Moment expansion method to calculate vibrational frequencies of molecules and solids

1980 ◽  
Vol 18 (1) ◽  
pp. 317-321 ◽  
Author(s):  
J. T. Devreese ◽  
P. E. Van Camp ◽  
V. E. Van Doren
Keyword(s):  
Expansion Method ◽  
Vibrational Frequencies ◽  
Moment Expansion

scholarly journals A general moment expansion method for stochastic kinetic models

2013 ◽  
Vol 138 (17) ◽  
pp. 174101 ◽  
Author(s):  
Angelique Ale ◽  
Paul Kirk ◽  
Michael P. H. Stumpf
Keyword(s):  
Kinetic Models ◽  
Expansion Method ◽  
Moment Expansion

scholarly journals Field moment expansion method for interacting bosonic systems

2021 ◽  
Vol 104 (8) ◽  
Author(s):  
Andrew Eberhardt ◽  
Michael Kopp ◽  
Alvaro Zamora ◽  
Tom Abel
Keyword(s):  
Expansion Method ◽  
Moment Expansion

Moment-expansion-method calculations of phonon line shapes in argon

1994 ◽  
Vol 50 (22) ◽  
pp. 16380-16385 ◽  
Author(s):  
E. Roger Cowley ◽  
Fathi Zekaria
Keyword(s):  
Expansion Method ◽  
Phonon Line ◽  
Line Shapes ◽  
Moment Expansion

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.

An empirical review of gambling expansion and gambling-related harm

2018 ◽  
Vol 64 (5-6) ◽  
pp. 295-306 ◽  
Author(s):  
Debi A. LaPlante ◽  
Heather M. Gray ◽  
Pat M. Williams ◽  
Sarah E. Nelson
Keyword(s):  
Literature Review ◽  
Peer Review ◽  
Empirical Data ◽  
Empirical Studies ◽  
Expansion Method ◽  
Responsible Gambling ◽  
Review Literature ◽  
Evidence Based ◽  
Empirical Comparison ◽  
Related Harm

Abstract. Aims: To discuss and review the latest research related to gambling expansion. Method: We completed a literature review and empirical comparison of peer reviewed findings related to gambling expansion and subsequent gambling-related changes among the population. Results: Although gambling expansion is associated with changes in gambling and gambling-related problems, empirical studies suggest that these effects are mixed and the available literature is limited. For example, the peer review literature suggests that most post-expansion gambling outcomes (i. e., 22 of 34 possible expansion outcomes; 64.7 %) indicate no observable change or a decrease in gambling outcomes, and a minority (i. e., 12 of 34 possible expansion outcomes; 35.3 %) indicate an increase in gambling outcomes. Conclusions: Empirical data related to gambling expansion suggests that its effects are more complex than frequently considered; however, evidence-based intervention might help prepare jurisdictions to deal with potential consequences. Jurisdictions can develop and evaluate responsible gambling programs to try to mitigate the impacts of expanded gambling.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

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