Changeset ac60a39 in sasmodels for doc/guide


Ignore:
Timestamp:
Nov 20, 2017 11:33:17 AM (7 years ago)
Author:
Paul Kienzle <pkienzle@…>
Branches:
master, core_shell_microgels, magnetic_model, ticket-1257-vesicle-product, ticket_1156, ticket_1265_superball, ticket_822_more_unit_tests
Children:
1f159bd
Parents:
4f5afc9 (diff), 146793b (diff)
Note: this is a merge changeset, the changes displayed below correspond to the merge itself.
Use the (diff) links above to see all the changes relative to each parent.
Message:

Merge branch 'master' into ticket-776-orientation

Location:
doc/guide
Files:
3 added
4 edited

Legend:

Unmodified
Added
Removed

  • doc/guide/index.rst

    rc0d7ab3 rda5536f  
    1313   resolution.rst 
    1414   magnetism/magnetism.rst 
     15   orientation/orientation.rst 
    1516   sesans/sans_to_sesans.rst 
    1617   sesans/sesans_fitting.rst 

  • doc/guide/magnetism/magnetism.rst

    r1f058ea r4f5afc9  
    55 
    66Models which define a scattering length density parameter can be evaluated 
    7  as magnetic models. In general, the scattering length density (SLD = 
    8  $\beta$) in each region where the SLD is uniform, is a combination of the 
    9  nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
    10  spin states of the neutrons. 
     7as magnetic models. In general, the scattering length density (SLD = 
     8$\beta$) in each region where the SLD is uniform, is a combination of the 
     9nuclear and magnetic SLDs and, for polarised neutrons, also depends on the 
     10spin states of the neutrons. 
    1111 
    1212For magnetic scattering, only the magnetization component $\mathbf{M_\perp}$ 
    1313perpendicular to the scattering vector $\mathbf{Q}$ contributes to the magnetic 
    1414scattering length. 
    15  
    1615 
    1716.. figure:: 
    … …  
    2827is the Pauli spin. 
    2928 
    30 Assuming that incident neutrons are polarized parallel (+) and anti-parallel (-) 
    31 to the $x'$ axis, the possible spin states after the sample are then 
     29Assuming that incident neutrons are polarized parallel $(+)$ and anti-parallel 
     30$(-)$ to the $x'$ axis, the possible spin states after the sample are then: 
    3231 
    33 No spin-flips (+ +) and (- -) 
     32* Non spin-flip $(+ +)$ and $(- -)$ 
    3433 
    35 Spin-flips    (+ -) and (- +) 
     34* Spin-flip $(+ -)$ and $(- +)$ 
     35 
     36Each measurement is an incoherent mixture of these spin states based on the 
     37fraction of $+$ neutrons before ($u_i$) and after ($u_f$) the sample, 
     38with weighting: 
     39 
     40.. math:: 
     41    -- &= ((1-u_i)(1-u_f))^{1/4} \\ 
     42    -+ &= ((1-u_i)(u_f))^{1/4} \\ 
     43    +- &= ((u_i)(1-u_f))^{1/4} \\ 
     44    ++ &= ((u_i)(u_f))^{1/4} 
     45 
     46Ideally the experiment would measure the pure spin states independently and 
     47perform a simultaneous analysis of the four states, tying all the model 
     48parameters together except $u_i$ and $u_f$. 
    3649 
    3750.. figure:: 
    … …  
    4154$\phi$ and $\theta_{up}$, respectively, then, depending on the spin state of the 
    4255neutrons, the scattering length densities, including the nuclear scattering 
    43 length density ($\beta{_N}$) are 
     56length density $(\beta{_N})$ are 
    4457 
    4558.. math:: 
    4659    \beta_{\pm\pm} =  \beta_N \mp D_M M_{\perp x'} 
    47     \text{ when there are no spin-flips} 
     60    \text{ for non spin-flip states} 
    4861 
    4962and 
    … …  
    5164.. math:: 
    5265    \beta_{\pm\mp} =  -D_M (M_{\perp y'} \pm iM_{\perp z'}) 
    53     \text{ when there are} 
     66    \text{ for spin-flip states} 
    5467 
    5568where 
    5669 
    5770.. math:: 
    58     M_{\perp x'} = M_{0q_x}\cos(\theta_{up})+M_{0q_y}\sin(\theta_{up}) \\ 
    59     M_{\perp y'} = M_{0q_y}\cos(\theta_{up})-M_{0q_x}\sin(\theta_{up}) \\ 
    60     M_{\perp z'} = M_{0z} \\ 
    61     M_{0q_x} = (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ 
    62     M_{0q_y} = (M_{0y}\sin\phi - M_{0x}\cos\phi)\sin\phi 
     71    M_{\perp x'} &= M_{0q_x}\cos(\theta_{up})+M_{0q_y}\sin(\theta_{up}) \\ 
     72    M_{\perp y'} &= M_{0q_y}\cos(\theta_{up})-M_{0q_x}\sin(\theta_{up}) \\ 
     73    M_{\perp z'} &= M_{0z} \\ 
     74    M_{0q_x} &= (M_{0x}\cos\phi - M_{0y}\sin\phi)\cos\phi \\ 
     75    M_{0q_y} &= (M_{0y}\sin\phi - M_{0x}\cos\phi)\sin\phi 
    6376 
    6477Here, $M_{0x}$, $M_{0x}$, $M_{0z}$ are the x, y and z components 
    … …  
    6679 
    6780.. math:: 
    68     M_{0x} = M_0\cos\theta_M\cos\phi_M \\ 
    69     M_{0y} = M_0\sin\theta_M \\ 
    70     M_{0z} = -M_0\cos\theta_M\sin\phi_M 
     81    M_{0x} &= M_0\cos\theta_M\cos\phi_M \\ 
     82    M_{0y} &= M_0\sin\theta_M \\ 
     83    M_{0z} &= -M_0\cos\theta_M\sin\phi_M 
    7184 
    7285and the magnetization angles $\theta_M$ and $\phi_M$ are defined in 
    … …  
    7689 
    7790===========   ================================================================ 
    78  M0_sld        = $D_M M_0$ 
    79  Up_theta      = $\theta_\mathrm{up}$ 
    80  M_theta       = $\theta_M$ 
    81  M_phi         = $\phi_M$ 
    82  Up_frac_i     = (spin up)/(spin up + spin down) neutrons *before* the sample 
    83  Up_frac_f     = (spin up)/(spin up + spin down) neutrons *after* the sample 
     91 M0:sld      $D_M M_0$ 
     92 mtheta:sld   $\theta_M$ 
     93 mphi:sld     $\phi_M$ 
     94 up:angle     $\theta_\mathrm{up}$ 
     95 up:frac_i    $u_i$ = (spin up)/(spin up + spin down) *before* the sample 
     96 up:frac_f    $u_f$ = (spin up)/(spin up + spin down) *after* the sample 
    8497===========   ================================================================ 
    8598 
    8699.. note:: 
    87     The values of the 'Up_frac_i' and 'Up_frac_f' must be in the range 0 to 1. 
     100    The values of the 'up:frac_i' and 'up:frac_f' must be in the range 0 to 1. 
    88101 
    89102*Document History* 
    90103 
    91104| 2015-05-02 Steve King 
    92 | 2017-05-08 Paul Kienzle 
     105| 2017-11-15 Paul Kienzle 

