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!!!!! VERIFICATION CHECK: vc-dimer-continuity-c1 !!!!!
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Description: Determines whether a model has a continuous energy and first
derivative, i.e. belongs to the C^1 continuity class, for all
possible dimers. For a model supporting N species, there are N +
N!/(2(N-2)! distinct dimers for all possible species combinations.
(For example if N=3, there are 3+3!/2=6 dimers. If the species are
A,B,C, the 6 dimers are AA, BB, CC, AB, AC, BC.) For each dimer,
the equilibrium separation and cutoff are determined. The
continuity across the cutoff is assessed. Then an analysis is
performed to detect any discontinuities from half the equilibrium
distance to the cutoff. Although the verification check only
requires C^1 continuity to pass, continuity up to 3rd order is
checked and reported.
Author: Ellad Tadmor
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Results for KIM Model : EAM_Dynamo_MishinMehlPapaconstantopoulos_2002_NiAl__MO_109933561507_005
Supported species : Al Ni
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DIMER Al--Al
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 2.76230230e+00 -8.38665123e-01 32 64 none
Cutoff separation: 5.95414401e+00 0.00000000e+00 28 30 none
C u t o f f S m o o t h n e s s
value continuous
Energy 0.00000000e+00 yes
1st-Deriv 2.75570940e-10 yes
2nd-Deriv 3.65881014e-07 yes
3rd-Deriv 8.42683052e-06 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.38115,5.95414] at 458 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-AlAl.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-AlAl.dat")
... No discontinuities found.
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-AlAl.dat")
... No discontinuities found.
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-AlAl.dat")
==> Suspected discontinuity encountered at r=1.48115115e+00 (|T^5| = 1.79454699e+01)
==> Suspected discontinuity encountered at r=1.49115115e+00 (|T^5| = 4.52101370e+01)
==> Suspected discontinuity encountered at r=1.50115115e+00 (|T^5| = 2.55511443e+01)
==> Suspected discontinuity encountered at r=1.51115115e+00 (|T^5| = 1.43880601e+01)
==> Suspected discontinuity encountered at r=1.52115115e+00 (|T^5| = 1.44966991e+01)
==> Suspected discontinuity encountered at r=1.53115115e+00 (|T^5| = 1.66621970e+00)
==> Suspected discontinuity encountered at r=1.54115115e+00 (|T^5| = 1.17610683e+00)
==> Suspected discontinuity encountered at r=1.55115115e+00 (|T^5| = 1.47037901e+00)
==> Suspected discontinuity encountered at r=1.58115115e+00 (|T^5| = 8.82293706e+00)
==> Suspected discontinuity encountered at r=1.59115115e+00 (|T^5| = 1.56382732e+01)
==> Suspected discontinuity encountered at r=1.60115115e+00 (|T^5| = 1.29748864e+01)
==> Suspected discontinuity encountered at r=1.61115115e+00 (|T^5| = 4.23902099e+00)
==> Suspected discontinuity encountered at r=1.62115115e+00 (|T^5| = 3.62810133e+00)
==> Suspected discontinuity encountered at r=1.63115115e+00 (|T^5| = 5.79507594e+00)
==> Suspected discontinuity encountered at r=1.65115115e+00 (|T^5| = 8.83143789e+00)
==> Suspected discontinuity encountered at r=1.66115115e+00 (|T^5| = 1.26823271e+01)
==> Suspected discontinuity encountered at r=1.67115115e+00 (|T^5| = 1.15742446e+01)
==> Suspected discontinuity encountered at r=1.68115115e+00 (|T^5| = 1.01878847e+01)
==> Suspected discontinuity encountered at r=1.69115115e+00 (|T^5| = 1.03150728e+01)
==> Suspected discontinuity encountered at r=1.70115115e+00 (|T^5| = 1.05027952e+01)
==> Suspected discontinuity encountered at r=1.71115115e+00 (|T^5| = 1.15380410e+01)
==> Suspected discontinuity encountered at r=1.72115115e+00 (|T^5| = 1.66597052e+01)
==> Suspected discontinuity encountered at r=1.73115115e+00 (|T^5| = 2.12337131e+01)
==> Suspected discontinuity encountered at r=1.74115115e+00 (|T^5| = 1.64501655e+01)
==> Suspected discontinuity encountered at r=1.75115115e+00 (|T^5| = 9.18893912e+00)
==> Suspected discontinuity encountered at r=1.76115115e+00 (|T^5| = 9.29161197e+00)
==> Suspected discontinuity encountered at r=1.77115115e+00 (|T^5| = 7.48603978e+00)
==> Suspected discontinuity encountered at r=1.80115115e+00 (|T^5| = 1.42637806e+01)
==> Suspected discontinuity encountered at r=1.81115115e+00 (|T^5| = 2.35921845e+01)
==> Suspected discontinuity encountered at r=1.82115115e+00 (|T^5| = 1.68756555e+01)
==> Suspected discontinuity encountered at r=1.83115115e+00 (|T^5| = 5.31706911e+00)
==> Suspected discontinuity encountered at r=1.85115115e+00 (|T^5| = 2.56559212e+00)
==> Suspected discontinuity encountered at r=1.86115115e+00 (|T^5| = 2.74581504e+00)
==> Suspected discontinuity encountered at r=1.87115115e+00 (|T^5| = 2.16835000e+00)
