A new asymptotic energy expansion method

2001 ◽  
Vol 289 (1-2) ◽  
pp. 39-43 ◽  
Author(s):  
Asiri Nanayakkara
Keyword(s):  
Expansion Method ◽  
Asymptotic Energy ◽  
Energy Expansion

Asymptotic behavior of eigen energies of non-Hermitian cubic polynomial systems

2007 ◽  
Vol 85 (12) ◽  
pp. 1473-1480 ◽  
Author(s):  
A Nanayakkara
Keyword(s):  
Asymptotic Behavior ◽  
Polynomial System ◽  
Expansion Method ◽  
Polynomial Systems ◽  
Level Spacing ◽  
Spacing Distribution ◽  
Cubic Polynomial ◽  
Asymptotic Energy ◽  
04.20 Jb ◽  
Energy Expansion

The asymptotic behavior of the eigenvalues of a non-Hermitian cubic polynomial system H = (P2/2) + µx3 + ax2 + bx, where µ, a, and b are constant parameters that can be either real or complex, is studied by extending the asymptotic energy expansion method, which has been developed for even degree polynomial systems. Both the complex and the real eigenvalues of the above system are obtained using the asymptotic energy expansion. Quantum eigen energies obtained by the above method are found to be in excellent agreement with the exact eigenvalues. Using the asymptotic energy expansion, analytic expressions for both level spacing distribution and the density of states are derived for the above cubic system. When µ = i, a is real, and b is pure imaginary, it was found that asymptotic energy level spacing increases with the coupling strength a for positive a while it decreases for negative a. PACS Nos.: 03.65.Ge, 04.20.Jb, 03.65.Sq, 02.30.Mv, 05.45

ENERGY EXPANSION AND VORTEX LOCATION FOR A TWO-DIMENSIONAL ROTATING BOSE–EINSTEIN CONDENSATE

2006 ◽  
Vol 18 (02) ◽  
pp. 119-162 ◽  
Author(s):  
RADU IGNAT ◽  
VINCENT MILLOT
Keyword(s):  
Topological Charge ◽  
Einstein Condensate ◽  
Two Dimensional ◽  
Precise Location ◽  
Ginzburg Landau ◽  
Bose Einstein Condensate ◽  
Mass Constraint ◽  
Asymptotic Energy ◽  
Bose Einstein ◽  
Energy Expansion

We continue the analysis started in [14] on a model describing a two-dimensional rotating Bose–Einstein condensate. This model consists in minimizing under the unit mass constraint, a Gross–Pitaevskii energy defined in ℝ2. In this contribution, we estimate the critical rotational speeds Ωd for having exactly d vortices in the bulk of the condensate and we determine their topological charge and their precise location. Our approach relies on asymptotic energy expansion techniques developed by Serfaty [20–22] for the Ginzburg–Landau energy of superconductivity in the high κ limit.

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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