Changes in / [4cdc4b1:dc76240] in sasmodels
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sasmodels/models/guinier.py
rc9fc873 r2d81cfe 7 7 .. math:: 8 8 9 I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2 R_g^2}{3} \right]}9 I(q) = \text{scale} \cdot \exp{\left[ \frac{-Q^2R_g^2}{3} \right]} 10 10 + \text{background} 11 11 … … 19 19 20 20 .. math:: q = \sqrt{q_x^2 + q_y^2} 21 22 In scattering, the radius of gyration $R_g$ quantifies the objects's23 distribution of SLD (not mass density, as in mechanics) from the objects's24 SLD centre of mass. It is defined by25 26 .. math:: R_g^2 = \frac{\sum_i\rho_i\left(r_i-r_0\right)^2}{\sum_i\rho_i}27 28 where $r_0$ denotes the object's SLD centre of mass and $\rho_i$ is the SLD at29 a point $i$.30 31 Notice that $R_g^2$ may be negative (since SLD can be negative), which happens32 when a form factor $P(Q)$ is increasing with $Q$ rather than decreasing. This33 can occur for core/shell particles, hollow particles, or for composite34 particles with domains of different SLDs in a solvent with an SLD close to the35 average match point. (Alternatively, this might be regarded as there being an36 internal inter-domain "structure factor" within a single particle which gives37 rise to a peak in the scattering).38 39 To specify a negative value of $R_g^2$ in SasView, simply give $R_g$ a negative40 value ($R_g^2$ will be evaluated as $R_g |R_g|$). Note that the physical radius41 of gyration, of the exterior of the particle, will still be large and positive.42 It is only the apparent size from the small $Q$ data that will give a small or43 negative value of $R_g^2$.44 21 45 22 References … … 65 42 66 43 # ["name", "units", default, [lower, upper], "type","description"], 67 parameters = [["rg", "Ang", 60.0, [ -inf, inf], "", "Radius of Gyration"]]44 parameters = [["rg", "Ang", 60.0, [0, inf], "", "Radius of Gyration"]] 68 45 69 46 Iq = """ 70 double exponent = fabs(rg)*rg*q*q/3.0;47 double exponent = rg*rg*q*q/3.0; 71 48 double value = exp(-exponent); 72 49 return value; … … 89 66 90 67 # parameters for demo 91 demo = dict(scale=1.0, background=0.001, rg=60.0)68 demo = dict(scale=1.0, rg=60.0) 92 69 93 70 # parameters for unit tests
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