Atomic integrals with the magnetic dipole- dipole operator.
Atomic integral obtained with magnetic dipole- dipole operator in form of finite sum of integrals over hypergeometric functions
INTEGRAL EQUATION↗
SEARCH · Engineering Papers
Results for “DIPOLE”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Computer-graphics studies of dipole-dipole collisions - Evidence for neutral collision complexes.
Extension of three-dimensional computer-graphics studies of orientation-dependent forces to multiple reflection behavior in dipole-dipole collisions. The collision pairs DCl-DCl and HCl-HCl are studied for rotational temperatures of 25, 77, and 300 K and translational temperatures of 77 and 300 K. The probability of a multiple reflection collision is a very sensitive inverse function of hard-core reflection distance for fixed temperatures. A brief comparison of the results is made with two-dimensional results of Clarke and Smith (1970) for CHF3-CHF3.
Dugan, J. V., Jr.↗
Geomagnetic eccentric dipole <gemagnitnyy ekstsentrichnyy dipol'<
Geomagnetic eccentric dipole
GEOMAGNETISM↗
Theoretical shape of the magnetosphere boundary taking into account the geomagnetic dipole inclination to the geographic axis and the non-dipole part of the geomagnetic field
Theoretical shape of magnetosphere boundary considering inclination of geomagnetic dipole and nondipole part of geomagnetic field
Rudneva, N. M.↗
Accurate Predictions of Mean Geomagnetic Dipole Excursion and Reversal Frequencies, Mean Paleomagnetic Field Intensity, and the Radius of Earth's Core Using McLeod's Rule
The geomagnetic spatial power spectrum R(sub n)(r) is the mean square magnetic induction represented by degree n spherical harmonic coefficients of the internal scalar potential averaged over the geocentric sphere of radius r. McLeod's Rule for the magnetic field generated by Earth's core geodynamo says that the expected core surface power spectrum (R(sub nc)(c)) is inversely proportional to (2n + 1) for 1 less than n less than or equal to N(sub E). McLeod's Rule is verified by locating Earth's core with main field models of Magsat data; the estimated core radius of 3485 kn is close to the seismologic value for c of 3480 km. McLeod's Rule and similar forms are then calibrated with the model values of R(sub n) for 3 less than or = n less than or = 12. Extrapolation to the degree 1 dipole predicts the expectation value of Earth's dipole moment to be about 5.89 x 10(exp 22) Am(exp 2)rms (74.5% of the 1980 value) and the expected geomagnetic intensity to be about 35.6 (mu)T rms at Earth's surface. Archeo- and paleomagnetic field intensity data show these and related predictions to be reasonably accurate. The probability distribution chi(exp 2) with 2n+1 degrees of freedom is assigned to (2n + 1)R(sub nc)/(R(sub nc). Extending this to the dipole implies that an exceptionally weak absolute dipole moment (less than or = 20% of the 1980 value) will exist during 2.5% of geologic time. The mean duration for such major geomagnetic dipole power excursions, one quarter of which feature durable axial dipole reversal, is estimated from the modern dipole power time-scale and the statistical model of excursions. The resulting mean excursion duration of 2767 years forces us to predict an average of 9.04 excursions per million years, 2.26 axial dipole reversals per million years, and a mean reversal duration of 5533 years. Paleomagnetic data show these predictions to be quite accurate. McLeod's Rule led to accurate predictions of Earth's core radius, mean paleomagnetic field intensity, and mean geomagnetic dipole power excursion and axial dipole reversal frequencies. We conclude that McLeod's Rule helps unify geo-paleomagnetism, correctly relates theoretically predictable statistical properties of the core geodynamo to magnetic observation, and provides a priori information required for stochastic inversion of paleo-, archeo-, and/or historical geomagnetic measurements.
