 Email:   jhomenuk at physics.ubc.ca 




Research: Finitedifference Approximations

Honours Thesis: Preliminary Results
 Simple activatorinhibitor system: This attempts to model a hypothetical biological system in development. The components begin with nearly equal and uniform distributions. The activator is given a slight defect, causing the system to react in a preferred direction, but eventually form a stable periodic structure.
 Small Field [ MPEG ]
 Large Field [ MPEG ]
 (2+1) Diffusion Equation using Multigrid [ diffusion2D.sdf ]. The above activatorinhibitor system will be extended to (2+1) dimensions.
 Putting Multigrid to the test: [ MPEG ] This animation is the convergence of an elliptic equation to its solution sin(2 pi x). The initial guess is 2 sin(2 pi x). There is a 1grid solution and a 2grid solution. Each "time step" contains 10 iterations of the GaussSeidel method. For the 2grid, 6 of those iterations are done on the coarse grid.
 (2+1) ReactionDiffusion Equation: [ D15.0a_0.sdf.1  D15.0h_0.sdf.1 ] A breakup instability in the weak interaction regime of the classical GiererMeinhardt model using homoclinic stripe initial conditions.
Solutions to Various Equations
Description  n points  2n points  4n points  8n points  16n points  Convergence Test Equality implies O(h^{2}) convergence 
Wave Equation (1+1) Cartesian Coordinates Dirichlet/Sommerfeld BCs  MPEG  MPEG  MPEG  MPEG  MPEG  MPEG 
Wave Equation (1+1) Spherical Coordinates Neumann/Sommerfeld BCs  MPEG  MPEG  MPEG  MPEG  MPEG  MPEG 
SineGordon Equation (1+1) Spherical Coordinates Neumann/Sommerfeld BCs  MPEG  MPEG  MPEG  MPEG  MPEG  MPEG 
KdV Equation (1+1)
 Cartesian coords: One Soliton [MPEG], Two Solitons [MPEG], convergence test [MPEG].
KleinGordon Equation with DoubleWell Potential (1+1)
 Based on Ethan Honda's PhD dissertation [PSPDF].
 Final Report [PSPDF]
Reference Material
 RNPL Reference Manual [HTMLPS]
 RNPL User's Guide [HTMLPS]
 Robert Marsa's PhD dissertation, chapters 8 and 9 [PS]
 My essay [PDF] for RELG 100