Nature
of Mathematical modelling MAS 864 
final projectpage  
Axel Kilian  
week one  bouncing ball  
Bouncing
ball in java 

bouncing
ball as postscript The balls path is drawn as a postscript path and saved as an eps file. The starting position and speeds can be 

chapter 6  ordinary differential equations  
runge kutta applet  varying stepsize  
applet source code  
chapter 9 cellular automata and lattice gas  
HPP  square lattice cellular automata  FHP  hexagon lattice grid cellular automata  earlier sketches of unfinished hex grid CA 
without random seeding  without random seeding  box1 box starting condition only 
with random seeding of surrounding area  with random seeding of surrounding area  box2 box + random 
source code  source code  box3 mouse seeding 
box4  hexagonal grid distorted into aligned shape and centered starting box  mouse seeding fluid.java  
Random  
10 random trajectory using LSFR random number generator with order 32 (takes about 20 sec to generate the 10000 points  sorry very slow implementation of LSFR)  
function fitting  
results as text file  error in a
and b depending on sig^2 n,i/sig^2gr = sum j (V^2 i,j/w^2 j) 

x = ran1(&idum)  
y = 2+3x+gaussrand  2.179988
+ 0.101654 2.650558 + 0.174769 Chisquared 99.425986 

gaussrand = gasdev(&idum)*SPREAD  
(b) 100 independent data sets  
(c) bootstrapping  
inverse wavelet transform  
the applet calculating the inverse wavelet transform of vector 2^12 with 1 at 5 and 30 (memory intensive  might run out of memory)  The source code in java  
all 12 steps static drawn into same graph  
animated applet  showing the 12 steps leading up to the result  
screenshot of vector of 2^12 length  


and screenshot with the x vector at eac of the 12 steps (on the far left is the starting condition with5 at 1and 30 at 1  
simplex search  
Applet showing the search  
source
code for simplex code of function f(x,y) = 0.2(x^2+y^2)2 *exp((x^2)+y^2))  exp((x^2+(y+4)^2))/2) 

polynomial fitting  
polynomial fitting of order 5,10 and 15 source code for polyfunc  function written in "R" used to find coefficients  fit is not correct  
order 5 coefficients [1,] 0.4153837165 [2,] 0.1341669391 [3,] 0.0036503410 [4,] 0.0009534706 [5,] 0.0001057958 order 10 coefficients [1,] 3.505278e01 [2,] 3.216823e01 [3,] 2.130687e02 [4,] 1.792592e02 [5,] 8.046099e04 [6,] 4.715427e04 [7,] 5.854754e06 [8,] 5.914938e06 [9,] 2.132643e09 [10,] 2.678003e08 order15 coefficients [1,] 2.356892e01 [2,] 4.519468e01 [3,] 1.179799e01 [4,] 5.303195e02 [5,] 1.512227e02 [6,] 3.209537e03 [7,] 8.446648e04 [8,] 1.094209e04 [9,] 2.568237e05 [10,] 1.978109e06 [11,] 4.228687e07 [12,] 1.744958e08 [13,] 3.487685e09 [14,] 5.886214e11 [15,] 1.121760e11 

Control Theory  
Inverted
pendulum 

final project  
OpenFEM site
 www.openfem.net cached version as site was down recently 

Project description  
The modeling
of form rarely takes into account structural performance of the elements
that are being modeled. The proposal is to study how optimization and
structural analysis can be used to influence form making in design process. 

Examples of formfinding through computational models  
Genetic Algorithm based approach to finding developable strips on arbitrary NURBS surfaces (final project 6.836 spring 2002)  hanging chain
model java applet 
