Showing papers on "Field (physics) published in 1986"

The statistics of peaks of Gaussian random fields

Abstract: A set of new mathematical results on the theory of Gaussian random fields is presented, and the application of such calculations in cosmology to treat questions of structure formation from small-amplitude initial density fluctuations is addressed. The point process equation is discussed, giving the general formula for the average number density of peaks. The problem of the proper conditional probability constraints appropriate to maxima are examined using a one-dimensional illustration. The average density of maxima of a general three-dimensional Gaussian field is calculated as a function of heights of the maxima, and the average density of 'upcrossing' points on density contour surfaces is computed. The number density of peaks subject to the constraint that the large-scale density field be fixed is determined and used to discuss the segregation of high peaks from the underlying mass distribution. The machinery to calculate n-point peak-peak correlation functions is determined, as are the shapes of the profiles about maxima.

Separation of large DNA molecules by contour-clamped homogeneous electric fields

Abstract: Electric fields can be manipulated by a method in which multiple electrodes are arranged along a closed contour and clamped to predetermined electric potentials. This method may be applied to a broad range of problems in the separation of macromolecules by gel electrophoresis. DNA molecules as large as 2 megabases can be well separated with a contour-clamped homogeneous electric field alternating between two orientations 120 degrees apart. The pattern of separation is independent of position in the gel, which is an advantage over previous methods. DNA less than 50 kilobases can be separated without distortion even at high voltage with a nonalternating contour-clamped homogeneous field. Decreased band broadening in DNA less than 200 bases can be achieved with a contour-clamped inhomogeneous field.

The self-consistent-field approach to polyatomic vibrations

Abstract: on the Born-Oppenheimer approximation which separates the motion of the electrons from that of the nuclei. The electronic motion produces an effective potential which holds molecules together and governs their vibrational motion. The complexity of this potential gives rise to the richness of much of chemistry. Thus, a theoretical picture of the vibrations of molecules is at the heart of many chemical questions. The traditional view of vibrational motion is based on an harmonic approximation to the full nuclear potential. This very simple approximation gives rise to

Energy and action flow through the internal wave field: An eikonal approach

Abstract: The energy and action flow through the small-scale part of the oceanic internal wave field is modeled by use of the eikonal technique, which is not subject to a weak interaction assumption. Both Monte Carlo calculations and a simplified model are presented and found to agree. It is found that the action flows toward slightly higher frequency (and thus the waves gain energy), in striking contrast to weak interaction predictions of a strong frequency decrease. The energy dissipation scales with depth as N2 cosh−1 (N/f), in agreement with measurements. The overall level is, however, a factor of 4 smaller than measurements. Possible sources of this discrepancy are discussed. A comparison is made with previous theoretical approaches for the depth dependence of dissipation.

Radiative gravitational fields in general relativity I. general structure of the field outside the source

Abstract: We present a well-defined formal framework, together with appropriate mathematical tools, which allow us to implement in a constructive way, and to investigate in full mathematical details, the Bonnor-Thorne approach to gravitational radiation theory. We show how to construct, within this framework, the general radiative (formal) solution of the Einstein vacuum equations, in harmonic coordinates, which is both past-stationary and past-asymptotically Minkowskian. We investigate the structure of the latter general radiative metric (including all tails and nonlinear effects) both in the near zone and in the far zone. As a side result it is proven that post-Newtonian expansions must be done by using the gauge functions (lg c)^p/c^n (p, n = positive integers).

Relation between electroabsorption in bulk semiconductors and in quantum wells: The quantum-confined Franz-Keldysh effect.

Abstract: We evaluate the interband optical absorption of a semiconductor quantum well in the presence of a uniform electric field perpendicular to the layer and neglecting excitonic effects. We show that this formally becomes the Franz-Keldysh effect in the limit of an infinitely thick layer. When the potential drop across the layer is small compared to the confinement energy we obtain behavior qualitatively different from the bulk Franz-Keldysh effect and we explain this in terms of a quantum-confined Franz-Keldysh effect; with increasing field we demonstrate numerically for a GaAs-like semiconductor that we recover Franz-Keldysh-like behavior, once the originally ``forbidden'' quantum-well transitions become strong. Our discussion gives an alternative physical picture for the Franz-Keldysh effect, including a simple explanation of the Franz-Keldysh oscillations.

