Representation of axisymmetric magnetic fields in computer programs

The standard expression for the off-axis fields in terms of the axial values and their differentials is examined. It is shown that if terms higher than the second are used, the accuracy becomes worse instead of better, unless the input data are mathematically perfect. It is not possible to remedy this by smoothing experimental data with a polynomial curve-fitting routine. Alternative expressions of the fields in terms of Legendre polynomials and of elliptic integrals are considered. It is shown that the elliptic integral method is the most convenient in practical cases, and a fast computer routine is given for the required K and E. In this method, the fields are defined by the parameters of a set of current loops, and the problem of finding these parameters is discussed. No general solution can be given, but a considerable class of cases is reduced to an explicit solution of a cubic equation by Cardan's method. It is shown that hybrid methods can also be used; the data is first represented by a set of current loops. A precise set of axial values is calculated from these loops, and the differential routine can then be used with acceptable accuracy, including terms up to the sixth order.     

Two-dimensional computer simulation models for MOSLSI fabrication processes

A two-dimensional process simulation program has been developed. The process models used for this program are oxidation, diffusion, ion implantation, and deposition/etching of CVD films. The numerical models are based on a finite-difference approximation to diffusion equation. A large number of equations derived from the diffusion equation are solved by Stone's method because of its excellent rate of convergence. Attention is paid primarily to lateral impurity diffusion and lateral oxidation near the edge of the oxidation mask. Oxidation enhanced diffusion of boron is also included. We have obtained good quantitative agreement between calculated and experimentally observed diffused line capacitance variation with reverse bias voltage which is strongly affected by the lateral channel stop diffusion in a locally oxidized process.     

Multiscale representations of Markov random fields

Recently, a framework for multiscale stochastic modeling was introduced based on coarse-to-fine scale-recursive dynamics defined on trees. This model class has some attractive characteristics which lead to extremely efficient, statistically optimal signal and image processing algorithms. The authors show that this model class is also quite rich. In particular, they describe how 1-D Markov processes and 2-D Markov random fields (MRFs) can be represented within this framework. The recursive structure of 1-D Markov processes makes them simple to analyze, and generally leads to computationally efficient algorithms for statistical inference. On the other hand, 2-D MRFs are well known to be very difficult to analyze due to their noncausal structure, and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification. In contrast, their multiscale representations are based on scale-recursive models and thus lead naturally to scale-recursive algorithms, which can be substantially more efficient computationally than those associated with MRF models. In 1-D, the multiscale representation is a generalization of the midpoint deflection construction of Brownian motion. The representation of 2-D MRFs is based on a further generalization to a “midline” deflection construction. The exact representations of 2-D MRFs are used to motivate a class of multiscale approximate MRF models based on one-dimensional wavelet transforms. They demonstrate the use of these latter models in the context of texture representation and, in particular, they show how they can be used as approximations for or alternatives to well-known MRF texture models     

Two-dimensional computer design of dual-ring thyristors

The main 2-dimensional equations are presented for the basic computer model of dual-ring amplifying gate thyristors (d.r.t.). These criteria ensure the maintenance of the very high di/dt capability of these devices in any possible triggering conditions.     

Two-dimensional orthogonal lattice structures for autoregressivemodeling of random fields

Two-dimensional orthogonal lattice filters are developed as a natural extension of the 1-D lattice parameter theory. The method offers a complete solution for the Levinson-type algorithm to compute the prediction error filter coefficients using lattice parameters from the given 2-D augmented normal equations. The proposed theory can be used for the quarter-plane and asymmetric half-plane models. Depending on the indexing scheme in the prediction region, it is shown that the final order backward prediction error may correspond to different quarter-plane models. In addition to developing the basic theory, the article includes several properties of this lattice model. Conditions for lattice model stability and an efficient method for factoring the 2-D correlation matrix are given. It is shown that the unended forward and backward prediction errors form orthogonal bases. A simple procedure for reduced complexity 2-D orthogonal lattice filters is presented. The proposed 2-D lattice method is compared with other alternative structures both in terms of conceptual background and complexity. Examples are considered for the given covariance case     

