!---------------------------------------------------------------------- 
!---------------------------------------------------------------------- 
!  Muensteranian Torturials on Nonlinear Science
!  edited by Uwe Thiele, Oliver Kamps, Svetlana Gurevich
!  (Center for Nonlinear Science, Universitaet Muenster)
!----------------------------------------------------------------------
!  Section: Continuation with auto07p
!  Tutorial: LINDROP: linear stability of steady states on a horizontal
!  homogeneous substrate
!  by Uwe Thiele (www.uwethiele.de), supported by Christian Schelte,
!  Frank Ehebrecht, Thomas Seidel, Simon Hartmann
!  Version 3, Jan 2022
!  for complete set of files and up to date version see
!  http://dx.doi.org/10.5281/zenodo.4546375
!----------------------------------------------------------------------
!  Files: README_lindrop - Further details and screen output for runs 
!  with auto07p of lindrop.f90 producing steady solutions of a thin film
!  equation for a horizontal homogeneous substrate
!----------------------------------------------------------------------
!----------------------------------------------------------------------

General
-------
Here the shell command line commands and screen output are given.
See accompanying LINDROP.pdf for alternative Python interface commands and 
detailed description of the tutorial

Commands and screen ouput
-------------------------

run 1
-----
Start at critical wavelength, increase domain size (PAR5), let C1 (PAR6) and EPS (PAR2) adapt
@cl
@@R lindrop 1
@sv ld1
  BR    PT  TY  LAB    PAR(5)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      MAX U(4)      PAR(6)        PAR(2)     
   1     1  EP    1   3.39292E+01   7.07107E-05   1.00000E-04   6.28319E-04   0.00000E+00   0.00000E+00   3.56653E-02   0.00000E+00
   1   207  UZ    2   2.50000E+01   9.96462E-01   1.23885E+00   3.75931E-01   0.00000E+00   0.00000E+00   6.91994E-02   1.16155E-13
   1   211  LP    3   2.45544E+01   1.08930E+00   1.35237E+00   4.22313E-01   0.00000E+00   0.00000E+00   7.51897E-02  -1.76021E-13
   1   218  UZ    4   2.50000E+01   1.17054E+00   1.46184E+00   4.49354E-01   0.00000E+00   0.00000E+00   7.74092E-02  -1.31590E-13
   1   437  UZ    5   5.00000E+01   2.00795E+00   3.12929E+00   5.26743E-01   0.00000E+00   0.00000E+00   5.59959E-02   5.96850E-11
   1   583  UZ    6   7.50000E+01   2.45169E+00   4.36855E+00   5.57692E-01   0.00000E+00   0.00000E+00   4.57191E-02   1.15024E-10
   1   680  UZ    7   1.00000E+02   2.77015E+00   5.40700E+00   5.77203E-01   0.00000E+00   0.00000E+00   3.95806E-02   2.28824E-10

run 11
------
start at drop with L=50 (LAB5 of ld1), change BETA (PAR7) and let C1 (PAR6) and EPS (PAR2) adapt
-> detect EV as BR
@@R lindrop 11 ld1
@sv ld11
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      MAX U(4)      PAR(6)        PAR(2)     
   1    11  UZ    8   1.00000E-03   2.00795E+00   3.12949E+00   5.26744E-01   0.00000E+00   0.00000E+00   5.59959E-02   2.52245E-11
   1    17  BP    9   1.56379E-03   2.00795E+00   3.12940E+00   5.26738E-01   0.00000E+00   0.00000E+00   5.59959E-02   3.07861E-11
   1   102  UZ   10   1.00000E-02   2.00795E+00   3.12973E+00   5.26724E-01   0.00000E+00   0.00000E+00   5.59959E-02   2.58445E-11
   1  1000       11   9.98000E-02   2.00795E+00   3.12980E+00   5.26719E-01   0.00000E+00   0.00000E+00   5.59959E-02   1.81018E-11
   1  1002  UZ   12   1.00000E-01   2.00795E+00   3.12980E+00   5.26719E-01   0.00000E+00   0.00000E+00   5.59959E-02   1.81928E-11
   1  2000       13   1.99800E-01   2.00795E+00   3.12970E+00   5.26725E-01   0.00000E+00   0.00000E+00   5.59959E-02   1.31000E-11
   1  2500  EP   14   2.49800E-01   2.00795E+00   3.12954E+00   5.26734E-01   0.00000E+00   0.00000E+00   5.59959E-02   1.85740E-11

