Generation of an arbitrary order Bessel beam in FDTD for time domain calculation

2019 ◽  
Author(s):  
Zhefeng Wu ◽  
Jiajie Wang ◽  
Paul Briard ◽  
Yiping Han ◽  
Antao Chen ◽  
...  
Keyword(s):  
Time Domain ◽  
Arbitrary Order ◽  
Bessel Beam

scholarly journals Novel Generic Analytical Model of Fractance Response

1970 ◽  
Vol 10 (1) ◽  
pp. 42-52
Author(s):  
Rawid Banchuin ◽  
Roungsan Chaisricharoen
Keyword(s):  
Analytical Model ◽  
Time Domain ◽  
Analog Circuits ◽  
Arbitrary Order ◽  
Voltage Response ◽  
Periodic Excitation ◽  
Control Engineering ◽  
Electronic Engineering ◽  
Engineering Control ◽  
Proposed Model

Fractance is often cited in various engineering disciplines for example, analog circuits and systems, biomedical engineering, control engineering and electronic engineering etc. In this research, a novel generic analytical model of the voltage response of fractance in time domain has been proposed. This model composes of two parts for fractance with order ranges from 0 to 1 and larger than 1 respectively. With this model, the asymptotic and transient voltage responses of fractance can also be determined. Unlike the results of the previous works which are applicable only to fractance with certain orders under certain excitations, this model can be applied to fractance of arbitrary order under arbitrary type of periodic excitation. Moreover, it has been shown that the proposed model is in a realistic format. So, this model has been found to be beneficial to various fractance involved engineering disciplines stated above.

A Versatile Analytical Expression of Time Domain Response of Arbitrary Order Fractance

2015 ◽  
Vol 781 ◽  
pp. 572-575
Author(s):  
Rawid Banchuin
Keyword(s):  
Control Systems ◽  
Time Domain ◽  
Analog Circuits ◽  
Arbitrary Order ◽  
Analytical Tool ◽  
Analytical Expression ◽  
Biomedical Electronics ◽  
Time Domain Response

In this research, a versatile analytical expression of time domain response of fractance with arbitrary order has been derived. Responses to various renowned inputs can be analytically determined by using the derived expression as the basis. This expression has been found to be an efficient analytical tool for various fractance involved disciplines such as biomedical electronics, control systems and analog circuits etc.

A transform of univariable time domain polynomial for extraction of temporal arcs

2020 ◽  
Vol 39 (6) ◽  
pp. 1363-1374
Author(s):  
Binesh Thankappan
Keyword(s):  
Time Domain ◽  
Design Methodology ◽  
Arbitrary Order ◽  
Special Functions ◽  
Time Derivative ◽  
Polynomial Functions ◽  
Content Type ◽  
Analysis And Synthesis ◽  
Novel Method ◽  
Practical Implications

Purpose This paper aims to present a special transformation that is applied to univariable polynomials of an arbitrary order, resulting in the generation of the proposed offset eliminated polynomial. This transform-based approach is used in the analysis and synthesis of temporal arc functions, which are time domain polynomial functions possessing two or more values simultaneously. Using the proposed transform, the submerged values of temporal arcs can also be extracted in measurements. Design/methodology/approach The methodology involves a two-step mathematical procedure in which the proposed transform of the weighted modified derivative of the polynomial is generated, followed by multiplication with a linear or ramp function. The transform introduces a stretching in the temporal or spatial domain depending on the type of variable under consideration, resulting in modifications for parameters such as time derivative and relative velocity. Findings Detailed analysis of various parameters in this modified time domain is performed and results are presented. Additionally, using the proposed methodology, the submerged value of any temporal arc function can also be extracted in measurements, thereby unraveling the temporal arc. Practical implications A typical implementation study with results is also presented for an operational amplifier-based temporal arc-producing square rooting circuit for the extraction of the submerged value of the function. Originality/value The proposed transform-based approach has major applications in extracting the values of temporal arc functions that are submerged in conventional experimental measurements, thereby providing a novel method in unraveling that class of special functions.

Time-Domain Implementation of Higher-Order Non-Reflecting Boundary Conditions for Turbomachinery Applications

2015 ◽  
Author(s):  
Stefan Henninger ◽  
Peter Jeschke ◽  
Graham Ashcroft ◽  
Edmund Kügeler
Keyword(s):  
Boundary Conditions ◽  
Time Domain ◽  
Arbitrary Order ◽  
Linear Time ◽  
Numerical Test ◽  
Acoustic Resonance ◽  
Inverse Laplace Transform ◽  
Test Case ◽  
Local Conditions ◽  
Blade Flutter

The present paper demonstrates the time-domain implementation of arbitrary-order non-reflecting boundary conditions for a 3d non-linear time-accurate RANS solver for turbomachinery applications. The conditions are based on the 2d circumferential mode decomposition of the linearized Euler equations. The exact linearized conditions are non-local since they involve space-time Fourier/Laplace transforms. Time-local conditions of arbitrary order are obtained by approximation of the inverse Laplace transform Bessel function convolution kernel by sums of exponential functions. Likewise, this corresponds to a rational function approximation of the exact non-reflecting boundary kernel in the frequency-domain. The boundary conditions are validated against two numerical test cases. The first test case mimics Tyler-Sofrin modes present in turbomachinery applications by prescribing 2d acoustic modes in a uniform flow. The second test case is concerned with the potential contamination of blade flutter analyses by spurious reflections on artificial boundaries. For the benchmark problem Standard Configuration 10, blade flutter with non-zero inter-blade phase angle, acoustic resonance generates spinning waves susceptible to reflection. Contrasting the results of non-reflecting boundary conditions of varying order of accuracy shows that low order conditions can fail for challenging cases, which emphasizes the need for an accurate non-reflecting boundary treatment.

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