Two-dimensional computer simulation for switching a bipolar transistor out of saturation

A two-dimensional numerical analysis for the turnoff of a bipolar transistor from high injection level (VBE= 900 mV) is carried out. VBCis being kept constant at 1 V. Distributions of potential, electron, and hole density are interpreted and lead to a subdivision of the total transient time into four time regions, each governed by a single phenomenon. These phenomena are 1) fast discharge of the sidewall transistor, 2) the "lateral wave" which has the dominating influence in the total switching time, 3) the vertical discharge, and 4) the emitter discharge. The transient behavior is essentially ruled by two-dimensional lateral effects. Hence one-dimensional models are not adequate for switching a transistor out of saturation.     

Factoring polynomials using binary representations of finite fields

The factorization of polynomials over finite fields is considered. A new deterministic algorithm is proposed that solves the equal-degree factorization problem by combining Berlekamp's (1970) trace algorithm iterative method with the concept of binary representations of finite fields. The interesting aspects of the new algorithm are its simple structure, the easy proof of its correctness, and its efficiency when an efficient realization of the mapping from the finite field to a binary representation is known. Some results about binary representations of finite fields are derived to show that the new factoring algorithm is also nonasymptotically efficient for every finite field. The only practical drawback may be the precomputation of some constants needed in the binary representation, but several suggestions are given to improve this when more about the finite field is known     

Two-dimensional computer analysis of dielectric-surface-loaded GaAs bulk element

Computer analysis based on a 2-dimensional model was performed to investigate the effect of dielectric surface loading on the growth of dipole domains in a GaAs bulk element. The results show that a dipole domain originally produced by an inhomogeneity in GaAs is prevented from developing, as most of the space charges are concentrated near the surface boundary of GaAs by the presence of dielectric material.     

Two-dimensional surface integral representations for a rotationallyinvariant anisotropic medium: applications to scattering

The Huygens' principle is presented for an electromagnetic field in a rotationally invariant anisotropic region. The representation is investigated by deriving surface integral equations for scattering, resulting, for instance, in scattering formulations for an impedance body and for a perfectly conducting electric sheet (both embedded in the anisotropic material). Validation is accomplished via application to a canonical geometry     

Modern computer tools for high frequency electromagnetic fields simulation

Modern numerical methods of electromagnetic field simulation are considered and computer codes based on these methods are described. A number of various microwave devices field calculations are presented, estimations of efficiency, accuracy and universality of the codes are given.     

Far-field approximations to the Kirchoff-Helmholtz representations of scattered fields

The standard far-field approximation to the Kirchhoff formula for the field scattered by a flat metallic plateSof arbitrary shape is given by a certain surface (double) integral. This double integral can be reduced to a line integral evaluated around the boundary of S. Moreover, ifSis a polygon, this line integral can be reduced to a closed form expression involving no integrations at all. The use of such line integral representations can easily reduce the costs of numerical calculation by orders of magnitude. If the integrands are to be sampledptimes per wavelength to achieve an acceptable degree of precision, and ifAis the area ofS, then the numerical evaluation of the double integral requiresp^{2}A/lambda^{2}functional evaluations whereas the line integral only requirespsqrt{A/lambda^{2}}. IfSis a polygon withNvertices, then only2Nfunctional evaluations are required to evaluate the closed form expression with no quadrature error at all.     

Singularity expansion representations of fields and currents in transient scattering

A unified treatment of the natural mode representations for induced currents and scattered fields is obtained by use of fundamental concepts regarding causality and superposition. The transient scattered field response is shown to have the form of a constant coefficient complex exponential sum only in the "late-time," after the last driven reponse is received from the object. Prior to this, the "early.time" response is found to be due to direct physical optics fields as well as a sum of temporally modulated natural modes produced by the progressive illumination of the incident wavefront. Alternate representations ands-plane behaviors are considered. The implications of these results on natural resonance target identification schemes are discussed.     

