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Plane wave packets and beams
Published in G. Someda Carlo, Electromagnetic Waves, 2017
This relation confirms that a tightly focused Gaussian beam (small spot size) diverges rapidly, away from the waist plane, while if one wants a well collimated beam, i.e., a beam consisting of almost parallel rays, it is necessary that the beam cross-section be not too small. This comment is fundamental not only in optics, but also in the case of aperture antennas. It expresses the so-called “uncertainty principle” between “conjugate variables,” i.e., between two quantities which span the domains of two functions related to each other by a Fourier transform. It is, in this sense, the same as the relationship between widths of a signal in the time domain and in the frequency domain, which we recalled in Section 4.7. In the present case, the Fourier transform is the plane-wave expansion of the field on the beam waist plane.
Experimental investigations on efficiency and instability of combustion process in a diesel engine fueled with ternary blends of hydrogen peroxide additive/biodiesel/diesel
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2022
Prabhakar Sharma, Ajay Chhillar, Zafar Said, Zuohua Huang, Van Nhanh Nguyen, Phuoc Quy Phong Nguyen, Xuan Phuong Nguyen
Increased cyclic variations over the combustion phase can cause engine roughness, loud noises, performance degradation, and increased exhaust emissions. The statistical method, wavelet analysis, and chaotic analysis may all be used to specify cyclic fluctuations in combustion. Each has advantages and disadvantages. The wavelet analysis is founded on a spectral-temporal approach and is based on continuous wavelet transformation (CWT) (Torrence and Compo 1998). Any signal processing method utilized should be capable of recognizing time and frequency data concurrently to determine the magnitude of tenacity and the existence of cyclic fluctuations. The exact measurement of these conjugate variables is a tough and complex task due to a lack of ways to indicate accurate frequency values at a particular time and vice versa. The CWT analysis is important in this context because it provides a suitable platform for dissecting frequency and time data together (Ali et al. 2015a).