Contents

Skiba at R=28: first connect intermediate p1 to FSS

sd0='FSS'; sp0='pt13'; sd1='p1'; sp1='pt16'; flip=1; % p1i to FSS
fn=setfnflip(sd0,sp0,sd1,sp1,flip);
alvin=[0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1];
opt.start=1; opt.tv=[]; opt.nti=60; opt.retsw=1;  opt.t1=150;
[alv,vv,sol,udat,tlv,tv,uv]=iscnat(alvin,[],[],opt,fn);

ans =
  Columns 1 through 7
    0.0300    0.0010    0.5000    0.0300    0.0050    0.9000    0.0010
  Columns 8 through 13
   28.0000    0.0100    0.1000    1.0000    1.1000    0.3000
ans =
  Columns 1 through 7
    0.0300    0.0010    0.5000    0.0300    0.0050    0.9000    0.0010
  Columns 8 through 13
   28.0000    0.0100    0.1000    1.0000    1.1000    0.3000
getting Psi, done in 0.210999s, n/2=164, d=0, suggested T=132.692
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 60, Maximum relative error = 0.00623473, order = 2 
al=0.1, flag=0 
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 60, Maximum relative error = 0.00211358, order = 2 
al=0.2, flag=0
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 60, Maximum relative error = 0.0139961, order = 2 
===> Non linear iteration  = 2, Linear iteration = 1 
...

save

tlv0=tlv; tv0=tv; uv0=uv; alv0=alv; vv0=vv;

now connect IC from uv0 to p1/pt34 (upper p1)

js=6; je=10; jl=js-je+1; % alpha-range; now set the target and Psi:
s1=loadp('p1','pt34'); getaux(s1)', pause
u1=s1.u(1:s1.nu); [Psi,muv,d,t1]=getPsi(s1); n=s1.nu;
a0l=length(alv0); tva=zeros(jl,opt.Nmax+1); % some prep. and fields to hold paths
opt.Nmax=200; opt.Itnlmax=10; opt.nti=30;
uva=zeros(jl,n+1,opt.Nmax+1); opt.start=0;  sol=[]; alva=[]; vva=[]; tavl=[];
opt.retsw=0; alvin=[0.05 0.2 0.4 0.6 0.8 1];
tv=linspace(0,opt.t1,opt.nti); se=2; opt.tv=tv.^se./opt.t1^(se-1); doplot=1;
opt.msw=0; opt.Stats_step='on'; v=[10,20];  % switch off stats
for j=js:je;
   fprintf('j=%i, al=%g\n', j, alv0(j)); s0.u(1:n)=uv0(j,1:n,1)';
   [alv,vv,sol,udat,tlv,tv,uv]=iscnat(alvin,[],[],opt,fn);
   if ~isempty(alv); Jd=vv0(j)-vv(end); fprintf('J1-J2=%g\n',Jd); % cont. success
      alva=[alva alv0(j)]; vva=[vva vv(end)]; tl=length(sol.x); % put vals in vector
      talv=[tavl tl]; tva(j,1:tl)=sol.x; uva(j,1:n,1:tl)=sol.y;
   end
end

ans =
  Columns 1 through 7
    0.0300    0.0010    0.5000    0.0300    0.0050    0.9000    0.0010
  Columns 8 through 13
   28.0000    0.0100    0.1000    1.0000    1.1000    0.3000
getting Psi, c-evals at i=161, mu=-0.188201, mu(i+1)=-0.188201, 
c-evals at i=167, mu=0.158192, mu(i+1)=0.158192, 
done in 0.219869s, n/2=164, d=0, suggested T=326.294
j=6, al=0.6
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 30, Maximum relative error = 0.282657, order = 2 
===> Non linear iteration  = 2, Linear iteration = 1 
     N= 30, Maximum relative error = 0.0107719, order = 2 
===> Non linear iteration  = 3, Linear iteration = 1 
     N= 30, Maximum relative error = 0.0102957, order = 2 
===> Non linear iteration  = 3, Linear iteration = 2 
     N= 80, Maximum relative error = 0.000351711, order = 2 
al=0.05, flag=0 
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 80, Maximum relative error = 0.0899376, order = 2 
...

plot value diagram

js=6; jep=10; figure(6); clf; plot(alv0(js:jep),vv0(js:jep),'-*b');hold on;
plot(alva,vva,'-*r');set(gca,'FontSize',s1.plot.fs); axis tight;
xlabel('\alpha','FontSize',s1.plot.fs); ylabel('J_{a}','FontSize',s1.plot.fs);

select j and plot paths

j=9; fprintf('j=%i, al=%g\n', j, alv0(j)); pause; s0.u(1:n)=uv0(j,1:n,1)';
[alv,vv,sol,udat,tlv,tv,uv]=iscnat(alvin,[],[],opt,fn);
sol0=[]; alp=alv0(j); % plot the paths to FSC and FSM alp
sol0.x=tv0(j,1:tlv0(j));sol0.y=squeeze(uv0(j,1:n,1:tlv0(j)));
psol3Db2(s1,sol0,sol,1,1,[]); xlabel('x'); ylabel('t'); zlabel('v'); view(v);
psol3Db2(s1,sol0,sol,2,2,[]); xlabel('x'); ylabel('t'); zlabel('w'); view(v);
psol3Db2(s1,sol0,sol,4,5,[]); xlabel('x'); ylabel('t'); zlabel('E'); view(v);

j=9, al=0.9
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 30, Maximum relative error = 0.155872, order = 2 
===> Non linear iteration  = 2, Linear iteration = 1 
     N= 30, Maximum relative error = 0.00635334, order = 2 
al=0.05, flag=0 
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 30, Maximum relative error = 0.0677208, order = 2 
===> Non linear iteration  = 2, Linear iteration = 1 
     N= 30, Maximum relative error = 0.0135594, order = 2 
===> Non linear iteration  = 2, Linear iteration = 2 
     N= 80, Maximum relative error = 0.00123751, order = 2 
al=0.2, flag=0
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 80, Maximum relative error = 0.0741019, order = 2 
===> Non linear iteration  = 2, Linear iteration = 1 
     N= 80, Maximum relative error = 0.00241351, order = 2 
al=0.4, flag=0
===> Non linear iteration  = 1, Linear iteration = 1 
     N= 80, Maximum relative error = 0.0698624, order = 2 
...

Published with MATLAB® 7.14