## Code for Figure 7.18

### main.m

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54% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING.  If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.

%
% compute the actual phi versus eta
%
Bbig   = 100;
Bsmall = 0.01;
nphi = 100;
phismall = 10^(-2);
phibig = 10^(4);
phi = [logspace(log10(phismall),log10(phibig),nphi)]';
B = Bbig;
etabig = 1./phi.*(1./tanh(3*phi) - 1./(3*phi))./ ...
( 1 + (phi./tanh(3*phi) - 1/3)/B );
B = Bsmall;
etasmall = 1./phi.*(1./tanh(3*phi) - 1./(3*phi))./ ...
( 1 + (phi./tanh(3*phi) - 1/3)/B );
tmp = [phi  etabig etasmall];
%save -ascii biotasy.dat tmp;
%
% compute the various straight line approximations for asymptotic plots
%
horiz  = [phismall 1; sqrt(Bbig) 1];
minus1 = [1 1; phibig 1/phibig];
minus2small = [sqrt(Bsmall) 1; phibig 1/(phibig*phibig/Bsmall)];
minus2big = [sqrt(Bbig) 1; phibig 1/(phibig*phibig/Bbig)];
auxvbl = [horiz minus1 minus2small minus2big];
%save -ascii biotasy_01.dat auxvbl;

save biotasy.dat tmp auxvbl

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
loglog (tmp(:,1), tmp(:,2:3), ...
auxvbl(:,1), auxvbl(:,2), ...
auxvbl(:,3), auxvbl(:,4), ...
auxvbl(:,5), auxvbl(:,6), ...
auxvbl(:,7), auxvbl(:,8));
% TITLE
end % PLOTTING

```