Showing papers on "Field (physics) published in 1990"

A general classification of three-dimensional flow fields

Abstract: The geometry of solution trajectories for three first‐order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three‐dimensional flow patterns defined by instantaneous streamlines for flow at and away from no‐slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three‐dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.

A class of mixed assumed strain methods and the method of incompatible modes

Abstract: A three-field mixed formulation in terms of displacements, stresses and an enhanced strain field is presented which encompasses, as a particular case, the classical method of incompatible modes. Within this frame-work, incompatible elements arise as particular ‘compatible’ mixed approximations of the enhanced strain field. The conditions that the stress interpolation contain piece-wise constant functions and be L2-ortho-gonal to the enhanced strain interpolation, ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation. The preceding conditions are formulated in a form particularly convenient for element design. As an illustration of the methodology three new elements are developed and shown to exhibit good performance: a plane 3D elastic/plastic QUAD, an axisymmetric element and a thick plate bending QUAD. The formulation described herein is suitable for non-linear analysis.

Nonlinear optical processes using electromagnetically induced transparency

Abstract: We show that by applying a strong-coupling field between a metastable state and the upper state of an allowed transition to ground one may obtain a resonantly enhanced third-order susceptibility while at the same time inducing transparency of the media. An improvement in conversion efficiency and parametric gain, as compared to weak-coupling field behavior, of many orders of magnitude is predicted.

Time-dependent density-functional theory

Abstract: Publisher Summary Density functional theory for stationary states or ensembles is a formulation of many-body theory in terms of the particle density Time-dependent density functional theory as a complete formalism is of more recent origin, although a time-dependent version This chapter describes the linear-response limit of time-dependent density functional theory along with applications to the photo-response of atoms, molecules and metallic surfaces Beyond the regime of linear response, the description of atomic and nuclear collision processes appears to be a promising field of application where the time-dependent Kohn and Sham (KS) scheme could serve as an economical alternative to time-dependent configuration-interaction calculation So far, only a simplified version of the time-dependent KS scheme has been implemented in this context Another possible application beyond the regime of linear response is the calculation of atomic multiphoton ionization which, in the case of hydrogen, has recently been found 54i55 to exhibit chaotic behavior A full-scale numerical solution of the time-dependent Schriidinger equation for a hydrogen atom placed in strong time-dependent electric fields has recently been reported A time-dependent Hartree–Fock calculation has been achieved for the multiphoton ionization of helium For heavier atoms an analogous solution of the time dependent Kohn-Sham equations offers itself as a promising application of time-dependent density functional theory

Interactions between Light Waves in a Nonlinear Dielectric

Abstract: The induced nonlinear electric dipole and higher moments in an atomic system, irradiated simultaneously by two or three light waves, are calculated by quantum-mechanical perturbation theory. Terms quadratic and cubic in the field amplitudes are included. An important permutation symmetry relation for the nonlinear polarizability is derived and its frequency dependence is discussed. The nonlinear microscopic properties are related to an effective macroscopic nonlinear polarization, which may be incorporated into Maxwell's equations for an infinite, homogeneous, anisotropic, nonlinear, dielectric medium. Energy and power relationships are derived for the nonlinear dielectric which correspond to the Manley-Rowe relations in the theory of parametric amplifiers. Explicit solutions are obtained for the coupled amplitude equations, which describe the interaction between a plane light wave and its second harmonic or the interaction between three plane electromagnetic waves, which satisfy the energy relationship ${\ensuremath{\omega}}_{3}={\ensuremath{\omega}}_{1}+{\ensuremath{\omega}}_{2}$, and the approximate momentum relationship ${\mathrm{k}}_{3}={\mathrm{k}}_{1}+{\mathrm{k}}_{2}+\ensuremath{\Delta}\mathrm{k}$. Third-harmonic generation and interaction between more waves is mentioned. Applications of the theory to the dc and microwave Kerr effect, light modulation, harmonic generation, and parametric conversion are discussed.

Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines

Abstract: The present investigation of three-dimensional reconnection of magnetic fields with nulls and of fields with closed lines gives attention to the geometry of the former, with a view to their gamma-line and Sigma-surface structures. The geometric structures of configurations with a pair of type A and B nulls permit reconnection across the null-null lines; these are the field lines which join the two nulls. Also noted is the case of magnetostatic reconnection, in which the magnetic field is time-independent and the electrostatic potential is constant along field lines.

