### 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 language | English |
---|---|

Title of host publication | 4th AIAA Theoretical Fluid Mechanics Meeting |

Publication status | Published - 2005 |

Event | 4th AIAA Theoretical Fluid Mechanics Meeting - Toronto, ON, Canada Duration: 2005 Jun 6 → 2005 Jun 9 |

### Other

Other | 4th AIAA Theoretical Fluid Mechanics Meeting |
---|---|

Country | Canada |

City | Toronto, ON |

Period | 05-06-06 → 05-06-09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mechanical Engineering
- Mechanics of Materials
- Condensed Matter Physics

### Cite this

*4th AIAA Theoretical Fluid Mechanics Meeting*

}

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 -