Several example problems are included with VBM which use a variety of visualization and computation modules.
This example is a seven dimensional ODE BVP. It models a naturally twisted strut to which a force is being applied at the end. After discretization we will have a system with approximately 600 equations and two more unknowns than equations. This is the same problem that is used in the tutorial part of this manual.
The command to run this demo (assuming you are in the VBM directory) is:
cd demos/planar_strut;../../bin/VBM.py -f strut.vbm
This file demos the VBM_1D_AUTO compute engine. Since it is the basis of the tutorial in Section it is a good place to start looking at VBM files.
This example, taken from the work of Maddocks in Bibliography, is a problem with six equations and eight unknowns. The system models the equilibrium configurations of a heavy rigid body.
The command to run this demo (assuming you are in the VBM directory) is:
bin/VBM.py -f continuation_data/MC2_2par/mc2.data
This file demos the VBM_1D_AUTO and VBM_2D_Rheinboldt compute engines. Note, you must have Matlab installed on your computer to use the VBM_2D_Rheinboldt module. An appropriate data probe is the "Numeric data at one point" module.
This demo is taken directly from the demo problems in AUTO94 (for more detail see Bibliography). It is a two dimensional ODE BVP. We provide it as an example of the changes that are necessary to take a problem originally for AUTO94 and use it in VBM.
The command to run this demo (assuming you are in the VBM directory) is:
bin/VBM.py -f continuation_data/bvp/bvp.vbm
This file demos the VBM_1D_AUTO_FORT8, VBM_1D_AUTO, and VBM_1D_remote_AUTO compute engines. Note, the file must be modified to have the first line of the VBM_1D_remote_AUTO block be the address of a machine running a VBM compute server. Appropriate data probes are "AUTO solution recontruction (Fort 8)" and "AUTO solution recontruction (IVP)".
This example is a fourteen dimensional Hamiltonian ODE BVP which has been used to model the equilibrium configurations of small DNA mini-circles. In this example VBM (or its predecessors) was used as part of the original research, and results have been published in Bibliography, Bibliography, Bibliography, and Bibliography.
After discretization we will have a system with approximately 1200 equations and six more unknowns then equations. We will not explicitly compute any six dimensional manifolds, but we can compute various one dimensional sub-bifurcation diagrams.
The command to run this demo (assuming you are in the VBM directory) is:
bin/VBM.py -f continuation_data/dna_1par/dna.data
This file demos VBM_1D_AUTO and VBM_1D_remote_AUTO compute engines. Note, the file must be modified to have the first line of the VBM_1D_remote_AUTO block be the address of a machine running a VBM compute server. Also, this demo can use VBM's ability to transmit binary problem files. There is a Makefile in VBM/continuation_data/dna_1par which may be used to compile a parallel version of AUTO94 on SunOS machines with the Sun Workshop Pro compilers. This Makefile can be used as an example for the compilation on your specific machine. An appropriate data probe is the "General rod problems (multiple ribbons)" module.
The demo directory from the VBM distribution contains several
demos concerning the circular elastic rod problem. They are set to be
used with the "General rod problems (multiple ribbons)" dataprobe. For
all of these problems, you have to compile the IVP problem.
All these demos use problems defined in the dna_problems
directory. They can be classified in the following categories:
Perfect problem
This category contains the perfect_with_energy_demo. It uses the
perfect_old problem, and only the natural ribbon can be defined
for it. For this demo, you must choose the preprocess option on when
compiling the IVP problem.
Formula uhats problems
This category contains the perfect_with_energy_demo. It uses
the formula_uhats problem, and only the natural ribbon can be
defined for it.
Uhats Problems
The demos under this category represent elastic rods with non zero
starting energy. They all use files in the rob_problem directory,
and both the natural and the real ribbon can be defined for them. Here
is the list of these demos: