Exploring the effects of compensation


In [ ]:
import scubic
import lda

profs = [ 
        #0 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':4.92,\
         's0':8.,\
         'extents':80.,\
         'T':0.20,\
         'direc':'111',\
         'mu0':1.0 ,\
         'aS':1000.,\
         'x2lims':(-60.,60),\
        },
        #1 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':0.,\
         's0':8.,\
         'extents':40.,\
         'T':0.192,\
         'direc':'111',\
         'x2lims':(-30.,30.),\
         'aS':1000.,\
        },
        #2 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':0.,\
         's0':8.,\
         'extents':60.,\
         'T':0.15,\
         'direc':'111',\
         'mu0':10.0 ,\
         'aS':1000. ,\
         'y2lims':(0.,2.1),\
         'x2lims':(-50.,50.)
        },
        #3 
        {'wIR':31.06,\
         'wGR':31.06/1.15,\
         'g0':4.14,\
         's0':7.,\
         'extents':50.,\
         'T':0.144,\
         'direc':'111'
        },
        #4
        {'wIR':500.,\
         'wGR':120.,\
         'g0':-4.2,\
         's0':7.,\
         'extents':50.,\
         'T':0.115,\
         'direc':'111'
        },
        #5
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':3.751,\
         's0':7.,\
         'extents':50.,\
         'T':0.119,\
         'direc':'111'
        },
        #6
        {'wIR':50.,\
         'wGR':50./1.05,\
         'g0':4.295,\
         's0':7.,\
         'extents':50.,\
         'T':0.096,\
         'direc':'111'
        },
        
        #7
        {'wIR':30.05,\
         'wGR':30.05/1.15,\
         'g0':4.14,\
         's0':7.,\
         'extents':50.,\
         'T':0.185,\
         'direc':'111'
        },
        #8
        {'wIR':500.,\
         'wGR':120.,\
         'g0':-4.51,\
         's0':7.,\
         'extents':50.,\
         'T':0.152,\
         'direc':'111'
        },
        #9
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':3.711,\
         's0':7.,\
         'extents':50.,\
         'T':0.153,\
         'direc':'111'
        },
        #10
        {'wIR':50.,\
         'wGR':50./1.05,\
         'g0':4.254,\
         's0':7.,\
         'extents':50.,\
         'T':0.122,\
         'direc':'111'
        },
        
        ]



tags = range(11) 
#tags = [2] 
#tags = [7,8,9,10]

for tag in tags:
    print '\n',tag

    s       = profs[tag]['s0']
    g       = profs[tag]['g0']
    wIR     = profs[tag]['wIR']
    wGR     = profs[tag]['wGR']
    T       = profs[tag]['T'] 
    extents = profs[tag]['extents']
    direc   = profs[tag]['direc'] 
    aS      = profs[tag].get('aS',650.)
    mu0     = profs[tag].get('mu0','halfMott')
    x2lims  = profs[tag].get('x2lims', (-50.,50.))
    y2lims  = profs[tag].get('y2lims', (0.,1.1))
    
    pot = scubic.sc(allIR=s, allGR=g, allIRw=wIR, allGRw=wGR)
    test = lda.lda(potential = pot, Temperature=T, a_s=aS, extents=extents, globalMu=mu0, verbose=True, \
                   ignoreExtents=False, ignoreSlopeErrors=True, ignoreMuThreshold=True)
    fig = lda.plotLine( test , line_direction=direc, extents=extents, \
                       x1lims=(-70.,70.), x2lims=x2lims, y2lims=y2lims, y3lims=(0.,24.)) 
    print test.getRadius()/wIR
    print test.Number
    plt.close()
    fig.savefig('profiles/%03d.png'%tag, dpi=300)


0
ERROR: Bottom of the band has a negative slope
[-1.78250019 -1.7825425  -1.78262535 -1.78274518 -1.78289668 -1.7830728
 -1.78326476 -1.78346212 -1.78365276 -1.78397332 -1.78452752 -1.78506972
 -1.78558128 -1.78604213 -1.78643085 -1.78672474 -1.7868999  -1.7869313
 -1.78679289 -1.78645766]
[ -4.23128288e-05  -8.28468952e-05  -1.19829629e-04  -1.51500824e-04
  -1.76118758e-04  -1.91966253e-04  -1.97356635e-04  -1.90639590e-04
  -3.20564685e-04  -5.54193916e-04  -5.42200868e-04  -5.11560512e-04
  -4.60851662e-04  -3.88721742e-04  -2.93891329e-04  -1.75158436e-04
  -3.14025103e-05   1.38411861e-04   3.35231550e-04]
[False False  True  True  True  True  True  True  True  True  True  True
  True  True  True  True False False False]
ERROR: Chemical potential exceeds the evaporation threshold 
 mu0 = -0.597
   T = 0.240
 Eth = -0.455
ERROR: Chemical potential exceeds the bottom of the band along 100
 mu0 = -0.597
   T = 0.240
E100 = -0.455
ERROR: Radial density profile along 111 has a positive slope


