A general analytical expression for evaluation of an arbitrary n-dimensional Franck-Condon overlap integral including the Duschinsky effect

Abstract The granulometric composition of most unconsolidated sediments is susceptible to general analytical expression and can be represented by simple algebraic functions defined by the two indices of evolution (n) and sorting (g).In the case of fine sediments, where dispersion is weak, these functions correspond rather precisely to the actual granulometric curves. Four granulometric facies corresponding to true sedimentary facies can be defined according to the index n.

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Complex Franck—Condon overlap integral in nonradiative decays

Chemical Physics ◽

10.1016/0301-0104(79)85052-1 ◽

1979 ◽

Vol 38 (1) ◽

pp. 89-96 ◽

Cited By ~ 2

Author(s):

Yuichi Fujimura ◽

Takeshi Nakajima

Keyword(s):

Overlap Integral ◽

Franck Condon

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A Simple and General Analytical Expression for Calculating Crosstalk in Multiwaveguide Directional Couplers Using Finite Differences Method

Journal of Kufa Physics ◽

10.31257/2018/jkp/2019/110202 ◽

2019 ◽

Vol 11 (02) ◽

pp. 6-14

Author(s):

Sabah M.M. Ameen ◽

Mansour H. Mansour ◽

Keyword(s):

Finite Differences ◽

Directional Couplers ◽

General Analytical Expression ◽

Analytical Expression ◽

Finite Differences Method

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The X (X = F, Cl, I) effect on the photoassociation of H+X→HX

Journal of Theoretical and Computational Chemistry ◽

10.1142/s0219633615500625 ◽

2015 ◽

Vol 14 (08) ◽

pp. 1550062

Author(s):

Wei Gao ◽

Bin-Bin Wang ◽

Yong-Chang Han ◽

Shu-Lin Cong

Keyword(s):

Schrödinger Equation ◽

Vibrational Level ◽

Ground State ◽

Schrodinger Equation ◽

Vibrational State ◽

Time Dependent ◽

Overlap Integral ◽

Target State ◽

Multiphoton Transition ◽

Franck Condon

This work explores the vibrational state-selective photoassociation (PA) in the ground state of the HX (X = F, Cl, I) molecule by solving the time-dependent Schrödinger equation. For the three systems, the vibrational level of [Formula: see text] is set to be the target state and the PA probability of the target state is calculated and compared by considering different initial collision momentums. It is found that the PA probabilities are in accordance with Franck–Condon overlap integral for the HI and HCl systems, but it is not the case for the HF system. Moreover, for the HF system, it is shown that the PA probability of the target state is largest and the multiphoton transition is more likely to occur.

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Vibrational Amplitude Frequency Characteristics Analysis of a Controlled Nonlinear Meso-Scale Beam

Actuators ◽

10.3390/act10080180 ◽

2021 ◽

Vol 10 (8) ◽

pp. 180

Author(s):

Zuguang Ying ◽

Yiqing Ni

Keyword(s):

Harmonic Balance ◽

Frequency Characteristics ◽

Vibration Response ◽

Periodic Response ◽

General Analytical Expression ◽

Analytical Expression ◽

Periodic Vibration ◽

Balance Solution ◽

Frequency Relation ◽

Meso Scale

Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration analyses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response variation have potential application to the vibration control design of nonlinear meso-scale structure systems.

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