Solutions of differential equations with regular coefficients by the methods of Richmond and Runge-Kutta

Numerical solutions of the differential equation which describe the electric field within an inhomogeneous layer of permittivity, upon which a perpendicularly-polarized plane wave is incident, are considered. Richmond's method and the Runge-Kutta method are compared for linear and exponential profiles of permittivities. These two approximate solutions are also compared with the exact solutions

Modified Hilbert transform pair and Kramers-Kronig relations for complex permittivities

Modified versions of the Hilbert transform pair and the Kramers-Kronig relations are derived for the complex permittivity of a plasma/dielectric medium which is singular at the frequency of the applied electric field equal to 0. Such a complex permittivity exists when the plasma/dielectric model allows a loss term but no restoring term. Permittivity, in which both loss and restoring terms are included, is shown to satisfy the standard Hilbert transform pair and, thus, the Kramers-Kronig relations

Angular power spectrums and their relationship to autocorrelation functions of aperture antennas

Normalized angular power spectrum representations have been derived for linear and circular aperture antennas in terms of their autocorrelation functions. Examples of their use are given

Electronic compensation for reflector surface distortion to improve radiation pattern characteristics of antennas

A simple procedure is described for determining the excitation coefficients of an array feed which compensates for the surface distortion of a reflector antenna to improve the radiation pattern in such a way as to approximate the performance of the undistorted antenna. A computer simulation for a practical feed array is presented as an example of compensation for the distortion of an actual antenna

An analysis of the effects of secondary reflections on dual-frequency reflectometers

The error-producing mechanism involving secondary reflections in a dual-frequency, distance measuring reflectometer is examined analytically. Equations defining the phase, and hence distance, error are derived. The error-reducing potential of frequency-sweeping is demonstrated. It is shown that a single spurious return can be completely nullified by optimizing the sweep width

Double universality of the transition in the supercritical state

Universality aids consistent understanding of physical properties and states of matter where a theory predicts how a property of a phase (solid, liquid, and gas) changes with temperature or pressure. Here, we show that the matter above the critical point has a remarkable double universality. The first universality is the transition between the liquid-like and gas-like states seen in the crossover of the specific heat on the dynamical length with a fixed inversion point. The second universality is the operation of this effect in many supercritical fluids, including N(2), CO(2), Pb, H(2)O, and Ar. Despite different structure and chemical bonding, the transition has the same fixed inversion point deep in the supercritical state. This advances our understanding of the supercritical state previously considered to be a featureless area on the phase diagram and a theoretical guide for improved deployment of supercritical fluids in green and environmental applications

Stochastic thermodynamics in a non-Markovian dynamical system

The developing field of stochastic thermodynamics extends concepts of macroscopic thermodynamics such as entropy production and work to the microscopic level of individual trajectories taken by a system through phase space. The scheme involves coupling the system to an environment—typically a source of Markovian noise that affects the dynamics of the system. Here we extend this framework to consider a non-Markovian environment, one whose dynamics have memory and which create additional correlations with the system variables, and illustrate this with a selection of simple examples. Such an environment produces a rich variety of behavior. In particular, for a case of thermal relaxation, the distributions of entropy produced under the non-Markovian dynamics differ from the equivalent case of Markovian dynamics only by a delay time. When a time-dependent external work protocol is turned on, the system's correlations with the environment can either assist or hinder its approach to equilibrium, and affect its production of entropy, depending on the coupling strength between the system and environment

Patterns of broad-beam antennas of different polarizations next to simple Hangar models

Broad-beam antennas of different polarizations radiating next to simple hangar models are investigated. Expressions that represent the elevation-plane patterns of slots in and 1/4 wavelength monopoles on a finite rectangular ground plane upon which a rectangular scattering object was placed were derived using geometrical theory of diffraction. These expressions were obtained by superposing the infinite ground plane solutions, reflected field solutions from the scattering object and diffracted field solutions in their respective regions of validity. Patterns for a 1/2 wavelength slot and 1/4 wavelength electric monopole are verified experimentally for a number of source locations. Data pertaining to the polarization question in regard to the multipath problem are presented

A Theoretical Investigation of the Input Characteristics of a Rectangular Cavity-Backed Slot Antenna

Equations which represent the magnetic and electric stored energies are derived for an infinite section of rectangular waveguide and a rectangular cavity. These representations which are referred to as being physically observable are obtained by considering the difference in the volume integrals appearing in the complex Poynting theorem. It is shown that the physically observable stored energies are determined by the field components that vanish in a reference plane outside the aperture. These physically observable representations are used to compute the input admittance of a rectangular cavity-backed slot antenna in which a single propagating wave is assumed to exist in the cavity. The slot is excited by a voltage source connected across its center; a sinusoidal distribution is assumed in the slot. Input-admittance calculations are compared with measured data. In addition, input-admittance curves as a function of electrical slot length are presented for several size cavities. For the rectangular cavity backed slot antenna, the quality factor and relative bandwidth were computed independently by using these energy relationships. It is shown that the asymptotic relationship which is usually assumed to exist between the quality bandwidth and the reciprocal of relative bandwidth is equally valid for the rectangular cavity backed slot antenna

Causality of plasma permittivity with loss and restoring terms

The causality of the complex permittivity for a plasma model in which both loss and restoring terms are included is shown. Discussions as to what occurs in this causality property when the loss and restoring terms vanish are presented. Results are shown to agree with earlier work