Thesis (Ph. D.)--University of Michigan, 1932. / Cover title. Thesis note on label attached to p. [487]. "Reprinted from the American mathematical monthly, vol. XLII, no. 8, October, 1935."

No description available.

No description available.

Thesis (Ph. D.)--University of Washington. / Bibliography: l. [111]-113.

Promotionsarbeit der Eidgenössischen Technischen Hochschule, Zürich. / Includes bibliographical references (p. 231-233).

Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (leaves 101-107).

Thesis (Honors)--College of William and Mary, 2009. / Includes bibliographical references (leaves 29-30). Also available via the World Wide Web.

It is known that a thermistor displays inductive reactance and negative resistance at low frequencies when biased with a current greater than turnover current. Thus when shunted by a capacitance in this condition sustained oscillations are possible. These oscillations range from a sinusoidal small - amplitude character, when the system is just above the threshold for oscillation, to a strongly relaxational type when a large shunt capacitance is employed. The investigation described in this thesis involved a study of the dynamic properties of these oscillations and their relation to the static properties of the thermistor. The relevant thermistor parameters which were measured included the dependence of resistance on temperature, the thermal conductance and the thermal time constant. For the determination of the latter, special very low frequency techniques were developed. Thermistors of high resistance and low thermal time constant were selected in order to avoid the necessity for very large capacitances in the study of relaxation oscillations. The oscillations were studied over a wide range of capacitances covering the transition from sinusoidal to relaxation type. The voltage extrema and period were measured as functions of capacitance, voltage supply resistance and operating point. Also, in order to elucidate the dynamic processes involved, the transient phenomena produced by abrupt pertubations were investigated. In parallel with the experimental program, an investigation was made of the features of the differential equations describing the behaviour of the system, especially for the limit cycles corresponding to relaxation oscillations. The asymptotic form of the cycles were derived for the case where the circuital time constant greatly exceeds the thermal time constant of the thermistor. The complicated nature of the equations precluded a solution in a closed form and approximational methods were found to be necessary. However, in the case of sinusoidal oscillations of small amplitude, the period can be exactly expressed in terms of the system parameters (Burgess, Nov. 1955) and this result was confirmed experimentally. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

This thesis describes experiments designed to test the prediction made by J. E. Robinson that adiabatic oscillations could be produced in liquid helium II. Oscillations have been observed in an experimental arrangement consisting of an adiabatic container placed in a helium II bath and connected with the bath by means of a "superleak". A "thermal pulse" introduced into the container caused the liquid level to oscillate. Containers of different geometries and employing two different types of superleak, were successfully used to observe oscillations. With one of these the temperature dependence of the frequency was measured between 1.38° and 2.065°K and found to be of the expected form and magnitude. The damping of the oscillations, the rate of fluid flow and the thermal relaxation of the container have also been investigated. Both quantitatively and in their general behaviour, the observed oscillations confirm the predictions of Robinson. An analogy is suggested between the oscillations in an adiabatic container in liquid helium II and those of a gas in a Helmholtz resonator. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The thesis is concerned principally with Gunn-effect oscillations, low-frequency oscillations due to field-enhanced trapping (FET), and the interaction of the Gunn effect with traps. In the first part of the thesis, the theory of these phenomena is developed in a form which is unified in that it applies to all three independently of their physical cause i.e. field-enhanced interband transfer or FET. The theory of the quasi-steady-state is treated, in which interlevel electron transfer is assumed to be "fast" compared with electric field changes. The theory of the Gunn effect and of FET instabilities is then reviewed in this framework, as well as experimental observations. Some complements to previous theoretical knowledge are included, such as a discussion of stationary electric distributions, a rigorous derivation of the smalls-signal equivalent circuit of a Gunn diode and its application to a domain-stability criterion. Various computational simulations were performed, of which the following seem not to have been reported previously. Gunn-domains oscillation in a diode with doping increasing linearly from cathode to anode was simulated. It was known experimentally that such a device has an interesting voltage-tunability, and this was confirmed and explored. The simulation of a subcritical diode showed that its negative differential conductance is associated with the launching of accumulation layers in synchronism with the voltage modulation, which was not previously made clear. High-field domains due to field-enhanced trapping were found to grow exponentially with time; some relations between their dynamic behaviour and the trapping parameters are inferred from the results. Field-independent trapping was found to have little effect on steadily-propagating Gunn domains; in a domain, traps are depleted. The result show, however, that cumulative trapping near the cathode, and at the anode, might alter the oscillation. Field-enhanced trapping can result in the trapping of the Gunn domain at the anode, These two results are important in connection with the performance of practical Gunn oscillators in that the material should not contain too many traps; impurities causing such traps should not enter the material by contamination from the electrodes at the surface. For the experimental part of the thesis, diodes were cleaved, from slices of N-type, high-resistivity gallium arsenide onto which ohmic contacts had been applied. Above a threshold field of about 0.3 MV/m, some of these diodes exhibited small current oscillations due to high-field domains propagating at some 1 m/s. The diode-current transients revealed the existence of a trap level just below the Fermi level. Illumination strongly enhanced the field-enhanced trapping. The use of the electro-optic effect to probe the electric-field distribution in the diode was investigated. The-experiments showed that, in a non-ohmic diode biased in the high-resistance direction, there exists a high-field region near the cathode. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate