The use of electroacoustic resonances to determine electron density profiles
Unknown electron density profiles determined from electroacoustic resonance frequencies by WKB approximation
Baird, A. W., III↗
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Electron tunneling as a basis for semiconduction in proteins
Electron tunneling is investigated as a possible mechanism for the conduction of electrical current in solids composed of protein molecules. An intermolecular potential barrier is assumed which takes into account the applied electric field and the possibility of image charge effects. The WKB approximation is used to calculate the net tunneling current density and resulting conductivity. The results suggest that electron tunneling per se is not a suitable mechanism for explaining the observed conductivities in such materials.
Flax, L.↗
On the theory of tunnelling in electron and proton transfer reactions.
The concept of tunnelling in the theory of electron and proton transfer reactions has recently been questioned on the ground that the situation is a nonstationary one. It has been suggested that time-dependent perturbation theory should be applied to obtain the quantum mechanical transition probability. We have done this for a square barrier. The result for most reactions is the same as obtained by the WKB approximation.
Sen, R. K.↗
Alfven waves in spiral interplanetary field
This paper presents a theoretical study of the Alfven waves in the spiral interplanetary magnetic field. The Alfven waves under consideration are arbitrary large-amplitude nonmonochromatic microscale waves of any polarization. They superpose on a mesoscale background flow of thermally anisotropic plasma. When the WKB approximation is used, an analytical solution for the amplitude vectors is obtained as a function of the background flow properties: density, velocity, Alfven speed, thermal anisotropy, and the spiral angle. The relative intensity of fluctuations compared with the magnitude of the background field has its maximum in the region near 1 AU. Thus outside of this region the solar wind is less turbulent. Owing to attenuation of microscale Alfven waves, fluctuation energy is converted into the kinetic energy of the solar wind.
Whang, Y. C.↗
Geodesic synchrotron radiation
This paper presents the results and methods of computing the high-frequency radiation emitted by freely falling particles moving in circular geodesic orbits in a spherically symmetric gravitational field. The high-frequency radiation, to which the methods of this paper apply, is the principal part of radiated energy only in the case of a particle moving in a highly relativistic, and therefore unstable, circular geodesic. The geodesic synchrotron radiation emitted in this case shows excitation of high-frequency harmonics and a narrow angular distribution. A Green's-function solution of the scalar wave equation is obtained using WKB methods. For application to relativistic circular orbits, a parabolic WKB approximation is required and yields solutions in terms of parabolic cylinder functions.
Breuer, R. A.↗
Large-amplitude hydromagnetic waves
Several aspects of the theory of large-amplitude hydromagnetic waves and their behavior in the interplanetary medium are examined. The characteristic modes of the full (i.e., nonlinearized) MHD equations and their modification by collisionless and finite-frequency effects are considered. Special attention is paid to the transverse Alfven mode, which is undamped and characterized by strictly constant pressure, density, and B; this seems to be the predominant propagating fluctuation at 1 AU. It is shown that its propagation in the small-wavelength (WKB) approximation is essentially identical to that of the small-amplitude Alfven wave of linearized theory. It is also suggested that its presence at 1 AU may provide a natural explanation of the observed power anisotropy of the fluctuations. A second-order analysis is used to study fluctuations that are not characteristic modes. It is found that for a small range of propagation directions, and subject to third-order effects, a finite-amplitude wave can exist that is linearly polarized with delta B perpendicular to both B sub zero and k; such a wave can damp nonlinearly.
Barnes, A.↗
An investigation of the stability of the Bondi-Hoyle model of accretion flow
The Bondi-Hoyle-Lyttleton (1944) accretion model is considered which involves accretion onto a massive body moving at a high Mach number with respect to the ambient medium and the production of a high-density accretion column along the axis where particle orbits intersect. The stability of steady-state solutions with respect to short-wavelength perturbations is analyzed using the WKB approximation, and the accretion column is shown to be unstable toward such perturbations. It is noted that this instability is not affected by the position of the stagnation point in the steady-state solution.