run 111
------
start at BP (LAB9 of ld11), switch branches (ISW=-1) change BETA (PAR7) and let C1 (PAR6), EPS (PAR2) and norm (PAR9) adapt
-> 'blow up' eigenfunction, stop at defined norm (PAR9)
@@R lindrop 111 ld11
@sv ld111
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      PAR(6)        PAR(2)        PAR(9)     
   2   160  UZ   15   1.56379E-03   2.00795E+00   3.13019E+00   5.26721E-01   1.49236E+00   5.59959E-02   1.64027E-10   1.00000E+00

run 1111
------
start at LAB15 of ld111, change QQ (PAR8) and let C1 (PAR6), BETA (PAR7) and EPS (PAR2) adapt
norm of eigenfunction fixed (PAR9), using QQ as principal continuation parameter we get the maximum of dispersion relation 
as fold; we also detect zero crossing
@@R lindrop 1111 ld111
@sv ld1111
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      PAR(8)        PAR(6)        PAR(2)     
   2   152  LP   16   1.83987E-03   2.00795E+00   3.13021E+00   5.26723E-01   1.48758E+00   6.45701E-02   5.59959E-02   1.64011E-10
   2   472  UZ   17   2.58240E-10   2.00795E+00   3.13011E+00   5.26710E-01   1.49873E+00   9.37718E-02   5.59959E-02   1.65741E-10
   2   559  UZ   18  -1.01354E-03   2.00795E+00   3.13022E+00   5.26725E-01   1.50589E+00   1.00000E-01   5.59959E-02   1.60095E-10

run 1111b
------
other direction
@@R lindrop 1111b ld111
@sv ld1111b
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      PAR(8)        PAR(6)        PAR(2)     
   2   109  LP   16   2.88299E-09   2.00795E+00   3.13026E+00   5.26730E-01   1.51371E+00  -5.55044E-05   5.59959E-02   1.67657E-10
   2   245  LP   17   1.83987E-03   2.00795E+00   3.13022E+00   5.26724E-01   1.48758E+00  -6.45690E-02   5.59959E-02   1.64165E-10
   2   309  UZ   18  -3.82611E-07   2.00795E+00   3.13018E+00   5.26720E-01   1.49875E+00  -9.37745E-02   5.59959E-02   1.61343E-10
   2   327  UZ   19  -1.01358E-03   2.00795E+00   3.13022E+00   5.26724E-01   1.50589E+00  -1.00000E-01   5.59959E-02   1.60018E-10

run 11111
---------
follow maximum as fold continuation (ISW=2), start-up run
start at LAB16 of ld1111, continue in QQ (PAR8) and let C1 (PAR6), BETA (PAR7) and EPS (PAR2) adapt,
add additional continuation parameter domain size PER (PAR5)
norm of eigenfunction fixed (PAR9), this follows the maximum of dispersion relation as fold and 
therefore gives maximal growth rate and transversal wavenumber with increasing domain (ie ridge cross section)
@@R lindrop 11111 ld1111
@sv ld11111
 Generating starting data : Restart at EP label below :
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      PAR(8)        PAR(6)        PAR(2)        PAR(5)     
   3     5  EP   19   1.83987E-03   2.00795E+00   3.13026E+00   5.26745E-01   6.45701E-02   5.59959E-02   1.77967E-10   5.00000E+01

