Showing papers on "Field (physics) published in 1981"

Rigorous coupled-wave analysis of planar-grating diffraction

Abstract: A rigorous coupled-wave approach is used to analyze diffraction by general planar gratings bounded by two different media. The grating fringes may have any orientation (slanted or unslanted) with respect to the grating surfaces. The analysis is based on a state-variables representation and results in a unifying, easily computer-implementable matrix formulation of the general planar-grating diffraction problem. Accurate diffraction characteristics are presented for the first time to the authors’ knowledge for general slanted gratings. This present rigorous formulation is compared with rigorous modal theory, approximate two-wave modal theory, approximate multiwave coupled-wave theory, and approximate two-wave coupled-wave theory. Typical errors in the diffraction characteristics introduced by these various approximate theories are evaluated for transmission, slanted, and reflection gratings. Inclusion of higher-order waves in a theory is important for obtaining accurate predictions when forward-diffracted orders are dominant (transmission-grating behavior). Conversely, when backward-diffracted orders dominate (reflection-grating behavior), second derivatives of the field amplitudes and boundary diffraction need to be included to produce accurate results.

Analysis of dispersive waves by wave field transformation

Abstract: The dispersive waves in a common‐shot wave field can be transformed into images of the dispersion curves of each mode in the data. The procedure consists of two linear transformations: a slant stack of the data produces a wave field in the phase slowness‐time intercept (p — τ) plane in which phase velocities are separated. The spectral peak of the one‐dimensional (1-D) Fourier transform of the p — τ wave field then gives the frequency associated with each phase velocity. Thus, the data wave field is linearly transformed from the time‐distance domain into the slowness‐frequency (p — ω) domain, where dispersion curves are imaged. All the data are present throughout the transformations. Dispersion curves for the mode overtones as well as the fundamental are directly observed in the transformed wave field. In the p — ω domain, each mode is separated from the others even when its presence is not visually detectable in the untransformed data. The resolution achieved in the result is indicated in the p — ω wave ...

Interpretation of magnetic resonance data from water nuclei in heterogeneous systems

Abstract: Nuclear magnetic resonance (NMR) data from water nuclei (1H, 2H, and 17O) can provide much information about the state of water in heterogeneous systems. In the present work, we present a theoretical framework for the interpretation of such data and discuss the implications of the theory. Due to the local anisotropy in heterogeneous systems, it is necessary to consider two components of water motion: a fast anisotropic reorientation superposed on a more extensive slow motion. On the basis of the experimentally verified assumption that these motions occur on different time scales, we develop a ’’two‐step’’ model of relaxation, showing that both motions may give important contributions to the relaxation. We derive a simple expression for the relevant correlation function, valid for isotropic systems. Anisotropic systems are also treated, making use of a new symmetry theorem for time correlation functions. The proof of this theorem is given in an Appendix. The magnitudes of the water 2H and 17O quadrupole coupling constants are estimated to 0.222 and 6.67 MHz, respectively. Results of ab initio quantum chemical calculations are presented, demonstrating the insensitivity of the water 17O field gradient to nearby ionic species. The possibilities and limitations of the NMR technique in answering the fundamental questions about water structure and dynamics in heterogeneous systems are discussed. We suggest a novel interpretation of the well‐known invariance of the ratio of 1H and 2H splittings. Furthermore, we argue that the available NMR data are consistent with a short‐ranged (≲2 molecular layers) perturbation of the water tumbling rate and anisotropy.

Magnetospheric asymmetries associated with the y-component of the IMF

Abstract: Observed magnetospheric asymmetries which occur in response to the y-component of the IMF are discussed in terms of the open model of the magnetosphere. The torque which the IMF exerts on the magnetosphere about the Earth-Sun axis results in asymmetric addition of open flux tubes to the tail lobes about the noon-midnight meridian. In response an IMF-associated By field appears across the tail lobes. The ratio between internal and external By fields will generally be same as the ratio between internal and external electric fields. If the tail flux asymmetry is related to an asymmetric distribution of the field normal to the tail magnetopause then an asymmetry in tail lobe electric field and plasma populations will immediately result, as observed. If the flux asymmetry is associated with a twist in the tail then the By field will appear but not necessary the electric field and plasma asymmetries. Generally both effects may occur together. Simple open tail lobe models are derived which demonstrate the asymmetry effects. These represent more physically satisfactory models of the tail and its plasma populations than available hitherto, but they remain somewhat unrealistic in a number of respects. Finally, it is shown that the observed asymmetry effects on closed (auroral zone) field lines may be at least qualitatively accounted for if the cross-magnetosphere IMF-associated By field pervades not only the open but also the closed field line regime, as may be generally expected.

