Reverse Drift Research Articles

Stochastic theory of a fluid model of producers and consumers coupled by a buffer

This paper analyzes, derives efficient computational procedures and numerically investigates the following fluid model which is of interest in manufacturing and communications: m producing machines supply a buffer, n consuming machines feed off it. Each machine independently alternates between exponentially distributed random periods in the ‘in service' and ‘failed' states. Producers/consumers have their own failure/repair rates and working capacities. When the buffer is either full or empty some of the machines in service are not utilized to capacity; otherwise they are fully utilized. Our main result is for the state distribution of the Markovian system in equilibrium which is the solution of a system of differential equations. The spectral expansion for its solution is obtained. Two important decompositions are obtained: the eigenvectors have the Kronecker-product form in lower-dimensional vectors; the characteristic polynomial is factored with each factor an explicitly given polynomial of degree at most 4. All eigenvalues are real. For each of various cases of the model, a system of linear equations is derived from the boundary conditions; their solution complete the spectral expansion. The count in operations of the entire procedure is O(m3n3): independence from buffer size exemplifies an important attraction of fluid models. Computations have revealed several interesting features, such as the benefit of small machines and the inelasticity of production rate to inventory. We also give results on the eigenvalues of a more general fluid model, reversible Markov drift processes.

Stochastic quantisation and killing symmetries of random systems

Recent results about the supersymmetries of random systems governed by stochastic differential equations have classical analogues in terms of geometrical symmetries in the configuration space of commuting variables. The related results are: (1) the reversible drift velocity of a stationary stochastic process is a Killing vector of the diffusion metric; (2) the irreversible drift velocity is a geodesic tangent vector; (3) the stationary current conservation equation is a special case of the general result that scalar products of Killing vectors with geodesic tangent vectors are constants of the motion. The physical postulate is that microscopic reversibility is to the normality of time translation generators what time reversal invariance is to the hermiticity of hamiltonians.

Light induced reversible drift mobility effect in a-asse thin films

Reversible photoinduced change of hole drift mobility was found in a-AsSe film. The drift mobility decreased by an order of magnitude due to He-Ne laser irradiation. The special peculiarity of this effect which differs significantly from photostructural changes observed is that thermal annealing of 6 hours at 80 °C, well below the transition temperature restores the initial larger drift mobility.

Behavior of mid-latitude F-region irregularities deduced from spaced-receiver VHF scintillation measurements

Using three closely spaced antennas, mid-latitude night-time scintillations at 136 MHz were observed under geomagnetically quiet conditions during June–July 1982. By means of correlation analysis, characteristics of ionospheric irregularities such as drift velocities, shapes and sizes were investigated for seven scintillation events. In the premidnight hours mostly southward or southwestward drifts were observed, while in the postmidnight hours the percentage of northward drifts increased. Mean northward and southward drift velocities were 25 m s −1 and 23 m s −1, respectively. Large northward drifts (> 80m s −1) were occasionally observed in the postmidnight hours. Peculiar drift reversals from northward to southward occurred abruptly in the midst of strong and high-pitch scintillations. They were accompanied by sharp increases in TEC. The directions of the major axes of the diffraction pattern ellipses are coincident with those of the geomagnetic field lines, which suggests that the irregularities are well field-aligned. The mean axial ratio and mean minor radius are 6.2 and 182 m, respectively. The axial ratio increases and the minor radius decreases with increasing S 4.

A study of hard X-ray associated meter-decameter bursts observed on December 19, 1979

We present the results of a study of the relationship of a complex meter-decameter wavelength radio burst observed with the Clark Lake E-W and N-S interferometers, with a hard X-ray burst observed with the X-ray spectrometer aboard ISEE-3. The radio burst consisted of several type III's, reverse drift type III's, a U burst, and type II and type IV bursts. The X-ray emission was also complex. The radio as well as hard X-ray emissions were observed before the flash phase of the flare; they were not always associated and we conjecture that this may constitute evidence for acceleration of electrons high in the corona. On the other hand, all components of the reverse drift burst were associated with hard X-ray subpeaks, indicating multiple injection of electron beams along field lines with different density gradients. While the type II burst appeared to be related to the hard X-ray burst, a detailed correspondence between individual features of the radio and hard X-ray burst emissions could not be found. The type IV burst started after all hard X-ray emissions ceased. Its source appeared to be a magnetic arch, presumably containing energetic electrons responsible for the gyrosynchrotron radiation of type IV.

