Analytic and numerical approaches for circular cylinder quantum nano jet

San-Yih Lin, Sheng Chang Shih, Yuan Hung Tai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The solutions of the axisymmetric circular cylinder quantum nano jet can be governed by the time-dependent linear Schrödinger equation that is solved by two approaches. One is a partial analytic method based on the Fourier-Bessel transform and the other is numerical method based on finite difference methods. Appropriate boundary conditions for the solutions of the circular cylinder quantum nano jet are derived. By the Fourier-Bessel transform method, several integral formulas for the solutions of the jet are obtained. The Gaussian quadrature numerical integration is then applied to evaluate the integrals. The fourth-order central and compact difference methods are used for the numerical approach. The fourth-order Runge-Kutta time integration is applied for the time marching. Detailed comparisons between the partial analytic and numerical methods are performed. The results indicate that the partial analytic method can obtain right solutions and the proposed numerical method can capture the dispersion wave very well.

Original languageEnglish
Title of host publication4th AIAA Theoretical Fluid Mechanics Meeting
Publication statusPublished - 2005
Event4th AIAA Theoretical Fluid Mechanics Meeting - Toronto, ON, Canada
Duration: 2005 Jun 62005 Jun 9

Other

Other4th AIAA Theoretical Fluid Mechanics Meeting
CountryCanada
CityToronto, ON
Period05-06-0605-06-09

Fingerprint

circular cylinders
Circular cylinders
Numerical methods
time marching
wave dispersion
linear equations
Linear equations
numerical integration
quadratures
Finite difference method
Boundary conditions
boundary conditions

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

Lin, S-Y., Shih, S. C., & Tai, Y. H. (2005). Analytic and numerical approaches for circular cylinder quantum nano jet. In 4th AIAA Theoretical Fluid Mechanics Meeting
Lin, San-Yih ; Shih, Sheng Chang ; Tai, Yuan Hung. / Analytic and numerical approaches for circular cylinder quantum nano jet. 4th AIAA Theoretical Fluid Mechanics Meeting. 2005.
@inproceedings{f830474da9a74f28a60ef990a1e2d5dd,
title = "Analytic and numerical approaches for circular cylinder quantum nano jet",
abstract = "The solutions of the axisymmetric circular cylinder quantum nano jet can be governed by the time-dependent linear Schr{\"o}dinger equation that is solved by two approaches. One is a partial analytic method based on the Fourier-Bessel transform and the other is numerical method based on finite difference methods. Appropriate boundary conditions for the solutions of the circular cylinder quantum nano jet are derived. By the Fourier-Bessel transform method, several integral formulas for the solutions of the jet are obtained. The Gaussian quadrature numerical integration is then applied to evaluate the integrals. The fourth-order central and compact difference methods are used for the numerical approach. The fourth-order Runge-Kutta time integration is applied for the time marching. Detailed comparisons between the partial analytic and numerical methods are performed. The results indicate that the partial analytic method can obtain right solutions and the proposed numerical method can capture the dispersion wave very well.",
author = "San-Yih Lin and Shih, {Sheng Chang} and Tai, {Yuan Hung}",
year = "2005",
language = "English",
isbn = "9781624100666",
booktitle = "4th AIAA Theoretical Fluid Mechanics Meeting",

}

Lin, S-Y, Shih, SC & Tai, YH 2005, Analytic and numerical approaches for circular cylinder quantum nano jet. in 4th AIAA Theoretical Fluid Mechanics Meeting. 4th AIAA Theoretical Fluid Mechanics Meeting, Toronto, ON, Canada, 05-06-06.

Analytic and numerical approaches for circular cylinder quantum nano jet. / Lin, San-Yih; Shih, Sheng Chang; Tai, Yuan Hung.

4th AIAA Theoretical Fluid Mechanics Meeting. 2005.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

TY - GEN

T1 - Analytic and numerical approaches for circular cylinder quantum nano jet

AU - Lin, San-Yih

AU - Shih, Sheng Chang

AU - Tai, Yuan Hung

PY - 2005

Y1 - 2005

N2 - The solutions of the axisymmetric circular cylinder quantum nano jet can be governed by the time-dependent linear Schrödinger equation that is solved by two approaches. One is a partial analytic method based on the Fourier-Bessel transform and the other is numerical method based on finite difference methods. Appropriate boundary conditions for the solutions of the circular cylinder quantum nano jet are derived. By the Fourier-Bessel transform method, several integral formulas for the solutions of the jet are obtained. The Gaussian quadrature numerical integration is then applied to evaluate the integrals. The fourth-order central and compact difference methods are used for the numerical approach. The fourth-order Runge-Kutta time integration is applied for the time marching. Detailed comparisons between the partial analytic and numerical methods are performed. The results indicate that the partial analytic method can obtain right solutions and the proposed numerical method can capture the dispersion wave very well.

AB - The solutions of the axisymmetric circular cylinder quantum nano jet can be governed by the time-dependent linear Schrödinger equation that is solved by two approaches. One is a partial analytic method based on the Fourier-Bessel transform and the other is numerical method based on finite difference methods. Appropriate boundary conditions for the solutions of the circular cylinder quantum nano jet are derived. By the Fourier-Bessel transform method, several integral formulas for the solutions of the jet are obtained. The Gaussian quadrature numerical integration is then applied to evaluate the integrals. The fourth-order central and compact difference methods are used for the numerical approach. The fourth-order Runge-Kutta time integration is applied for the time marching. Detailed comparisons between the partial analytic and numerical methods are performed. The results indicate that the partial analytic method can obtain right solutions and the proposed numerical method can capture the dispersion wave very well.

UR - http://www.scopus.com/inward/record.url?scp=84884766691&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84884766691&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781624100666

BT - 4th AIAA Theoretical Fluid Mechanics Meeting

ER -

Lin S-Y, Shih SC, Tai YH. Analytic and numerical approaches for circular cylinder quantum nano jet. In 4th AIAA Theoretical Fluid Mechanics Meeting. 2005