Schrödinger operators with magnetic fields. III. Atoms in homogeneous magnetic field

Abstract: We prove a large number of results about atoms in constant magnetic field including (i) Asymptotic formula for the ground state energy of Hydrogen in large field, (ii) Proof that the ground state of Hydrogen in an arbitrary constant field hasL z = 0 and of the monotonicity of the binding energy as a function ofB, (iii) Borel summability of Zeeman series in arbitrary atoms, (iv) Dilation analyticity for arbitrary atoms with infinite nuclear mass, and (v) Proof that every once negatively charged ion has infinitely many bound states in non-zero magnetic field with estimates of the binding energy for smallB and largeL z .

Introduction to the Background Field Method

Abstract: The background field approach to calculations in gauge field theories is presented. Conventional functional techniques are reviewed and the background field method is introduced. Feynman rules and renormalization are discussed and, as an example, the Yang--Mills $\beta$ function is computed.

The direction of growth of differentiating neurones and myoblasts from frog embryos in an applied electric field.

Abstract: 1. Disaggregated single neurones and myoblasts obtained from the neural tube and somites of Xenopus laevis embryos (stages 17-21) were cultured in the presence of steady small electric fields. 2. Neurites grew preferentially towards the negative pole, or cathode, in field strengths of 7-190 mV/mm. Many turned through considerable angles to do so. This effect disappeared below a threshold level of about 7 mV/mm. 3. Greater numbers of neurones sprouted neurites in cultures exposed to an electric field compared to control cultures. The difference could be as much as tenfold. The threshold level of this phenomenon was about 6-8 mV/mm. Other cell types such as pigment cells and fibroblasts were also stimulated to differentiate in culture by an electric field, although to a lesser extent than neurones. 4. Applied electric fields had no effect on the location of the origin of neurites on the cell body. 5. Spherical myoblasts cultured in applied electric fields (36-170 mV/mm) elongated with a bipolar axis of growth which was perpendicular to the electric field. The response was graded and disappeared at field strengths below 36 mV/mm. 6. It is suggested that in vivo, the direction of neural outgrowth from the neural tube and the strict spatial organization of somites might be under the control, in part, of endogenous electric fields. Possible sources of these are discussed.

Transport of ion‐exchanging solutes in groundwater: Chromatographic theory and field simulation

Abstract: Equations describing the transport of ion-exchanging solutes governed by local chemical equilibrium through a saturated porous medium are well established in the literature. Concentration profiles resulting from the numerical solution of the general multispecies equations typically exhibit unusual and complicated features such as multiple fronts and plateau zones. This paper presents an analytical framework, based upon the theory of chromatography, which permits a priori characterization of certain key concentration profile features. The cases studied include both homovalent and heterovalent exchange in binary and ternary systems. In order to test its validity, the chromatographic analysis is applied to a field project involving direct injection of advanced treated municipal effluent into an aquifer. All of the major features observed in the available field data are accurately predicted by the chromatographic theory.

Critical conditions for magnetic instabilities in force-free coronal loops

Abstract: The remarkable magnetohydrodynamic stability of solar coronal loops has been attributed to the anchoring of the ends of loops in the dense photosphere. However, all the previous analyses of such line-tying have been approximate, in the sense that they give only upper or lower bounds on the critical amount of twist (or the critical loop-length) required for the breakdown of stability. The object of the present paper is to remove these approximations and determine the exact value for the critical twist. When it is exceeded the magnetic field becomes kink unstable and a flare may be initiated. A simple analytic stability calculation is described for an idealised loop. This is followed by the development of a general numerical technique for any loop profile, which involves solving the partial differential equations of motion. It is found, for example, that a force-free field of uniform twist possesses a critical twist of 2.49 π, by comparison with the previous bounds of 2π, for stability, and 3.3π, f...

Theory of electron spin resonance of magnetic ions in metals

Abstract: Reviewed at both a relatively elementary and more advanced level is the interpretative theory of the electron spin resonance of magnetic ions in metals. The various theoretical possibilities are illustrated by experimental examples wherever possible. Initially the development is based upon the Bloch-Hasegawa equations. The relationship of the advanced theory to this more elementary theory is emphasized. Multimagnetic-impurity experiments, the skin depth problem, the analysis of exchange, hyperfine and crystal field parameters, Redfield theory, ionic and virtual bound state models and the Kondo effect, all in relation to E.S.R. in metals, are each covered in some detail. A discussion of some outstanding problems and projections for the future are also included.

