Sab Models: renamed freegas -> recoil

Scripts/Models/Specialized/sab_diffusion.m

@@ -13,6 +13,10 @@
 %   An incoherent solid type diffusion is obtained for small 'c' values (e.g. 0.01).
 %   The model satisfies the detailed balance.
 %
+%   The characteristic time for a diffusion step is t0=MD/kT, usually around 
+%   t0 = 1-4 E-12 s in liquids.
+%   The diffusion constant D is usally around D= 1 -10  1E-3 mm2/s in liquids.
+%
 %   The dispersion has the form:
 %      S(a,b) = 2*c*wt/pi*a * exp(2*c^2*a-b/2) 
 %               * sqrt( (c^2+1/4)./(b^2+4*c^2*wt^2*a^2) )

Scripts/Models/Specialized/sab_recoil.m

@@ -0,0 +1,81 @@
+function signal=sab_recoil(varargin)
+% model = sab_recoil(p, alpha ,beta, {signal}) : Free-gas/recoil dispersion(Q)
+%
+%   iFunc/sab_recoil: a 2D S(alpha,beta) with a free-gas/recoil dispersion
+%
+%   This is a 2D free-gas model appropriate to model the scattering law of a gas
+%     molecule, as well as the translational component of a liquid. 
+%     This is a pure incoherent scattering law (no structure).
+%
+%   The input parameter 'wt' is the translational weight, which quantifies the 
+%   fraction of the scattering originating from recoil/diffusion, e.g. wt=Mdiff/M
+%   A pure recoil is obtained with wt=1. The model satisfies the detailed balance.
+%
+%   The dispersion has the form:
+%      S(alpha,beta) = 1/sqrt(4*pi*wt*alpha)*exp( (wt*alpha + beta)^2/4/wt/a)
+%
+%   where we commonly define (h stands for hbar):
+%     alpha=  h2q2/2MkT = (Ei+Ef-2*mu*sqrt(Ei*Ef))/AkT   unit-less moment
+%     beta = -hw/kT     = (Ef-Ei)/kT                     unit-less energy
+%     A    = M/m                
+%     mu   = cos(theta) = (Ki.^2 + Kf.^2 - q.^2) ./ (2*Ki.*Kf)
+%     m    = mass of the neutron
+%     M    = mass of the scattering target [g/mol]
+%     wt   = translational weight, wt=Mdiff/M e.g. in [0-1]
+%
+% conventions:
+% w = omega = Ei-Ef = energy lost by the neutron [meV]
+%     omega > 0, neutron looses energy, can not be higher than Ei (Stokes)
+%     omega < 0, neutron gains energy, anti-Stokes
+%
+%   You can build a freegas model for a given translational weight with:
+%      sab = sab_recoil(wt)
+%
+%   Evaluate the model with syntax:
+%     sab(p, alpha, beta)
+%
+% input:  p: sab_recoil model parameters (double)
+%             p(1)= wt          Translational weight Mdiff/M [1]
+%             p(2)= Amplitude 
+%         alpha:  axis along unitless wavevector/momentum (row,double)
+%         beta:   axis along unitless energy (column,double)
+% output: signal: model value [iFunc_Sab]
+%
+%
+% Example:
+%   s=sab_recoil;
+%   plot(log10(iData(s, [], 0:.1:20, -50:50)))  % alpha=0:20, beta=-50:50
+%
+% Reference: 
+%  M.Mattes and J.Keinert, IAEA INDC (NDS)-0470 (2005) https://www-nds.iaea.org/publications/indc/indc-nds-0470/
+%  R.E.McFarlane, LA-12639-MS (ENDF 356) (March 1994) https://t2.lanl.gov/nis/publications/thermal.pdf
+%  
+%
+% Version: $Date$
+% See also iData, iFunc
+%   <a href="matlab:doc(iFunc,'Models')">iFunc:Models</a>
+% (c) E.Farhi, ILL. License: EUPL.
+
+signal.Name           = [ 'sab_recoil dispersion(Q) free-gas/recoil dispersion [' mfilename ']' ];
+signal.Description    = 'A 2D S(alpha,beta) recoil/free-gas/translational dispersion.';
+
+signal.Parameters     = {  ...
+  'wt             Translational weight; wt=Mdiff/M [1]' ...
+  'Amplitude' };
+
+signal.Dimension      = 2;         % dimensionality of input space (axes) and result
+signal.Guess          = [ 1 1 ];
+
+signal.Expression     = { ...
+ 'a = x; b = y; wt = p(1);' ...
+ 'if isvector(a) && isvector(b) && numel(a) ~= numel(b), [a,b] = meshgrid(a,b); end' ...
+ 'signal  = p(2)./sqrt(4*pi*wt*a).*exp(-(wt*a + b).^2/4/wt./a);' ...
+ };
+
+signal= iFunc(signal);
+signal= iFunc_Sab(signal); % overload Sab flavour
+
+if nargin == 1 && isnumeric(varargin)
+  p = varargin{1};
+  if numel(p) >= 1, signal.ParameterValues(1) = p(1); end
+end