UNDER ETERNAL CONSTRUCTION...

You might want to have a look at these for the time being:

• Movies
  
  
  • NUCLEATION OF VORTICES IN ROTATING BECs
    
  • γ=0.01, μ=5, Ω=0.2, Ω_rot=0.37 [ movie (avi, 31Mb) ] , [ movie (mpeg, 7Mb) ].
  • γ=0.01, μ=10, Ω=0.2, Ω_rot=0.3 [ movie (avi, 72Mb) ] , [ movie (mpeg, 16Mb) ].
  • γ=0.01, μ=5, Nv=5, Ω=0.2, Ω_rot=0.37, perturb every 105s [ movie (avi, 19Mb) ] , [ movie (mpeg, 3.5Mb) ].
  
  
  • γ=0.1, μ=5, Ω=0.2, Ω_rot=0.37 [ movie (avi, 14Mb) ] , [ movie (mpeg, 3Mb) ].
  • γ=0.1, μ=10, Ω=0.2, Ω_rot=0.3 [ movie (avi, 10Mb) ] , [ movie (mpeg, 2.5Mb) ].
  
  
  
  • SLOSHING OF BACKGROUND CLOUD DUE TO VORTEX DIPOLE
    
  • Two vortices of same charge => no sloshing: [ movie ] , [ trajectory (ps) ].
  • Two vortices of opposite charge => sloshing: [ movie ] , [ trajectory (ps) ], [ phase diff. steady state and seeded vortices (jpg) ].
  
  
  • 2D BREATHERS IN ELECTRICAL LATTICES
    
  • Experimental: two interacting breathers in hexagonal lattice:
    [ all frames [72 Mb] ], [ every 2 frames [36 Mb] ], [ every 4 frames [18 Mb] ], [ every 4 frames AVI [1 Mb] ]
  • Experimental: a traveling front in a 6x6 square lattice:
    [ Tfin=4ms [96 Mb] ], [ Tfin=2ms [48 Mb] ], [ Tfin=1ms frames [24 Mb] ]
  • Numerical: traveling patterns in a 12x12 square lattice:
    [ Tfin=3.3314ms [121 Mb] ], [ Tfin=2.099ms [62 Mb] ], [ Tfin=1.220ms frames [16 Mb] ]
  
  
  • VORTEX DYNAMICS IN PT POTENTIALS (μ=2)
    
  • Bifurcation movie for even number of vortices: [ even ]
  • 1 vortex: [ ε=0.2 ], [ ε=0.35 ]
  • 2 vortices: [ ε=0.2 ]
  • Depression (comming from 2 annihilated vortices): [ ε=0.4 ]
  • 3 asymmetric vortices: [ ε=0.2 ]
  • one vortex + one depression (comming from 2 annihilated vortices): [ ε=0.35 ]
  
  
  • CHASING DARK SOLITONS?
    
  • Destabilization of a stationary DS [Rb87, ND=87,696, (fx,fy,fz)=(85,133,5.9) Hz, (Nx,Ny,Nz)=(31,31,451)]
    [ t=1:400 ms ], [ t=50:100 ms ].
  • Two interacting Vortex Lines (VLs): [ND=87,740, (Nx,Ny,Nz)=(43,29,439)]
    » Centered about the y-axis: [ 2D integrated ], [ Density isosurface ]
    » Slightly displaced in the y-direction: [ 2D integrated ], [ Density isosurface ]
    » Slightly more displaced in the y-dir (larger leapfrogging dist): [ 2D integrated ], [ Density isosurface ]
    » frac_z02_2.2_x00_00: [ 2D integrated ], [ Density isosurface (+ x-cut) ], [ Density isosurface (+ y-cut) ]
    » frac_z04_05_x00_00: [ 2D integrated ], [ Density isosurface (+ x-cut) ], [ Density isosurface (+ y-cut) ]
    
  • Two chasing DSs:
    » x1=-10, x2=-30, vel_1 [ 2D integrated ], [ Density isosurface (+ x-cut) ].
    » x1=-10, x2=-30, vel_2 (‹ vel_1) [ 2D integrated ], [ Density isosurface (+ x-cut) ].
    » x1=10, x2=-10, vel_1 [ 2D integrated ], [ Density isosurface (+ x-cut) ], [ Density isosurface (+ y-cut) ].
    » x1=10, x2=-10, vel_2 (‹ vel_1) [ 2D integrated ], [ Density isosurface (+ x-cut) ], [ Density isosurface (+ y-cut) ].
    