Augmented Langevin approach to fluctuations in nonlinear irreversible processes

A Fokker-Planck equation derived from statistical mechanics by M. S. Green (J. Chem. Phys. 20:1281 (1952)) has been used by Grabert et al. (Phys. Rev. A 21:2136 (1980)) to study fluctuations in nonlinear irreversible processes. These authors remarked that a phenomenological Langevin approach would not have given the correct reversible part of the Fokker--Planck drift flux, from which they concluded that the Langevin approach is untrustworthy for systems with partly reversible fluxes. Here it is shown that a simple modification of the Langevin approach leads to precisely the same covariant Fokker--Planck equation as that of Grabert et al., including the reversible drift terms. The modification consists of augmenting the usual nonlinear Langevin equation by adding to the deterministic flow a correction term which vanishes in the limit of zero fluctuations, and which is self-consistently determined from the assumed form of the equilibrium distribution by imposing the usual potential conditions. This development provides a simple phenomenological route to the Fokker--Planck equation of Green, which has previously appeared to require a more microscopic treatment. It also extends the applicability of the Langevin approach to fluctuations in a wider class of nonlinear systems.

Structure and dynamics of the winter polar cap F region

All‐sky imaging photometer measurements and ionospheric soundings taken at Thule, Greenland (86° corrected geomagnetic latitude), in December 1979 and January 1982 reveal the large‐scale organization of the winter polar cap ionosphere. Three groups of forms have been identified: (1) The most predominant features are sun‐aligned, generally unstructured, subvisual, F region arcs, extending for more than 1000 km (limit of all‐sky field of view) across the polar cap. In general, these arcs drift from dawn to dusk at speeds between 100 and 250 m s−1; however, stagnation of arc drift and drift reversals have been observed. The arcs are produced by soft particle precipitation. (2) During a magnetically disturbed period the arcs disappeared, and large patches of enhanced F region ionization drifted at speeds of 250 to 700 m s−1 across the field of view in the antisunward direction. Although arcs are produced by soft particle precipitation, preliminary results from the Dynamics Explorer satellite do not indicate any localized soft electron precipitation into the patches. (3) On a few occasions both forms were observed simultaneously. Between F region sun‐aligned arcs, which were drifting from dawn to dusk, small patches of ionization were observed moving at much higher speed in the antisunward direction. Both the arcs and the patches appear as strong localized irregularities in the ionospheric soundings. The Doppler information provided by the aircraft's Digisonde 128PS was used to relate backscatter traces to individual arcs or patches and to track individual features over more than 1500 km. For a large number of observations the time variation of measured Doppler velocities suggests specular reflection from electron density enhancements associated with the optical forms, rather than scatter from field‐aligned irregularities imbedded in the arcs or patches. A simple velocity filter applied to the ionogram data permitted the generation of range‐time characteristics for selected ionization drift velocities. A tendency for high velocities to occur during magnetically active periods was found. The ionospheric soundings showed that the F region arcs are bands of enhanced ionization, imbedded in a background ionosphere with a base height (h′F) of approximately 250 km and a critical frequency of approximately 4 MHz (∼2 × 105 el cm−3). The virtual heights in the ionograms did not change during transit of the arcs through the zenith. During the active periods, when the antisunward moving patches were observed, the background ionization dropped to less than 3 MHz (105 el cm−3) while the base height (h′F) moved up to heights above 400 km. The strongly ionized patches (f0 F2 > 8 MHz), however, were observed to reach a minimum virtual range of ∼250 km during the zenith transit, leading during their passage through the zenith to rapid h′F fluctuations of the order of 200 km within minutes.

Radio Evidence for Electron Acceleration by Transverse Shock Waves in Herringbone Type II Solar Bursts

Perhaps the most direct evidence to date for shock wave acceleration of electrons in the solar corona is provided by radio observations of Type II bursts containing herringbone structure (Roberts 1959). On spectral records the herringbones appear to resemble miniature forward and reverse drift Type III bursts extending above and below the Type II backbone.

