Calculations of the dynamic dipole polarizabilities for the Li
                    <sup>+</sup>
                    ion

Zhang, Yonghui; Tang, Li-Yan; Zhang, Xianzhou; Shi, Ting-Yun

doi:10.1088/1674-1056/25/10/103101

Cited by 6 publications

(4 citation statements)

References 53 publications

(72 reference statements)

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“…The dense‐bed external catalyst coolers, which are mostly widely seen in FCC units, are usually operated in bubbling or turbulent flow regime. The heat tube often adopts a concentrically double‐tube design . Figure shows a schematic of the design of a typical FCC external catalyst cooler widely used in China's refineries .…”

Section: Introductionmentioning

confidence: 99%

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Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Yao

Zhang

et al. 2014

AIChE Journal

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Bed-to-wall heat transfer properties of a vertical heat tube in a fluidized bed of fine fluid catalytic cracking (FCC) particles are measured systematically using a specially designed heat tube. Two important surface hydrodynamic parameters, i.e. the packet fraction (d pa ) and mean packet residence time (s pa ) based on the packet renewal theory, are determined by an optical fiber probe and a data processing method. The experimental results successfully reveal the axial and radial profiles of heat-transfer coefficient, the effects of superficial gas velocity, and static bed height on heat-transfer coefficient, most of which can be explained successfully by the measured s pa , an indicator of packet renewal frequency. s pa is found to play a more dominant role than d pa on bed-to-wall heat transfer. With a fitted correction factor, the modified Mickley and Fairbanks model is able to predict the heat-transfer coefficients with enough accuracy based on the determined packet parameters. Figure 23. Effect of static bed height on heat-transfer coefficients.

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Section: Introductionmentioning

confidence: 99%

“…The heat tube often adopts a concentrically double‐tube design . Figure shows a schematic of the design of a typical FCC external catalyst cooler widely used in China's refineries . Hot particles enter into the cooler through the top entrance, then flow downward in the cooler and leave from the bottom exit.…”

Section: Introductionmentioning

confidence: 99%

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Yao

Zhang

et al. 2014

AIChE Journal

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show abstract

“…[1][2][3][4][5][6][7] However, accurate experimental and theoretical data for this pivotal electric property are widely available mainly for neutral atomic and molecular species. [6][7][8][9][10][11][12][13][14][15] As for ions, the reliable literature values are predominately limited to singly and doubly charged monoatomic cations, [16][17][18][19][20][21][22][23] whereas both for highly charged atomic cations and especially for anions (both atomic and molecular) there is a lack of established data on polarizability. Indeed, the information available in the literature on the isotropic (scalar) polarizability values for multiply charged atomic species is essentially fragmentary, [16,21,22,[24][25][26] and the polarizability estimates for negative monoatomic ions reported elsewhere can differ by tens of percent and even several times.…”

Section: Introductionmentioning

confidence: 99%

A simple semiempirical model for the static polarizability of ions

Sharipov

Loukhovitski

2023

Chinese Phys. B

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A concise analytical model for the static dipole polarizability of ionized atoms and molecules is created for the first time. As input, it requires, alongside the polarizability of neutral counterpart of a given ion, only the charge and elemental composition. This physically motivated semiempirical model is based on a number of established regularities in polarizability of charged monatomic and polyatomic compounds. In order to adjust it, the results of quantum chemistry calculations and gas-phase measurements available for a broad range of ionized multielectron species are employed. To counteract the appreciable bias in the literature data toward polarizability of monoatomic ions, for some molecular ions of general concern the results of the authors’ own density functional theory calculations are additionally invoked. A total of 541 data points are used to optimize the model. It is demonstrated that the model we suggested has reasonable (given the substantial uncertainties of the reference data) accuracy in predicting the static isotropic polarizability of arbitrarily charged ions of any size and atomic composition. The resulting polarizability estimates are found to achieve a coefficient of determination of 0.93 for the assembled data set. The created analytic tool is universally applicable and might be advantageous for some applications, where there is an urgent need for rapid low-cost evaluation of the static gas-phase polarizability of ionized atoms and molecules. This is especially relevant to constructing the complex models of nonequilibrium chemical kinetics aimed at precise describing the observable refractive index (dielectric permittivity) of plasma flows. The data sets that support the findings of this study are openly available in Science Data Bank at https://...

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“…[15] To solve this problem, Patchkovskii et al have proposed a parallel method, [18] and achieved the spa-tial derivatives of the radial coordinate by using the finitedifference method (FDM), which leads to an increase in the grids for the larger sized problem, [17] and finally significantly increasing the amount of computation in the case of higher accuracy. [19] Guan et al solved TDSE of two-electron quantum system in spherical coordinates efficiently based on the finite-element (FE) discrete-variable-representation (DVR) and Short-Iteration-Lanczos (SIL) propagator, [20] because the FE-DVR can offer higher computing accuracy [21] and make the Hamiltonian matrix very sparse, whose effects are similar to those provided by the B-spline [22,23] and sine-DVR, [24] and the efficiency of the wave function evolution strongly relies on the sparsity of the Hamiltonian matrix for the SIL propagator. [25] The most ideal structure of the Hamiltonian matrix is expected to have diagonal or similarly sparse elements for the SIL propagator.…”

Section: Introductionmentioning

confidence: 99%

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

Zhou¹,

Liu²,

Liu³

et al. 2019

Chinese Phys. B

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We present a parallel numerical method of simulating the interaction of atoms with a strong laser field by solving the time-depending Schrödinger equation (TDSE) in spherical coordinates. This method is realized by combining constructing block diagonal matrices through using the real space product formula (RSPF) with splitting out diagonal sub-matrices for short iterative Lanczos (SIL) propagator. The numerical implementation of the solver guarantees efficient parallel computing for the simulation of real physical problems such as high harmonic generation (HHG) in these interaction systems.

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Calculations of the dynamic dipole polarizabilities for the Li ⁺ ion

Cited by 6 publications

References 53 publications

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

A simple semiempirical model for the static polarizability of ions

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

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Calculations of the dynamic dipole polarizabilities for the Li + ion

Cited by 6 publications

References 53 publications

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

Systematic study on heat transfer and surface hydrodynamics of a vertical heat tube in a fluidized bed of FCC particles

A simple semiempirical model for the static polarizability of ions

Efficient solver for time-dependent Schrödinger equation with interaction between atoms and strong laser field*

Contact Info

Product

Resources

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Calculations of the dynamic dipole polarizabilities for the Li ⁺ ion