[5054e80] | 1 | #correlation length model |
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| 2 | # Note: model title and parameter table are inserted automatically |
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| 3 | r""" |
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| 4 | Definition |
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| 5 | ---------- |
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| 6 | |
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| 7 | The scattering intensity I(q) is calculated as |
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| 8 | |
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| 9 | .. math:: |
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| 10 | I(Q) = \frac{A}{Q^n} + \frac{C}{1 + (Q\xi)^m} + B |
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| 11 | |
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| 12 | The first term describes Porod scattering from clusters (exponent = n) and the |
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| 13 | second term is a Lorentzian function describing scattering from polymer chains |
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| 14 | (exponent = m). This second term characterizes the polymer/solvent interactions |
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| 15 | and therefore the thermodynamics. The two multiplicative factors A and C, the |
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| 16 | incoherent background B and the two exponents n and m are used as fitting |
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| 17 | parameters. The final parameter ξ is a correlation length for the polymer |
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| 18 | chains. Note that when m=2 this functional form becomes the familiar Lorentzian |
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| 19 | function. |
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| 20 | |
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| 21 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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| 22 | where the q vector is defined as |
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| 23 | |
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| 24 | .. math:: |
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| 25 | q = \sqrt{q_x^2 + q_y^2} |
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| 26 | |
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| 27 | .. figure:: img/correlation_length_1d.jpg |
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| 28 | |
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| 29 | 1D plot using the default values (w/500 data points). |
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| 30 | |
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| 31 | REFERENCE |
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| 32 | B Hammouda, D L Ho and S R Kline, Insight into Clustering in |
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| 33 | Poly(ethylene oxide) Solutions, Macromolecules, 37 (2004) 6932-6937 |
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| 34 | """ |
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| 35 | |
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| 36 | from numpy import inf, sqrt |
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| 37 | |
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| 38 | name = "correlation_length" |
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| 39 | title = """Calculates an empirical functional form for SAS data characterized |
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| 40 | by a low-Q signal and a high-Q signal.""" |
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| 41 | description = """ |
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| 42 | """ |
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| 43 | category = "shape-independent" |
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| 44 | # pylint: disable=bad-continuation, line-too-long |
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| 45 | # ["name", "units", default, [lower, upper], "type","description"], |
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| 46 | parameters = [ |
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| 47 | ["lorentz_scale", "", 10.0, [0, inf], "", "Lorentzian Scaling Factor"], |
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| 48 | ["porod_scale", "", 1e-06, [0, inf], "", "Porod Scaling Factor"], |
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| 49 | ["cor_length", "Ang", 50.0, [0, inf], "", "Correlation length"], |
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| 50 | ["exponent_p", "", 3.0, [0, inf], "", "Porod Exponent"], |
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| 51 | ["exponent_l", "1/Ang^2", 2.0, [0, inf], "", "Lorentzian Exponent"], |
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| 52 | ] |
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| 53 | # pylint: enable=bad-continuation, line-too-long |
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| 54 | |
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| 55 | def Iq(q, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l): |
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| 56 | """ |
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| 57 | 1D calculation of the Correlation length model |
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| 58 | """ |
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| 59 | porod = porod_scale / pow(q, exponent_p) |
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| 60 | lorentz = lorentz_scale / (1.0 + pow(q * cor_length, exponent_l)) |
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| 61 | inten = porod + lorentz |
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| 62 | return inten |
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| 63 | |
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| 64 | def Iqxy(qx, qy, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l): |
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| 65 | """ |
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| 66 | 2D calculation of the Correlation length model |
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| 67 | There is no orientation contribution. |
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| 68 | """ |
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| 69 | q = sqrt(qx ** 2 + qy ** 2) |
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| 70 | return Iq(q, lorentz_scale, porod_scale, cor_length, exponent_p, exponent_l) |
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| 71 | |
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| 72 | # parameters for demo |
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| 73 | demo = dict(lorentz_scale=10.0, porod_scale=1.0e-06, cor_length=50.0, |
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| 74 | exponent_p=3.0, exponent_l=2.0, background=0.1, |
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| 75 | ) |
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| 76 | |
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| 77 | # For testing against the old sasview models, include the converted parameter |
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| 78 | # names and the target sasview model name. |
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| 79 | oldname = 'CorrLengthModel' |
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| 80 | # pylint: disable=bad-continuation |
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| 81 | oldpars = dict( |
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| 82 | lorentz_scale='scale_l', porod_scale='scale_p', |
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| 83 | cor_length='length_l', exponent_p='exponent_p', |
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| 84 | exponent_l='exponent_l' |
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| 85 | ) |
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| 86 | |
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| 87 | tests = [ |
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| 88 | [{}, 0.001, 1009.98], |
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| 89 | [{}, 0.150141, 0.174645], |
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| 90 | [{}, 0.442528, 0.0203957] |
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| 91 | ] |
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| 92 | # pylint: enable=bad-continuation |
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