scholarly journals An Alternative Approach to Energy Eigenvalue Problems of Anharmonic Potentials

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Okan Ozer ◽  
Halide Koklu
Keyword(s):  
Series Expansion ◽  
Excellent Agreement ◽  
Taylor Series ◽  
Taylor Expansion ◽  
Eigenvalue Problems ◽  
Energy Eigenvalue ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Energy Eigenvalues ◽  
Alternative Approach

Energy eigenvalues of quartic and sextic type anharmonic potentials are obtained by using an alternative method called asymptotic Taylor expansion method (ATEM) which is an approximate approach based on the asymptotic Taylor series expansion of a function. It is shown that the energy eigenvalues found by ATEM are in excellent agreement with the existing results.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

Rationalize the irrational and fractional expressions in nonlinear analysis

2016 ◽  
Vol 30 (04) ◽  
pp. 1650068 ◽  
Author(s):  
Yongfeng Yang ◽  
Tingdong Jiang ◽  
Zhong Ren ◽  
Junyao Zhao ◽  
Zheng Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Series Expansion ◽  
Taylor Series ◽  
Impact Force ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Stochastic Bifurcation ◽  
Bifurcation And Chaos ◽  
Integral Process ◽  
Series Expansion Method

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

A novel method for computing the vertical gradients of the potential field: Application to downward continuation

2019 ◽  
Author(s):  
Kha Van Tran ◽  
Trung Nhu Nguyen
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Potential Field ◽  
Continuation Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Downward Continuation ◽  
Source Distribution ◽  
Vertical Derivative ◽  
Series Expansion Method

Summary Downward continuation is a very useful technique in the interpretation of potential field data. It would enhance the short wavelength of the gravity anomalies or accentuate the details of the source distribution. Taylor series expansion method has been proposed to be one of the best downward continued methods. However, the method using high-order vertical derivatives leads to low accuracy and instability results in many cases. In this paper, we propose a new method using a combination of Taylor series expansion and upward continuation for computing vertical derivatives. This method has been tested on the gravitational anomaly of infinite horizontal cylinder in both cases with and without random noise for higher accurate and stable than Hilbert transform method and Laplace equation method, especially in the case of noise input data. This vertical derivative method is applied successfully to calculate the downward continuation according to Taylor series expansion method. The downward continuation is also tested on both complex synthetic models and real data in the East Vietnam Sea (South China Sea). The results reveal that by calculating this new vertical derivative, the downward continuation method gave higher accurate and stable than the previous downward continuation methods.

A Tabular Taylor Series Expansion Method for Fast Calculation of Steam Properties

1997 ◽  
Vol 119 (2) ◽  
pp. 485-491 ◽  
Author(s):  
K. Miyagawa ◽  
P. G. Hill
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
International Association ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
The State ◽  
Steam Power ◽  
Direct Use ◽  
Derivatives Of ◽  
Plane Grid

A new method is proposed for rapid and accurate calculation of steam properties in the regions of the state plane of greatest importance to the steam power industry. The method makes direct use of the derivatives of that Helmholtz function that is the best available wide-ranging scientific formulation of the properties of steam. It is rapid because, with a six-term Taylor series expansion, it uses property values and derivatives evaluated once and for all from the Helmholtz function and stored in tables pertaining to an optimized state plane grid configuration. The method eliminates the need for iterative property calculations and is amenable to any region of the state plane. For properties in the ranges of temperature from 0 to 800°C and pressure from 0 to 100 MPa the core memory requirement for three functions of any given pair of independent properties is less than 1 Mb. With this memory allocation it is possible everywhere in the stated range to satisfy the specific volume and enthalpy tolerances specified by the International Association for the Properties of Water and Steam. An optimized formulation of the method is demonstrated in this paper for enthalpy, entropy, and volume functions of pressure and temperature in the superheat region.

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