William Streifer

A New Model For Age-Size Structure of a Population

An equation describing the dynamics of single species populations is derived. The model allows for variations in the physiological characteristics of animals of different ages and sizes. An analytical solution which holds under certain specific conditions is found. It is shown that Von Foersters equation, the logistic equation and other prior models are special cases of the new model. See full-text article at JSTOR

Complex Rays with an Application to Gaussian Beams

The use of rays to construct fields is illustrated by finding the field in the region z>0 when the field is given on the plane z = 0. This construction is valid for complex rays as well as real ones. The method is applied to a gaussian field in the plane z = 0, in which case a gaussian beam results. The calculation involves only complex rays. Exactly the same results are also obtained by applying the method of stationary phase to an integral representation of the field. However, the ray method is simpler than the stationary-phase method, and it is also applicable to problems for which the stationary-phase method cannot be used because no integral representation of the field is known.

Scalar Analysis of Radially Inhomogeneous Guiding Media

Inhomogeneities in refractive index have been suggested as a means of guiding waves in the submillimeter through optical wavelength range. In this paper, asymptotic techniques are applied to the scalar wave equation to determine propagation constants and mode patterns in radially inhomogeneous transmission systems with circular cross sections. Results are obtained with the variation of refractive index specified only as a general class of functions. Rectangular geometries are treated as a special case.

Analytic Solution of Ray Equations in Cylindrically Inhomogeneous Guiding Media. 1: Meridional Rays

Analytic methods are employed to solve the meridional ray equations for propagation in inhomogeneous cylindrical systems such as gas lenses and GRIN rods, which focus rays by virtue of a gradual radial decrease in refractive index. Digital computer programs are used to carry out the necessary algebraic manipulations, and the results apply for arbitrary index variations and initial conditions. Comparisons are made with known exact solutions.

Comparison of laser mode calculations.

In this paper we show that numerical and kernel expansion procedures for solving the laser mode problem do not differ in essence; both convert the integral equation into a matrix equation. Furthermore, the Fox and Li iterative method is shown to be a matrix diagonalization technique. A particular kernel expansion using Gaussian-Hermite functions is discussed, as are matrix diagonalization techniques. Numerical results are compared with other published values. We conclude that the optimum procedure is to use gaussian quadrature numerical integration to convert to a matrix equation and diagonalize the matrix with the computer program ALLMAT. This method is computationally simple and simultaneously determines many modes. Also, it is applicable to unstable and/or tilted mirror resonators with selectively coated reflectors.

Unstable Laser Resonator Modes

In this paper, mode patterns and losses are determined for unstable laser resonators with finite, rectangular reflectors of spherical curvature. An analysis of the uniform intensity mode, based upon the Cornu spiral is given. For more general calculations, gaussian quadrature integration is used to convertthe integral equation for the modes into a matrix equation. The latter is solved using ALLMIAT on a digital computer, thereby simultaneously determining many modes. The mode competition effectreported by Siegman and Arrathoon is shown to occur because the unstable modes do not generally retain their ordering, according to relative loss, as the reflector size changes. We also discuss a perturbation calculation in which the infinite mirror solutions of Bergstein are used as expansion functions.

Laser Resonators with Tilted Reflectors

In this paper we solve the mode problem for laser resonators having identical tilted spherical reflectors of rectangular shape in both stable and unstable configurations. Gaussian quadrature integration is employed to convert the integral equation for the modes into a matrix equation which is solved with the matrix diagonalization program ALLMAT. Plane parallel and aligned concentric resonators have identical losses; however, the latter are shown to be much less sensitive to alignment. We find that for low loss modes in the tilted stable resonator the loss can be approximated by the average loss of two aligned resonators; the region of validity for this approximation is given. Stable resonator losses increase monotonically with tilt; however, this is not always true for the unstable resonator where the loss may decrease for small tilts.

A Model for Population Reproducing by Fission

A partial differential equation which describes the dynamics of a single species population for animals reproducing by fission is set forth. The equation is then applied to Dugesia tigrina. Whenever possible, experimental results are used to determine pertinent parameters. Tests are performed to determine those parameters upon which the model has a critical dependence. The model gives results which are qualitatively in agreement with empirical populations. See full-text article at JSTOR

Optical Resonator Modes—Rectangular Reflectors of Spherical Curvature*

A combined analytic and numerical technique for solving the integral equation for optical-resonator modes based on the work of Schmidt is introduced. The method involves a kernel expansion which converts the integral equation to a matrix equation. Numerical diagonalization of the matrix then yields all modes simultaneously.The potentialities of the method in treating resonator configurations such as those with tilted or irregular mirrors, which are intractable by present analytic or semi-analytic theories, are discussed. Numerical results of mode patterns, including both magnitude and phase, losses, and resonance conditions are presented for a resonator formed by two spherical mirrors of differing curvature and rectangular cross section. These results are for a moderately large Fresnel number and include “high-loss” geometries.

Applying Models Incorporating Age‐Size Structure of a Population to Daphnia

Partial differential equations which describe the dynamics of single species populations are applied to Daphnia pulex. Whenever possible, experimental results are used to determine pertinent parameters. Tests are performed to find parameters upon which the model has a critical dependence. The model gives results which are qualitatively in agreement with empirical populations. See full-text article at JSTOR