DSPC Standard Layers#
This shows an example of using a standard layers model to analyse reflectivity from a floating bilayer of DSPC.
The model is set up in the script, we set Gaussian priors on some of the parameters, build the two contrasts, run the calculation and plot the results.
This example can be run as a script or interactively using the instructions below.
Run Script:
root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'normalReflectivity', 'standardLayers'));
standardLayersDSPCScript
Run Interactively:
root = getappdata(0, 'root');
cd(fullfile(root, 'examples', 'normalReflectivity', 'standardLayers'));
edit standardLayersDSPCSheet.mlx
Standard Layers Analysis of a DSPC Floating Bilayer
In this worksheet, we will carry out an analysis of a floating bilayer sample using a 'standard layers' model.
The sample consists of a DSPC bilayer, on a silane SAM on Silicon as follows.....
So we are going to need layers for Oxide, SAM tails, SAM heads, and the Heads/Tails of the Bilayer. We also need to consider hydration of the submerged bilayer.
Start by making a project....
% Make the project
problem = createProject(name='original_dspc_bilayer', calcType='normal', model='standard layers', geometry='substrate/liquid', absorption=false);
% Make priors visible..
problem.showPriors = true;
The add the parameters we are going to need to this....
paramGroup = {
{'Oxide thick', 5, 19.54, 60, true, 'uniform', 0, Inf};
{'Oxide SLD', 3.39e-06, 3.39e-06, 3.41e-06, false, 'uniform', 0, Inf};
{'Sam tails thick', 15, 22.66, 35, true, 'uniform', 0, Inf};
{'Sam tails SLD', -5e-07, -4.01e-07, -3e-07, false, 'uniform', 0, Inf};
{'Sam tails hydration', 1, 5.253, 50, true, 'uniform', 0, Inf};
{'Sam rough', 1, 5.64, 15, true, 'uniform', 0, Inf};
{'cw thick', 10, 17.12, 28, true, 'uniform', 0, Inf};
{'cw SLD', 0, 0, 1e-09, false, 'uniform', 0, Inf};
{'SAM head thick', 5, 8.56, 17, true, 'gaussian', 10, 2};
{'SAM head SLD', 1e-07, 1.75e-06, 2e-06, false, 'uniform', 0, Inf};
{'SAM head hydration', 10, 45.45, 50, true, 'uniform', 30, 3};
{'Bilayer head thick', 7, 10.70, 17, true, 'gaussian', 10, 2};
{'Bilayer head SLD', 5e-07, 1.47e-06, 1.5e-06, false, 'uniform', 0, Inf};
{'Bilayer rough', 2, 6.014, 15, true, 'uniform', 0, Inf};
{'Bilayer tails thick', 14, 17.82, 22, true, 'uniform', 0, Inf};
{'Bilayer tails SLD', -5e-07, -4.610e-07, 0, false, 'uniform', 0, Inf};
{'Bilayer tails hydr', 10, 17.64, 50, true, 'uniform', 0, Inf};
{'Bilayer heads hydr', 10, 36.15, 50, true, 'gaussian', 30, 3};
{'cw hydration', 99.9, 100, 100, false, 'uniform', 0, Inf};
{'Oxide Hydration', 0, 23.61, 60, true, 'uniform', 0, Inf};
};
problem.addParameterGroup(paramGroup);
% In addition to these, there is also Substrate Roughness which is always
% parameter 1. Increase the allowed range of this a bit....
problem.setParameter(1,'max',10);
Now we can group these parameters into the layers we need, and add them to the project......
% Group these into layers....
Layers = {
{'Oxide', 'Oxide thick', 'Oxide SLD', 'substrate roughness', 'Oxide Hydration', 'bulk out'};
{'Sam tails', 'Sam tails thick', 'Sam tails SLD', 'Sam rough', 'Sam tails hydration', 'bulk out'};
{'Sam heads', 'SAM head thick', 'SAM head SLD', 'Sam rough', 'SAM head hydration', 'bulk out'};
{'Central water', 'cw thick', 'cw SLD', 'Bilayer rough', 'cw hydration', 'bulk out'};
{'Bilayer heads', 'Bilayer head thick', 'Bilayer head SLD', 'Bilayer rough', 'Bilayer heads hydr', 'bulk out'};
{'Bilayer tails', 'Bilayer tails thick', 'Bilayer tails SLD','Bilayer rough', 'Bilayer tails hydr', 'bulk out'};
};
problem.addLayerGroup(Layers);
Now deal with the experimental params. We need a bulk in of Silicon, and two Bulk outs - D2O and SMW
% Remove the existing default first (we could just rename it and change the
% values, of course....)