Photon Counting Probabilities in Quantum Optics

Abstract: We reconsider various approaches to the quantum theory of photodetection from the point of view of the quantum theory of measurement, and show that important differences between them depend upon the manner in which they take into account the modification of the field distribution produced by the presence of the detector. We show that the Mandel photon counting formula may lead to unphysical results, such as negative probabilities, in some situations just because this modification is not incorporated into the model. We also show that the recently developed quantum theory of continuous measurements provides a completely satisfactory framework for discussing photon counting experiments. As an illustration, an exact derivation of the photon statistics of a single-mode free field is presented, and some of the results are shown to be identical to those derived earlier by Mollow and others. We also indicate how our approach can be extended to discuss the photon statistics of fields in interaction with sources an...

An investigation of finite-element modeling for electrical and electromagnetic data in three dimensions

Abstract: The finite-element method can be used to solve the differential equations which describe electrical and electromagnetic (EM) field behavior. The equations are, respectively, Poisson's equation and the vector, damped wave equation. The finite-element equations are derived, in both cases, using the minimum theorem. While both tetrahedral and hexahedral elements may be used for the modeling of the resistivity problem, only hexahedral elements give satisfactory results for the EM problem. A disadvantage of the relatively simple mesh design used in the approach described here is the presence of long thin elements. Such elements have very poor interpolating properties, and they adversely affect the rate of convergence of the overrelaxation technique used in solving the resulting system of linear equations.For the modeling of resistivity data over an earth with one plane of symmetry, the system of equations typically has about 9000 unknowns. About 50,000 unknowns are needed to give a satisfactory solution to an EM problem where the earth has one plane of symmetry. The advantage of solving these problems with a technique such as the finite-element method is that earths with an almost arbitrary distribution of conductivity can be modeled. On the other hand, an integral-equation method can be far more cost effective for small inhomogeneities. The results from the resistivity algorithm show the adverse effect of an irregular, conducting, and polarizable overburden on dipole-dipole, induced polarization surveys. Modeling of a horizontal loop EM survey illustrates the importance of assessing the host rock conductivity before attempting to interpret inhomogeneity responses.

London approach to anisotropic type-II superconductors

Abstract: The London equations with a phenomenlogical mass tensor are used to analyze the vortex structure near the lower critical field. The anisotropy results in a transverse magnetic field in the Abrikosov vortex. This field attenuates exponentially at large distances from the vortex axis. The strongly anisotropic attenuation length is evaluated. The line energy is found in the London approximation.

Giant resonances in nuclei

Abstract: A review is given of the present situation of electric giant resonances in nuclei. Starting with the properties of the well-known electric dipole resonances the authors summarise the known experimental facts on resonances with other angular momenta and parities. They mainly discuss the giant quadrupole and giant monopole resonances which are known best. The difficulties connected with the extraction of nuclear structure information from the experimental cross sections are discussed in detail. They also review the theoretical developments in this field and emphasise especially microscopic models and the corresponding results. As far as possible the experimental facts are compared with the theoretical results.

Convective and pore scale dispersive solute transport in unsaturated heterogeneous fields

Abstract: Transport of an inert solute in unsaturated horizontally heterogeneous field soils, which differs from that in laboratory conditions, is investigated. Four solute transport factors and their variabilities have been examined: (1) convection by vertical velocity V, which changes in plane because of variability in soil properties, (2) recharge R, applied on the surface, constant in time but varying in plane, (3) pore scale dispersivity λ, variable in the field, and (4) average dispersivity λ, with field condition value. The variables V, R, λ, and solute concentration C are regarded as random. Closed form equations (requiring a numerical quadrature at most) for the probability distribution of C are derived by using several simplifying assumptions concerning the water flow regime. The mathematical solutions are capable of determining detailed statistical information about solute distribution in the field. Two soils are examined: (1) Panoche soil (150 hectares in area) with low average saturated conductivity and relatively large variance and (2) Bet Dagan soil (0.8 hectare in area) with larger average conductivity and a smaller variance. It is found that for both soils the variability of λ has very little influence and that adopting the value of λ for the entire field is sufficient. The variability of R when it is moderate has a modest effect. The three major factors are the variability in soil hydraulic conductivity, average values of rate of recharge R, and pore scale dispersion λ. It is concluded that (1) average concentration profile in the heterogeneous field cannot be modeled as the solution of convective-diffusion equation with constant coefficients and (2) if λ is taken at its laboratory-measured value, its effect upon solute distribution is negligible compared with that of soil variability, but if the large field value is adopted, it has an impact upon solute distribution. The dominant spreading mechanism in Panoche soil is heterogeneity combined with convection. Accounting for both mechanisms is warranted in most cases.