Time evolution of Bloch electrons in a homogeneous electric field

Abstract: The theory of a Bloch electron moving in the presence of a homogeneous electric field is reviewed and objections to the conventional derivations are discussed. A new derivation of the time development of a Bloch electron moving in a homogeneous, but time-dependent, electric field is presented using a vector potential to describe the field rather than the usual scalar potential. This new treatment avoids all the basic assumptions of the conventional derivations and demonstrates that a Bloch electron will oscillate in a single band with the Bloch period if a homogeneous electric field is abruptly turned on, with a tunneling probability into other bands given by the conventional expression. It is also shown that the calculated optical absorption will have the same ladderlike structure that would be obtained if Wannier-Stark quantized energy levels are assumed, although the present calculation makes no such assumption. The previous objections to the existence of Bloch oscillations for electrons in a perfect periodic potential are examined and found to be irrelevant provided the tunneling probability per Bloch oscillation period is much less than one, a condition that is generally satisfied for typical elemental and compound semiconductors for electric fields smaller than ${10}^{6}$ V/cm.

Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations

Abstract: 0 The stability (i) of fully three-dimensional magnetostatic equilibria of arbitrarily complex topology, and (ii) of the analogous steady solutions of the Euler equations of incompressible inviscid flow, are investigated through construction of the second variations S2M and S2K of the magnetic energy and kinetic energy with respect to a virtual displacement field q(x) about the equilibrium configuration. The expressions for S2M and S2K differ because in case (i) the magnetic lines of force are frozen in the fluid as it undergoes displacement, whereas in case (ii) the vortex lines are frozen, so that the analogy between magnetic field and velocity field on which the existence of steady flows is based does not extend to the perturbed states. It is shown that the stability condition S2M > 0 for all q(x) for the magnetostatic case can be converted to a form that does not involve the arbitrary displacement q(x), whereas the condition S2K > 0 for all q for the stability of the analogous Euler flow cannot in general be so transformed. Nevertheless it is shown that, if S2M and S2K are evaluated for the same basic equilibrium field, then quite generally S2M+S2K > 0 (all non-trivial q). A number of special cases are treated in detail. In particular, it is shown that the space-periodic Beltrami field BE = (B, cosaz+B, sinuy, B, cosax+ B, sinuz, B, cosay+ B, sinux) is stable (i.e. S2M > 0 for all q) and that the medium responds in an elastic manner to perturbations on a scale large compared with a-l. By contrast, it is shown that S2K is indefinite in sign for the analogous Euler flow, and it is argued that the flow is unstable to certain large-scale helical perturbations having the same sign of helicity as the unperturbed flow. It is conjectured that all topologically non-trivial Euler flows are similarly unstable. 0

Electric-field dependence of linear optical properties in quantum well structures: Waveguide electroabsorption and sum rules

Abstract: We summarize the electric-field dependence of absorption and luminescence in quantum wells for fields perpendicular to the layers, present extended discussion of electroabsorption spectra and devices in waveguide samples, and derive sum rules for electroabsorption. Optical bistability, self-linearized modulation, and optical level shifting are demonstrated in self-electrooptic effect device configurations, with good modulation contrast and polarization-dependent properties. The electroabsorption spectra enable quantitative comparison of theory and experiment for absorption strengths in quantum wells with field. The sum rules enable excitonic effects to be included in the comparison, and good agreement is seen. One sum rule is also more generally applicable to electroabsorption in semiconductors.

Dissipation in a fundamental model of quantum optical resonance

Abstract: The fully quantum-electrodynamical model of a two-level atom interacting with a single-cavity mode predicts an atomic evolution whose form is dictated by the discrete nature of the field energy and its statistical distribution. We demonstrate that the revivals of atomic excitation which are the signature of the quantum nature of the evolution are strongly affected by field dissipation even when the damping hardly affects the underlying Rabi oscillations.

Active magnetic screening of coils for static and time-dependent magnetic field generation in NMR imaging

Abstract: A new method is introduced for screening or reducing extraneous magnetic fields outside coil structures The method utilises a set of current-carrying conductors or a discrete wire array to simulate the induced surface currents which occur in superconducting magnetic screens or which occur in high conductivity thick metal screens when placed around coils producing time-dependent fields or field gradients The active screens have the advantage that they work at any frequency including DC Field gradient coil structures utilising the principle can be compact and of low inductance Strong external fields can be made arbitrarily low thus making it feasible to generate large rapidly switched gradients within and in close proximity to a superconductive magnet Such gradients can be especially useful in the implementation of high speed NMR imaging methods

The average magnetic field draping and consistent plasma properties of the Venus magnetotail

Abstract: The detailed average draping pattern of the magnetic field in the deep Venus magnetotail is examined. The variability of the data ordered by spatial location is studied, and the groundwork is laid for developing a coordinate system which measured locations with respect to the tail structures. The reconstruction of the tail in the presence of flapping using a new technique is shown, and the average variations in the field components are examined, including the average field vectors, cross-tail current density distribution, and J x B forces as functions of location across the tail. The average downtail velocity is derived as a function of distance, and a simple model based on the field variations is defined from which the average plasma acceleration is obtained as a function of distance, density, and temperature.