  
  
  • VORTEX RING (VR) DYNAMICS IN REPULSIVE BECs (courtesy of Ron Caplan)
    
  • Two annihilating VRs: [ far ], [ close ]
  • Two chasing VRs: [ movie1 ] [ movie2 ] [ movie3 ] [ movie4 ]
  • Two opposite charge VRs colliding (offset): [ movie ]
  • Transversal cuts of a VR after optimization: [ movie ]
  • 5 colliding/merging/splitting VRs: [ movie1 ], [ movie2 (closer to each other) ]
  • 4 merging VRs shooting a VR back: [ movie ]
  • Quadrupole oscillations of a single VRs: [ Vol 3D ], [ 2D cuts ]
  • An approximate m=2 (double) VR splits into leapfrooging: [ Vol 3D ], [ 2D cuts (phase) ]. [ 2D cuts (density) ]
  • A stable double ring VR: [ Vol 3D ], [ 2D cuts (phase) ]. [ 2D cuts (density) ]
  
  
  • BRIGHT-DARK SOLITON OSCILATIONS IN A CIGAR-SHAPED BEC
    
  • Harmonic oscillations
    » Rb87, ND=4,410 and NB=1,116, fz=fy=133 Hz, fx=75.9, (Nx,Ny,Nz)=(21,21,351) [ movie ]
    » Rb87, ND=5 and NB=672, fz=fy=133 Hz, fx=75.9, (Nx,Ny,Nz)=(21,21,351) [ movie ]
    » Rb87, ND=15 and NB=132, fz=fy=133 Hz, fx=75.9, (Nx,Ny,Nz)=(21,21,351) [ movie ]
    » Rb87, ND=88,251 and NB=1,048, fz=fy=133 Hz, fx=75.9, (Nx,Ny,Nz)=(21,21,351) [ movie ]
    » Sengstock's experiment: Rb87, ND=92,432 and NB=7,973, fz=85 Hz, fy=133 Hz, fx=5.9, (Nx,Ny,Nz)=(21,21,351) [ movie ]
    » 2 out-of-phase (attractive) DB collisions: Rb87, ND=5,243 and NB=817, fz=fy=133 Hz, fx=5.9, (Nx,Ny,Nz)=(15,15,151) [ movie ]
    » 2 in-phase (repulsive) DB collisions: Rb87, ND=5,331 and NB=907, fz=fy=133 Hz, fx=5.9, (Nx,Ny,Nz)=(15,15,151) [ movie ]
    
  
  
  • FARADAY PATTERNS IN CIGAR SHAPED BECs
    
  • Patterns
    » mass = 120K atoms, fr=160.5 Hz, fz=7 Hz, Nr=801, Nz=801, [ movie ]
    
  
  
  • BECs COLLISIONS
    
  • Three 3D BEC fragments colliding (Brian P. Anderson's experiment)
    » Ramp down time = 0 ms: Density, phase and vorticity for phases=(0,0,0):
    [ 2D movie ], [ vorticity (zoom out) ], [ vorticity (0<t<40) ], [ vorticity (18<t<35) ], [ density ], [ both ].
    » Ramp down time = 0 ms: Density, phase and vorticity for phases=(0,2*pi/3,4*pi/3):
    [ 2D movie ], [ vorticity (zoom out) ], [ vorticity (0<t<40) ], [ vorticity (18<t<35) ], [ density ], [ both ].
    » Ramp down time = 50 ms: Density, phase and vorticity for phases=(0,0,0):
    [ 2D movie ], [ vorticity ], [ density ].
    » Ramp down time = 50 ms: Density, phase and vorticity for phases=(0,2*pi/3,4*pi/3):
    [ 2D movie ], [ vorticity ], [ density ].
    
  • Two component BEC collisions
    » Two fragments, one in each component, colliding (cropped domain): [ movie ]
    » Two fragments, one in each component, colliding (full domain): [ movie ]
    
    
    
  • MULTIPOLES IN BESSEL OLs
    
  • Instabilities
    » Unstable dipole (b=0.9, p=15) [ movie ]
    » Unstable quadrupole (b=1, p=20) [ movie (t=[0,100]) ], [ movie (t=[100,200]) ]
    
  
  
  • Different mesh and domain sizes (b=0.9, p=15)
    » N=[64x64], L=[-8,8] and N=[128x128], L=[-16,16] [ movie ]
    » N=[128x128], L=[-16,16] and N=[256x256], L=[-16,16] [ movie ]
    
  
  
  • TWO COMPONENT BECs
    
  • 50-50 of 360K atoms and all parameters from David Hall's experiment (no expansion)
    » 3D view with side and bottom projections and with slice removed:
    * Cuts at 60% and 30% for |1> and |2> respectively: [ movie ]
    * Cuts at 50% and 55% for |1> and |2> respectively: [ movie ]
    