==> Suspected discontinuity encountered at r=1.88115115e+00 (|T^5| = 1.98466721e+00)
==> Suspected discontinuity encountered at r=1.89115115e+00 (|T^5| = 1.94991688e+00)
==> Suspected discontinuity encountered at r=1.90115115e+00 (|T^5| = 1.56456118e+00)
==> Suspected discontinuity encountered at r=1.91115115e+00 (|T^5| = 1.05882981e+00)
==> Suspected discontinuity encountered at r=1.95115115e+00 (|T^5| = 2.17957599e+00)
==> Suspected discontinuity encountered at r=1.96115115e+00 (|T^5| = 2.54136853e+00)
==> Suspected discontinuity encountered at r=1.97115115e+00 (|T^5| = 1.61231440e+00)
==> Suspected discontinuity encountered at r=2.02115115e+00 (|T^5| = 1.50458637e+00)
==> Suspected discontinuity encountered at r=2.03115115e+00 (|T^5| = 2.74228022e+00)
==> Suspected discontinuity encountered at r=2.04115115e+00 (|T^5| = 2.53396054e+00)
==> Suspected discontinuity encountered at r=2.05115115e+00 (|T^5| = 1.30079945e+00)
==> Suspected discontinuity encountered at r=2.10115115e+00 (|T^5| = 1.09769336e+00)
==> Suspected discontinuity encountered at r=2.21115115e+00 (|T^5| = 1.02627102e+00)
==> Suspected discontinuity encountered at r=2.24115115e+00 (|T^5| = 1.30954571e+00)
==> Suspected discontinuity encountered at r=2.25115115e+00 (|T^5| = 1.27079956e+00)
==> Suspected discontinuity encountered at r=2.26115115e+00 (|T^5| = 1.06104188e+00)
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DIMER Ni--Ni
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 2.17910631e+00 -1.26820925e+00 31 62 none
Cutoff separation: 5.95414401e+00 0.00000000e+00 26 28 none
C u t o f f S m o o t h n e s s
value continuous
Energy 0.00000000e+00 yes
1st-Deriv -1.64691437e-09 yes
2nd-Deriv 1.67832930e-08 yes
3rd-Deriv -1.27505052e-05 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.08955,5.95414] at 487 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-NiNi.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-NiNi.dat")
... No discontinuities found.
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-NiNi.dat")
... No discontinuities found.
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-NiNi.dat")
==> Suspected discontinuity encountered at r=1.47955315e+00 (|T^5| = 1.34885933e+00)
==> Suspected discontinuity encountered at r=1.48955315e+00 (|T^5| = 2.90132134e+00)
==> Suspected discontinuity encountered at r=1.50955315e+00 (|T^5| = 3.28992231e+00)
==> Suspected discontinuity encountered at r=1.51955315e+00 (|T^5| = 2.01651017e+00)
==> Suspected discontinuity encountered at r=1.52955315e+00 (|T^5| = 1.36525561e+00)
==> Suspected discontinuity encountered at r=1.53955315e+00 (|T^5| = 3.33809688e+00)
==> Suspected discontinuity encountered at r=1.54955315e+00 (|T^5| = 3.02931681e+00)
==> Suspected discontinuity encountered at r=1.55955315e+00 (|T^5| = 2.08884646e+00)
==> Suspected discontinuity encountered at r=1.56955315e+00 (|T^5| = 2.01605196e+00)
==> Suspected discontinuity encountered at r=1.57955315e+00 (|T^5| = 1.03923952e+00)
==> Suspected discontinuity encountered at r=1.62955315e+00 (|T^5| = 1.71269118e+00)
==> Suspected discontinuity encountered at r=1.63955315e+00 (|T^5| = 3.58238729e+00)
==> Suspected discontinuity encountered at r=1.64955315e+00 (|T^5| = 4.62018869e+00)
==> Suspected discontinuity encountered at r=1.65955315e+00 (|T^5| = 3.70264351e+00)
==> Suspected discontinuity encountered at r=1.66955315e+00 (|T^5| = 1.86945479e+00)
==> Suspected discontinuity encountered at r=1.67955315e+00 (|T^5| = 1.28752622e+00)
==> Suspected discontinuity encountered at r=1.68955315e+00 (|T^5| = 1.39819670e+00)
==> Suspected discontinuity encountered at r=1.71955315e+00 (|T^5| = 1.55641888e+00)
==> Suspected discontinuity encountered at r=1.72955315e+00 (|T^5| = 1.30107928e+00)
==> Suspected discontinuity encountered at r=1.76955315e+00 (|T^5| = 1.66675070e+00)
==> Suspected discontinuity encountered at r=1.77955315e+00 (|T^5| = 1.14687570e+00)
==> Suspected discontinuity encountered at r=1.85955315e+00 (|T^5| = 1.60165444e+00)
==> Suspected discontinuity encountered at r=1.86955315e+00 (|T^5| = 1.59166229e+00)
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DIMER Al--Ni
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 2.34089261e+00 -1.20291410e+00 32 64 none
Cutoff separation: 5.95414400e+00 0.00000000e+00 27 29 none
C u t o f f S m o o t h n e s s
value continuous
Energy 0.00000000e+00 yes
1st-Deriv 4.05945259e-10 yes
2nd-Deriv 3.71813220e-07 yes
3rd-Deriv 4.86352215e-06 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.17045,5.95414] at 479 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-AlNi.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-AlNi.dat")
... No discontinuities found.
