A variational principle for nonconservative power systems

Recent results for nonconservative dynamical systems involve a variational principle of the Hamilton type. In this approach the velocity of variation and the variation of velocity are not commutative as in the case of mechanics governing conservative dynamical systems. In this paper we adapt the above approach to power systems which include the effects of transfer conductances. For such power systems we show that if certain noncommutative rules (which are consistent with the ones used for the variation of velocities in nonconservative dynamical systems) are used, then it is possible to employ a variational principle of the Hamilton type to derive the classical model for power systems. Numerous simulations of specific postfault multimachine power systems have verified that the above noncommutative rules are indeed satisfied for the types of power systems which we consider.The present results give additional understanding for the types of energy functions that have recently been used in transient stability studies of power systems. In these works, several attributes of energy functions have been ascertained by means of simulations and heuristic reasoning, rather than analysis (e.g., path-dependent terms of energy functions have been approximated by making linear trajectory assumptions).The work of the first author was supported by the National Science Foundation under Grant No. ECS84-51091. The work of the second author was supported by the National Science Foundation under Grant No. ECS84-19918.     

A variational coupled-mode theory including radiation loss forgrating-assisted couplers

We calculate higher order effects such as frequency shifts and radiation loss in grating waveguides and grating couplers. The approach follows a vector variational principle which incorporates the Floquet components correct to first order. It is unnecessary to bring radiation modes into the formalism. This yields a simple coupled-mode formulation which includes attenuation due to radiation loss, and is correct to third order in the index contrast of the grating. Numerous examples are given which show excellent agreement with rigorous numerical simulations     

Application of variational principle for calculation of resonant frequencies of cylindrical dielectric resonators

In the letter we present a new method for the calculations of resonant frequencies of cylindrical dielectric resonators using the variational principle. This method is applicable for determining the resonant frequencies of cylindrical isolated and shielded dielectric resonators. Computations for all modes (TE, TM and HEM) are given.     

A coupled mode formulation by reciprocity and a variational principle

A coupled mode formulation for parallel dielectric waveguides is presented via two methods: a reciprocity theorem and a variational principle. In the first method, a generalized reciprocity relation for two sets of field solutions(E^{(1)}, H^{(1)})and(E^{(2)}, H^{(2)})satisfying Maxwell's equation and the boundary conditions in two different mediaepsilon^{(1)}(x,y)andepsilon^{(2)}(x,y), respectively, is derived. Based on the generalized reciprocity theorem, we then formulate the coupled mode equations. The second method using a variational principle is also presented for a general waveguide system which can be lossy. The results of the variational principle can also be shown to be identical to those from the reciprocity theorem. The exact relations governing the "conventional" and the new coupling coefficients are derived. It is shown analytically that our formulation satisfies the reciprocity theorem and power conservation exactly, while the conventional theory violates the power conservation and reciprocity theorem by as much as 55 percent and the Hardy-Streifer theory by 0.033 percent, for example.     

Bimodal packet distribution in loss systems using maximum Tsallis entropy principle

A theoretical model of loss system is proposed and analysed within the framework of maximum Tsallis entropy principle. The study provides an explicit expression for state probability distribution of packets in presence of long-range dependent traffic. The unimodal state probability distribution corresponding to well-known Erlang?s loss formula is recovered for Tsallis entropy parameter q = 1. As the parameter q is lowered from unity, it is shown that the state probability distribution makes a transition from unimodal to bimodal. The emergence of bimodality can be regarded as a consequence of long-range dependence. The implication of the model in the design of loss systems is discussed.     

Application of maximum entropy principle in paralleled repairable systems

This paper investigates the application of the maximum entropy principle (MEP) to study the stochastic behavior of a repairable system. The system to be analyzed is a two-unit paralleled system whose failure rates are time-independent and whose repair time distribution is gamma. The exact distribution of some operating characteristics are compared with those obtained using MEP. Tables and graphs are provided.     

New principle to measure loss and mode-conversion parameters of multimode fibres

We derive an equation that relates the differences between the mean transit times of modes of a multimode fibre with loss, multimode dispersion and mode-conversion parameters. The concept of dynamic equilibrium is developed for the temporal difference. Further, we propose a new method of simultaneous measurement of loss and mode-conversion parameters which utilises the temporal difference.     