run 111111
----------
follow maximum as fold continuation (ISW=2), continuation run starting at LAB19 of ld11111
description as run11111
@@R lindrop 111111 ld11111
@sv ld111111
mdat07fold maxdisp_L_h3
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      PAR(8)        PAR(6)        PAR(2)        PAR(5)     
   3   500       20   1.08553E-03   2.74804E+00   5.33143E+00   5.75937E-01   4.49444E-02   3.99752E-02   2.17936E-12   9.80410E+01
   3   518  UZ   21   1.06943E-03   2.77015E+00   5.40779E+00   5.77222E-01   4.44713E-02   3.95806E-02   2.09245E-12   1.00000E+02
   3  1000       22   5.98551E-04   3.71278E+00   9.22230E+00   6.22736E-01   2.90288E-02   2.64435E-02   4.59320E-11   2.23407E+02
   3  1104  UZ   23   5.54014E-04   3.85350E+00   9.88539E+00   6.28194E-01   2.73605E-02   2.49923E-02   6.36886E-11   2.50000E+02
   3  1500       24   4.03159E-04   4.47959E+00   1.31426E+01   6.49121E-01   2.13267E-02   1.96873E-02   4.38652E-10   4.02220E+02
   3  1755  UZ   25   3.50131E-04   4.78497E+00   1.49098E+01   6.57657E-01   1.90394E-02   1.76517E-02   6.55620E-10   5.00000E+02
   3  2000       26   2.98880E-04   5.15057E+00   1.71704E+01   6.66701E-01   1.67291E-02   1.55810E-02   1.00050E-09   6.41273E+02
   3  2500       27   2.37276E-04   5.73194E+00   2.11268E+01   6.78899E-01   1.38021E-02   1.29351E-02   2.87931E-09   9.29590E+02
   3  2623  UZ   28   2.26901E-04   5.85171E+00   2.19928E+01   6.81128E-01   1.32910E-02   1.24704E-02   2.87614E-09   1.00000E+03

run 111111b
----------
follow maximum as fold continuation (ISW=2), continuation run starting at LAB19 of ld11111
description as run11111 - BACKWARDS
@@R lindrop 111111b ld11111
@sv ld111111b
mdat07fold maxdisp_L_h3_b
  BR    PT  TY  LAB    PAR(7)      L2-NORM U(1)    MAX U(1)      MAX U(2)      PAR(8)        PAR(6)        PAR(2)        PAR(5)     
   3   500       20   1.99310E-02   4.58119E-01   6.06934E-01   1.29659E-01   1.53161E-01   4.06766E-02  -1.32264E-12   3.17739E+01
   3  1000       21   1.10740E-03   2.71865E+00   5.23095E+00   5.74217E-01   4.55824E-02   4.05068E-02   3.99874E-12   9.54919E+01
   3  1028  UZ   22   1.06943E-03   2.77015E+00   5.40768E+00   5.77215E-01   4.44713E-02   3.95806E-02   2.35018E-12   1.00000E+02
   3  1500       23   6.15090E-04   3.66415E+00   8.99853E+00   6.20786E-01   2.96369E-02   2.69708E-02   3.98328E-11   2.14789E+02
   3  1645  UZ   24   5.54014E-04   3.85350E+00   9.88655E+00   6.28194E-01   2.73605E-02   2.49923E-02   6.85166E-11   2.50000E+02
   3  2000       25   4.18806E-04   4.40023E+00   1.27042E+01   6.46737E-01   2.19835E-02   2.02692E-02   2.20674E-10   3.79529E+02
   3  2331  UZ   26   3.50131E-04   4.78497E+00   1.49087E+01   6.57651E-01   1.90394E-02   1.76517E-02   5.57073E-10   5.00000E+02
   3  2500       27   3.14197E-04   5.03237E+00   1.64255E+01   6.63905E-01   1.74307E-02   1.62114E-02   7.56315E-10   5.92501E+02
   3  3000       28   2.47818E-04   5.61779E+00   2.03103E+01   6.76688E-01   1.43158E-02   1.34014E-02   2.57299E-09   8.66176E+02
   3  3245  UZ   29   2.26901E-04   5.85171E+00   2.19899E+01   6.81125E-01   1.32910E-02   1.24704E-02   3.24648E-09   1.00000E+03

