The diffraction field of a Gaussian planar velocity distribution is a Gaussian beam function under the condition (ka } 2•, 1. This property makes a series of Gaussian functions attractive as a possible base function set. The new approach presented enables one to express any axisymmetric beam field in a simple analytical form-the superposition of Gaussian beams about the same axis but with beam waists of different sizes located at different positions along the axis. A computer optimization is used to evaluate the coefficients, as well as the beam waists and their positions. The extreme case of a piston radiator is used to test the approach. Good agreement between a ten-term Gaussian beam solution and the results of numerical integration (or analytical solution on axis) is obtained throughout the beam field: in the farfield, the transition region, and the nearfield. Discrepancies exist only in the extreme nearfield (< 0.1 times the Fresnel distance). For surface velocity distributions that are less discontinuous (smoother), the number of terms in the Gaussian beam solution is reduced. In the extreme case of a Gaussian radiator, only one term is needed. The approach, then, reduces the study of any axisymmetric beam field to the study of the much simpler Gaussian beam.
The electrode shape required to produce a Gaussian electric field distribution at the surface of a transducer was calculated. Such electrodes were made and tried with both quartz and PZT transducers with promising results. These transducers have an advantage over those made by taking advantage of electrical fringing [Breazeale et al., J. Acoust. Soc. Am. 70, 1791–1793 (1981)] in that they do not have the limitation 2 < W/T < 4. Results of measurement of the ultrasonic field produced at 4 MHz by quartz and PZT are given, and application to NDE and acoustical microscopy is considered. [Research sponsored, in part, by UTORNL Science Alliance, A State of Tennessee Center of Excellence. PZT provided by S. Fujishima, Murata Corp.]
In large public places such as scenic tourist areas, shopping malls, stations, squares, and so on, there is a wide demand for people counting and pedestrian flow monitoring. Based on the feedback from the pedestrian flow monitoring system, resources can be optimally allocated to maximize social and economic benefits. Moreover, trampling accidents can be avoided because pedestrian guidance is carried out in time. In order to meet these requirements, we propose a method of pedestrian flow monitoring based on the received signal strength (RSS) of wireless sensor networks. This method mainly utilizes the shadow attenuation effect of pedestrians on RF signals of effective links. In this paper, a deployment structure of a radio frequency wireless sensor network is firstly designed to monitor the pedestrians. Secondly, the features are extracted from the wavelet decomposition of RSS signal series with a short time. Lastly, the support vector machine (SVM) algorithm is trained by an experimental data set to distinguish the instantaneous number of pedestrians passing through the monitoring point. The experimental results show that the accuracy is about 92.9% in the context of real-time pedestrian flow monitoring.In large public places such as scenic tourist areas, shopping malls, stations, squares, and so on, there is a wide demand for people counting and pedestrian flow monitoring. Based on the feedback from the pedestrian flow monitoring system, resources can be optimally allocated to maximize social and economic benefits. Moreover, trampling accidents can be avoided because pedestrian guidance is carried out in time. In order to meet these requirements, we propose a method of pedestrian flow monitoring based on the received signal strength (RSS) of wireless sensor networks. This method mainly utilizes the shadow attenuation effect of pedestrians on RF signals of effective links. In this paper, a deployment structure of a radio frequency wireless sensor network is firstly designed to monitor the pedestrians. Secondly, the features are extracted from the wavelet decomposition of RSS signal series with a short time. Lastly, the support vector machine (SVM) algorithm is trained by an experimental data set to distinguish the instantaneous number of pedestrians passing through the monitoring point. The experimental results show that the accuracy is about 92.9% in the context of real-time pedestrian flow monitoring.
Wave propagations are best described by three major approaches: the spherical wave approach represented by Rayleigh integral, the planar wave approach represented by spatial Fourier analysis, and the Gaussian beam approach. Spherical and planar wave approaches, both in form of double integrals, are analytically inconvenient and computationally expensive. In contrast, the Gaussian beam approach, with huge advantages in analytical operability and computational efficiency, has been quietly but firmly winning popularity. Dr. Breazeale’s article: A diffraction beam field expressed as the superposition of Gaussian beams, co-authored with Wen, is not only a most representative work for Gaussian beam approach but also a most cited academic work in sound field analysis and computation. As a memory of Dr. Breazeale’s pioneer role in the raise of Gaussian beam method, this article presents a new enhancement to the existing Gaussian beam method. A modified form of Gaussian beam function introduced as the base function set for wave field analysis greatly reduces the error rooted from the parabolic approximation, the number of Gaussian beams needed, and the run-time computation burden. The process for calculating the beam coefficients and beam parameters is also greatly simplified.
A new method of analysis is described to represent the resultant field when a wave beam is subjected to any physical process (e.g., propagation, focusing, reflection, diffraction, etc.). Instead of expressing the field solution as a continuous distribution of plane waves through spatial Fourier analysis, a set of Gaussian beams is employed as the basic unit. The Gaussian beam representation is introduced to replace the traditional planewave representation so that the solution is an analytical one rather than a symbolic integral. This replacement is made possible by a computer optimization routine that overcomes problems introduced by use of nonorthogonal functions, and enables the expression of the field solution in a simple closed analytical form—the sum of Gaussian functions. The technique is applied to the description of the reflected field of a bounded beam incident at the Rayleigh angle with very satisfactory results. [Research sponsored by the Science Alliance, a State of Tennessee Center of Excellence.]
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