Transient electromagnetic fields of a vertical magnetic dipole on a two-layer earth

The transient fields of a vertical magnetic dipole on a two-layer earth model are expressed in analytical form using two different approaches. In the first, the fields in the time domain are obtained as the inverse Laplace transforms of derived full wave time-harmonic solutions, while in the second, the concept of natural frequencies of the stratified earth is utilized. Comparison with a previously obtained approximate solution reveals that the latter is the late time part of the present solution. Important features in the waveforms of the surface fields due to step and pulsed current excitations are demonstrated by a variety of numerical examples. These features provide diagnostic means of sensing the earth's stratification, overburden thickness, and the ratio of conductivities of the layers.     

High precision approximate analytical solutions to ODE using LS-SVM

The problem of solving differential equations and the properties of solutions have always been an important content of differential equation the study. In practical application and scientific research, it is difficult to obtain analytical solutions for most differential equations. In recent years, with the development of computer technology, some new intelligent algorithms have been used to solve differential equations. They overcomes the drawback of traditional methods and provide the approximate solution in closed form (i.e., continuous and differentiable). The least squares support vector machine (LS-SVM) has nice properties in solving differential equations. In order to further improve the accuracy of approximate analytical solutions and facilitative calculation, a novel method based on numerical methods and LS-SVM methods is presented to solve linear ordinary differential equations (ODEs). In our approach, a high precise of the numerical solution is added as a constraint to the nonlinear LS-SVM regression model, and the optimal parameters of the model are adjusted to minimize an appropriate error function. Finally, the approximate solution in closed form is obtained by solving a system of linear equations. The numerical experiments demonstrate that our proposed method can improve the accuracy of approximate solutions.     

On the efficient evaluation of probabilistic similarity functions for image retrieval

Probabilistic approaches are a promising solution to the image retrieval problem that, when compared to standard retrieval methods, can lead to a significant gain in retrieval accuracy. However, this occurs at the cost of a significant increase in computational complexity. In fact, closed-form solutions for probabilistic retrieval are currently available only for simple probabilistic models such as the Gaussian or the histogram. We analyze the case of mixture densities and exploit the asymptotic equivalence between likelihood and Kullback-Leibler (KL) divergence to derive solutions for these models. In particular, 1) we show that the divergence can be computed exactly for vector quantizers (VQs) and 2) has an approximate solution for Gauss mixtures (GMs) that, in high-dimensional feature spaces, introduces no significant degradation of the resulting similarity judgments. In both cases, the new solutions have closed-form and computational complexity equivalent to that of standard retrieval approaches.     

A uniform approximation to the scattering and propagation problem for a stratified Bi-anisotropic slab

The scattering and propagation problem for time-harmonic waves in a stratified bi-anisotropic slab is considered. Based upon the identification of the left- and right-moving modes, and on a boundedness assumption concerning the space and frequency dependence of the physical parameters, a sequence of approximate solutions which converge absolutely and uniformly to the exact solution are derived. In particular, if the magnetoelectric coupling is small and the permittivity and permeability vary slowly, the approximate solutions converge so fast that the first approximation already gives a satisfactory approximation. With the present approximation method, approximate solutions valid for all frequencies can be obtained in explicit form.     

Impedance comparisons for the asymmetrically driven thin cylindrical antenna

The results from various approximate methods of solution to three basic equations for the impedance of the asymmetrically driven perfectly conducting thin cylindrical antenna are briefly discussed and compared. Generally good agreement is found between method-of-moment solutions and the three-term King-Wu theory. Largest disagreement with those approximate methods is found with the Shen-Wu-King solution and the joining procedure.     

New analytical expressions for dark current calculations of highlydoped regions in semiconductor devices

We studied highly doped quasi-neutral regions of semiconductor devices with position dependent doping concentration in the absence of illumination. An important parameter of a highly doped region is its dark current. To clarify how the doping profile influences the dark current, simple analytical expressions are useful. To this end, we first transformed the transport equations to a simple dimensionless form. This enables us to write already existing analytical expressions in an elegant way. It is demonstrated how, from any analytical dark current expression, a direct counterpart can be derived. Next, we derived a dimensionless form for a nonlinear first-order differential equation for the effective recombination velocity. Starting from the analytical solution of this differential equation for uniformly doped regions and using linearization techniques, we obtained two new simple and accurate expressions for the dark current. The expressions are valid for general doping profiles with different minority carrier transparencies. The exact solution is included between both new approximate solutions. The new expressions are compared with previous approximate solutions     

A treatment of impurity diffusion in oxidizing ambients

The linear diffusion equation may be transformed to a moving reference frame which corresponds to a linear-parabolic or experimental oxide growth law. The resulting partial differential equation is separable and may be Laplace transformed. If the semiconductor is initially uniformly doped and semi-infinite, solutions in the Laplace transform domain are expressible as parabolic cylinder functions. Integration constants for constant interface concentration or deposition diffusions as well as leaching boundary conditions may be determined.A space-time solution for the deposition problem is derived. Leaching from a uniformly doped substrate is treated in some detail. Residue techniques are used to develop analytic expressions for the dominant solution term, which is compared to published results. The complete solution may be obtained by using approximate analytic inversion, which requires numerical computations. Results are compared with data from existing theories, which are special cases of the present model.     

基于不确定集的稳健Capon波束形成算法性能分析

该文针对常规Capon波束形成易受期望信号导向矢量失配影响,研究了基于导向矢量误差不确定集的稳健Capon自适应波束形成算法。推导出期望信号导向矢量属于球形不确定集时的自适应权矢量近似闭式解,并由此进行性能评估,得到目标功率估计和输出信号干扰噪声比的近似表达式,从而明确了各种因素对性能的影响关系。计算机仿真结果证明了该文分析的合理性。     

Accurate asymptotic solution for the surface field due to apertures in a conducting cylinder

Asymptotic solutions for the surface field due to a magnetic point source on a cylinder can simplify the computational task in the analysis of mutual coupling-e.g. in conformal arrays. Although several asymptotic solutions are at present available, their accuracy is limited. The aim here is to obtain a new approximate solution with improved accuracy. An asymptotic solution of the exact modal solution for the field on a cylinder which contains terms up to(k_{0}t)^{-2}, wheretis the distance from the source, is derived. Approximate terms up to(k_{0}t)^{-3}are included from the solution for a source on a plane conductor and an earlier asymptotic solution. The new approximate solution consists of the exact solution for a plane conductor, modulated by a Fock function, plus a contribution associated with the cylinder which vanishes in the limit of infinite radius. Typically for cylinders of radius greater than one and half wavelengths it agrees to within 0.5 dB in magnitude and1degin phase of the modal solution. Results for dominant mode mutual and self-admittances of rectangular apertures on a cylinder obtained from this solution are presented. A formula is also given for calculating self-admittances from an asymptotic solution. There is excellent agreement between admittances computed from the asymptotic solution and the modal solution. One exception is the self-susceptance of an axial slot where the error is larger than expected, although the error is low enough to be acceptable in most practical cases.     

Surface-potential solutions to the Pao–Sah voltage equation

Surface potential is one of the most important quantities in compact MOSFET (metal-oxide-semiconductor field-effect transistor) modeling. Current trend in compact modeling is moving from the threshold-voltage-based to the surface-potential-based models. The latter require a very accurate solution of the nonlinear implicit Pao–Sah voltage equation. Another past difficulty of the surface-potential-based models was the imaginary and thus unphysical solution when the gate voltage is very close to the flatband voltage. This was recently resolved by Sah physically, consequently mathematical conditioning is no longer necessary, although nonlinearity remains. The solutions to the Pao–Sah voltage equation are graphically demonstrated to illustrate the multiplicity of roots and to help attain the correct solution, but not suitable for numerical computation and analytical compact modeling. The main advantage of the analytical approximate solutions over the numerical one is their faster computation speed. However, all approximate solutions suffer from poor accuracy, in addition to some unexpected results. On the other hand, iterative algorithms may also return erroneous solutions by converging to the wrong roots for the surface potential. With properly chosen initial guess, the Newton–Raphson algorithm for the Pao–Sah voltage equation can converge to the correct solution with controllable high accuracy and computation speed comparable to that of the approximate explicit algorithms. An initial guess that ensures convergence to correct surface potential solution for the newly derived 2004-Sah voltage equation is proposed, which can be used to benchmark other approximate solutions. Comparisons among various approximate solutions with the iterative one are presented, both in wide gate voltage ranges (from strong accumulation to strong inversion) with coarse gate voltage step size and narrow gate voltage range near flatband with fine gate voltage step size.     

Multiple scattering of EM waves by spheres part I--Multipole expansion and ray-optical solutions

Solution to the multiple scattering of electromagnetic (EM) waves by two arbitrary spheres has been pursued first by the multipole expansion method. Previous attempts at numerical solution have been thwarted by the complexity of the translational addition theorem. A new recursion relation is derived which reduces the computation effort by several orders of magnitude so that a quantitative analysis for spheres as large as10lambdain radius at a spacing as small as two spheres in contact becomes feasible. Simplification and approximation for various cases are also given. With the availability of exact solution, the usefulness of various approximate solutions can be determined quantitatively. For high frequencies, the ray-optical solution is given for two conducting spheres. In addition to the geometric and creeping wave rays pertaining to each sphere alone, there are rays that undergo multiple reflections, multiple creeps, and combinations of both, called the hybrid rays. Numerical results show that the ray-optical solution can be accurate for spheres as small aslambda/4in radius is some cases. Despite some shortcomings, this approach provides much physical insight into the multiple scattering phenomena.     

On nonlinear fractional Klein-Gordon equation

Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Gordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order α are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation.     

Scattering by a Ferrimagetic Circular Cylinder in a Rectangular Waveguide

A general and rigorous formulation of the scattering by a dc magnetized ferrimagnetic cylinder in a rectangular waveguide is derived. This formulation leads to an approximate solution whose error can be quantitatively estimated. As an example, the case in which the ferrimagnetic cylinder is centrally placed is solved. It is shown that previously existing approximate solutions are not valid for the resonant situation in view of their accuracy.     

An Analytic Model to Account for Quantum–Mechanical Effects of MOSFETs Using a Parabolic Potential Well Approximation

An analytic model to account for the quantum–mechanical effects (QMEs) of the MOSFETs using a parabolic potential well approximation is presented in this paper. Based on the solution of the coupled SchrÖdinger and Poisson equations following the Wentzel–Kramer–Brillouin method, a transcendental equation of the subband energy level has been rigorously derived to obtain an approximate analytic solution for the subband energy levels and the inversion charge centroid. Calculated results from the obtained analytical solution are compared with the previous approximate solutions reported in the literature and the numerically simulated data. A good agreement between the analytical and numerical is obtained, proving the validity of the analytic modeling of QMEs.     

Approximate maximum likelihood estimators for array processing inmultiplicative noise environments

We consider the problem of localizing a source by means of a sensor array when the received signal is corrupted by multiplicative noise. This scenario is encountered, for example, in communications, owing to the presence of local scatterers in the vicinity of the mobile or due to wavefronts that propagate through random inhomogeneous media. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to-noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML₁) estimator is derived. The performance of the AML₁ estimator in the presence of additive noise is studied, and a theoretical expression for its asymptotic variance is derived. Its performance is shown to be close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered, and the corresponding AML₂ solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to both the multiplicative and additive noise powers, leaving out a two-dimensional (2-D) minimization problem instead of a four-dimensional (4-D) problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis     

Cold-cavity vectorial eigenmodes of VCSELs

An analytical approximate solution of Maxwell's equations for the cold-cavity eigenmodes of cylindrical etched air-post vertical-cavity surface-emitting lasers (VCSELs) is presented. In radial and azimuthal directions, the modes correspond to the hybrid modes of cylindrical optical waveguides. A vectorial transform matrix approach is derived which takes into account coupling of bound eigenmodes in VCSEL structures. The method is illustrated for the case of noncoupled modes and the corresponding simplified transform matrix approach is used to calculate the field profiles in longitudinal direction and predict the resonance wavelengths for the VCSEL eigenmodes. Although approximate, the resulting eigenmodes may be viewed as a useful alternative to full numerical solutions, especially with regard to future more comprehensive modeling of VCSELs     

On filtered binary processes

The problem of calculating the probability density function of the output of anRCfilter driven by a binary random process with intervals generated by an equilibrium renewal process is studied. New integral equations, closely related to McFadden's original integral equations, are derived and solved by a matrix approximation method and by iteration. Transformations of the integral equations into differential equations are investigated and a new closed-form solution is obtained in one special case. Some numerical results that compare the matrix and iteration solutions with both exact solutions and approximate solutions based upon the Fokker-Planck equation are presented.     

A Comparison of Point Target Spectra Derived for Bistatic SAR Processing

The existence of a double hyperbola in the bistatic range equation makes it difficult to find an exact analytical solution for the 2-D point target spectrum. Several approximate solutions for the spectrum have been derived and used to focus bistatic synthetic aperture radar data. In this paper, we establish the relationship between three independently derived bistatic point target spectra. The first spectrum is Loffeld's bistatic formula, which consists of a quasi-monostatic and a bistatic phase term. The second spectrum makes use of Rocca's smile operator, which transforms bistatic data in a defined configuration to a monostatic equivalent. The third spectrum is derived using a power series—called the method of series reversion (MSR). The MSR spectrum is the most general among the three. This paper shows that this spectrum can be reduced to the same formulation as the former two when certain conditions are met. In addition, a new approximate spectrum is derived using a Taylor series expansion about the two stationary phase points of the transmitter and receiver. We also give an alternative geometrical proof of the relationship between Rocca's smile operator and Loffeld's bistatic deformation term. The accuracies of the point target spectra are demonstrated using simulations of an X-band bistatic airborne radar with a fixed baseline.      

New approximations to J0 and J1 Besselfunctions

New approximate solutions to the 0th- and 1st order Bessel functions of the first kind are derived. The formulations are based upon using a new integral with no previously known solution. The new integral in the limiting case is identical to the 0th-order Bessel function integral. It is solved in closed form, and the solution is expressed as a simple even order polynomial with integer coefficients. The polynomial coefficients are all of integer value. The 1st-order Bessel function approximation can then be found through a simple derivative. Comparisons are made between the exact solution, classic solutions, and the new approximation. The new approximation proves to be much more accurate than the classic small argument approximation. It is also sufficiently accurate to bridge the gap between the classic large and small argument approximations and has potential applications in allowing one to analytically evaluate integrals containing Bessel functions