Voorhies, Coerte V.↗
Applicability of the single equivalent point dipole model to represent a spatially distributed bio-electrical source
Although the single equivalent point dipole model has been used to represent well-localised bio-electrical sources, in realistic situations the source is distributed. Consequently, position estimates of point dipoles determined by inverse algorithms suffer from systematic error due to the non-exact applicability of the inverse model. In realistic situations, this systematic error cannot be avoided, a limitation that is independent of the complexity of the torso model used. This study quantitatively investigates the intrinsic limitations in the assignment of a location to the equivalent dipole due to distributed electrical source. To simulate arrhythmic activity in the heart, a model of a wave of depolarisation spreading from a focal source over the surface of a spherical shell is used. The activity is represented by a sequence of concentric belt sources (obtained by slicing the shell with a sequence of parallel plane pairs), with constant dipole moment per unit length (circumferentially) directed parallel to the propagation direction. The distributed source is represented by N dipoles at equal arc lengths along the belt. The sum of the dipole potentials is calculated at predefined electrode locations. The inverse problem involves finding a single equivalent point dipole that best reproduces the electrode potentials due to the distributed source. The inverse problem is implemented by minimising the chi2 per degree of freedom. It is found that the trajectory traced by the equivalent dipole is sensitive to the location of the spherical shell relative to the fixed electrodes. It is shown that this trajectory does not coincide with the sequence of geometrical centres of the consecutive belt sources. For distributed sources within a bounded spherical medium, displaced from the sphere's centre by 40% of the sphere's radius, it is found that the error in the equivalent dipole location varies from 3 to 20% for sources with size between 5 and 50% of the sphere's radius. Finally, a method is devised to obtain the size of the distributed source during the cardiac cycle.
NASA Discipline Cardiopulmonary↗
A Dynamo Simulation Generating Saturn-Like Small Magnetic Dipole Tilts
Abstract Among planetary dynamos, the magnetic field of Saturn stands out in its exceptional level of axisymmetry. One of its peculiar features is that the magnetic dipole mode is tilted with respect to the planetary rotation axis by only ≈0.007° or less. Numerical dynamo simulations performed in this context have had great difficulty in producing such small dipole tilt angles without introducing ad hoc ingredients such as a latitudinally varying heat flux pattern in the outer layers or stably stratified layers (SSLs). Here we present a numerical dynamo simulation that generates a highly axisymmetric dynamo with a dipole tilt of about ≈0.0008° on average. The model consists of a deep dynamo layer and an overlying low-conductivity layer but without any SSLs. We highlight a novel mechanism where strong differential rotation generated in the atmospheric layer penetrates into the dynamo region, helping to maintain a very small magnetic dipole tilt. Plain Language Summary Saturn's dipole-dominant magnetic field exhibits a very peculiar feature: the dipole component of the planetary magnetic field is tilted by less than ≈0.007° with respect to the planetary spin axis. Numerical simulations performed in this context suggest that if a spatial heat-flux variation is imposed, along with a stably stratified region, on top of an active dynamo layer, then small dipole tilt values can be realized. Here we present a model where extremely small dipole tilt values can be achieved without these ad hoc ingredients. Our simulations demonstrate that dynamo theory allows extremely small dipole tilt values in a relatively simple model configuration.
Rakesh Kumar Yadav↗
Analysis of microstrip dipoles and slots transversely coupled to a microstrip line using the FDTD method
Printed dipole elements and their complement, linear slots, are elementary radiators that have found use in low-profile antenna arrays. Low-profile antenna arrays, in addition to their small size and low weight characteristics, offer the potential advantage of low-cost, high-volume production with easy integration with active integrated circuit components. The design of such arrays requires that the radiation and impedance characteristics of the radiating elements be known. The FDTD (Finite-Difference Time-Domain) method is a general, straight-forward implementation of Maxwell's equations and offers a relatively simple way of analyzing both printed dipole and slot elements. Investigated in this work is the application of the FDTD method to the analysis of printed dipole and slot elements transversely coupled to an infinite transmission line in a multilayered configuration. Such dipole and slot elements may be used in dipole and slot series-fed-type linear arrays, where element offsets and interelement line lengths are used to obtain the desired amplitude distribution and beam direction, respectively. The design of such arrays is achieved using transmission line theory with equivalent circuit models for the radiating elements. In an equivalent circuit model, the dipole represents a shunt impedance to the transmission line, where the impedance is a function of dipole offset, length, and width. Similarly, the slot represents a series impedance to the transmission line. The FDTD method is applied to single dipole and slot elements transversely coupled to an infinite microstrip line using a fixed rectangular grid with Mur's second order absorbing boundary conditions. Frequency-dependent circuit and scattering parameters are obtained by saving desired time-domain quantities and using the Fourier transform. A Gaussian pulse excitation is applied to the microstrip transmission line, where the resulting reflected signal due to the presence of the radiating element is used to determine the equivalent element impedance.
