core_shell_microgelscostrafo411magnetic_modelrelease_v0.94release_v0.95ticket-1257-vesicle-productticket_1156ticket_1265_superballticket_822_more_unit_tests
Last change
on this file since ec87470 was
2c74c11,
checked in by Paul Kienzle <pkienzle@…>, 8 years ago
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implicit Iqxy; fix divide by 0 for q=0
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Property mode set to
100644
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File size:
1.2 KB
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1 | r""" |
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2 | This model fits the Porod function |
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3 | |
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4 | .. math:: |
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5 | |
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6 | I(q) = C/q^4 |
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7 | \\ |
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8 | C = 2\pi (\Delta\rho)^2 S_v |
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9 | |
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10 | to the data directly without any need for linearisation (cf. Log I(q) vs Log q). |
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11 | |
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12 | Here $C$ is the scale factor and $S_v$ is the specific surface area (ie, surface area / volume) |
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13 | of the sample, and $\Delta\rho$ is the contrast factor. |
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14 | |
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15 | For 2D data: The 2D scattering intensity is calculated in the same way as 1D, |
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16 | where the q vector is defined as |
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17 | |
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18 | .. math:: |
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19 | q = \sqrt{q_x^2+q_y^2} |
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20 | |
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21 | References |
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22 | ---------- |
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23 | |
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24 | G Porod. *Kolloid Zeit*. 124 (1951) 83. |
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25 | L A Feigin, D I Svergun, G W Taylor. *Structure Analysis by Small-Angle X-ray and Neutron Scattering*. Springer. (1987) |
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26 | """ |
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27 | |
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28 | from numpy import power, inf, errstate |
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29 | |
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30 | name = "porod" |
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31 | title = "Porod function" |
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32 | description = """\ |
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33 | I(q) = scale/q^4 + background |
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34 | """ |
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35 | |
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36 | category = "shape-independent" |
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37 | |
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38 | parameters = [] |
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39 | |
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40 | def Iq(q): |
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41 | """ |
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42 | @param q: Input q-value |
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43 | """ |
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44 | with errstate(divide='ignore'): |
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45 | return power(q, -4) |
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46 | |
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47 | Iq.vectorized = True # Iq accepts an array of q values |
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48 | |
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49 | demo = dict(scale=1.5, background=0.5) |
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50 | |
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51 | tests = [ |
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52 | [{'scale': 0.00001, 'background':0.01}, 0.04, 3.916250], |
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53 | [{}, 0.0, inf], |
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54 | ] |
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