Title page for etd-0807112-154404


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URN etd-0807112-154404
Author Han-long Shiu
Author's Email Address fh51025@yahoo.com.tw
Statistics This thesis had been viewed 5349 times. Download 503 times.
Department Applied Mathematics
Year 2011
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Computing Energy Levels of Rotating Bose-Einstein Condensates on Curves
Date of Defense 2012-06-28
Page Count 61
Keyword
  • Bose-Einstein condensates
  • finite difference method
  • continuation method
  • bifurcation
  • Abstract Recently the phenomena of Bose-Einstein condensates have been observed in laboratories, and the related problems are extensively studied. In this paper we consider the nonlinear Schrödinger equation in the laser beam rotating magnetic field and compute its corresponding energy functional under the mass conservative condition. By separating time and space variables, factoring real part and image part, and discretizing via finite difference method, the original equation can be transformed to a large scale parametrized polynomial systems. We use continuation method to find the solutions that satisfy the mass conservative condition. We will also explore bifurcation points on the curves and other solutions lying on bifurcation branches. The numerical results show that when the rotating angular momentum is small, we can find the solutions by continuation method along some particular curves and these curves are regular. As the angular momentum is increasing, there will be more bifurcation points on curves.
    Advisory Committee
  • Tzon-Tzer Lu - chair
  • Chen-Chang Peng - co-chair
  • Chen-Chang Peng - co-chair
  • Chen-Chang Peng - co-chair
  • Chen-Chang Peng - co-chair
  • Yueh-Cheng Kuo - co-chair
  • Chien-Sen Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Chien-Sen Huang - co-chair
  • Tsung-Lin Lee - advisor
  • Files
  • etd-0807112-154404.pdf
  • indicate access worldwide
    Date of Submission 2012-08-07

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