Tulintseff, A. N.↗
Dual frequency, dual polarized, multi-layered microstrip slot and dipole array antenna
An antenna array system is disclosed which uses subarrays of slots and subarrays of dipoles on separate planes. The slots and dipoles respectively are interleaved, which is to say there is minimal overlap between them. Each subarray includes a microstrip transmission line and a plurality of elements extending perpendicular thereto. The dipoles form the transmission elements and the slots form the receive elements. The plane in which the slots are formed also forms a ground plane for the dipoles--hence the feed to the dipole is on the opposite side of this ground plane as the feed to the slots. HPAs are located adjacent the dipoles on one side of the substrate and LNAs are located adjacent the slots on the other side of the substrate. The dipoles and slots are tuned by setting different offsets between each element and the microstrip transmission line.
Tulintseff, Ann N.↗
Dipole receiver characteristics in the presence of sea water
The receive properties for a dipole in the presence of sea water were obtained by solving integral equations for currents along the unloaded dipole and its image. For dipoles of 0.1 wavelength or higher above the sea surface, the performance resembled that of a dipole over a perfectly conducting plane; for dipoles within 0.1 wavelength above the sea surface, the relative gain dropped in about the same proportion as the relative reduction in the strength of the resultant electric field. An insulated wavelength/2 dipole with a conjugate load matched in free space had a relative power gain of 17 db below isotropic at the sea surface.
Kao, P. S.↗
Radiation patterns of interfacial dipole antennas
The radiation pattern of an infinitesimal electric dipole is calculated for the case where the dipole is vertically located on the plane interface of two dielectric half spaces and for the case where the dipole is lying horizontally along the interface. For the vertical case, it is found that the radiation pattern has nulls at the interface and along the dipole axis. For the horizontal case, it is found that the pattern has a null at the interface; that the pattern in the upper half space, whose index of refraction is taken to be less than that of the lower half space, has a single lobe whose maximum is normal to the interface; and that in the lower half space, in the plane normal to the interface and containing the dipole, the pattern has three lobes, whereas in the plane normal to the interface and normally bisecting the dipole, the pattern has two maxima located symmetrically about a minimum. Interpretation of these results in terms of the Cerenkov effect is given.
Engheta, N.↗
Dipole Field Effects on Ion Ejections from a Paul Ion Trap
Attempts at improving the quality of mass spectra obtained from a Paul trap mass spectrometer prompted an investigation of the effects of additional fields to supplement the primary rf quadrupole trapping field. Reported here are the results of the first in a series of tests that focuses on the application of a single dipole field to augment the trapping and subsequent ejections of ions stored within a Paul trap. Measurements are presented for a fixed quadrupole frequency with varying dipole frequencies. The presence of the dipole field during the quadrupole trapping phase causes ion ejections of single m/z species at discrete dipole frequencies. During the mass analysis phase, the varying dipole frequency produces a complex set of resonant structures that impact ejection time (mass range), as well as mass spectral peak intensity and width
dipole↗
Estimation of dipole-quadrupole dispersion energies.
The calculation of the dipole-quadrupole dispersion coefficient is discussed through a perturbation and a variation method. Accurate combination rules are obtained from both methods, one new and one already known. Further approximations permit computations in terms of accessible parameters. Values are calculated for the interactions of atomic pairs formed from hydrogen, alkali, and rare-gas atoms. A new relation giving the dipole-quadrupole coefficient in terms of the dipole-dipole coefficient and the dipole and quadrupole polarizabilities seems accurate, but needs further testing.