Structure of the temperature field downwind of a line source in grid turbulence

Abstract: A Lagrangian stochastic model is used in conjunction with detailed wind-tunnel measurements to examine the structure and development of the temperature field behind a line source in grid turbulence. It is shown that on the scale of these experiments molecular diffusion and viscosity have an important influence on temperature fluctuations (particularly on the intensity of these fluctuations) and must be explicitly modelled. The model accounts for a wide range of the measured properties of the temperature field and provides a unified treatment of temperature fluctuations through all stages of the development of the temperature field. This development is discussed in terms of a simple physical picture in which the hot plume is initially smooth and is moved about bodily by the turbulence, but gradually develops increasing internal structure or patchiness as it grows with distance downstream until a self-similar state is reached in which this internal structure maintains the temperature fluctuations.

Evolution of Experimental Techniques for the Study of the Electrical Properties of Insulating Materials

Abstract: When an electric field is applied to an insulating material three basic processes can take place: the dipoles tend to rotate, ions migrate and space charge can be injected at the interfaces, depending on such parameters as temperature or applied electric field. For many years, a direct analysis was impossible since the experimentally observable variables gave only an average of what was taking place in the samples under study. Many methods were developed over the years combining available measuring techniques with theoretical hypotheses. They led to phenomenological descriptions but it appeared that a direct measurement of space charge or polarization distributions in the materials would be a way for understanding the physical processes involved. In this paper we will present the evolution of these methods and will describe on which at present seems the most promising. It uses the propagation in the sample of a pressure wave which acts as a virtual probe sensitive to charge, field or potential. A very elegant technique to generate this pressure wave involves the use of a short-duration laser pulse. It will be shown how this can find applications in a very large number of areas. Examples will be given in such different fields as electrets, HV insulation, and transducer materials.

New Results in Dielectric-Loaded Resonators

Abstract: Analysis of cylindrical dielectric-loaded resonators is reviewed. The fields within the dielectric-loaded region are postulated as the superposition of hybrid, TE, or TM modes of the infinite dielectric-loaded waveguide, while the fields in the end regions of the resonators are described by the superposition of the normal modes of a homogeneously filled waveguide. Numerical results are presented which reveal that accurate representation of the fields in the resonant structure generally require several modes. Hence, the resonant modes cannot be correlated directly with single waveguide modes. A new method for mode identification is proposed. For a wide range of parameters, the resonant frequencies, mode charts, field expansion coefficients, field intensity, and distributions are presented. Excellent agreement of the mode charts with resonant frequency measurement results are obtained.

Compton scattering in strong magnetic fields

Abstract: The relativistic cross section for Compton scattering by electrons in strong magnetic fields is derived. The results confirm and extend earlier work which has treated only transitions to the lowest or first excited Landau levels. For the teragauss field strengths expected in neutron star magnetospheres, the relative rates for excited state transitions are found to be significant, especially for incident photon energies several times the cyclotron frequency. Since these transitions must result in the rapid emission of one or more cyclotron photons as well as the Compton-scattered photon, the scattering process actually becomes a photon 'splitting' mechanism which acts to soften hard photon spectra, and also provides a specific mechanism for populating higher Landau levels in the electron distribution function. The results should be significant for models of gamma-ray bursters and pulsating X-ray sources.

Theory of the interaction of light with large inhomogeneous molecular aggregates. I. Absorption

Abstract: A general method to describe the spectroscopy of large, internally inhomogeneous particles is presented. The theory utilizes an approach similar to the one used by DeVoe in the treatment of the optical properties of polymers. The particle is divided into groups and the internal field is calculated by solving a self‐consistent set of linear equations in the field amplitude at each group in the particle. It is found that if the particle is dense the intermediate and radiation coupling mechanisms must be included in addition to the dipole–dipole coupling. Through these coupling mechanisms it is found that the excitation generated at each group in the chromophore can delocalize over regions comparable to the size of the wavelength of light. The response of the particle to the light can then be described in terms of ‘‘collective modes’’ of excitation of the entire particle, the amplitude of each mode being controlled by the geometrical relation between the groups and the efficiency in energy transfer between any two groups in the aggregate. The spatially averaged equations of the absorbance for a collection of large inhomogeneous arbitrarily shaped aggregates are derived.