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-AlNi.dat")
... No discontinuities found.
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-AlNi.dat")
==> Suspected discontinuity encountered at r=1.48044631e+00 (|T^5| = 1.85430176e+00)
==> Suspected discontinuity encountered at r=1.49044631e+00 (|T^5| = 2.86987086e+00)
==> Suspected discontinuity encountered at r=1.50044631e+00 (|T^5| = 4.67366295e+00)
==> Suspected discontinuity encountered at r=1.51044631e+00 (|T^5| = 1.32191711e+01)
==> Suspected discontinuity encountered at r=1.52044631e+00 (|T^5| = 1.07558477e+01)
==> Suspected discontinuity encountered at r=1.53044631e+00 (|T^5| = 3.77953742e+00)
==> Suspected discontinuity encountered at r=1.55044631e+00 (|T^5| = 1.25467311e+00)
==> Suspected discontinuity encountered at r=1.56044631e+00 (|T^5| = 1.84501447e+00)
==> Suspected discontinuity encountered at r=1.57044631e+00 (|T^5| = 1.40467203e+00)
==> Suspected discontinuity encountered at r=1.60044631e+00 (|T^5| = 1.40295961e+00)
==> Suspected discontinuity encountered at r=1.61044631e+00 (|T^5| = 1.08985640e+00)
==> Suspected discontinuity encountered at r=1.63044631e+00 (|T^5| = 1.12533921e+00)
==> Suspected discontinuity encountered at r=1.64044631e+00 (|T^5| = 1.48471710e+00)
==> Suspected discontinuity encountered at r=1.65044631e+00 (|T^5| = 1.46077347e+00)
==> Suspected discontinuity encountered at r=1.66044631e+00 (|T^5| = 1.73549267e+00)
==> Suspected discontinuity encountered at r=1.67044631e+00 (|T^5| = 1.87327360e+00)
==> Suspected discontinuity encountered at r=1.68044631e+00 (|T^5| = 1.57191347e+00)
==> Suspected discontinuity encountered at r=1.69044631e+00 (|T^5| = 1.41020073e+00)
==> Suspected discontinuity encountered at r=1.70044631e+00 (|T^5| = 1.20427858e+00)
==> Suspected discontinuity encountered at r=1.74044631e+00 (|T^5| = 1.61074540e+00)
==> Suspected discontinuity encountered at r=1.75044631e+00 (|T^5| = 1.83528296e+00)
==> Suspected discontinuity encountered at r=1.76044631e+00 (|T^5| = 1.39683634e+00)
==> Suspected discontinuity encountered at r=1.81044631e+00 (|T^5| = 1.03429285e+00)
==> Suspected discontinuity encountered at r=1.82044631e+00 (|T^5| = 2.52006460e+00)
==> Suspected discontinuity encountered at r=1.83044631e+00 (|T^5| = 3.54000213e+00)
==> Suspected discontinuity encountered at r=1.84044631e+00 (|T^5| = 3.09645299e+00)
==> Suspected discontinuity encountered at r=1.85044631e+00 (|T^5| = 1.98941758e+00)
==> Suspected discontinuity encountered at r=1.86044631e+00 (|T^5| = 1.07026353e+00)
==> Suspected discontinuity encountered at r=1.92044631e+00 (|T^5| = 1.20467628e+00)
==> Suspected discontinuity encountered at r=1.93044631e+00 (|T^5| = 1.40913720e+00)
==> Suspected discontinuity encountered at r=1.94044631e+00 (|T^5| = 1.30277609e+00)
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SUMMARY of Model Continuity Results Across All Dimers:
continuous
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Energy yes
1st-Deriv yes
2nd-Deriv yes
3rd-Deriv ** NO **
=====================================================================================================
Continuity must be C^1 or higher to pass this verification check.
Grade: P
Comment: The model is C^2 continuous. This means that the model has continuous energy and continuous derivatives up to order 2.