Cowie, L. L.↗
Pulse asymptotics of the Charney baroclinic instability problem
The asymptotic response of the Charney baroclinic instability problem to a localized perturbation is determined using the formalism of Briggs (1964) and exploiting a recently obtained highly accurate WKB approximate dispersion relation (Lindzen and Rosenthal, 1981). Comparison is made with previous results for two-level and Eady models. Small scales and rapid growth characteristic of the initial stages of cyclogenesis are found and the linear dispersion relation, which can be obtained from observation of zonal wind and stability, emerges as a forecast tool for prediction of geographically local cyclogenesis.
Farrell, B. F.↗
The local dispersion relation for magneto-atmospheric waves
The local dispersion relation for magneto-atmospheric waves is discussed in terms of the linearized theory of waves in a plane-stratified, inviscid, perfectly conducting atmosphere under uniform gravity. The normally used local dispersion relation is demonstrated to not be unique, depending instead on the order of derivation from the fundamental first-order perturbation equations of continuity, momentum, energy, and induction. Furthermore, it is shown that the local dispersion relation predicts that the cutoff frequency decreases with increasing magnetic field strength, while the WKB approximation method projects an increase in the cutoff frequency with increasing magnetic field strength. A new form of the local dispersion relation is developed, and consideration is given to the special case of a global dispersion relation in conditions of an isothermal atmosphere with a horizontal magnetic field.
Thomas, J. H.↗
Forced, stationary waves in a linear, stratified, quasi-geostrophic atmosphere
A finite difference model and an approximate WKB analysis were employed to test the validity of three of the Smagorinsky conclusions (1953) regarding the influence of diabatic heating upon the resultant stationary eddies. The conclusions comprised a necessity of including surface friction to avoid resonance, to account for stratospheric influence to accurately estimate the magnitude of the disturbances in the upper third of the troposphere, and the adequacy of the linear model for describing the gross features of sea-level normals at middle and high latitudes. Results of the WKB analysis of the effects of orography and diabatic heating demonstrate that streamfunctions are produced when orography forces a stationary solution. The surface friction is concluded to have a negligible effect on the solutions when the wind speeds are low. The solutions, however, require the presence of a lid for the middle troposphere to eliminate resonance responses.
Roads, J. O.↗
Observation of millimeter-wave oscillations from resonant tunneling diodes and some theoretical considerations of ultimate frequency limits
Recent observations of oscillation frequencies up to 56 GHz in resonant tunneling structures are discussed in relation to calculations by several authors of the ultimate frequency limits of these devices. It is found that calculations relying on the Wentzel-Kramers-Brillouin (WKB) approximation give limits well below the observed oscillation frequencies. Two other techniques for calculating the upper frequency limit were found to give more reasonable results. One method employs the solution of the time-dependent Schroedinger equation obtained by Kundrotas and Dargys (1986); the other uses the energy width of the transmission function for electrons through the double-barrier structure. This last technique is believed to be the most accurate since it is based on general results for the lifetime of any resonant state. It gives frequency limits on the order of 1 THz for two recently fabricated structures. It appears that the primary limitation of the oscillation frequency for double-barrier resonant-tunneling diodes is imposed by intrinsic device circuit parameters and by the transit time of the depletion layer rather than by time delays encountered in the double-barrier region.
Sollner, T. C. L. G.↗
Dynamics of dendritic sidebranching in the two-dimensional symmetric model of solidification
Within a WKB approximation, the evolution of time-dependent deformations of the needle crystal solution of the two-dimensional symmetric model of solidification is studied. It is found that perturbations with fixed small frequencies are initially amplified as they propagate from near the tip down the dendrite but ultimately decay. Localized wave packets behave rather differently; the packet continues to grow exponentially as it moves to arbitrarily large distances from the tip. The relevance of these results to sidebranching of dendrites is discussed.