The effect of parallel inhomogeneity on magnetospheric hydromagnetic wave coupling

Abstract: In a cold homogeneous plasma, fast mode and transverse mode MHD waves can be independently excited. Inhomogeneities couple the modes and allow the excitation of field line resonances by compressional (fast mode) perturbations of the magnetosphere. Past discussions have focused on inhomogeneities in the radial direction (or its equivalent in simpler geometries), ignoring gradients of the Alfv6n velocity along the unperturbed field direction. The nature of the coupling and the effectiveness of excitation are significantly modified by the presence of such gradients. One essential change is that the compressional and transverse field perturbations differ in their structure along the field. This reduces the effectiveness of the coupling between the fast (global) mode and standing (localized) field line resonances for identical harmonics of the parallel structure but allows different harmonics to couple. A fast mode wave propagating in from the outer boundary can, therefore, drive field line resonances in the region exterior to its turning point, or effective reflection point, where its amplitude has not yet decayed.

Propagation properties and condensate formation of the confined Yang-Mills field.

Abstract: The dynamical generation of a pole in the self-energy of a Yang-Mills field: an extension of the Schwinger mechanism: establishes a link between the tendency of the field to form nonperturbative vacuum condensates and its ''noninterpolating'' property in the confining phase: the fact that it has no particles associated with it. The nonvanishing residue of such a pole: a parameter b/sup 4/ of dimension (mass)/sup 4/: on the one hand provides for a nonvanishing value of , a contribution to the ''gluon condensate.'' On the other hand, it implies a dominant nonperturbative form of the propagator that has no particle singularity on the real k/sup 2/ axis; instead, it describes a quantized field whose elementary excitations are short lived. The dispersion law for these excitations is given and shows that they grow more particlelike (are asymptotically free) at large momenta, thus providing a qualitative description of the short-lived excitation at the origin of a gluon jet. At large k/sup 2/, the nonperturbative propagator reproduces nonperturbative corrections derived from the operator-product expansion.

Geomagnetic field analysis—IV. Testing the frozen-flux hypothesis

Abstract: Summary. We present a model of the magnetic field at the core–mantle boundary, for epoch 1959.5, based on a large set of observatory and survey measurements. Formal error estimates for the radial field at the core are 50 μT, compared with 30 and 40 μT for our previous MAGSAT (1980) and POGO (1970) models. Current work on the determination of the velocity of the core fluid relies on the assumption that the core behaves as a perfect conductor, so that the field lines remain frozen to the fluid at the core surface. This frozen-flux condition requires that the integrated flux over patches of the core surface bounded by contours of zero radial field remain constant in time. A new method is presented for constructing core fields that satisfy these frozen-flux constraints. The constraints are non-linear when applied to main field data, unlike the case of secular variation which was considered in an earlier paper. The method is applied to datasets from epochs 1969.5 and 1959.5 to produce fields with the same flux integrals as the 1980 model. The frozen-flux hypothesis is tested by comparing the changes in the flux integrals between 1980/1969.5, 1969.5/1959.5 and 1980/1959.5 with their errors. We find that the hypothesis can be rejected with 95 per cent confidence. The main evidence for flux diffusion is in the South Atlantic region, where a new null flux curve appears between 1960 and 1970, and continues to grow at a rapid rate from 1970 to 1980. However, the statistical result depends critically on our error estimates for the field at the core surface, which are difficult to assess with any certainty; indeed, doubling the error estimates negates the statistical argument. The conclusion is therefore, at this stage, tentative, and requires further evidence, either from older data, if good enough, or from future satellite measurements.

Development of a steady relief at the interface of fluids in a vibrational field

Abstract: The vibrations of a vessel strongly influence the behavior of the interface of the fluids in it. Thus, vertical vibrations can lead both to the parametric excitation of waves (Faraday ripples) and to the suppression of the Rayleigh-Taylor instability [1–2]. At the present time, the influence of vertical vibrations on the behavior of a fluid surface have been studied in sufficient detail (see, for example, review [3]). The behavior of an interface of fluids in the case of horizontal vibrations has been studied less. An interesting phenomenon has been revealed in the experimental papers [4, 5]: in the case of fairly strong horizontal vibrations of a vessel containing a fluid with a free surface, the fluid collects near one of the vertical vessel walls, the free surface being practically plane and stationary with respect to the vessel, while its angle of inclination to the horizon depends on the vibration rate. But if there is a system of immiscible fluids with comparable but different densities in the vessel, horizontal vibrations lead to the formation of a steady wave relief at the interface. An explanation of the behavior of a fluid with a free boundary was given in [6] on the basis of averaged equations of fluid motion in a vibrational field. The present paper is devoted to an analysis of the behavior of the interface of fluids with comparable densities in a high-frequency vibrational field.