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ABSTRACT The principles of electrostatics are applied to dimensions both lower and higher than 3. Specifically, Laplace's equations are solved in n dimensions subject to hyper-spherical symmetry in order to [...]

The finite element method is used to solve Laplace's equation for ion-atom chambers. We first consider a simplified model chamber for which an analytical solution can be obtained; the model chamber serves as a test case to verify the accuracy and convergence of the finite element method. We apply the finite element method to an experimental chamber consisting of five equipotential rings in a grounded cylindrical shell. We determine the strength and homogeneity of the electric field in the region of the chamber where the atoms undergo laser excitation into a Rydberg state. [DOI: 10.1119/1.3000255]

In this work, a novel procedure to solve the Navier-Stokes equations in the vorticity-velocity formulation is presented. The vorticity transport equation is solved as an ordinary differential equation (ODE) problem on each node of the spatial discretization. Evaluation of the right-hand side of the ODE system is computed from the spatial solution for the velocity field provided by a new partial differential equation expression called the kinematic Laplacian equation (KLE). This complete decoupling of the two variables in a vorticity-in-time/velocity-in-space split algorithm reduces the number of unknowns to solve in the time-integration process and also favors the use of advanced ODE algorithms, enhancing the efficiency and robustness of time integration. The issue of the imposition of vorticity boundary conditions is addressed, and details of the implementation of the KLE by isoparametric finite element discretization are given. Validation results of the KLE method applied to the study of the classical case of a circular cylinder in impulsive-started pure-translational steady motion are presented. The problem is solved at several Reynolds numbers in the range 5 < Re < 180 comparing numerical results with experimental measurements and flow visualization plates. Finally, a recent result from a study on periodic vortex-array structures produced in the wake of forced-oscillating cylinders is included. [DOI: 10.1115/1.2198245]

Abstract In this note there are introduced two new concepts of e-harmonic numbers, and a new concept of e-perfect number. Their initial study is provided. Keywords Exponential divisors, harmonic numbers, [...]

Scaling factors for 40 combinations of theory and basis set, intended for predicting the fundamental frequencies from computed harmonic frequencies are reported. An empirical scaling factor partially compensates for the errors arising from vibrational anharmonicity and incomplete treatment of electron correlation.

Abstract We present some inequalities for the polygamma funtions. As an application, we give the upper and lower bounds for the expression [n.summation over (k=1)] 1/k - 1n n - [...]

The results on occurrence of high-order harmonic generation are presented in a two-electron quantum dot molecule. The model system is in very good agreement with a model system based on level crossing theory that is used for the derivation of a relation for the cutoff frequency of the harmonics.

A presentation is made in this study where hyperspherical harmonics for triatomic systems are generated in terms of row-orthonormal hyperspherical coordinates. The harmonics of all values of the hyperangular momentum quantum number up to 40 are obtained using this approach.

High-order harmonic generation spectra of atoms and molecules in intense laser fields show a wide plateau of odd harmonics, with photon energies high up to the soft X-ray regime. The analysis of these experiments provides the conditions for which the hyper-Raman lines are missing and the conditions for which they are observable.

It is uniformly known that the buckling modes of uniform columns are given by trigonometric, namely, harmonic, functions. For inhomogeneous columns the buckling modes usually are derived via special functions including Bessel and Lommel functions. Recently it was demonstrated that the buckling modes of specific inhomogeneous columns assume a simple polynomial form. The question posed in the title of this study therefore naturally arises. It is shown that the reply to this query is affirmative. Four cases of harmonically varying buckling modes are postulated and semi-inverse problems are solved that result in the distributions of the flexural rigidity compatible to the preselected modes and to specified axial load distributions. In all cases the closed-form solutions are obtained for the eigenvalue parameter.

Research was conducted to provide a solution to the problem of electrostatics of the conducting double spheres of arbitrary radii placed in an arbitrary potential field. The approach was based on Kelvin's transformation combined with reflection and translation characteristics for harmonic functions. The proposed theorem admits interpretation of the image system for several imposed potentials in the presence of the two-sphere assembly.

The necessary and sufficient conditions for applicability of spatial harmonic expansions (the Rayleigh hypothesis) for plasma wave branches in periodic plasma-loaded waveguides have been obtained for the first time, based on the exact solution for the relevant boundary-value problem. Conditions of oscillation appearance beyond the scope of such expansions and their expected effect on the operation of plasma-filled backward-wave oscillators are discussed. Index Terms - High power backward wave oscillator, microwave tube, periodic structure, plasma-filled waveguide.

