Contents
stat. BD for vegOC; set matlab paths and init FSS branch
clear all; path('../p2poclib',path);
close all; p=[]; lx=5; nx=40; ny=1; ly=lx/nx; sw=1; rho=0.03;
p=veginit(p,lx,ly,nx,ny,sw,rho); p=setfn(p,'FSS'); p0=p; screenlayout(p);
inires=0.223704
first res=7.05917e-14
Problem directory name: FSS
find bif.points from FSS branch
p=p0; p.nc.ilam=8; p.sol.ds=-1; p.nc.nsteps=100; p=findbif(p,10);
step lambda y-axis residual iter meth ds
0 got first point with lam=34, res=7.05917e-14
- now lam=34
1 got second point with lam=34, res=4.85464e-13
warning: mu-min=-3.57912, mu-max=3.54912; consider increasing p.nc.neig
Starting findbif, 25 negative EVals at lam=34
2 34.00000 807.18266 6.36e-14 2 nat 0.97162
warning: mu-min=-3.57849, mu-max=3.54849; consider increasing p.nc.neig
- lam=33.5, ineg=25
warning: mu-min=-3.57818, mu-max=3.54818; consider increasing p.nc.neig
...
recalculate branch to get usr-lam points
delete('FSS/pt*.mat');
p=p0; p.sol.ds=-1; p.sw.bifcheck=0; p=cont(p,45);
p.sol.ds=-0.5; p.nc.dsmax=0.5; p=cont(p,100);
step lambda y-axis residual iter meth ds
0 got first point with lam=34, res=7.05917e-14
- now lam=33.9
1 got second point with lam=33.9, res=5.3273e-11
2 33.38888 784.32318 5.97e-14 2 nat -1.00000
3 32.87340 765.26388 6.28e-14 2 nat -1.00000
4 32.35388 746.26045 6.09e-14 2 nat -1.00000
5 31.83025 727.31448 7.37e-14 2 nat -1.00000
6 31.30243 708.42758 7.29e-14 2 nat -1.00000
7 30.77037 689.60146 6.05e-14 2 nat -1.00000
...
bif from FSS
p=swibra('FSS','bpt1','p1',-1); p.sw.bifcheck=0; p=cont(p,70);
p=swibra('FSS','bpt2','p2',-2); p.sw.bifcheck=0; p=cont(p,100);
p=swibra('FSS','bpt3','p3',-2); p.sw.bifcheck=0; p=cont(p,35);
lambda=21.8644, zero eigenvalue is 6.03683e-07
al0=0.615546, a1=-1.19499e-07, b1=0.00105236, al1b=-0.00210465
Problem directory name: p1
step lambda y-axis residual iter meth ds
1 21.94290 407.85609 4.60e-11 2 arc -1.00000
2 22.16323 414.10662 4.42e-10 2 arc -1.00000
3 22.48862 423.36166 5.93e-09 2 arc -1.00000
4 22.88529 434.68450 2.70e-11 2 arc -1.00000
5 23.32942 447.41790 9.52e-12 2 arc -1.00000
6 23.80529 461.13049 3.94e-12 2 arc -1.00000
...
plot the BD, max v over R
figure(3); clf; pcmp=1;
plotbraf('FSS','pt140',3,pcmp,'cl','k','lab',[13,17,28,44,91],'labo',0,-40);
plotbraf('FSS','bpt4',3,pcmp,'cl','k');
plotbraf('p1','pt74',3,pcmp,'cl','b', 'lab',[11,16,34,38, 49, 65],'labo',1,0);
plotbraf('p2','pt97',3,pcmp,'cl','r', 'lab',[23 38],'labo',1,0);
plotbraf('p3','pt37',3,pcmp,'cl','m','lab',[8],'labo',1,0);
text(31,400,'FSS','fontsize',16);text(30,520,'p1','fontsize',16);
text(13.5,200,'p2','fontsize',16);text(24.5,570,'p3','fontsize',16);
xlabel('R'); ylabel('max v');
plot the BD, J_{c,a} over R
figure(3); clf; pcmp=4;
plotbraf('FSS','pt140',3,pcmp,'cl','k','lab',[13,17,28,44,72],'labo',0,1);
plotbraf('FSS','bpt4',3,pcmp,'cl','k');
plotbraf('p1','pt74',3,pcmp,'cl','b', 'lab',[11,16,34,38, 49, 65],'labo',1,0);
xlabel('R'); ylabel('J_{c,a}'); axis([19 30 12 29]);
soln plots
plot1Df('p1','pt11',1,10,10,10,3);pause; plot1Df('p1','pt16',1,10,10,10,3);pause
plot1Df('p1','pt34',1,10,10,10,3);pause; plot1Df('p1','pt38',1,10,10,10,3);pause
plot1Df('p1','pt49',1,10,10,10,3);pause; plot1Df('p1','pt65',1,10,10,10,3);pause
plot1Df('p2','pt23',1,10,10,10,3);pause; plot1Df('p3','pt8',1,10,10,10,3);
lam=26
p1/pt11, lam=26, (v,w,lam,mu,E,P=311.63&10.05&0.56&1.0187&11.2060&22.0012)
lam=28
p1/pt16, lam=28, (v,w,lam,mu,E,P=337.92&10.37&0.53&1.0596&13.4642&25.0649)
lam=28
p1/pt34, lam=28, (v,w,lam,mu,E,P=283.31&13.17&0.35&1.0560&17.0876&25.0205)
lam=26
p1/pt38, lam=26, (v,w,lam,mu,E,P=252.46&13.34&0.34&1.0253&15.2125&22.1437)
lam=20
p1/pt49, lam=20, (v,w,lam,mu,E,P=175.49&13.28&0.34&0.9244&9.6781&14.4264)
...
values for table
valf('FSS','pt13'); valf('FSS','pt17');
FSS/pt13, lam=28, (v,w,lam,mu,E,P=376.31&9.25&0.58&1.0946&12.6471&25.8521)
FSS/pt17, lam=26, (v,w,lam,mu,E,P=335.36&9.30&0.59&1.0419&10.7558&22.4486)