581hw6sc - AMATH 581 Autumn Quarter 2011 Homework 6:...

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Unformatted text preview: AMATH 581 Autumn Quarter 2011 Homework 6: Bose-Einstein Condensation in 3D DUE: Wednesday, December 7, 2011 (actually Thursday, 12/8 at 3 a.m.) Consider the Gross-Pitaevskii system (nonlinear Schrodinger with potential) modeling a condensed state of matter i t + 1 2 2 - | | 2 + [ A 1 sin 2 ( x ) + B 1 ][ A 2 sin 2 ( y ) + B 2 ][ A 3 sin 2 ( z ) + B 3 ] = 0 (1) where 2 = 2 x + 2 y + 2 z (you can google this to learn more... or see the extra pages here). Consider periodic boundaries and using the 3D FFT ( fftn ) to solve for the evolution. Step forward using ode45 . VISUALIZE USING isosurface or slice . WARNING: 3D problems involve working with vectors of size n 3 , so pick n small to begin playing around. ANSWERS : Let x,y,z [- , ], tspan = 0 : 0 . 5 : 4, n = 16, and parameters A i =- 1 and B j =- A j , with initial conditions ( x,y,z ) = cos( x )cos( y )cos( z ) (2) write out the solution of your numerical evolution from ode45 as A1.dat. (NOTE: your solution will be in the Fourier domain when your write it out.) ANSWERS : Now solve with initial conditions ( x,y,z ) = sin( x )sin( y )sin( z ) (3) write out the solution of your numerical evolution from ode45 as A2.dat. (NOTE: your solution will be in the Fourier domain when your write it out.) Background on BECs...
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This note was uploaded on 03/23/2012 for the course AMATH 581 taught by Professor Staff during the Fall '08 term at University of Washington.

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581hw6sc - AMATH 581 Autumn Quarter 2011 Homework 6:...

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