheet and hence in the rate of field line crossing of the neutral sheet. For the two models, particles are accelerated and turned toward the earth within the neutral sheet and are ejected from the neutral sheet with small pitch angles to a magnetic line of force, with energies of tens of kilovolts. For the first model, a dipole and tail model, electrons are ejected at about 150 RE and protons about 50 RE back in the tail. For the second model, an extended tail model, electrons are ejected at about 500 RE, and protons at about 400 RE. Proton auroras would be expected about ½° lower latitude than electron auroras, and isotropic fluxes should be measurable out to distances of the order of 2.5 RE from the earth. Extremely thin sheets of incoming particles are produced, about 1 km for electrons between 1 and 10 kev. These results are obtained from an approximate, nonadiabatic theory and are verified by machine computations. To map the thin output sheets onto the earth, a three-dimensional dipole and tail model is used for the numerical computations of many proton trajectories. Thin output sheets of accelerated particles are found using Liouville's theorem. These thin sheets or spatially intense regions are near the auroral zones when mapped onto the earth; they move to lower latitudes on the earth with an increase in the strength of the tail field, and their thickness is roughly proportional to the thermal velocity of the particles incident on the tail. The geomagnetic tail may sometimes be quite long without field-line merging and may sometimes be shorter with merging. These models may therefore be useful in the description of auroral acceleration whenever the merging process is going on. The models may be applicable to other situations where neutral points or sheets may exist, such as the day-side magnetospheric current sheet, the interplanetary field, solar flares, etc. If He auroral emission occurs as suggested by Eather, these results imply that alphas should be found equatorward of precipitating protons with about twice the proton energy.