The Weierstrass function is continuous everywhere and differentiable nowhere. It is used advantageously for modeling fractally coarse media. The frequency domain expression is analyzed using the Laplace transform of a...
The Weierstrass function is continuous everywhere and differentiable nowhere. It is used advantageously for modeling fractally coarse media. The frequency domain expression is analyzed using the Laplace transform of a truncated Weierstrass function. The poles of this function constitute a geometric sequence on the imaginary axis of the complex frequency plane. computer calculations show that the zeros change little as the order is increased. Theoretical development reveals the nature of the dependence of the zeros on order and the parameters of the function. The effect of the scale of observation on the function's properties is examined in both time and frequency domains.
Although researchers often describe a particular medium with only a single grain size or an average grain size, distributions of grain sizes can have significant effects on the physical characteristics of the material...
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Although researchers often describe a particular medium with only a single grain size or an average grain size, distributions of grain sizes can have significant effects on the physical characteristics of the material. Ultrasonic attenuation due to energy scattered at the grain boundaries depends on the ultrasonic wavelength, the grain size, and certain material properties such as elastic constants. This paper examines the relationship between the wavelength dependency of ultrasonic attenuation and grain-size distributions. A transformation is developed which solves a general class of Fredholm equations of the first kind. The equation relating attenuation to grain-size distributions belongs to this class of equations. The transformation allows attenuation to be calculated by discrete convolution, and provides a method for estimating the grain-size distribution directly from attenuation measurements. (C) 1997 Acoustical Society of America.
Numerical techniques based upon boundary integral methods like charge simulation or Galerkin boundary elements are still warmly received in the HV community because they are relatively easy to implement and use, and b...
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Numerical techniques based upon boundary integral methods like charge simulation or Galerkin boundary elements are still warmly received in the HV community because they are relatively easy to implement and use, and because they are accurate. However, the results can be sensitive to the quality of the discretization. In this work we introduce an efficient refinement scheme that automatically chooses the sections of conducting and dielectric boundaries where new nodes should be placed. The numerical results compare favorably to canonical solutions, and the method is shown to be effective on more complicated practical geometries.
A unified theoretical formulation describing the electro-acoustic transduction processes governing an electromagnetic acoustic transducer is presented. This new approach establishes separate electrical, mechanical and...
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A unified theoretical formulation describing the electro-acoustic transduction processes governing an electromagnetic acoustic transducer is presented. This new approach establishes separate electrical, mechanical and material subsystem descriptions based on the momentum conservation forms of Maxwell's field equations in the quasi-static limit and Cauchy's law of motion. Instead of accounting for the electromagnetic acoustic material interaction by direct linkage of mechanical stress and magnetic flux through constitutive relations, the coupling of the field tensors is achieved as part of an additional material subsystem. As a result, the complete set of governing equations and associated boundary conditions can be derived from first principles in a concise way that lends itself to a quantitative numerical implementation in the time domain. Aspects of the numerical formulation and the subsequent computer model predictions are discussed in a companion paper.
A new recombination mechanism, via the high density of shallow donor and acceptors present in the base-emitter junction of integrated circuit transistors, is suggested. In contrast to the recombination via deep center...
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A new recombination mechanism, via the high density of shallow donor and acceptors present in the base-emitter junction of integrated circuit transistors, is suggested. In contrast to the recombination via deep centers, this mechanism has an ideal voltage dependence, leading to a beta essentially independent of the base-emitter voltage. It appears to be the dominant component to the base current of integrated circuit transistors. The temperature dependence of the beta of the transistors arises from the ionization energy of the donors and acceptors. The rate-setting capture cross section by neutral acceptor and donors is 1.3(5) x 10(-15) cm2.
A finite-element time-domain (FETD) method for solving Maxwell's equations was developed by combining prism-based edge elements with central differencing in the time domain. This method solves for the electric fie...
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A finite-element time-domain (FETD) method for solving Maxwell's equations was developed by combining prism-based edge elements with central differencing in the time domain. This method solves for the electric field as a vector function of space and time in finite cylindrical cavity geometries of arbitrary geometry. Two stability analyses of this method are performed using the growth factor technique and the Z-transform. Furthermore, the computational complexity of the present approach is also investigated. This method has been implemented and its validity tested by studying the resonant frequencies of various microwave cavities.