Alvarez-Rizzatti, M.↗
Magnetic dipole moment of a spherical shell with TRM acquired in a field of internal origin
The acquisition of thermoremanent magnetization (TRM) by a cooling spherical shell is studied for internal magnetizing dipole fields, using Runcorn's (1975) theorems on magnetostatics. If the shell cools progressively inward, inner regions acquire TRM in a net field composed of the dipole source term plus a uniform field due to the outer magnetized layers. In this case, the global dipole moment and external remanent field are nonzero when the whole shell has cooled below the Curie point and the source dipole has disappeared. The remanent field outside the shell is found to depend on the thickness, radii, and cooling rate of the shell, as well as the coefficient of TRM and the intensity of the magnetizing field. Some implications for the moon's remanent dipole moment are discussed.
Srnka, L. J.↗
Is the earth's dipole actually inclined with respect to the rotation axis?
Planetary exploration by deep space probes in recent years has shown that the dipole moment of some magnetized planets has a surprisingly large inclination angle with respect to the rotation axis. Applying the method developed for the source surface magnetic field of the sun (a spherical surface of 2.5 solar radii), it is suggested that the main dipole of the earth and the magnetized planets may actually be axial (the magnetic moment being parallel or antiparallel to the rotation axis), and that two or three smaller dipoles near the core surface could be responsible for the apparent inclination of the main dipole. In formulating a dynamo theory of the planetary magnetic field, such a possibility should be considered, as well as the inclined dipole case.
Akasofu, S.-I.↗
Dipole and quadrupole tests of the isotropy of gamma-ray burst locations
Dipole and quadrupole tests of the isotropy of locations on the sphere are discussed. The statistics (cos theta), the dipole moment to the Galactic center, and mean (sin-squared b - 1/3), the quadrupole moment about the Galactic plane, can be used to search for significant anisotropies in galactic coordinates. Such coordinate-system-based tests are the most powerful tests of dipole and quadrupole anisotropies in the particular coordinate system. Two statistics which have not been previously applied to gamma-ray burst data are described. The Rayleigh-Watson statistic measures the size of the dipole moment of the locations and the Bingham statistic measures the deviation of the eigenvalues of a quadrupole-like matrix from the values expected for isotropy. Tests based upon these two statistics search for dipole and quadrupole moments in spherical location data in a coordinate-system-independent, and thus model-independent, manner. They can detect an anisotropy in any direction and yield an analytic statistical significance to any detected anisotropy. The statistical tests are demonstrated herein using a variety of data sets.
Briggs, Michael S.↗
Mutual impedance of nonplanar-skew sinusoidal dipoles
The mutual impedance of nonplanar-skew sinusoidal dipoles is presented as a summation of several exponential integrals with complex arguments. Mathematical models are developed to show the near-zone field of the sinusoidal dipole. The mutual impedance of coupled dipoles is expressed as the sum of four monopole-mobopole impedances to simplify the analysis procedure. The subroutines for solving the parameters of the dipoles are discussed.
Richmond, J. H.↗
Dipole and quadrupole anisotropy of the 2.7 K radiation
Results of measurements of the dipole and quadrupole anisotropy of the microwave background radiation are reported. Balloon-borne measurements of the temperature difference between two horn antennas pointed 90 deg apart and 45 deg from the zenith were carried out at frequencies of 24.8, 31.4 and 46.0 GHz to determine three dipole and four quadrupole parameters. When combined with data from two previous balloon flights, a dipole anisotropy of 3.78 + or - 0.30 mK in the direction 11.6 + or - 0.2 h RA, -12 + or - 5 deg dec is obtained. The measurements reveal a spectral index of 0.04 + or - 0.28 between 19.0 and 46.0 GHz, indicating that the dipole effect arises from an intrinsic anisotropy in the temperature of the background and/or a first-order Doppler shift due to solar motions. A statistically significant quadrupole effect is also detected which is attributed to the intrinsic anisotropy of the 2.7 K background.
Boughn, S. P.↗