Analysis of particle orbits in an ultra-high-current plasma column

Electron collisionless motion in an infinite plasma column is studied under the conditions of relaxed Bennet equilibrium in order to understand the macroscopic structure of the equilibrium, and serve as a preliminary step in an expanded study aimed at determining the relative importance of drift reversed currents. The model assumes, in the framework of the Vlasov theory, a Bennett equilibrium released of the constraint of a constant transverse temperature, a constant macroscopic speed of the charged particles with a constant ratio of their densities; the particles, however, are not required to be monoenergetic, which leads to a diffuse plasma edge. The results, in graphical form, define the values of the parameters for which drift reversals occur, and the conditions under which variations of the parameter values do not affect drift reversals, thus suggesting simplifications in the parametric study of particle trajectories.

Position and Polarization of Solar Drift Pair Bursts

Reverse drift pairs were first described by Roberts (1958) and later by Ellis (1969) and de la Nòe and Moller-Pedersen (1971). Figure 1 shows a 10-min section of the spectrograph record and the corresponding section of the polarimeter record. The figure contains several reverse drift pairs and illustrates the main features of RDPs, namely: (1) frequency drift rate of about 4 MHz s-1 (i.e. a factor of ~50 faster than Type lis and a factor of ~2 slower than type Ills); (2) drift to higher frequencies (i.e. opposite to that of Type II and III bursts, hence the name ‘reverse’); and (3) an apparent ‘echo’ of the burst some 1 to 2 s later to form a pair. On 1979 February 17/18 a noise storm consisting of Type 1 bursts, Type III bursts and an underlying continuum was observed with the Culgoora spectropolarimeter, spectrograph, and radioheliograph. During this noise storm, the spectrograph record showed several hundred RDP bursts, and about fifty FDPs. Here we report new results on the polarization-of drift pair bursts, present further data on RDP positional and frequency characteristics, and then comment on existing theories concerning RDPs.

Takapoto. La prospérité, retour aux îles

A temporary movement of Tuamotuan people back to their atoll of Takapoto was noted in 1975. This is seen as an example of reverse drift from the cities, as these people had been resident in Tahiti prior to their return, but with unemployment there and the economic possibilities of making copra and pearl shell money on their home atoll, life looked better on the atoll. A regular air service to and from Tahiti was an additional positive factor in this move. But this may be only a temporary or 'boom' period of increase in the atoll population, for the economic advantages may be short-lived.

Reliability Study of GaAs MESFET's

Failure modes have been studied phenomenologically on a small-signal GaAs MESFET with a 1mu m aluminum gate. Three major failure modes have been revealed, i.e., gradual degradation due to source and drain contact degradation, catastrophic damage due to surge pulse, and instability or reversible drift of electrical characteristics during operation. To confirm the product quality and to assure the device reliability, a quality assurance program has been designed and incorporated in a production line. A cost-effective lifetime prediction method is presented that utilizes correlations between RF parameters and dc parameters calculated using an equivalent circuit model. Mean time to failure (MTTF) value of over 10/sup 8/ h has been obtained for the GaAs MESFET for an operating channel temperature of 100/spl deg/C.

Solutions of the Fokker-Planck equation in detailed balance

The solutions of the Fokker-Planck equation in detailed balance are investigated. Firstly the necessary and sufficient conditions obtained by Graham and Haken are derived by an alternative method. An equivalent form of these conditions in terms of an operator equation for the Fokker-Planck Liouville operator is given. Next, the transition probability is expanded in terms of an biorthogonal set of eigenfunctions of a certain operatorL. The necessary and sufficient conditions for detailed balance leads to a simple operator equation forL. This operator equation guarantees that on!y half of the biorthogonal set needs to be calculated. Finally the dependence of the eigenvalues on the reversible and irreversible drift coefficient is discussed.

Effects of chemical treatment of germanium surfaces on reverse current drift

Effects of chemical treatment of germanium surfaces on reverse current drift

The influence of surface treatment, ambient gas and temperature on the reverse characteristics of alloyed silicon p-n junctions

A study has been made of the electrical characteristics of silicon alloyed p+-n diodes in a variety of ambient gases, at temperatures between 20°C and 250°C, and after several types of surface chemical treatment. Results obtained on devices before heating are interpretable in terms of accepted theory for device characteristics under the influence of channels and accumulation layers but after heating to 250°C in oxygen or nitrogen several complicating features are observed. Results indicate that heating in oxygen produces slow surface states giving rise to reverse current drifts in wet atmospheres over periods of the order of 15 minutes, while heating in nitrogen produces a lowered surface potential with resulting low-voltage surface breakdown, which suggests that nitrogen may be unsuitable as an encapsulation gas in devices designed to operate at high temperatures.