Q-factor computation of radiation loss corresponding to surfacewave in a patch circular resonator

The authors present a new approach for the Q-factor computation of radiation loss in a circular patch with surface wave TM₀. The circular patch resonant frequency (f) problem is formulated in terms of an integral equation using the transverse resonance method. First, the computed real part of f is found to compare closely with the published results considering space wave TM₁₁. Next, the Q-factor of the surface wave as a function of physical resonator parameters is presented     

Dissipation loss of mid-infrared radiation in a dielectric waveguide

Dissipation loss of electromagnetic radiation with wavelengths of 20–55 μm was theoretically studied in a three-layer planar dielectric insulating waveguide combined with a heterolaser. It was shown that the dependence of the loss on the waveguide layer thickness behaves differently for different wavelengths in the range of 20–55 μm. The lowest loss (several inverse centimeters) is characteristic of radiation with wavelength λ = 20 μm. The losses increase with the wavelength and reach a value of 150 cm^-1 at λ = 40 μm, which is almost independent of the waveguide layer thickness. For electromagnetic radiation with λ = 50 and 55 μm, a sharp (hundreds of times) decrease in the loss with an increase in the waveguide layer thickness is observed.     

Application of the superposition principle to solar-cell analysis

The principle of superposition is used to derive from fundamentals the widely used shifting approximation that the current-voltage characteristic of an illuminated solar cell is the dark current-voltage characteristic shifted by the short-circuit photocurrent. Thus the derivation requires the linearity of the boundary-value problems that underlie the electrical characteristics. This focus on linearity defines the conditions that must hold if the shifting approximation is to apply with good accuracy. In this regard, if considerable photocurrent and considerable dark thermal recombination current both occur within the junction space-charge region, then the shifting approximation is invalid. From a rigorous standpoint, it is invalid also if low-injection concentrations of holes and electrons are not maintained throughout the quasi-neutral regions. The presence of sizable series resistance also invalidates the shifting approximation. Methods of analysis are presented to treat these cases for which shifting is not strictly valid. These methods are based on an understanding of the physics of cell operation. This understanding is supported by laboratory experiments and by exact computer solution of the relevant boundary-value problems. For the case of high injection in the base region, the method of analysis employed accurately yields the dependence of the open-circuit voltage on the short-circuit current (or the illumination level).     

Packet loss due to encryption in space data systems

This paper analyzes the probabilities of data packet loss for both an encrypted channel in self-synchronous cipher feedback mode and a nonencrypted channel, in the space data systems. Simulation results show reasonable agreement with analytical results. When channel bit error probability is 10^-5 and the total number of packets per frame is 3, the analytical model gives 0.39% packet loss while the simulation gives 0.22% packet loss due to encryption. Although the analysis is performed for the space data systems, the resulting derived equations with minor change will be useful in many packet communication applications     

Application of expert systems to systems reliability evaluation

An expert system for diagnosing rough ride problems in heavy trucks has been developed and can be used on a personal computer. The system operates on two levels of knowledge data base: shallow — acquired from truck service personnel and causal obtained from a multiprobe vibration analysis system (MVAS) through a preprocessing neural network. The justification for selecting neural networks is presented as are virtues and drawbacks of the developed system.     

Analysis of radiation loss in grating-assisted codirectionalcouplers

In this paper, we present a new accurate numerical method, named leaky mode propagation method, to analyze the radiation loss in grating-assisted codirectional couplers. The complex propagation constant and electromagnetic field distribution of the normal modes are evaluated by using a space harmonic field expansion derived from the Floquet theorem. In order to prove the accuracy of our method, a comparison between our results and those calculated by the most used method, i.e., the transfer matrix method, is carried out in terms of power attenuation coefficient and total radiation loss. Quantitative and qualitative discrepancies between the two methods are widely discussed. In particular, an oscillatory variation of radiation loss with grating depth and gap thickness in contrast to the monotonic behavior predicted by the transfer matrix method has been found     

Matrix-variate variational auto-encoder with applications to image process

Variational Auto-Encoder (VAE) is an important probabilistic technology to model 1D vectorial data. However, when applying VAE model to 2D image, vectorization is necessary. Vectorization process may lead to dimension curse and lose valuable spatial information. To avoid these problems, we propose a novel VAE model based on matrix variables named as Matrix-variate Variational Auto-Encoder (MVVAE). In this model, input, hidden and latent variables are all in matrix form, therefore inherent spatial structure of 2D images can be maintained and utilized better. Especially, the latent variable is assumed to follow matrix Gaussian distribution which is more suitable for describing 2D images. To solve the weights and the posterior of latent variable, the variational inference process is given. The experiments are designed for three real-world application: reconstruction, denoising and completion. The experimental results demonstrate that MVVAE shows better performance than VAE and other probabilistic methods for modeling and processing 2D data.     