X-ray lasers

Abstract: The first in its field, this book is both an introduction to x-ray lasers and a how-to guide for specialists. It provides new entrants and others interested in the field with a comprehensive overview and describes useful examples of analysis and experiments as background and guidance for researchers

The response of living cells to very weak electric fields: the thermal noise limit

Abstract: A physical model in which cells are considered as possible detectors of very weak periodic electric fields yields a general relation between cell size and both thermally induced fluctuations in membrane potential and the maximum change in membrane potential caused by an applied field. The simplest version of the model provides a broad-band estimate of the smallest applied electric field to which membrane macromolecules can directly respond (about 10(-3) volt per centimeter). Much smaller fields (10(-6) volt per centimeter) can be detected if there is a response in only a narrow band of frequencies or if signal averaging occurs through field-induced variation in the catalytic activity of membrane-associated enzymes. Both extensions of the simplest version remove the apparent violation of the thermal noise limit found in some experiments.

Properties of displaced number states.

Abstract: Recent developments in quantum optics have led to new proposals to generate number states of the electromagnetic field using conditioned measurement techniques or the properties of atom-field interactions in microwave cavities in the micromaser. The number-state field prepared in such a way may be transformed by the action of a displacement operator; for the microwave micromaser state this could be implemented by the action of a classical current that drives the cavity field. We evaluate some properties of such displaced number states, especially their description in phase space. The photon number distribution is shown to display unusual oscillations, which are interpreted as interference in phase space, analogous to Franck-Condon oscillations in molecular spectra. The possibility of detecting these oscillations is discussed, through the photodetection counting statistics of the displaced number states. We show that the displaced-number-state quantum features are relatively robust when dissipation of the field energy is included.

Modeling solar force-free magnetic fields

Abstract: A class of nonlinear force-free magnetic fields is presented, described in terms of the solutions to a second-order, nonlinear ordinary differential equation. These magnetic fields are three-dimensional, filling the infinite half-space above a plane where the lines of force are anchored. They model the magnetic fields of the sun over active regions with a striking geometric realism. The total energy and the free energy associated with the electric current are finite and can be calculated directly from the magnetic field at the plane boundary using the virial theorem. In the study of solar magnetic fields with data from vector magnetographs, there is a long-standing interest in devising algorithms to extrapolate for the force-free magnetic field in a given domain from prescribed field values at the boundary. The closed-form magnetic fields of this paper open up an opportunity for testing the reliability and accuracy of algorithms that claim the capability of performing this extrapolation. The extrapolation procedure as an ill-posed mathematical problem is discussed. 22 refs.

The gradient tensor of potential field anomalies: Some implications on data collection and data processing of maps

Abstract: The full gradient tensor is presently not measured routinely onboard airplanes or on land. This paper describes some improvements that can be made in strategies of data collection and in processing of potential field maps if such tensor measurements were available. We suggest that, in addition to producing for example standard total field anomaly maps, the invariants of the tensor be mapped. Strikes of magnetic or gravimetric structures may be determined from minimizing the power in the first row and column of the tensor. Invariants can be looked upon as nonlinear filters enhancing sources with big volumes. Their lateral resolution is superior to that of the field proper and, for a given resolution, the flight altitude and separation between flight lines can be increased compared with the standard mode of operation. In airborne surveys the distance between flight lines is normally much larger than the height above the ground. This may introduce severe aliasing effects in the direction perpendicular to the...

Transformation of vector magnetograms and the problems associated with the effects of perspective and the azimuthal ambiguity

Abstract: Off-center vector magnetograms which use all three components of the measured field provide the maximum information content from the photospheric field and can provide the most consistent potential field independent of the viewing angle by defining the normal component of the field. The required transformations of the magnetic field vector and the geometric mapping of the observed field in the image plane into the heliographic plane have been described. Here we discuss the total transformation of specific vector magnetograms to detail the problems and procedures that one should be aware of in analyzing observational magnetograms. The effect of the 180-deg ambiguity of the observed transverse field is considered as well as the effect of curvature of the photosphere. Specific results for active regions AR 2684 (September 23, 1980) and AR 4474 (April 26, 1984) from the Marshall Space Flight Center Vector magnetograph are described which point to the need for the heliographic projection in determining the field structure of an active region.