radius check start =  0.001
[  1.01039381e+00   1.01042412e+00   1.01048476e+00   1.01057582e+00
   1.01069736e+00   1.01084950e+00   1.01103235e+00   1.01124602e+00
   1.01149062e+00   1.01177669e+00   1.01211331e+00   1.01248498e+00
   1.01289184e+00   1.01333394e+00   1.01381113e+00   1.01432312e+00
   1.01486935e+00   1.01544895e+00   1.01606075e+00   1.01670312e+00
   1.01740547e+00   1.01820037e+00   1.01903726e+00   1.01990552e+00
   1.02080131e+00   1.02171991e+00   1.02265570e+00   1.02363860e+00
   1.02473970e+00   1.02585024e+00   1.02696081e+00   1.02806062e+00
   1.02913750e+00   1.03029839e+00   1.03156743e+00   1.03279356e+00
   1.03395906e+00   1.03504464e+00   1.03606002e+00   1.03724693e+00
   1.03831273e+00   1.03923188e+00   1.04002114e+00   1.04071099e+00
   1.04152001e+00   1.04209776e+00   1.04241043e+00   1.04242282e+00
   1.04239719e+00   1.04226318e+00   1.04176776e+00   1.04087017e+00
   1.03951789e+00   1.03830525e+00   1.03655424e+00   1.03420793e+00
   1.03120483e+00   1.02794440e+00   1.02428703e+00   1.01980780e+00
   1.01441387e+00   1.00812222e+00   1.00164715e+00   9.94019942e-01
   9.85125487e-01   9.74841321e-01   9.63812193e-01   9.51716700e-01
   9.37975745e-01   9.22488561e-01   9.05188515e-01   8.87696156e-01
   8.68463887e-01   8.47548824e-01   8.25063158e-01   8.01644744e-01
   7.78674486e-01   7.54999253e-01   7.30963718e-01   7.06912770e-01
   6.83676098e-01   6.62445105e-01   6.41732782e-01   6.21413967e-01
   6.01122504e-01   5.80519315e-01   5.61439652e-01   5.41347983e-01
   5.19692556e-01   4.96151555e-01   4.70582327e-01   4.43709754e-01
   4.17612468e-01   3.90208041e-01   3.61858699e-01   3.33107820e-01
   3.04459200e-01   2.76385278e-01   2.51391883e-01   2.27725224e-01
   2.05251969e-01   1.84149965e-01   1.64536031e-01   1.46471231e-01
   1.29968576e-01   1.15707971e-01   1.03180481e-01   9.18166110e-02
   8.15620294e-02   7.23481365e-02   6.41004541e-02   5.67418523e-02
   5.01950930e-02   4.43847547e-02   3.95686860e-02   3.52907068e-02
   3.14742816e-02   2.80743252e-02   2.50488412e-02   2.23590451e-02
   1.99693795e-02   1.78474482e-02   1.59638923e-02   1.42922273e-02
   1.28086397e-02   1.15493293e-02   1.04442361e-02   9.45509621e-03
   8.56955096e-03   7.77649764e-03   7.06598212e-03   6.42909562e-03
   5.85787682e-03   5.34522004e-03   4.88478993e-03   4.47094277e-03
   4.09865443e-03   3.76345462e-03   3.46136743e-03   3.18885747e-03
   2.94278149e-03   2.72034494e-03   2.52515205e-03   2.35144631e-03
   2.19320137e-03   2.04890328e-03   1.91719486e-03   1.79685913e-03
   1.68680456e-03   1.58605176e-03   1.49372158e-03   1.40902452e-03
   1.33125116e-03   1.25976373e-03   1.19398847e-03   1.13340890e-03
   1.07755977e-03   1.02602169e-03   9.78416291e-04   9.34401985e-04]
[False False False  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False]
0.95511238578
2708644.2959

1
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.200093376909
23637.5956254

2
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.732341759488
2217546.76447

3
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.70144345962
299586.152208

4
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.0435736677116
300268.631553

5
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.456879877276
300072.944547

6
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.429467084639
300112.686314

7
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.704155561003
299850.856949

8
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.0429467084639
300134.643761

9
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.450210098046
300176.99891

10
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.423197492163
300784.859313
scubic.py:271: RuntimeWarning: invalid value encountered in sqrt
  nu.append( (1./2./np.pi) * np.sqrt(c2) * factor )