Results of a study revealed that the second harmonic (SH) intensity at gold electrodes modified with self-assembled monolayers (SAMs) of two novel molecules, which have trans-ferrocenyl-nitrophenyl ethylene and thiol groups as the second harmonic generation and surface-attached groups, was dependent on the oxidation state of the ferrocene group. The SH intensity rose when the ferrocene moiety of the SAMs was oxidized to the ferricenium cation. The molecular orientation change in each SAM upon reduction/oxidation of the ferrocene moiety was also studied by Fourier transform infrared reflection.

Research was conducted to examine the analytical dependence of the free-electron laser saturated power on the cavity detuning as well as the dependence of the higher harmonics generated power on the quantity. It was observed that a suitable modulation of the cavity detuning may provide a pulsed behavior of the laser, superimposed to the natural mode locking. The impact of the modulation on the harmonic generation was also investigated.

A theoretical investigation of the backward second-harmonic generation (SHG) process using subpicosecond and nanosecond laser pulses in periodically poled lithium niobate crystals was conducted. The amounts of pulse broadening and conversion efficiencies were different for the two configurations despite the fact that the temporal behaviors of the second-harmonic radiation were determined by the same functions as those for the forward SHG. The saturation of the conversion efficiencies and the effective third-harmonic generation were also investigated.

The boundary mode Laplace approximation to the Bayes factor was utilized for testing extrabinomial variation. The chance of forming a boundary mode was high when the boundary mode Laplace approximation to the Bayes factor occurred at the boundary of the parameter space. The half-normal density function and the exponential density function can also be utilized for boundary mode Laplace approximations depending on the difference of the boundary mode from the true value., 1. INTRODUCTION For testing or choosing between two competing hypotheses [H.sub.0] and [H.sub.1], the Bayes factor measures the strength of evidence provided by the data y. The Bayes factors (B) [...]

In this paper, analytical expressions for calculating the capacitance of an isolated pixel diode as well as a pixel diode in an array are presented. These expressions fit the three-dimensional numerical solution of the Laplace equation better than 10% as previously calculated for these diodes, covering most practical cases. The total pixel capacitance [C.sub.P] is obtained by a simple substitution of parameters in the analytical expressions. In addition, a simple method to obtain the real diode capacitance, the parasitic capacitance, and the substrate concentration is proposed on the basis of the analytical equation for the capacitance for an isolated diode. The coincidence of measured and calculated data for the capacitance is shown. The procedures presented permit a very precise description of the real C-V curve for an isolated diode as well as for diodes in a pixel array, allowing the design of the best coupling between each pixel and its corresponding readout preamplifier with a minimum calculation effort. Index Terms - Detectors, diode capacitance, p-i-n diodes.

A modified form of Laplace's equation, based on coordinate stretching, is proposed, that lends itself to a new convenient numerical grid truncation methodology for the solution of Laplace's equation in open regions. The proposed method eliminates the need for approximate local boundary conditions on the truncation boundary of the numerical grid. Thus, it provides for a simple, robust, computationally efficient and very accurate grid truncation scheme. First, an analytic justification of the proposed grid truncation methodology is presented. Next, its numerical implementation is discussed in conjunction with the numerical solution of Laplace's equation in unbounded two-dimensional regions. Numerical studies are used to illustrate the choice of the parameters used in the numerical implementation of this new truncation scheme, and quantify their impact on solution accuracy.

A novel technique for obtaining superconvergent derivatives of finite element solutions for Laplace and Poisson type equations is presented. This is achieved by analytical integration of Green's function over single triangles. Superconvergent derivatives of FEM potential solutions have an accuracy of higher order than predicted by the finite element theory. Compared to direct evaluation the number of significant digits doubles. The procedure is illustrated by application to several test examples. It is notable that no restrictive regularity assumptions on the mesh topology are made.

The circular-harmonic-function correlation filter originally proposed by Hsu and Arsenault [Appl. Opt. 21, 4016 (1982)] for in-plane rotation invariance uses only one harmonic, which results in poor discrimination capability of the filter. Various methods to use multiple harmonics were explored previously by different researchers. We present a new method to combine multiple circular harmonics into a single filter that can provide the desired correlation response to in-plane rotation while minimizing the correlation-plane energy. Since multiple harmonics are included, the filter can discriminate well, and since correlation-plane energy is minimized, correlation peaks tend to be sharp. Since the designer can specify the desired in-plane rotation response, a variety of filter behaviors (including complete invariance to input rotations) can be obtained. Underlying theory is discussed, and simulation results are presented.

Kautz functions constitute a complete orthonormal basis for square-summable functions both on a continuous as well as a discrete semi-infinite axis. A special case of the Kautz functions are the well-known Laguerre functions. The Kautz functions can be used as series expansions for causal impulse responses. Convergence of such series depends on the parameters in the Kautz functions. The conditions for the optimal parameters in a truncated Kautz series are derived.

Prior assumptions under the null and alternative hypotheses are required to compute a Bayes factor for testing a nested hypotheses in the presence of a nuisance parameter. It is shown that the Schwartz criterion can give a reasonably approximate solution to a Bayesian testing problem. In certain cases, the log of the Bayes factor can be approximated by the Schwartz criterion with an acceptable degree of error.

The analogue of L(super 1)(G//K) of Wiener's Tauberian theorum has been obtained by using the resolvent transform with exact decay condition and no superfluous technicalities. An application of the analog is for Furstenberg's theorem. A generalization of Furstenberg's theorem characterizing harmonic functions on the unit disk has been proved by a mean property and a two-circles Morera-type theorem.

Recent surveys of 208/120 V three-phase four-wire electric systems, buildings, and industrial plants with computers and nonlinear loads show excessive currents in the neutral. These neutral currents are fundamentally third harmonic, and their presence is tied to wiring failures, elevating of neutral potentials, transformer overheating, etc. In response to these concerns, this paper proposes a new active power filter scheme to cancel neutral current harmonics. The proposed approach employs a star/delta transformer along with a two-switch PWM-controlled active filter. The closed loop control of the active power filter guarantees cancellation of neutral current harmonics under varying load conditions. The proposed system drastically improves the overall system performance and virtually eliminates transformer overheating due to harmonics. Experimental results from a prototype active power filter confirm the suitability of the proposed approach.

Eigenfunction and eigenvalues of the Laplacian are analyzed by a numerical package of Mathieu, developed by modifying Mathieu functions and constructing profiles of the eigenfunction sequence. The package enables visualization of the eigenfunctions and provides a new type of transition state, known as focusing modes, which have complementary features such as bouncing modes.

A method for the solution of the three dimensional Laplace equation is presented. The method applies to planar geometry cases, such as pixel detector devices, characterized by mixed boundary conditions. Through this algorithm the capacitances associated with pixel detectors are calculated. These capacitances, which are the pixel to substrate and the interpixel capacitances, are of great importance in the design of a pixel detector since they influence the noise and the cross talk effects between pixels. Capacitances for various pixel and interpixel dimensions are presented along with an analytical approximation for the calculation of the total pixel capacitance.

The Laplace method as an analytical tool for estimating expected values of functions of parameters and marginal densities in the Bayesian context is presented. Specifically, asymptotic expansions for posterior expectations of functions of parameters have been derived when the mode is on the edge of the parametric space. Second-order accuracy is obtained even if the mode is situated on the boundary.

An improved version of a Newton-type algorithm is used for adaptively searching for the minimum eigenvector of the asymptotic matrix of data that includes sinusoids of white noise. The proof of convergence is developed by the assumption of a suitable initialization. The new algorithm exhibits faster convergence properties than the earlier version, especially in low SNR cases.

The paper proposes an extension of the Monte Carlo procedures to the solution of axisymmetric problems. The stochastic techniques are illustrated with specific practical applications to the solution of Laplace's and Poisson's equations. The method requires no input data and provides results as accurate as those obtained using the finite element method.

A method that determines exactly the two-dimensional capacitance per unit length of a single dielectrically-insulated interconnection line above a conducting plane is introduced. The technique, which is analogous to a Fourier series, is based on a solution of Laplace's equation using Bernoulli's approach and may be applied to more complex configurations. A comparison with its counterparts in the literature is also provided.

A study was conducted to examine the microscopic characteristics of fluid dynamics and heat conduction. The study considers an evaporating extended meniscus of heptane which is developed between a horizontal substrate and a washer set at minimal heat fluxes. Results show that fluid flow and evaporation exhibit importance as dimensionless parameters of the intermolecular force field.

An improved floating-random-walk algorithm for solving the multi-dielectric Dirichlet problem is outlined. The improvement is achieved by using statistically generated Green's functions that are calculated before hand and stored as look-up tables. These tables have been used to solve the multi-dielectric Dirichlet problem for an arbitrary two dimensional geometry. The improved algorithm is also compared with the conventional floating-random-walk algorithm and is found to be at least two times more efficient. Results are presented for two types of parallel plate geometries.

Taylor's formula is used to derive the Euler-Maclaurin summation formula for a more accessible study of infinite series. The former formula is a virtual corollary of the latter when the error in the midpoint rule for integration is estimated. This can be achieved by replacing a sum with an integral, resulting in a good estimate because of a small derivative and a bounded step size. Thus, this is a reserval of the standard effect. The Cauchy form of the remainder in Taylor's formula also determines the Euler-Maclaurin formula's error term. This is incidentally related to Bernoulli numbers.

Numerical solution methods of Laplace's equation Delta-V = 0 when boundary values of potential V are specified abound, and many computer programs employing relaxation techniques, finite-element techniques, etc. have been discussed in the literature. The finite-mesh relaxation method of numerical iteration is discussed in many physics and electrical engineering texts, but little attention is given to the error analysis, which, moreover, is incorrect more often than not in these texts. We show that the error in the iterated solution can be found by a relatively simple analysis, and discuss its implications.

Temperature tunability in AgGaSe2 crystals are investigated to enable the application of AgGaSe2 in nonlinear optics. For various temperatures of the crystal, tunable second harmonic generation from the carbondioxide laser radiation is determined. The tuning is small, and experimental results agree with results obtained from dispersion experiments.

A full set of 34 empirically determined harmonic force constants F (sub i, k) for benzene in symmetries co-ordinates is investigated. The study can lead to refinement of the empirically determined harmonic force through a better fit of calculated and experimentally measured vibrational energy levels.

In this paper, the Floquet theory is combined with harmonic balance for the in-depth analysis of a Chua's family circuit, exhibiting intermittence. Floquet multipliers are calculated along the periodic solution paths obtained through harmonic balance by means of a continuation algorithm. The analysis of both the stable and unstable solution sections enhances the information about the system and permits a better understanding of the different phenomena that take place. Index Terms--Continuation algorithm, Floquet multipliers, harmonic balance, intermittency, route to chaos.

A method is presented based on second harmonic generation for detection of proteins adsorbed to interfaces and in the presence of bulk species. The free energy of adsorption of cytochrome c to glass was determined from an adsorption isotherm measurement of the second harmonic signal as a function of the bulk protein concentration.

Pressure-induced structure ordering of long-chain fluorescein O322 molecules within the monolayer at the air/water interface was studied by rotating a sample trough using the second-harmonic generation technique. The result shows that the transition of an initially disordered and heterogeneous dye monolayer into a fairly regular crystalline-like structure was characterized by continuous changes in the structure ordering of constituent molecules.

The problem of extracting sinusoid signals from noisy observations made at equally spaced times is considered. Eigenanalysis methods, such as Pisarenko's method and the extended Prony method, find the eigenvector [...]

The Variable Speed Air Conditioner (VSAC) is a large domestic distorting load. We investigate the impact of a large number of VSAC's on domestic harmonic levels. We present * a general method to build a harmonic numerical model of a passive filtered rectifier supplied by a distorted voltage, * a statistical method to assess the total harmonic currents produced by a large number of units running at various power levels and supplied by various distorted voltages. These two methods are applied to a rectifier used by many VSACS. We also present results for two other rectifiers. Index Terms--Analytical model, diversity, harmonic cancellation, single phase air conditioner, VSAC.

A synchronous-reference-frame (SRF)-based controller for the dominant harmonic active filter (DHAF) system has already been proposed by the authors. The SRF controller is designed to achieve harmonic isolation at the dominant harmonic frequencies (such as at the 5th and/or 7th) between the supply and load. This allows implementation of the DHAF system by square-wave inverters switching at the 5th or 7th harmonic frequency. Compared to conventional active filter systems which require high-switching-frequency pulsewidth modulation inverters, the square-wave-inverter-based DHAF system provides a viable and cost-effective solution to achieve harmonic isolation for high-power nonlinear loads (10 MW and above) or cluster of nonlinear loads, to meet the IEEE 519 recommended harmonic standard. In this paper, a new feedforward command of the SRF controller is proposed which provides better dynamic performance. The improved feedforward command of the SRF controller can suppress any system resonances at the dominant harmonic frequencies and meet IEEE 519 harmonic current limits. Experimental results are presented to validate the effectiveness of the SRF controller and the DHAF system. Index Terms--Active filter, dominant harmonic active filter, harmonic filtering, harmonic isolation, square-wave inverter, synchronous reference frame.

Abstract. The k-server problem is a generalization of the paging problem, and is the most studied problem in the area of competitive online problems. The Harmonic algorithm is a very […]

A new battery configuration technique and accompanying control circuitry, termed a Synergetic Battery Pack (SBP), is design to work with Lithium batteries, and can be used as both an inverter for an electric vehicle AC induction motor drive and a battery charger. In this paper, we compare the performance of the Synergetic Battery Pack as a battery charger with several simple conventional battery charging circuits via computer simulation. The factors of comparison were power factor, harmonic distortion, and circuit efficiency. The simulations showed that the SBP is superior to the conventional charging circuits since the power factor is unity and harmonic distortion is negligible.