Stability of uniform electronic wavepackets in chains and fullerenes

2015 ◽  
Vol 26 (12) ◽  
pp. 1550133 ◽  
Author(s):  
Valdemir L. Chaves Filho ◽  
Rodrigo P. A. Lima ◽  
F. A. B. F. de Moura ◽  
Marcelo L. Lyra
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Modulational Instability ◽  
The Other ◽  
Nonlinear Coupling ◽  
Phonon Coupling ◽  
Instability Analysis ◽  
Nonlinear Dynamic Equation ◽  
Electron Phonon Coupling ◽  
The Stability

In this paper, we investigate the influence of electron-lattice interaction on the stability of uniform electronic wavepackets on chains as well as on several types of fullerenes. We will use an effective nonlinear Schrödinger equation to mimic the electron–phonon coupling in these topologies. By numerically solving the nonlinear dynamic equation for an initially uniform electronic wavepacket, we show that the critical nonlinear coupling above which it becomes unstable continuously decreases with the chain size. On the other hand, the critical nonlinear strength saturates on a finite value in large fullerene buckyballs. We also provide analytical arguments to support these findings based on a modulational instability analysis.

scholarly journals Oscillation Criteria of Singular Initial-Value Problem for Second Order Nonlinear Dynamic Equation on Time Scales

2018 ◽  
Vol 5 (1) ◽  
pp. 102-112 ◽  
Author(s):  
Shekhar Singh Negi ◽  
Syed Abbas ◽  
Muslim Malik
Keyword(s):  
Time Scales ◽  
Initial Value Problem ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Type Inequality ◽  
Second Order ◽  
Oscillation Criterion ◽  
Initial Value ◽  
Nonlinear Dynamic Equation ◽  
Singular Initial Value Problem

AbstractBy using of generalized Opial’s type inequality on time scales, a new oscillation criterion is given for a singular initial-value problem of second-order dynamic equation on time scales. Some oscillatory results of its generalizations are also presented. Example with various time scales is given to illustrate the analytical findings.

FINITE DIFFERENCE METHOD FOR SOLVING THE NONLINEAR DYNAMIC EQUATION OF UNDERWATER TOWED SYSTEM

2014 ◽  
Vol 11 (04) ◽  
pp. 1350060 ◽  
Author(s):  
ZHIJIANG YUAN ◽  
LIANGAN JIN ◽  
WEI CHI ◽  
HENGDOU TIAN
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Computational Time ◽  
Algebraic Equations ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

A wide body of work exists that describes numerical solution for the nonlinear system of underwater towed system. Many researchers usually divide the tow cable with less number elements for the consideration of computational time. However, this type of installation affects the accuracy of the numerical solution. In this paper, a newly finite difference method for solving the nonlinear dynamic equations of the towed system is developed. The mathematical model of tow cable and towed body are both discretized to nonlinear algebraic equations by center finite difference method. A newly discipline for formulating the nonlinear equations and Jacobian matrix of towed system are proposed. We can solve the nonlinear dynamic equation of underwater towed system quickly by using this discipline, when the size of number elements is large.

scholarly journals Kamenev-Type Oscillation Criteria for the Second-Order Nonlinear Dynamic Equations with Damping on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
M. Tamer Şenel
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Oscillatory Solutions ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations ◽  
Generalized Riccati Transformation ◽  
Type Oscillation

The oscillation of solutions of the second-order nonlinear dynamic equation(r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t))γ+f(t,x(g(t)))=0, with damping on an arbitrary time scaleT, is investigated. The generalized Riccati transformation is applied for the study of the Kamenev-type oscillation criteria for this nonlinear dynamic equation. Several new sufficient conditions for oscillatory solutions of this equation are obtained.

