scholarly journals (G'/G)-expansion method and novel fractal structures for high-dimensional nonlinear physical equation

2010 ◽  
Vol 59 (3) ◽  
pp. 1409
Author(s):  
Li Bang-Qing ◽  
Ma Yu-Lan ◽  
Xu Mei-Ping
Keyword(s):  
Expansion Method ◽  
High Dimensional ◽  
Fractal Structures ◽  
Physical Equation

scholarly journals Model of fractal aggregates induced by shear

2013 ◽  
Vol 17 (5) ◽  
pp. 1403-1408 ◽  
Author(s):  
Zhanhong Wan ◽  
Jiawang Chen ◽  
Zhenjiang Youc ◽  
Zhiyuan Lia
Keyword(s):  
Evolution Equations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Fractal Dimensions ◽  
Expansion Method ◽  
Geometric Standard Deviation ◽  
Order Moment ◽  
Fractal Structures ◽  
Powerful Approach ◽  
Fractal Characteristics

It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.

scholarly journals New exact solutions of the(2+1)-dimensional Broer-Kaup equation by the consistent Riccati expansion method

2017 ◽  
Vol 21 (4) ◽  
pp. 1783-1788 ◽  
Author(s):  
Ying Jiang ◽  
Da-Quan Xian ◽  
Zheng-De Dai
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Expansion Method ◽  
High Dimensional ◽  
Solitary Wave Solutions ◽  
New Exact Solutions ◽  
Dynamical Behaviors ◽  
Wave Solutions ◽  
Linear Waves ◽  
Consistent Riccati Expansion

In this work, we study the (2+1)-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models

scholarly journals A 2D Expansion Method Using Fractal Shapes for High Dimensional Data

2009 ◽  
Vol 29-1 (2) ◽  
pp. 1319-1319
Author(s):  
Takanori Fujiwara ◽  
Manabu Tange ◽  
Satoshi Someya ◽  
Koji Okamoto
Keyword(s):  
High Dimensional Data ◽  
Expansion Method ◽  
High Dimensional

A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation

2016 ◽  
Author(s):  
F. Wang ◽  
F. Xiong ◽  
S. Yang ◽  
Y. Xiong
Keyword(s):  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Data Driven ◽  
High Dimensional ◽  
Chaos Expansion ◽  
Least Angle Regression ◽  
Structure Problem

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

Fractal Map: Fractal-Based 2D Expansion Method for Multi-scale High-Dimensional Data Visualization

2010 ◽  
pp. 306-315 ◽  
Author(s):  
Takanori Fujiwara ◽  
Ryo Matsushita ◽  
Masaki Iwamaru ◽  
Manabu Tange ◽  
Satoshi Someya ◽  
...  
Keyword(s):  
Data Visualization ◽  
High Dimensional Data ◽  
Expansion Method ◽  
High Dimensional ◽  
Multi Scale

scholarly journals Exact solutions with arbitrary functions of the (4+1)-dimensional fokas equation

2019 ◽  
Vol 23 (4) ◽  
pp. 2403-2411 ◽  
Author(s):  
Bo Xu ◽  
Sheng Zhang
Keyword(s):  
Exact Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Trigonometric Function ◽  
High Dimensional ◽  
Hyperbolic Function ◽  
Jacobi Elliptic Function ◽  
New Exact Solutions ◽  
Hyperbolic Function Solutions ◽  
Trigonometric Function Solutions

In this paper, the (4+1)-dimensional Fokas equation is solved by the generalized F-expansion method, and new exact solutions with arbitrary functions are obtained. The obtained solutions include Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the generalized F-expansion method can be used for constructing exact solutions with arbitrary functions of some other high dimensional partial differential equations in fluids.

scholarly journals New application of (G′/G)-expansion method to high-dimensional nonlinear physical equations

2009 ◽  
Vol 58 (11) ◽  
pp. 7402 ◽  
Author(s):  
Ma Yu-Lan ◽  
Li Bang-Qing ◽  
Sun Jian-Zhi
Keyword(s):  
Expansion Method ◽  
High Dimensional

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

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