    
  • 43-57 mix for a total of 375K atoms, dissipation=0.0010, Tf=200ms (no expansion)
    » 3D view with side and bottom projections [ movie ]
    » 3D view with side and bottom projections and with slice removed [ movie ]
    » 3D isocontours pics of the dynamics:
    » High definition snapshots [ 54 ms ] , [ 72 ms ] , [ 144 ms ] , [ 151 ms ]
    
    
  • 50-50 mix for a total of 350K atoms, dissipation=0.0016, Tf=200ms (no expansion)
    » 3D view (both components together) [ movie ]
    
    
  • 50-50 mix for a total of 350K atoms, dissipation=0.002, Tf=200ms (no expansion)
    » Top view (z-integrated) [ movie ]
    » 3D view (both components together) [ movie ]
    » R-Z view (computational coordinates) [ movie ]
    
    
  • 50-50 mix for a total of 350K atoms, no dissipation, Tf=200ms (no expansion)
    » Top view (z-integrated) [ movie ]
    » 3D view (both components together) [ movie ]
    » R-Z view (computational coordinates) [ movie ]
    
    
  • 50-50 mix for a total of 332K atoms (no expansion)
    » Top view (z-integrated) [ movie ]
    » 3D view (both components together) [ movie ]
    » 3D view (each components on its own) [ movie ]
    
    
  • 80-20 mix for a total of 1,096K atoms (no expansion)
    » Top view (z-integrated) [ movie ]
    » 3D view (both components together) [ movie ]
    » 3D view (each components on its own) [ movie ]
    » R-Z view (computational coordinates) [ movie ]
    
    
  • 80-20 mix for a total of 10,827K atoms (no expansion)
    » Top view (z-integrated) [ movie ]
    » 3D view (both components together) [ movie ]
    » 3D view (each components on its own) [ movie ]
    » R-Z view (computational coordinates) [ movie ]
    
    
  • VORTICES IN BECs
    
  • Vortex interactions with higher charge
    » two vortices: charges -2 and +1 [ movie (0-400s) ], [ movie (400-800s) ]
    
    
  • Vortex formation by phase engineering
    » one vortex [ movie ] [ phase IC ]
    » two vortices [ movie ] [ phase IC ]
    
    
  • Vortex dynamics for two vortices
    » two vortices: same charge [ movie ]
    » two vortices: opposite charge [ movie ]
    
    
  • Vortex dynamics for four vortices
    » four nearby vortices (2+ and 2-) [ movie ]
    » four vortices (2+ and 2-) [ movie ]
    » four off-center vortices (4+) [ movie ]
    
    
  • Vortex dynamics for many vortices from GPE eq.
    » top view |u(x,y,t)|² [ movie ]
    » side view 1-|u(x,y,t)|² [ movie ]
    
    
  • PDE (GPE) vs ODE approximation
    » 3 vortices (circles) [ movie ]
    » 3 vortices (flowers) [ movie ]
    
    
  • VORTEX LATTICES IN BECs BY PHASE IMPRINTING
    
  • Imprinting only the phase (\Omega=0.04)
    » with absorbing BCs [ side view ]
    » without absorbing BCs [ top view ] [ side view ]
    
    
  • Imprinting phase AND using Pade approximation
    » Same vorticity [ top view ] [ side view ]
    » Alternating vorticities [ top view ]
    
    
  • MOLECULAR DYNAMICS FOR VORTEX LATTICES
    
  • N_v=249, non periodic boundary conditions: triangular core with circular shells.
    » same charge [ movie ]
    » mixed charges [ movie ]
    
    
  • N_v=100, periodic box + fixed box angle = 90°: triangular lattice
    » random ICs [ movie ]
    » IC = perturbed square lattice [ movie ]
    
    
  • N_v=225, periodic box: triangular lattice
    » box angle = 60° + square lattice in box [ movie ]
    » box angle = 90° + random ICs [ movie ]
    » box angle = 90° + random ICs + friction (final box angle = 60°) [ movie ]
    
    
  • Oscillatory (Tkachenko) modes of the triangular lattice:
    » N_v=240, IC = perturbed square lattice [ movie ]
    
    
  • CHEMOTAXIS
    
  • Formation of aggregates
    » moving mesh vs. static mesh [ movie ]
    » two moving meshes with different monitor functions [ movie ]
    
    
  • Metastability
    » Two chemotactic aggregates attracting each other using a moving mesh PDE [ movie ]
    » Aggregate-boundary interactions:
       > moving mesh vs. static mesh [ movie ]
       > double vs. quad precision [ movie ]
    

• Bose Einstein Condensates (BEC)
  • Localized Breathers
  • Impurities => Moving Breathers
  • Extended Breathers

  
  

• Chemotaxis - cross diffusion equations
  • Blowup and Metastability
  • Understanding blowup in the chemotaxis model
  • Adaptive mesh application (loads of films here!)