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DiffRotDiscreteCircle

Description

Summary

This fitting function models the dynamics structure factor of a particle undergoing discrete jumps on N-sites evenly distributed in a circle. The particle can only jump to neighboring sites. This is the most common type of discrete rotational diffusion in a circle.

Markov model for jumps between neighboring sites:

ddtpj(t)=1τ[pj1(t)2pj(t)+pj+1(t)]

The Decay fitting parameter τ is the inverse of the transition rate. This, along with the circle radius r, conform the two fundamental fitting parameters of the structure factor S(Q,E):

S(Q,E)≡=eiEt/I(Q,t)dt=A0(Q,r)δ(E)+1πN1l=1Al(Q,r)τ1l(τ1l)2+E2
Al(Q,r)=1NNk=1j0(2Qrsin(πkN))cos(2πlkN)
τ1l=4τ1sin2(πlN)

The transition rate, expressed in units of energy is hτ1, with h = 4.135665616 meV ps.

This function is a composite of ElasticDiffRotDiscreteCircle and InelasticDiffRotDiscreteCircle.

When using DiffRotDiscreteCircle, the value of Q can be obtained either though the Q attribute or can be calculated from the input workspace using the WorkspaceIndex property. The value calculated using the workspace is used whenever the Q attribute is empty.

Example: Methyl Rotations

Methyl Rotations can be modelled setting N=3. In this case, the inelastic part reduces to a single Lorentzian:

S(Q,E)=A0(Q,r)δ(E)+2πA1(Q,r)3τ1(3τ1)2+E2

If, alternatively, one models these dynamics using the Lorentzian function provided in Mantid:

S(Q,E)=Aδ(ω)+Bπ(Γ2(Γ2)2+(ω)2)

Then:

B=1πhA1
Γ=3πhτ1=3.949269754meVTHzτ1

Attributes (non-fitting parameters)

Name Type Default Description
N      
NumDeriv      
Q      
f0.N      
f0.Q      
f0.WorkspaceIndex      
f1.N      
f1.Q      
f1.WorkspaceIndex      

N (integer, default=3) number of sites - NumDeriv (boolean, default=true) carry out numerical derivative - Q (double, default=0.5) Momentum transfer .. properties:

.. categories::

Source

C++ header: DiffRotDiscreteCircle.h

C++ source: DiffRotDiscreteCircle.cpp