Nonlinear Vibration Analysis of Viscoelastic Isolator

2012 ◽  
Vol 160 ◽  
pp. 140-144
Author(s):  
Chao Zhou ◽  
Cai Mao Zhong
Keyword(s):  
Dynamic Response ◽  
Fractional Derivative ◽  
Nonlinear Dynamic ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Response Characteristics ◽  
Nonlinear Dynamic Equation ◽  
The Stability ◽  
Stiffness And Damping

Research on nonlinear dynamic response of passive vibration isolator, which was excited by foundation vibration and isolated by viscoelastic material was done. Nonlinear stiffness was expressed by the cubic polynomial function of deformation and nonlinear damping was characterized by viscoelastic fractional derivative operator. Then the fractional derivative nonlinear dynamic equation of passive vibration isolator was established. The dynamic response characteristics were analyzed by harmonic balance method and the frequency response equation and amplitude-frequency curve were obtained, and furthermore, the influence of nonlinearity on system was analyzed. Finally, the stability and the stable interval of the periodic solution were argued by the Floquet theory. The result s indicates that the proposed equation can precisely describe the dynamic characteristics of viscoelastic vibration isolator. The ignorance of nonlinearity of stiffness and damping will result in obvious error. The proposed method provides theoretic reference for design of viscoelastic isolator and the evaluation of its effect.

scholarly journals Oscillation Criteria for Functional Dynamic Equations with Nonlinearities Given by Riemann-Stieltjes Integral

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yuangong Sun ◽  
Taher S. Hassan
Keyword(s):  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Second Order ◽  
Dynamic Equations ◽  
Stieltjes Integral ◽  
Oscillation Criteria ◽  
Nonlinear Dynamic Equation ◽  
Nonlinear Dynamic Equations

We present new oscillation criteria for the second order nonlinear dynamic equation[r(t)ϕγ(xΔ(t))]Δ+q0(t)ϕγ(x(g0(t)))+∫ab‍q(t,s)ϕα(s)(x(g(t,s)))Δζ(s)=0under mild assumptions. Our results generalize and improve some known results for oscillation of second order nonlinear dynamic equations. Several examples are worked out to illustrate the main results.

STRONG ELECTRON-PHONON COUPLING AND THE ORTHORHOMBIC TO TETRAGONAL TRANSITION IN La2CuO4

1988 ◽  
Vol 02 (05) ◽  
pp. 827-836 ◽  
Author(s):  
S. Barišić ◽  
I. Batistić
Keyword(s):  
Metal Oxides ◽  
Hole Concentration ◽  
Coupling Constant ◽  
Phonon Coupling ◽  
Strong Electron ◽  
Electron Phonon Coupling ◽  
The Stability ◽  
Electron Photon ◽  
Small Polarons ◽  
Photon Coupling

It is proposed that the main contribution to the electron-photon coupling in ionic metals arises from the deformation induced variation of the crystal field on the ionic sites which are involved in conduction. The latter are assumed here to be the oxygen sites in the CuO 2 planes of the layered metal oxides. The coupling of holes on those sites to the tilting mode of the La 2 CuO 4 lattice is investigated in detail. Although the coupling is quadratic in small tilting displacement the large value of the corresponding coupling constant explains the destabilization of the tilted (orthorhombic) La 2 CuO 4 lattice on increasing the hole concentration. It is shown that the holes are suppressing the tilt locally, creating the regions of the tetragonal please, as observed recently in the photogeneration experiments. The stability of the corresponding small polarons (tiltons) is discussed in detail.

scholarly journals On Hyers–Ulam and Hyers–Ulam–Rassias Stability of a Nonlinear Second-Order Dynamic Equation on Time Scales

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1507
Author(s):  
Alaa E. Hamza ◽  
Maryam A. Alghamdi ◽  
Mymonah S. Alharbi
Keyword(s):  
Time Scales ◽  
Dynamic Equation ◽  
Nonlinear Dynamic ◽  
Sufficient Conditions ◽  
Second Order ◽  
Nonlinear Dynamic Equation ◽  
Theoretical Results ◽  
Rassias Stability

In this paper, we obtain sufficient conditions for Hyers–Ulam and Hyers–Ulam–Rassias stability of an abstract second–order nonlinear dynamic equation on bounded time scales. An illustrative example is given to show the applicability of the theoretical results.

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