Determination of anisotropy field distribution in particle assemblies taking into account thermal fluctuations

Abstract: The anisotropy field distribution in assemblies of single domain particles is calculated from remanence curves. Thermal fluctuations are taken into account which are essential for particle volumes approaching the superparamagnetic critical volume. The calculations are carried out for aligned and randomly oriented assemblies. Using these results the temperature dependence of the mean anisotropy field is determined and simple expressions for the variation of the coercivity with the particle volume are given. The influence of the anisotropy field distribution and the particle–particle interaction on the magnetic properties of the assembly is discussed. Die Anisotropiefeldverteilung in Ensembles von Einbereichsteilchen wird aus Remanenzkurven berechnet. Es werden thermische Fluktuationen einbezogen, die wesentlich werden, wenn sich die Teilchenvolumina dem kritischen Volumen fur superparamagnetische Teilchen nahern. Die Rechnungen werden fur gerichtete und zufallig orientierte Ensembles durchgefuhrt. Auf der Basis dieser Resultate wird die Temperaturabhangigkeit des mittleren Anisotropiefeldes bestimmt, und es werden einfache Ausdrucke fur die Veranderung der Koerzitivfeldstarke mit dem Teilchenvolumen angegeben. Der Einflus der Anisotropiefeldverteilung und der Teilchenwechselwirkung auf die magnetischen Eigenschaften des Ensembles wird diskutiert.

Spin relaxation in small free iron clusters.

Abstract: Stern-Gerlach deflections of cold iron clusters in a molecular beam, with from 15 to 650 atoms per cluster, have been measured. It is found that the clusters deflect uniquely in the direction of the increasing field, indicating spin relaxation within the isolated clusters. The measured average magnetic moments increase with increasing cluster temperature and with increasing field, and in all cases they are found to be below the bulk value.

Homogeneous turbulence in the presence of rotation

Abstract: Turbulence in solid-body rotation is generated by a flow of air passing through a rotating cylinder containing a dense honeycomb structure and a turbulence-producing grid. The velocity field is probed downstream of this device by hot-wire probes. Using the statistical quantities characterising the fluctuating field, it is shown that the rotation affects mainly the components normal to the rotation axis and that these effects are triggered when the Rossby numbers, constructed from macroscopic turbulent quantities, are less than unity. These results are discussed in the framework of other experimental results on the subject. A theoretical interpretation, chiefly based on spectral analysis is proposed to explain the trends of the observations.

Shear-layer pressure fluctuations and superdirective acoustic sources

Abstract: We consider a sequence of boundary-value problems for the acoustic wave equation, with the pressure specified on the boundary as a function of space and time, and simulating features of the pressure field measured just outside a turbulent shear layer supporting large-scale coherent structures. The boundary pressure field has the form of a travelling subsonic plane wave, modulated by a large-scale envelope function. Three models for the envelope distribution are studied in detail, and the particular features which they exhibit are shown to be representative of large classes of amplitude functions.We start by looking at the hydrodynamic near field of the boundary pressure fluctuations, over spatial regions throughout which the motion can be taken as incompressible. Very close to the boundary, the pressure fluctuations decay exponentially with transverse distance, while at sufficiently large distances from the whole wave packet on the boundary, the pressure fluctuations have a dipole algebraic decay. We investigate the transition from exponential to algebraic decay, and find that it is effected through quite a complicated multilayer structure which depends crucially on the detailed form of the envelope.Acoustic fields are then determined both from exact solutions to the wave equation, and from matching arguments. In some cases, where the boundary source is compact, the distant acoustic fields have a simple compressible dipole type of behaviour. In other cases, however, when the boundary source is non-compact, the acoustic field has a superdirective character, the angular variation being described by exponentials of cosines of the angle with the streamwise direction. It is shown how the superdirective acoustic sources are completely compatible with the features of the inner incompressible field, and a criterion for the occurrence of the superdirective acoustic fields will be given. Superdirective fields of this kind have been observed in measurements by Laufer & Yen (1983) on a low-speed round jet of Mach number 0.1, and the general relation of our results to those experiments is explained.