Barber, Michael N.↗
Dendritic sidebranching in the three-dimensional symmetric model in the presence of noise
The time-dependent behavior of sidebranching deformations in the three-dimensional symmetric model of dendritic solidification is studied within a WKB approximation. Localized wave packets generated by pulses in the neighborhood of the tip are found to grow in amplitude and to spread and stretch as they move down the sides of the dendrite. This behavior is shown to imply that noise in the solidifying medium is selectively amplified in such a way as to produce a fluctuating train of sidebranches in qualitative agreement with experimental observations. A rough estimate indicates that purely thermal noise is probably not quite strong enough to fit the data.
Langer, J. S.↗
Velocity selection at large undercooling in a two-dimensional nonlocal model of solidification
The formation of needle-crystal dendrites from an undercooled melt is investigated analytically, applying the method of Caroli et al. (1986) to Langer's (1980) symmetric two-dimensional nonlocal model of solidification with finite anisotropy in the limit of large undercooling. A solution based on the WKB approximation is obtained, and a saddle-point evaluation is performed. It is shown that needle-crystal solutions exist only if the capillary anisotropy is nonzero, in which case a particular value of the growth velocity can be selected. This finding and the expression for the dependence of the selected velocity on the singular perturbation parameter and the strength of the anisotropy are found to be in complete agreement with the results of a boundary-layer model (Langer and Hong, 1986).
Barbieri, Angelo↗
A numerical model for gravity wave dissipation in the thermosphere
Two simplified models have been developed for the internal gravity wave dissipation due to viscosity, thermal conduction, and ion-drag in a multilayered, isothermal thermosphere. Both models use the WKB approximation, ray theory, and the time-averaged equations of gravity wave energy conservation. One model uses all the equations appropriate to a dissipative atmosphere, while the other uses the dispersion equation and polarization relations applicable to a nondissipative atmosphere, neglecting the viscous and thermal conduction contributions to the energy flux. Results from these models are compared to each other and to the results obtained by Klostermeyer (1973), using a full-wave model.
Hickey, M. P.↗
Nonparallel stability of boundary layers
The asymptotic formulations of the nonparallel linear stability of incompressible growing boundary layers are critically reviewed. These formulations can be divided into two approaches. The first approach combines a numerical method with either the method of multiple scales, or the method of averaging, of the Wentzel-Kramers-Brillouin (WKB) approximation; all these methods yield the same result. The second approach combined a multi-structure theory with the method of multiple scales. The first approach yields results that are in excellent agreement with all available experimental data, including the growth rates as well as the neutral stability curve. The derivation of the linear stability of the incompressible growing boundary layers is explained.
Nayfeh, Ali H.↗
Stability analysis of the accretion line
The stability of the flow along the accretion line in the Bondi-Hoyle-Lyttleton-type accretion flow is studied. The WKB approximation is used to analyze short wavelength linear perturbations of the axisymmetric steady state flow. The viscosity terms in the gasdynamical equations are included in the analysis. The radial modes are studied both in two- and three-dimensional accretion flow. Since a displaced accretion line cannot be defined in three-dimensional flow, the tangential modes are only analyzed in the two-dimensional flow. The analysis of the perturbed gasdynamical equations are made simpler as a result of the radial and tangential modes being decoupled in the linear regime. As was shown before, the three-dimensional accretion flow is unstable against radial modes. The two-dimensional accretion flow is found to be unstable against tangential modes, as well as against radial modes. Using typical numerical parameters which are in common use, the wavelength which gives the maximum growth rate of a small perturbation is found to be about 0.5 r(a), where r(a) is the accretion radius.
Soker, Noam↗
Remarks on transport theories of interplanetary fluctuations
The structure of a transport theory presented by Zhou and Matthaeus (1989), in which coupling of 'inward' and 'outward'-type fluctuations appears in the leading order, is studied. Allowance is made for the dynamic behavior of the 'fast' scale variables, which are averaged over to obtain slow-scale transport equations. The relationship of the two-scale transport models to transport models derived from the WKB approximation (Jeffreys and Jeffreys, 1980: Weinberg 1962; Dewar, 1970) as it has been applied to the solar wind MHD wave problem (Parker, 1965; Hollweg, 1973, 1974) is discussed.
Zhou, YE↗