problem.removeBulkIn(1);
problem.addBulkIn('Silicon', 2e-06, 2.073e-06, 2.1e-06, false);
%.... ditto bulk out....
problem.removeBulkOut(1);
problem.addBulkOut('D2O', 5.50e-06, 5.98e-06, 6.4e-06, true);
problem.addBulkOut('SMW', 1e-06, 2.21e-06, 4.99e-06, true);
Likewise the scalefactors and backgrounds......
% Set the scalefactors - use one for each contrast
problem.removeScalefactor(1);
problem.addScalefactor('Scalefactor 1', 0.05, 0.10, 0.2, true);
problem.addScalefactor('Scalefactor 2', 0.05, 0.15, 0.2, true);
% Now deal with the backgrounds....
problem.removeBackgroundParam(1);
problem.addBackgroundParam('Backs parameter D2O', 5e-10, 2.23e-06, 7e-06, true);
problem.addBackgroundParam('Backs parameter SMW', 1e-10, 3.38e-06, 4.99e-06, true);
problem.removeBackground(1);
problem.addBackground('D2O Background','constant','Backs parameter D2O');
problem.addBackground('SMW Background','constant','Backs parameter SMW');
Now load in and add the data....
d2o_dat = readmatrix('DSPC_D2O.dat');
problem.addData('dspc_bil_d2O', d2o_dat);
smw_dat = readmatrix('DSPC_SMW.dat');
problem.addData('dspc_bil_smw', smw_dat);
Finally, we build everything up into the two contrasts.....
stack = {'Oxide',...
'Sam tails',...
'Sam heads',...
'Central water',...
'Bilayer heads',...
'Bilayer tails',...
'Bilayer tails',...
'Bilayer heads',...
};
problem.addContrast('name', 'D2O',...
'BulkIn', 'Silicon',...
'BulkOut', 'D2O',...
'background', 'D2O Background',...
'resolution', 'Resolution 1',...
'scalefactor', 'Scalefactor 1',...
'data', 'dspc_bil_d2o',...
'model', stack);
problem.addContrast('name', 'SMW',...
'BulkIn', 'Silicon',...
'BulkOut', 'SMW',...
'background', 'SMW Background',...
'resolution', 'Resolution 1',...
'scalefactor', 'Scalefactor 2',...
'data', 'dspc_bil_smw',...
'model', stack);
Display our project, to check what we have....
% Just the name of the project with no semicolon.....
problem
Running the Project....
To run a project in RAT, we first need to define a controls block....
controls = controlsClass()
The devaults action ('procedure') is just a single caclulation. So send out project to RAT with this, and then plot our our initial starting position...
[problem,results] = RAT(problem,controls);
figure
plotRefSLD(problem,results);
We are as expected, a little off. Run some Differential Evolution on this.....
controls.procedure = 'DE';
controls.display = 'final' % Turn off per-iteration updates....
Note that now, the relevant parameters for Differential Evoultion appear in Controls. We can change these at this point if we want (e.g. controls.populationSize = 50 etc), but we'll go with the defaults for now....
[problem,results] = RAT(problem,controls);
figure
plotRefSLD(problem,results)
This is decent starting point, but we really want a Bayesian analysis. To do this just select DREAM in controls.....
controls.procedure = 'dream'
Again we'll just go with the defaults.....
[problem,results] = RAT(problem,controls)
Finally, plot out what we have....
h1 = figure;
bayesShadedPlot(problem,results,'KeepAxes',true,'interval',65,'q4',false);
h3 = figure;
plotHists(results,'figure',h3,'smooth',true);
figure
plotChain(results);
h4 = figure; % Need a figure handle....
cornerPlot(results,'figure',h4,'smooth',false);