An improved return stroke model with specified channel-base current

Abstract: An improved return stroke model that is both physically oriented and has a relatively straightforward mathematical basis is proposed. The current at the channel base is specified, and a time-dependent discharging of the charge stored on the leader channel determines the channel current as a function of height and time. The discharging process is separated into (1) the exponential discharge of the leader head and leader core with a relatively short time constant, less than 1 μs, which we call the “breakdown” time constant, and (2) the exponential discharge of the charge stored around the leader core with a longer time constant, of the order of microseconds. If a typical measured channel-base current is assumed and if the discharge time constants are properly chosen, electric and magnetic field wave shapes calculated with the model exhibit all the significant characteristics of measured fields. From a comparison of calculated and measured field wave shapes, we find a ratio of the breakdown time constant to the channel-base current rise time between 1 and 5. Comparison of typical characteristics of field wave shapes from natural and from artificially initiated (triggered) lightning indicates a faster discharging process for triggered lightning. Depending on the breakdown time constant, the return stroke speed determined using the well-known formula for the transmission-line model, with inputs being the peak electric field and peak current from the present model, are in the range from about 50 percent to 90 percent of the return stroke speed assumed in the present model. The corresponding transmission-line model speeds determined from the peak derivatives of the electric field and current are in the range from about 140 percent to 160 percent of the assumed return stroke speed. These results supply some indication of why transmission-line model speeds determined from the ratio of measured peak current and field derivatives in triggered lightning are greater than the speeds determined from the ratio of measured peak currents and fields. For a given channel-base current, the initial peak electric field and field derivative derived from the model increases as the height above ground of the strike point increases. The new model can therefore explain the differences in the data obtained from the triggered lightning studies at Kennedy Space Center in 1985 and in 1987 as being due to the different height of the triggering structures in those two years. If natural lightning strikes an elevated object, the increase of the initial electric field and field derivative can result in an additional substantial error in determining the peak current and peak current derivative from the transmission-line model.

Electrodynamic coupling of the magnetosphere and ionosphere

Abstract: The auroral zone ionosphere is coupled to the outer magnetosphere by means of field-aligned currents. Parallel electric fields associated with these currents are now widely accepted to be responsible for the acceleration of auroral particles. This paper will review the theoretical concepts and models describing this coupling. The dynamics of auroral zone particles will be described, beginning with the adiabatic motions of particles in the converging geomagnetic field in the presence of parallel potential drops and then considering the modifications to these adiabatic trajectories due to wave-particle interactions. The formation of parallel electric fields can be viewed both from microscopic and macroscopic viewpoints. The presence of a current carrying plasma can give rise to plasma instabilities which in a weakly turbulent situation can affect the particle motions, giving rise to an effective resistivity in the plasma. Recent satellite observations, however, indicate that the parallel electric field is organized into discrete potential jumps, known as double layers. From a macroscopic viewpoint, the response of the particles to a parallel potential drop leads to an approximately linear relationship between the current density and the potential drop. The currents flowing in the auroral circuit must close in the ionosphere. To a first approximation, the ionospheric conductivity can be considered to be constant, and in this case combining the ionospheric Ohm's Law with the linear current-voltage relation for parallel currents leads to an outer scale length, above which electric fields can map down to the ionosphere and below which parallel electric fields become important. The effects of particle precipitation make the picture more complex, leading to enhanced ionization in upward current regions and to the possibility of feedback interactions with the magnetosphere. Determining adiabatic particle orbits in steady-state electric and magnetic fields can be used to determine the self-consistent particle and field distributions on auroral field lines. However, it is difficult to pursue this approach when the fields are varying with time. Magnetohydrodynamic (MHD) models deal with these time-dependent situations by treating the particles as a fluid. This class of model, however, cannot treat kinetic effects in detail. Such effects can in some cases be modeled by effective transport coefficients inserted into the MHD equations. Intrinsically time-dependent processes such as the development of magnetic micropulsations and the response of the magnetosphere to ionospheric fluctuations can be readily treated in this framework. The response of the lower altitude auroral zone depends in part on how the system is driven. Currents are generated in the outer parts of the magnetosphere as a result of the plasma convection. The dynamics of this region is in turn affected by the coupling to the ionosphere. Since dissipation rates are very low in the outer magnetosphere, the convection may become turbulent, implying that nonlinear effects such as spectral transfer of energy to different scales become important. MHD turbulence theory, modified by the ionospheric coupling, can describe the dynamics of the boundary-layer region. Turbulent MHD fluids can give rise to the generation of field-aligned currents through the so-called α-effect, which is utilized in the theory of the generation of the Earth's magnetic field. It is suggested that similar processes acting in the boundary-layer plasma may be ultimately responsible for the generation of auroral currents.