run 11112
---------
follow zero crossing where BETA=0, start at LAB17 of ld1111, continue in QQ (PAR8) and let C1 (PAR6), EPS (PAR2) and
parameter domain size PER (PAR5) adapt; fix BETA=0 (PAR7) and norm of eigenfunction (PAR9)
@@R lindrop 11112 ld1111
@sv ld11112
mdat07 zerodisp_L_h3
  BR    PT  TY  LAB    PAR(8)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      PAR(6)        PAR(2)        PAR(5)     
   2   500       19   6.64343E-02   2.72093E+00   5.23892E+00   5.74348E-01   1.83537E+00   4.04652E-02   1.26723E-12   9.56874E+01
   2   538  UZ   20   6.49060E-02   2.77015E+00   5.40714E+00   5.77216E-01   1.86031E+00   3.95806E-02   1.48570E-12   1.00000E+02
   2  1000       21   4.78231E-02   3.44205E+00   8.01349E+00   6.11354E-01   2.21690E+00   2.95619E-02   2.06535E-11   1.78907E+02
   2  1417  UZ   22   4.01725E-02   3.85350E+00   9.88607E+00   6.28194E-01   2.44691E+00   2.49923E-02   7.33079E-11   2.50000E+02
   2  1500       23   3.77532E-02   4.00612E+00   1.06360E+01   6.33771E-01   2.53398E+00   2.35359E-02   9.61576E-11   2.81775E+02
   2  2000       24   2.88576E-02   4.70876E+00   1.44573E+01   6.55614E-01   2.94411E+00   1.81313E-02   3.07081E-10   4.73976E+02
   2  2068  UZ   25   2.80746E-02   4.78497E+00   1.49102E+01   6.57656E-01   2.98938E+00   1.76517E-02   3.57722E-10   5.00000E+02
   2  2500       26   2.28145E-02   5.38846E+00   1.87366E+01   6.71983E-01   3.35192E+00   1.44131E-02   1.13628E-09   7.49103E+02
   2  2936  UZ   27   1.96823E-02   5.85171E+00   2.19904E+01   6.81124E-01   3.63431E+00   1.24704E-02   2.93401E-09   1.00000E+03

run 11112b
---------
same as run 11112, but opposite direction
@@R lindrop 11112b ld1111
@sv ld11112b
mdat07 zerodisp_L_h3_b
  BR    PT  TY  LAB    PAR(8)      L2-NORM U(1)    MAX U(1)      MAX U(2)      MAX U(3)      PAR(6)        PAR(2)        PAR(5)     
   2   500       19   2.37586E-01   4.68453E-01   6.19749E-01   1.33068E-01   1.70854E+00   4.09311E-02  -1.02822E-12   3.16760E+01
   2  1000       20   8.47336E-02   2.21612E+00   3.68047E+00   5.41793E-01   1.59164E+00   5.09202E-02  -1.08171E-12   6.04733E+01
   2  1412  UZ   21   6.49060E-02   2.77015E+00   5.40680E+00   5.77220E-01   1.86031E+00   3.95806E-02   9.72454E-13   1.00000E+02
   2  1500       22   6.00092E-02   2.93782E+00   6.00425E+00   5.86600E-01   1.94662E+00   3.67337E-02   2.57182E-12   1.16048E+02
   2  2000       23   4.42909E-02   3.62024E+00   8.79934E+00   6.18990E-01   2.31562E+00   2.74589E-02   3.89869E-11   2.07248E+02
   2  2235  UZ   24   4.01725E-02   3.85350E+00   9.88704E+00   6.28190E-01   2.44692E+00   2.49923E-02   7.59374E-11   2.50000E+02
   2  2500       25   3.52020E-02   4.18222E+00   1.15359E+01   6.39806E-01   2.63541E+00   2.19939E-02   1.31972E-10   3.22517E+02
   2  3000  EP   26   2.93272E-02   4.66444E+00   1.41983E+01   6.54397E-01   2.91786E+00   1.84186E-02   3.51363E-10   4.59348E+02