Mathy plots


In [ ]:
import scubic
import lda

profs = [ 
        #0 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':4.92,\
         's0':8.,\
         'extents':80.,\
         'T':0.20,\
         'direc':'111',\
         'mu0':1.0 ,\
         'aS':1000.,\
         'x2lims':(-2.5,8.),\
        },
        #1 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':0.,\
         's0':8.,\
         'extents':40.,\
         'T':0.192,\
         'direc':'111',\
         'x2lims':(7.,8.),\
         'aS':1000.,\
        },
        #2 
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':0.,\
         's0':8.,\
         'extents':60.,\
         'T':0.15,\
         'direc':'111',\
         'mu0':10.0 ,\
         'aS':1000. ,\
         'y2lims':(0.,2.1),\
        },
        #3 
        {'wIR':31.06,\
         'wGR':31.06/1.15,\
         'g0':4.14,\
         's0':7.,\
         'extents':50.,\
         'T':0.144,\
         'direc':'111'
        },
        #4
        {'wIR':500.,\
         'wGR':120.,\
         'g0':-4.2,\
         's0':7.,\
         'extents':50.,\
         'T':0.115,\
         'direc':'111'
        },
        #5
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':3.751,\
         's0':7.,\
         'extents':50.,\
         'T':0.119,\
         'direc':'111'
        },
        #6
        {'wIR':50.,\
         'wGR':50./1.05,\
         'g0':4.295,\
         's0':7.,\
         'extents':50.,\
         'T':0.096,\
         'direc':'111'
        },
        
        #7
        {'wIR':30.05,\
         'wGR':30.05/1.15,\
         'g0':4.14,\
         's0':7.,\
         'extents':50.,\
         'T':0.185,\
         'direc':'111'
        },
        #8
        {'wIR':500.,\
         'wGR':120.,\
         'g0':-4.51,\
         's0':7.,\
         'extents':50.,\
         'T':0.152,\
         'direc':'111'
        },
        #9
        {'wIR':47.,\
         'wGR':47./1.15,\
         'g0':3.711,\
         's0':7.,\
         'extents':50.,\
         'T':0.153,\
         'direc':'111'
        },
        #10
        {'wIR':50.,\
         'wGR':50./1.05,\
         'g0':4.254,\
         's0':7.,\
         'extents':50.,\
         'T':0.122,\
         'direc':'111'
        },
        
        ]


tags = range(7) 
#tags = [2] 
tags = range(11)

for tag in tags:
    print '\n',tag

    s       = profs[tag]['s0']
    g       = profs[tag]['g0']
    wIR     = profs[tag]['wIR']
    wGR     = profs[tag]['wGR']
    T       = profs[tag]['T'] 
    extents = profs[tag]['extents']
    direc   = profs[tag]['direc'] 
    aS      = profs[tag].get('aS',650.)
    mu0     = profs[tag].get('mu0','halfMott')
    x2lims  = profs[tag].get('x2lims', None)
    y2lims  = profs[tag].get('y2lims', (0.,1.1))
    
    pot = scubic.sc(allIR=s, allGR=g, allIRw=wIR, allGRw=wGR)
    test = lda.lda(potential = pot, Temperature=T, a_s=aS, extents=extents, globalMu=mu0, verbose=True, \
                   ignoreExtents=False, ignoreSlopeErrors=True, ignoreMuThreshold=True)
    fig = lda.plotMathy( test , line_direction=direc, extents=extents, \
                       x2lims=x2lims, y2lims=y2lims) 
    print test.getRadius()/wIR
    print test.Number
    plt.close()
    savef = 'profilesMathy/%03d.png'%tag
    fig.savefig(savef, dpi=300)
    print savef


0
ERROR: Bottom of the band has a negative slope
[-1.78250019 -1.7825425  -1.78262535 -1.78274518 -1.78289668 -1.7830728
 -1.78326476 -1.78346212 -1.78365276 -1.78397332 -1.78452752 -1.78506972
 -1.78558128 -1.78604213 -1.78643085 -1.78672474 -1.7868999  -1.7869313
 -1.78679289 -1.78645766]
[ -4.23128288e-05  -8.28468952e-05  -1.19829629e-04  -1.51500824e-04
  -1.76118758e-04  -1.91966253e-04  -1.97356635e-04  -1.90639590e-04
  -3.20564685e-04  -5.54193916e-04  -5.42200868e-04  -5.11560512e-04
  -4.60851662e-04  -3.88721742e-04  -2.93891329e-04  -1.75158436e-04
  -3.14025103e-05   1.38411861e-04   3.35231550e-04]
[False False  True  True  True  True  True  True  True  True  True  True
  True  True  True  True False False False]
ERROR: Chemical potential exceeds the evaporation threshold 
 mu0 = -0.597
   T = 0.240
 Eth = -0.455
ERROR: Chemical potential exceeds the bottom of the band along 100
 mu0 = -0.597
   T = 0.240
E100 = -0.455
ERROR: Radial density profile along 111 has a positive slope


radius check start =  0.001
[  1.01039381e+00   1.01042412e+00   1.01048476e+00   1.01057582e+00
   1.01069736e+00   1.01084950e+00   1.01103235e+00   1.01124602e+00
   1.01149062e+00   1.01177669e+00   1.01211331e+00   1.01248498e+00
   1.01289184e+00   1.01333394e+00   1.01381113e+00   1.01432312e+00
   1.01486935e+00   1.01544895e+00   1.01606075e+00   1.01670312e+00
   1.01740547e+00   1.01820037e+00   1.01903726e+00   1.01990552e+00
   1.02080131e+00   1.02171991e+00   1.02265570e+00   1.02363860e+00
   1.02473970e+00   1.02585024e+00   1.02696081e+00   1.02806062e+00
   1.02913750e+00   1.03029839e+00   1.03156743e+00   1.03279356e+00
   1.03395906e+00   1.03504464e+00   1.03606002e+00   1.03724693e+00
   1.03831273e+00   1.03923188e+00   1.04002114e+00   1.04071099e+00
   1.04152001e+00   1.04209776e+00   1.04241043e+00   1.04242282e+00
   1.04239719e+00   1.04226318e+00   1.04176776e+00   1.04087017e+00
   1.03951789e+00   1.03830525e+00   1.03655424e+00   1.03420793e+00
   1.03120483e+00   1.02794440e+00   1.02428703e+00   1.01980780e+00
   1.01441387e+00   1.00812222e+00   1.00164715e+00   9.94019942e-01
   9.85125487e-01   9.74841321e-01   9.63812193e-01   9.51716700e-01
   9.37975745e-01   9.22488561e-01   9.05188515e-01   8.87696156e-01
   8.68463887e-01   8.47548824e-01   8.25063158e-01   8.01644744e-01
   7.78674486e-01   7.54999253e-01   7.30963718e-01   7.06912770e-01
   6.83676098e-01   6.62445105e-01   6.41732782e-01   6.21413967e-01
   6.01122504e-01   5.80519315e-01   5.61439652e-01   5.41347983e-01
   5.19692556e-01   4.96151555e-01   4.70582327e-01   4.43709754e-01
   4.17612468e-01   3.90208041e-01   3.61858699e-01   3.33107820e-01
   3.04459200e-01   2.76385278e-01   2.51391883e-01   2.27725224e-01
   2.05251969e-01   1.84149965e-01   1.64536031e-01   1.46471231e-01
   1.29968576e-01   1.15707971e-01   1.03180481e-01   9.18166110e-02
   8.15620294e-02   7.23481365e-02   6.41004541e-02   5.67418523e-02
   5.01950930e-02   4.43847547e-02   3.95686860e-02   3.52907068e-02
   3.14742816e-02   2.80743252e-02   2.50488412e-02   2.23590451e-02
   1.99693795e-02   1.78474482e-02   1.59638923e-02   1.42922273e-02
   1.28086397e-02   1.15493293e-02   1.04442361e-02   9.45509621e-03
   8.56955096e-03   7.77649764e-03   7.06598212e-03   6.42909562e-03
   5.85787682e-03   5.34522004e-03   4.88478993e-03   4.47094277e-03
   4.09865443e-03   3.76345462e-03   3.46136743e-03   3.18885747e-03
   2.94278149e-03   2.72034494e-03   2.52515205e-03   2.35144631e-03
   2.19320137e-03   2.04890328e-03   1.91719486e-03   1.79685913e-03
   1.68680456e-03   1.58605176e-03   1.49372158e-03   1.40902452e-03
   1.33125116e-03   1.25976373e-03   1.19398847e-03   1.13340890e-03
   1.07755977e-03   1.02602169e-03   9.78416291e-04   9.34401985e-04]
[False False False  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True  True  True
  True  True  True  True  True  True  True  True  True  True False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False False False False False False False False False False
 False False False]
0.95511238578
2708644.2959
profilesMathy/000.png

1
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.200093376909
23637.5956254
profilesMathy/001.png

2
OK: Bottom of the band has positive slope up to r111 = 10 um
OK: Chemical potential is below evaporation threshold.
OK: Chemical potential is below the bottom of the band along 100
OK: Radial density profile along 111 decreases monotonically.
0.732341759488

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