Dynamic phase transition in the kinetic Ising model under a time-dependent oscillating field

Abstract: We analyze within a mean-field approach the stationary states of the kinetic Ising model described by the Glauber stochastic dynamics and subject to a time-dependent oscillating external field We have found that the magnetization of the system oscillates in time around a certain value that is zero at high temperatures or large field amplitudes and nonzero at low temperatures and small field amplitudes The transition from one regime to the other, which corresponds to a spontaneous symmetry breaking, is found to be continuous for sufficiently small values of the field amplitudes For higher values the transition becomes discontinuous and the system exhibits a dynamical tricritical point

Noncommutative differential geometry and new models of gauge theory

Abstract: The noncommutative differential geometry of the algebra C∞(V)⊗Mn(C) of smooth Mn(C)‐valued functions on a manifold V is investigated. For n≥2, the analog of Maxwell’s theory is constructed and interpreted as a field theory on V. It describes a U(n)–Yang–Mills field minimally coupled to a set of fields with values in the adjoint representation that interact among themselves through a quartic polynomial potential. The Euclidean action, which is positive, vanishes on exactly two distinct gauge orbits, which are interpreted as two vacua of the theory. In one of the corresponding vacuum sectors, the SU(n) part of the Yang–Mills field is massive. For the case n=2, analogies with the standard model of electroweak theory are pointed out. Finally, a brief description is provided of what happens if one starts from the analog of a general Yang–Mills theory instead of Maxwell’s theory, which is a particular case.

On the derivation of Hawking radiation associated with the formation of a black hole

Abstract: We show how in gravitational collapse the Hawking radiation at large times is precisely related to a scaling limit on the sphere where the star radius crosses the Schwarzschild radius (as long as the back reaction of the radiation on the metric is neglected). For a free quantum field it can be exactly evaluated and the result agrees with Hawking's prediction. For a realistic quantum field theory no evaluation based on general principles seems possible. The outcoming radiation depends on the field theoretical model.

Evidence of Bragg scattering in microwave Doppler spectra of sea return

Abstract: Microwave signals backscattered from the ocean (and one lake) have been collected at many different windspeeds and fetches. Doppler spectra of some signals obtained at low microwave frequencies exhibit double peaks clearly indicating Bragg scattering. At higher microwave frequencies, high wind speeds, long fetches, or in the presence of substantial swell, these splittings disappear. A model of microwave Doppler spectra based on Bragg-scattering, composite-surface theory is developed and used to show that the results obtained in these field studies are compatible with the hypothesis that Bragg scattering dominates microwave backscatter from rough water surfaces under many wind speed and incidence angle conditions. In particular, the model shows double peaks of the proper separation which disappear under the same conditions as those of the actual spectra. Furthermore, Doppler bandwidths given by the model agree with those of the field data under a variety of conditions. A rough angular dependence of the amplitudes of Bragg waves traveling in different directions with respect to the wind is deduced from the measurements. Finally, the implications of these findings for synthetic aperture radar imagery of the ocean are briefly discussed.

Configuration transition in a nematic liquid crystal confined to a small spherical cavity.

Abstract: The director-field configuration of a nematic liquid crystal confined to a spherical cavity within a urethane polymer is observed to transform from a radial- to axial-type structure as the radius of the cavity, temperature, or strength of an applied electric field are varied. The phase diagram, anchoring strength at the droplet wall, and a value of the reduced field inside the droplet are determined for different polymer/liquid crystal interfaces.