Approximate formulas for the thermal resistance of IMPATT diodes compared with computer calculations

Two analytical formulas, which allow the thermal resistance to be calculated approximately for layered heat sinks with finite radii, are presented. They are shown to agree closely with finite-difference computer solutions of the steady-state heat equation for typical diode structures. The approximations allow rapid calculations without recourse to a computer.     

Three-dimensional computer model of electric fields in internaldefibrillation

The automatic internal defibrillator delivers a low-energy shock directly to the heart. Optimal strategies for these shock deliveries are determined by studying a three-dimensional computer model of the electric fields produced by initial defibillation electrodes. A finite-element analysis technique is used to calculate energy and current density distributions in three commonly used electrode configurations: (1) patch-patch (PP), (2) catheter-patch (CP), and (3) catheter-catheter (CC). analysis of these simulations indicates that : (1) the PP and CP configurations are more effective at channeling energy to the myocardium than the CC configuration; (2) small electrodes and the edges of the electrodes give rise to high local current densities which might cause damage to the myocardium: (3) energy delivered to the myocardium is not significantly altered for different electrode placements tested; (4) electrode size influences current density distribution, especially near the electrodes; and (5) energy distribution is sensitive to the relative conductances of the myocardial tissue and blood     

The application of the Gibbs-Bogoliubov-Feynman inequality in meanfield calculations for Markov random fields

The Gibbs-Bogoliubov-Feynman (GBF) inequality of statistical mechanics is adopted, with an information-theoretic interpretation, as a general optimization framework for deriving and examining various mean field approximations for Markov random fields (MRF's). The efficacy of this approach is demonstrated through the compound Gauss-Markov (CGM) model, comparisons between different mean field approximations, and experimental results in image restoration.     

Two-dimensional quantum-mechanical confinement of electrons in LED by strong magnetic fields

Two-dimensional quantum-mechanical confinement of electrons in a GaAlAs light emitting diode (LED) is realized by applying strong magnetic fields, in which electrons can move freely only in the direction of magnetic fields, and the dimensionality of the free carrier motion is reduced from three to one. With this confinement of electrons, considerable suppression of half-value width of the spectrum broadening from 80 to 60 Å at 80 K in the LED is observed. The systematic shift of the emission peak toward shorter wavelength is also observed in accordance with the theory, which takes into account the Landau level broadening due to finite electron mobility.     

Two-dimensional computer analysis of a microwave flat antenna arrayfor breast cancer tomography

In this paper, we report a two-dimensional computer simulation of a microwave flat antenna array for breast cancer tomography. This new technology promises reduction of X-ray exposure and easier access to peripheral areas of the breast. Using our version of the Newton algorithm, we studied two simple mathematical objects and a more sophisticated two-dimensional model of the breast that takes into account dielectric properties of different human tissues and malignant tumors. Our calculations show that, operating at 2 GHz, this device may give very reasonable images of tissues located up to 3-4 cm beneath the surface     

Two-dimensional quantum-mechanical confinement of electrons in DH lasers by strong magnetic fields

Two-dimensional quantum-mechanical confinement of electrons in DH lasers is realized near room temperature by applying strong magnetic fields up to 32 T. In order to confirm the realization of two-dimensional quantum-mechanical confinement of electrons in such lasers, the spectral characteristics are measured. The observed shift of the lasing wavelength with magnetic fields is shown to correspond to the upward shift of the lowest Landau level with the increase of magnetic fields.     

Two-dimensional computer simulation of the breakdown characteristics of a multi-element avalanche photodiode array

A two-dimensional computer simulation of the breakdown characteristics of a silicon multi-element avalanche photodiode array has been carried out. The effect of the interaction of the depletion layers of two adjacent avalanche photo diode (APD) elements on the breakdown voltage of the multi-element array has been modeled. The influence of the various physical parameters of the device on its breakdown voltage is investigated. Five different device structures are considered. Design guidelines for realizing true bulk breakdown in the device are presented. With the aid of these two-dimensional computer simulation results, the effect of scaling down the device dimensions, in an effort to increase the packing density of the device, on its breakdown voltage is also outlined.