Incoherent Summing with Standard Layers#

Analysing data containing domains using standard layers models is done in a similar way to a normal standard layers model, but with a couple of additional steps.

A normal standard layers model defines parameters, which are grouped into layers, and then these are arranged into contrasts. For sample containing domains, the layers are first grouped into domain contrasts, which are just groupings of layers with none of the additional parameters of a contrast (such as resolutions etc). Then, the actual experimental contrasts are built in the usual way, but with the model set as any two of the domains.

To control the ratio between the domains, we can add domain ratios as described in Standard Layers Domains. And each contrast has an additional field for domain ratios which is set as one of the values from this block.

This example can be run as a script or interactively using the instructions below.

Run Script:

root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'domains', 'standardLayers'));
domainsStandardLayersScript

Run Interactively:

root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'domains', 'standardLayers'));
edit domainsStandardLayersSheet.mlx

Domains Samples Using Standard Layers

Domains Standard Layers projects proceed in much the same way as a normal SL problem, except that there is an additional grouping step between layers an contrasts.

Layers are grouped into 'Domain Contrasts'. The model for the actual experimental contrast is built from these domains rather than from layers. Thhere are exactly two domains for each contrast, with the the ratio of them controlled by a fittable 'domain ratio' parameter.

In this we will set up a simple example of a simulated system consisting of two layered domains to illustrate this process.

Start by making the project, specifying that this is a domains model...

problem = createProject(calcType="domains");

Define the parameters we need to define our two domains...

Parameters = {
    %   Name            min         val         max     fit?
    {'L1 thick',         5,         20,         60,     true   };
    {'L1 SLD',           3e-6,      4.1e-6,    5e-6,    false  };
    {'L1 rough'          2,          5,         20,     true   };
    {'L1 Hydr'           10,        20,         30,     true   };
    {'L2 thick',         5,         60,        100,     true   };
    {'L2 SLD',           2.1e-6,    3e-6,      5e-6,    false  };
    {'L2 rough'          2,          5,         20,     true   };
    {'L2 Hydr'           10,        20,         30,     true   };
    {'L3 thick',         5,         200,       300,     true   };
    {'L3 SLD',           3e-6,      7e-6,      8e-6,    false  };
    {'L3 rough'          2,          5,         20,     true   };
    {'L3 Hydr'           10,        20,         30,     true   };
    };
 
problem.addParameterGroup(Parameters);

..now group these into layers as usual....

 
Layer1 = {'Layer 1',...         % Name of the layer
    'L1 thick',...              % Layer thickness
    'L1 SLD',...                % Layer SLD
    'L1 Rough',...              % Layer roughness
    'L1 Hydr',...               % hydration (precent)
    'bulk out' }; 
 
Layer2 = {'Layer 2',...         % Name of the layer
    'L2 thick',...              % Layer thickness
    'L2 SLD',...                % Layer SLD
    'L2 Rough',...              % Layer roughness
    'L2 Hydr',...               % hydration (precent)
    'bulk out' }; 
 
Layer3 = {'Layer 3',...         % Name of the layer
    'L2 thick',...              % Layer thickness
    'L2 SLD',...                % Layer SLD
    'L2 Rough',...              % Layer roughness
    'L2 Hydr',...               % hydration (precent)
    'bulk out' };
 
problem.addLayerGroup({Layer1, Layer2, Layer3});
 

If we look at the project, there are two extra groups as compared to a normal standard layers - Domain Contrasts and Domain Ratios...

disp(problem)
         modelType: 'standard layers'
    experimentName: ''
          geometry: 'air/substrate'


    Parameters: ---------------------------------------------------------------------------------------------- 

    p             Name               Min       Value      Max     Fit? 
    __    _____________________    _______    _______    _____    _____

     1    "Substrate Roughness"          1          3        5    true 
     2    "L1 thick"                     5         20       60    true 
     3    "L1 SLD"                   3e-06    4.1e-06    5e-06    false
     4    "L1 rough"                     2          5       20    true 
     5    "L1 Hydr"                     10         20       30    true 
     6    "L2 thick"                     5         60      100    true 
     7    "L2 SLD"                 2.1e-06      3e-06    5e-06    false
     8    "L2 rough"                     2          5       20    true 
     9    "L2 Hydr"                     10         20       30    true 
    10    "L3 thick"                     5        200      300    true 
    11    "L3 SLD"                   3e-06      7e-06    8e-06    false
    12    "L3 rough"                     2          5       20    true 
    13    "L3 Hydr"                     10         20       30    true 


    Bulk In: -------------------------------------------------------------------------------------------------- 

    p      Name       Min    Value    Max    Fit? 
    _    _________    ___    _____    ___    _____