New effective field theory for the transverse Ising model

Abstract: A new type effective field approach is used to derive the thermodynamical properties of the transverse Ising model. The method is based on an exact formal identity for the two-state transverse Ising model and utilizes an exponential operator technique. The lines of critical points in the Ω-T plane are derived and the critical transverse fields ΩC are obtained analytically, for lattices with coordination numbers z = 2, 4 and 6. This simple method yields results which represent a remarkable improvement on the usual mean field approximation. Our results are also compared with those from series expansion method.

Electromagnetic backscattering from a sparse distribution of lossy dielectric scatterers

Abstract: Electromagnetic backscattering from a sparse distribution of lossy dielectric particles having random orientation and position is studied. The paper begins by using the Foldy approximation to find an equation for the mean field. From this equation, an effective permittivity for the scattering medium is obtained. The correlation of the scattered field is found by employing the distorted Born approximation, i.e., particles embedded in the effective medium are assumed to be single scatterers. The above method is then used to find the backscattering coefficients from a leaf canopy. The leaf canopy is modeled by a half space of dielectric discs that are small in comparison to a wavelength. Numerical results show that the depolarized cross section is a sensitive function of leaf inclination angle statistics.

Mode suppression means for gyrotron cavities

Abstract: In a gyrotron electron tube of the gyro-klystron or gyro-monotron type, having a cavity supporting an electromagnetic mode with circular electric field, spurious resonances can occur in modes having noncircular electric field. These spurious resonances are damped and their frequencies shifted by a circular groove in the cavity parallel to the electric field.

Main field and convex covariant density for quasi-linear hyperbolic systems : relativistic fluid dynamics

Abstract: © Gauthier-Villars, 1981, tous droits réservés. L’accès aux archives de la revue « Annales de l’I. H. P., section A » implique l’accord avec les conditions générales d’utilisation (http://www.numdam. org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

Bose-Einstein Condensation, Spontaneous Symmetry Breaking, and Gauge Theories

Abstract: Bosonic chemical potentials for a variety of relativistic field theories are introduced via the methods of functional integrals with the aim of studying the relationship between Bose-Einstein condensation and spontaneous symmetry breaking. The models studied include the noninteracting and the self-interacting charged scalar field, scalar electrodynamics and the Higgs model, and the Weinberg-Salam model. In general the chemical potential acts as an effective symmetry-breaking parameter although the phase diagrams for the two cases (${m}^{2}l0$ and ${m}^{2}g0$) look very different. It is found that the symmetry-restoring temperature in the Weinberg-Salam model increases with increasing electric charge density. Finally, the analysis of Jakobsen, Kon, and Segal of a conserved isotropic total angular momentum for the cosmic background radiation is shown to be erroneous.

Applications of scaling to problems in high-field electronic transport

Abstract: Utilizing changes in the carrier distribution function by magnitude and momentum scaling of scattering rates, the author a number of interesting results concerning ionization coefficients and transient drift and diffusion. Starting with a general definition of the ionization coefficient which includes nonlocal effects, the behavior of this coefficient under scaling is determined and used to find a simple analytical expression in terms of physical parameters valid for all field strengths. When fit to data for silicon, surprisingly large but consistent high‐field, effective ionization energies are found for electrons (3.6 eV) and holes (5.0 eV). This expression can also relate ionization near an interface to that in the bulk. Rate scaling is also used to predict changes in velocity overshoot and diffusion‐limited rise times between bulk and interface behavior. These comparisons are facilitated by a novel relationship between the time dependence of the spacial diffusion of a carrier pulse and it spacial displacement in an applied field. A classification of scattering rates suggested by momentum scaling as well as alternative scaling procedures applicable in special cases are briefly included. The former provides information on the behavior under momentum scaling of the positional‐displacement correlation factor of surface‐roughness scattering. The latter shows how scattering‐rate scaling and momentum scaling can be made to transform into each another.