Showing papers by "Worcester Polytechnic Institute published in 1973"

Energy Spectrum of the Dicke Hamiltonian

Abstract: In this paper we analyze the energy eigenvalues of the Dicke Hamiltonian which describes the interaction of $N$ two-level atoms with an electromagnetic field. Using as a starting point the classification of the collective states proposed by Tavis and Cummings, we first derive approximate analytic expressions for the energy eigenvalues which are appropriate for special values of the collective parameters. We next evaluate a first-order correction which allows the application of our results to a wider class of collective states. An accurate description of the energy spectrum for arbitrary values of the collective parameters is provided using a method first introduced by Scharf for the case of resonant interaction, suitably generalized to account for possible frequency detuning between the radiation and the atomic resonant frequency. The limit of validity of the approximation is analyzed and the results compared with the numerical diagonalization of the Dicke Hamiltonian. With the exception of asymptotically small ranges of values of the parameters, the analytic expression for the density of energy eigenvalues derived in this paper compares very well with the results of the numerical diagonalization.

A method of simplifying large dynamic systems

Abstract: Large interconnected power systems demand complex computational schemes requiring excessive time and cost for the dynamic performance analyses. A method for simplifying such large systems described by linear differential equations, using Schwarz canonical form, is presented. This method docs not require the computation of eigenvalues and eigenvectors of the system matrix as in the case of other methods (Davison 1966, Chidambara and Davison 1967, Kuppurajulu and Elangovan 1971). A linearized power system model of order 7 is considered for this type of simplification and the response of the original and the reduced fourth-order system is compared. The results are also compared with the method of state variable grouping discussed by Kuppurajulu nnd Elangovan (1971).

Measurement of semiconductor junction parameters using lock-in amplifiers

Abstract: A phase-sensitive detection scheme is described that allows the equivalent circuit of semiconductor diodes to be determined over a wide range of operating conditions. Under reverse bias, a direct plot may be obtained of the bias dependence of the exhaustion region width through impedance measurements. In the forward sense, the diode admittance may be measured even when large currents are flowing through the diode. The capability of the method, both to yield valuable information regarding physical conditions at the junction of the device and to give insight into the charge-transport mechanisms at the interface, is illustrated through a series of measurements on selenium rectifiers.

Embedding near domains

Abstract: A class of near rings which generalizes the class of integral domains is defined. The definition of near domain is derived from the desirability of embedding near domains in near fields. The near domains presented here are shown to contain the D-rings of Berman and Siverman.

A field test for molecular sieve zeolites

Abstract: A simple field test for molecular sieve zeolites is described. The test utilizes the temperature rise (12"C to 23"C for natural zeolites) from the heat of immersion in water of an activated sample. A rugged, portable kit was designed for practical field trse and maintenance. fntroduction Since the discovery in the 1950's of large deposits of zeolites occurring as small (<25 pm) crystals in altered siliceous pyroclastics and flows, it has been recognized that a simple field test for determining the presence and percent of zeolite content would be useful for exploration and mining. It has been difficult in the field to differentiate diatomite, vitric ash, or bentonite-bearing beds from zeolitl.u,ed pyro. clastics in some deposits. A test to detect the presence of zeolite was reported by Helfferich (1964) using a combination of ion exchange and pH measurement, but the test is qualitative and highexchange-capacity interfere. Molecular sieve zeolites have several unique properties which make it possible to distinguish them from other fine-grained minerals and even other zeolites such as analcime. The molecular sieve zeolites contain intracrystalline pores which are interconnected to the crystal surfaces by ports of 8-, 10-, or 12-membered rings of oxygens. Their porous crystal structure gives them high sorptive capacities to 50 percent pore volume or to 30 wt percent water sorbed (with accompanying high heats of sorption or immersion up to 100 cal/gm) and selective sorption of smaller molecules, such as water and COz, with exclusion of larger molecules. Being network aluminosilicates, the Al3. for Sia* substitutions provide active sites for exchangeable cations located in the crystal pores. As with other minerals the zeolites are best identified by X-ray diffraction analysis, but the instrument is too expensive and bulky for general field use. The optical

Simulation of Dissolved Oxygen Profile

Abstract: A stochastic mathematical model is developed to describe the probability distribution of dissolved oxygen in streams which have received an input of both thermal and organic pollution. The stochastic model is simulated under conditions of constant and variable temperature, and the results of the simulation are compared with the mean values predicted by recent deterministic models. The simulation provides an estimate of the variability of the DO level to be expected at different points as well as a means of generating typical oxygen sag curves for a stream.

On the approximation of periodic solutions of equations with bounded nonlinearities

Abstract: We present a method for obtaining a closed-form approximation to harmonic periodic solutions of a class of ordinary differential equations containing a bounded, Lipschitzian nonlinearity and a sinusoidal forcing term. Our technique replaces the continuous nonlinearity with a suitable step-function nonlinearity and uses the Phase-Shift-Averaging Method to write the solution of the piecewise-linear problem in closed form.

Oxygen Sag Curve with Thermal Overload

Abstract: A deterministic model is developed for the oxygen sag curve for a variable temperature condition under thermal overload. With the help of this model, optimal locations of thermal and organic outlets with respect to each other can be determined for a predetermined minimum dissolved oxygen concentration in the river. In the presence of the thermal overload, the critical oxygen concentration (lowest) is much lower than that under constant temperature conditions of the stream, and it occurs earlier, the recovery of DO could be faster, and indeed the DO level downstream may be higher than under the constant temperature condition. The critical DO concentration and the critical oxygen deficit do not necessarily occur at the same point in the presence of the thermal overload. The mathematical models presented herein could be used in place of the constant temperature models.

Adjustment of Friction in Hydraulic Models of Lakes

Abstract: For complete dynamic similarity between a hydraulic model of a lake or closed basin and its prototype, both the Froude number and the Proudman number must be equal in the model and the prototype. For turbulent flow the Proudman number can not be explicitly determined and adjustment of model friction may be required. A method for adjustment of model friction is described which requires comparison of the damping of a standing long wave (or seiche) in the prototype and in the model basin. Assuming that the model frictional resistance could be decomposed into smooth boundary resistance and the resistance due to the addition of roughness elements, a mathematical formulation was developed for use in predicting the decay modulus for a roughened model basin. Good agreement was found between the analytical predictions and experimental results.

Closed-form approximation of the periodic response of a system with a saturating non-linearity†

Abstract: A technique for approximating harmonic, periodic solutions of a class of non-linear equations involving u saturation non-linearity is applied to a fourth-order equation which describes an electrical circuit containing a non-linear amplifying element. The computational effort required to obtain the closed-form approximation which this method yields is compared with that required for a numerical solution by the conventional methods of quasilinearization and patching. The various methods use comparable amounts of computer time, but the other classical methods do not offer the advantage of the closed-form approximation which our technique provides.

Finite dimensional representations of the ${\rm SU}(2)$-current Lie algebra

Abstract: We give a complete classification of the finite dimensional solutions for the Lie functional equations ofSU(2)

Graphics software for BASIC

Abstract: This article was prompted by the article written by Jon Meads in the Fall 1973 SIGGRAPH report. (1) A graphics package has been developed for use on Digital Equipment Corporation's GT40 and GT44 series of minicomputer-based graphics systems. Within the limitations of the machines, a package of graphics software was written to allow almost complete control of the display processor by a programmer using the language BASIC.