An analytical one-dimensional series solution for the time-domain displacement response of a piezoelectric plate is derived. Rather than the usual charge driven electric boundary value formulation, this paper develops...
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An analytical one-dimensional series solution for the time-domain displacement response of a piezoelectric plate is derived. Rather than the usual charge driven electric boundary value formulation, this paper develops the solution for a voltage-driven step function excitation where one electrode is stress-free and the other is displacement fixed. The advantage of this rapidly converging series lies in the ability to test numerical methods such as piezoelectric finite element time domain (FETD) algorithms.
The vibration of a machine carries important information about the health of its internal components; this information, if properly extracted, can be extremely useful in the detection of developing faults within the m...
The vibration of a machine carries important information about the health of its internal components; this information, if properly extracted, can be extremely useful in the detection of developing faults within the machine. One of the most effective methods to extract this information is the computation of the vibration power spectrum, but since the statistical properties of the vibration signal are generally unknown, the power spectrum has to be estimated from the available finite-length data. A number of methods have been proposed for vibration spectral estimation, each presenting advantages and disadvantages. In each specific application, it is often necessary to evaluate and choose the optimum spectral estimation method. This paper presents an analysis of four widely accepted non-parametric spectral estimation methods: Periodogram, Blackman-Tukey, Welch, and Nuttall-Carter. It compares them based on their mean, variance, resolution, and computational requirements. It is found that all methods, except the Periodogram, can achieve the same mean, variance, and resolution but differ in leakage suppression and computational complexity. The Welch method has the best leakage suppression and the Nuttall-Carter method has the lowest computational burden in most cases.
A cooperative method is proposed in which image intensity (brightness) and optical-flow information are integrated into a single stereo technique by modeling the input data as coupled Markov random fields (MRF’s). Th...
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A cooperative method is proposed in which image intensity (brightness) and optical-flow information are integrated into a single stereo technique by modeling the input data as coupled Markov random fields (MRF’s). The Bayesian probabilistic estimation method and the MRF–Gibbs equivalence theory are used to integrate the optical flow and the gray-level intensity information to obtain an energy function that will explicitly represent the depth discontinuity and occlusion constraints on the solution. This energy function involves the similarity in intensity (or edge orientation) and the optical flow between corresponding sites of the left and right images as well as the smoothness constraint on the disparity solution. If a simple MRF is used to model the data, the energy function will yield a poor disparity by smoothing across object boundaries, particularly when occluding objects are present. We use optical-flow information to indicate object boundaries (depth discontinuities) and occluded regions, in order to improve the disparity solution in occluded regions. A stochastic relaxation algorithm (simulated annealing) is used to find a favorable disparity solution by minimization of the energy equation.
Setup Planning is to determine the number/sequence of setups in a production line and operation details in each setup. To bridge the gap between computer-aided process planning (CAPP) and computer-aided fixture design...
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Setup Planning is to determine the number/sequence of setups in a production line and operation details in each setup. To bridge the gap between computer-aided process planning (CAPP) and computer-aided fixture design (CAFD), an automated setup planning and tolerance decomposition method is developed. Directed graph is extended to represent feature/dimension/tolerance relationships (FTG) and datum/machining feature relationships (DMG). According to different production schemes and manufacturing resource capabilities, setup planning principles and algorithms are explored to automatically extract DMG from FTG. Under the true positioning frame, tolerance decomposition models are concluded to partition a tolerance into interoperable machining errors, such as locating error, tool alignment error, and random process error. As one of the deterministic components of machining errors, locating error is primarily caused by positional variations of locating elements in fixture design and dimensional variations of locating features on workpieces. In this research, mathematical models are developed to analyze locating variations and their influences on machining features. The analysis results of locating error effects can be used in budgeting the locating precision and improving the setup plan. The technique has been implemented on a commercial CAD system with applications to automobile manufacturing industry.
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