A study on the radiation loss from a bent transmission line

This paper deals with the radiation loss of bent transmission lines in order to determine the most optimal design for a bent line from the standpoint of radiation loss. We have used the method of moments (MoM) for a numerical analysis on the radiation for different structures of bent lines and we have found that the simplest right-angle bend is the best with the least radiation loss. This theoretical expectation was confirmed experimentally     

Characterization of radiation loss from microstrip discontinuitiesusing a multiport network modeling approach

A convenient method for evaluating radiation loss from microstrip discontinuities is presented. A planar multiport network model of the discontinuity configuration and the segmentation method are used to evaluate the voltage distribution around the edges of the discontinuity. This voltage distribution is expressed as an equivalent magnetic current line source distribution which is used to calculate the far-zone field (for radiation loss). As an example, the results show that for a 90° bend in a 50-Ω line on a 10-mil-thick substrate with ϵ_r =2.2, the radiation loss is 0.1 dB at 30 GHz. Typical power levels radiated by several other discontinuities are reported. The analysis model was verified experimentally by fabricating microstrip resonators with discontinuities incorporated therein and measuring the Q factors of these resonators     

Excited state absorption of pump radiation as a loss mechanism insolid-state lasers

The characteristics of optical pumping dynamics in laser-pumped, rare-earth-doped, solid-state laser materials are investigated by using a tunable alexandrite laser to pump Y₃Al₅O₁₂ :Nd³⁺ in an optical cavity. It is found that the slope efficiency of the Nd laser operation depends strongly on the wavelength of the pump laser. For pump wavelengths resulting in low slope efficiencies, intense fluorescence emission is observed from the sample in the blue-green spectral region. This is attributed to the excited-state absorption of pump photons which occurs during radiationless relaxation from the pump band to the metastable state. This type of process is an important loss mechanism for monochromatic pumping of laser systems at specific pump wavelengths     

Application of the mutual information principle to spectral density estimation

The power spectrum of a stationary Gaussian random process is estimated when partial knowledge of the autocorrelation function is available {em a priori}. Particular attention is paid to the case when the {em a priori} knowledge is not precise, i.e., when there are errors in the measurements, perhaps due to the presence of noise. In the special case when the {em a priori} knowledge consists ofnpoints of the autocorrelation function, Burg's method of picking the spectrum which maximizes the entropy of the Gaussian process has been recently extended by Newman to account for a weighted average error in the estimates of the correlation function points. A new method is suggested here that uses the mutual information principle (MIP) of Tzannes and Noonan. The firstnpoints of the correlation function (obtained with errors) are used to derive an approximate spectrum by Burg's or any other method. This spectrum, as well as the error constraints involved, is then used to arrive at the underlying spectrum in the framework of the MIP approach.     

Design of a low loss SAW reflector filter with extremely widebandwidth for mobile communication systems

The design and performance of a low-loss surface acoustic wave (SAW) reflector filter are presented. The structure is a dual-track configuration incorporating two interdigital transducers (IDTs) and reflectors in each track. Extremely wide bandwidth can be obtained if chirped IDTs and reflectors are used. From the theoretical conditions for low-loss operation of the reflector filter, a design rule for the distances between the chirped components and for their lengths is derived. Because the transfer function of the filter is predominantly determined by the reflectors, a new synthesis method for chirped reflectors has been developed. For the design of the reflectors, phase-weighting and finger-width-weighting techniques were used to reduce passband distortions and improve the shape factor and stopband rejection. The filter has been fabricated on 128° YX-LiNbO₃ . The center frequency and fractional bandwidth are 200 MHz and 100%, respectively, the minimum insertion loss is 4 dB, a passband ripple is about 1 dB, and the stopband rejection is better than 35 dB     

Anomalous radiation loss of curved dielectric ridge waveguides

The radiation loss of curved ridge dielectric waveguides can show an oscillatory dependence on radius for the TM-polarisation. This effect is predicted only by a three-dimensional full vectorial analysis and is confirmed experimentally in S-bend dielectric ridge waveguides