Package nl.tudelft.simulation.sne.c1

Lithium-Cluster Dynamics (C1).

See:
Description

Class Summary

C1TaskA	The C1 Test Model.
C1TaskB	The C1 Test Model.
C1TaskC	The C1 Test Model.
FCenter	The concentration of aggregates consisting of F-centers.

Package nl.tudelft.simulation.sne.c1 Description

Lithium-Cluster Dynamics (C1).

The first model to be compared is taken from solid state physics. The special features to be compared are rate equations (application area), stiff systems (numerical integration), parameter sweep and steady-state calculation (experimentation).

The model describes formation and decay of defect ("F-centers") aggregates in alcali halides. The defects are produced by electron bombardment near the surface of the crystal and can either form aggregates or will evaporate if they reach the surface.

The variable f(t) denotes the concentration of F-centers, m(t) and r(t) respectively denote the concentration of aggregates consisting of two (M-center) or three F-centers (R-center). In principle the system can be easily extended taking into account formation of larger aggregates (n F-centers). The variable p(t) is the production term of F-centers due to electron bombardement (irridiation):

dr/dt = -d_rr + k_rmf

dm/dt = d_rr - d_mm + k_ff² - k_rmf

df/dt = d_rr + 2d_mm - k_rmf - 2k_ff² - l_ff + p

The parameter l_f measures the loss of F-centers at the surface. k_r and k_f are rate constants describing the formation of an M-center out of two F-centers, or the formation of an R-center out of an M-center and an F-center. The decay of an R-center into an M-center and an F-center is described by the rate constant d_r and the decay of an M-center into two F-centers by the rate constant d_m. Investigations are started after constant electron bombardment p(t) = p_c = 10⁴ of approximately 10 s; the production term has to be set to zero (p(t) = 0), the initial values are:

f(0) = 9.975

m(0) = 1.674

r(0) = 84.99

The parameter values are:

k_r = 1

k_f = 0.1

l_f = 1000

d_r = 0.1

d_m = 1

The following tasks should be performed
1. simulation of the stiff system over [0,10] with indication of computing time depending on different integration algorithms
2. parameter variation of l_f from 1.0E2 to 1.0E4 and a plot of all f(t;l_f), logarithmic steps preferred.
3. calculation of steady states during constant bombardment (p(t) = p_c = 1.0E4) and without bombardment (p(t) = 0).