Variable-characteristic p—n-junction devices based on reversible ion drift

It has been found that germanium wafers containing a p-type impurity and lithium, a high atomic mobility n-type impurity, may be used to construct junction devices, called flexodes, whose I–V characteristics may be reversibly transformed between resistive and rectifying states. These transformations result from the application of electric fields at intrinsic temperatures (≳ 100°C). They are due to field-enhanced diffusion of Li+ ions. Reverse bias is thought to cause electric-field-controlled precipitation of excess lithium in the region of the p—n junction. Such precipitation can degrade the rectification by causing breakdown and shorting of the junction. The precipitates may be removed from the junction region and the rectification may be restored by the application of forward bias. Methods of making flexodes and of obtaining the junction transformations are described, and a qualitative model for the growth of precipitates in the applied electric field is discussed. Several proposed practical applications of flexodes are also included.

Current-Carrier Transport and Photoconductivity in Semiconductors with Trapping

Fundamental differential equations are derived under the unrestricted approximation of electrical neutrality that admits trapping. Applied magnetic field is taken into account. The general transport equations derived hold without explicit reference to detailed trapping and recombination statistics. Modified ambipolar diffusivity, drift velocity, and lifetime function, which depend on two phenomenological differential "trapping ratios," apply in the steady state. The same diffusion length is shown to hold for both carriers, and a general "diffusion-length lifetime" is defined. Mass-action statistics are considered for cases of (one or) two energy levels. Certain "effective"---rather than physically proper---electron and hole capture and release frequencies or times that apply to concentration increments are defined, and a restriction from detailed balance to which they are subject is derived. Found widely useful is "capture concentration," the concentration of centers at equilibrium that are occupied times the fraction unoccupied. Criteria are given for minority-carrier trapping, recombination, and majority-carrier trapping, and for "shallow" and "deep" traps. Applications of the formulation include: the diffusion-length lifetime corresponding to the Shockley-Read electron and hole lifetimes, and that for recombination centers in the presence of (nonrecombinative) traps; linear and nonlinear steady-state and transient photoconductivity; the photomagnetoelectric effect; and drift of an injected pulse. The small- and large-signal nonlinearities that may occur with saturation of deep traps provide a single-level model for superlinearity. Photomagnetoelectric current is found to be decreased by minority-carrier trapping, through an increase in diffusion length. A simple general criterion is given for the local direction of drift of a concentration disturbance. With trapping, there may be "reverse drift," whose direction is normally that for the opposite conductivity type. With solutions of one type obtained for drift of an injected pulse, multiple trapping ultimately results in Gaussian mobile-carrier distributions which spread as if through diffusion and which drift at a fraction of the ambipolar velocity. With solutions of another type, related to reverse drift is the occurrence of local regions of mobile-carrier depletion which may in practice extend over appreciable distances.

Theory of Current-Carrier Transport and Photoconductivity in Semiconductors with Trapping

Fundamental differential equations are derived under the unrestricted approximation of electrical neutrality that admits trapping. Extension is made for applied magnetic field. The transport equations derived hold without explicit reference to detailed trapping and recombination statistics. Modified ambipolar diffusivity, drift velocity and lifetime function apply in the steady state. The same diffusion length is shown to hold for both carriers, and a general “diffusion-length lifetime” is defined. Atass-action statistics are considered for cases of (one or) two energy levels. Certain “effective” — rather than physically proper — electron and hole capture and release frequencies or times that apply to concentration increments are defined. Criteria are given for minority-carrier trapping, recombination and majority-carrier trapping, and for “shallow” and “deep” traps. Applications of the formulation include: the diffusion-length lifetime for the Shock-ley-Read electron and hole lifetimes; linear and nonlinear steady-state and transient photoconductivity; negative photoconductivity; the photoconductive decay observed by Hornbeck and Haynes in p-type silicon; the photomagnctoelcctric effect; and drift of an injected pulse. Photomagnetoeleclric current is found to be decreased by minority-carrier trapping, through an increase in diffusion length. A simple general criterion is given for the local direction of drift of a concentration disturbance. With trapping, there may be “reverse drift,” whose direction is normally that for the opposite conductivity type, and also local regions of carrier depletion that may extend in practice over appreciable distances.