  • doc/guide/pd/polydispersity.rst

    r1f058ea reda8b30  
    66.. ZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ 
    77 
     8.. _polydispersityhelp: 
     9 
    810Polydispersity Distributions 
    911---------------------------- 
    1012 
    11 With some models in sasmodels we can calculate the average form factor for a 
     13With some models in sasmodels we can calculate the average intensity for a 
    1214population of particles that exhibit size and/or orientational 
    13 polydispersity. The resultant form factor is normalized by the average 
     15polydispersity. The resultant intensity is normalized by the average 
    1416particle volume such that 
    1517 

  • doc/guide/resolution.rst

    r1f058ea r0db85af  
    209209$x'_0 = x_0 \cos(\theta) + y_0 \sin(\theta)$ and 
    210210$y'_0 = -x_0 \sin(\theta) + y_0 \cos(\theta)$. 
    211 Note that the rotation angle is zero for a $x$\ -\ $y$ symmetric 
     211Note that the rotation angle is zero for a $x$-$y$ symmetric 
    212212elliptical Gaussian distribution. The $A$ is a normalization factor. 
    213213 
    … …  
    233233 
    234234Since the weighting factor on each of the bins is known, it is convenient to 
    235 transform $x'$\ -\ $y'$ back to $x$\ -\ $y$ coordinates (by rotating it 
     235transform $x'$-$y'$ back to $x$-$y$ coordinates (by rotating it 
    236236by $-\theta$ around the $z$\ -axis). 
    237237 
    … …  
    254254    y'_0 &= 0 
    255255 
    256 while for a $x$\ -\ $y$ symmetric smear 
     256while for a $x$-$y$ symmetric smear 
    257257 
    258258.. math:: 
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