    1    "SLD Air"     0       0       0     false


    Bulk Out: ------------------------------------------------------------------------------------------------- 

    p      Name         Min       Value        Max       Fit? 
    _    _________    _______    ________    ________    _____

    1    "SLD D2O"    6.2e-06    6.35e-06    6.35e-06    false


    Scalefactors: ------------------------------------------------------------------------------------------------- 

    p         Name          Min     Value    Max     Fit? 
    _    _______________    ____    _____    ____    _____

    1    "Scalefactor 1"    0.02    0.23     0.25    false


   Domain Ratios: ----------------------------------------------------------------------------------------------- 

    p          Name          Min    Value    Max    Fit? 
    _    ________________    ___    _____    ___    _____

    1    "Domain Ratio 1"    0.4     0.5     0.6    false


    Backgrounds: ----------------------------------------------------------------------------------------------- 

    (a) Background Parameters: 

    p            Name             Min     Value     Max     Fit? 
    _    ____________________    _____    _____    _____    _____

    1    "Background Param 1"    1e-07    1e-06    1e-05    false

    (b) Backgrounds:  

    p         Name            Type              Source           Value 1    Value 2    Value 3    Value 4    Value 5
    _    ______________    __________    ____________________    _______    _______    _______    _______    _______

    1    "Background 1"    "constant"    "Background Param 1"      ""         ""         ""         ""         ""   


    Resolutions: --------------------------------------------------------------------------------------------- 

    (a) Resolutions Parameters: 

    p           Name           Min     Value    Max     Fit? 
    _    __________________    ____    _____    ____    _____

    1    "Resolution par 1"    0.01    0.03     0.05    false

    (b) Resolutions:  

    p         Name            Type             Source          Value 1    Value 2    Value 3    Value 4    Value 5
    _    ______________    __________    __________________    _______    _______    _______    _______    _______

    1    "Resolution 1"    "constant"    "Resolution par 1"      ""         ""         ""         ""         ""   


    Layers: -------------------------------------------------------------------------------------------------- 

    p      Name       Thickness       SLD       Roughness     Hydration    Hydrate with
    _    _________    __________    ________    __________    _________    ____________

    1    "Layer 1"    "L1 thick"    "L1 SLD"    "L1 rough"    "L1 Hydr"     "bulk out" 
    2    "Layer 2"    "L2 thick"    "L2 SLD"    "L2 rough"    "L2 Hydr"     "bulk out" 
    3    "Layer 3"    "L2 thick"    "L2 SLD"    "L2 rough"    "L2 Hydr"     "bulk out" 


    Custom Files: ------------------------------------------------------------------------------------------------------ 

    Name    Filename    Function Name    Language    Path
    ____    ________    _____________    ________    ____

     ""        ""            ""             ""        "" 


    Data: ------------------------------------------------------------------------------------------------------ 

        Name          Data       Data Range      Simulation Range   
    ____________    _________    __________    _____________________

    "Simulation"    "No Data"       "-"        "[ 0.0050 , 0.7000 ]"


   Domains Contrasts: ----------------------------------------------------------------------------------------------- 

       p   
    _______

    "Name" 
    "Model"


   Contrasts: ----------------------------------------------------------------------------------------------- 

             p         
    ___________________

    "Name"             
    "Data"             
    "Background"       
    "Background Action"
    "Bulk in"          
    "Bulk out"         
    "Scalefactor"      
    "Resolution"       
    "Resample"         
    "Repeat Layers"    
    "Domain Ratio"     
    "Model"            

Now, make a couple of Domain Contrasts, and define which layers make up which domains....

problem.addDomainContrast('name', 'Domain1', 'model', 'Layer 1');
problem.addDomainContrast('name', 'Domain2', 'model', {'Layer 2','Layer 3'});

Now make a contrast as with standard models, but this time also including the default domain ratio ("Domain Ratio 1). To set the model for our contrast, each physical contrast must have exactly two domain contrasts.

problem.addContrast('name','Domain Test',...
    'background',   'Background 1',...
    'resolution',   'Resolution 1',...
    'scalefactor',  'Scalefactor 1',...
    'resample',     false,...
    'BulkIn',       'SLD Air',...        
    'BulkOut',      'SLD D2O',...        
    'domainRatio',  'Domain Ratio 1',...
    'data',         'Simulation',...
    'model',        {'Domain1', 'Domain2'});

Now we can run our simulation as usual, and plot the results....

% Make a controls class....

controls = controlsClass();

% Send everything to RAT....

[problem,results] = RAT(problem,controls);

Starting RAT ______________________________________________________________________________________________

Elapsed time is 0.005070 seconds.

Finished RAT ______________________________________________________________________________________________

plotRefSLD(problem,results);