A simple network consisting of two species and four reactions. Details can be found in [Vigelius2010]. The source code is available in ABReaction.xml. A standard analysis can be done by:
$python -m gpgmp.test.abreaction <output-file>
The same reaction network as in Simple Reaction Network is modelled with individual species. The source code is available in ABReactionIndividual.xml. A standard analysis can be done by:
$python -m gpgmp.test.abreaction <output-file> individual
The same reaction network as in Simple Reaction Network is modelled with individual species, where all newly created individuals are initialized with a random diffusivity and drift. The source code is available in ABReactionIndividualNew.xml. A standard analysis can be done by:
$python -m gpgmp.test.abreaction <output-file> individual
In addition, you can use any HDF5 viewer to check, if the individual properties were set correctly, i.e. uniformly-random distributed.
The famous Fisher problem, a non-linear reaction-diffusion problem [Vigelius2010]. The source code is in FisherProblem.xml and standard analysis can be done by:
$python -m gpgmp.test.fisher_problem <output-file>
The same as Fisher Problem except that the species are individuals. The source code is in FisherProblemIndividual.xml and standard analysis can be done by:
$python -m gpgmp.test.fisher_problem <output-file> individual
A simple example to test the homogeneous solver involving one diffusing species (no drift) and no reactions [Vigelius2012a]. The source code is in HomogeneousDiffusion.xml and standard analysis can be done by:
$python -m gpgmp.test.homogeneous_diffusion <output-file>
The same example as Homogeneous Diffusion with a drift field [Vigelius2012a]. The source code is in HomogeneousDrift.xml and standard analysis can be done by:
$python -m gpgmp.test.homogeneous_drift_diffusion <output-file>
Exactly the same as Homogeneous Diffusivity and Drift only that the diffusivity and drift field is now set using a field parameter. The source code is in HomogeneousDriftField.xml and standard analysis can be done by:
$python -m gpgmp.test.homogeneous_drift_diffusion <output-file>
Exactly the same as Homogeneous Diffusivity and Drift only that the diffusing species are individuals. The source code is in HomogeneousDriftIndividual.xml and standard analysis can be done by:
$python -m gpgmp.test.homogeneous_drift_diffusion <output-file>
An example to test the inhomogeneous solver. It contains one species and position-dependent diffusivity and drift [Vigelius2012a]. The source code is in MultiplicativeNoise.xml and standard analysis can be done by:
$python -m gpgmp.test.multiplicative_noise <output-file>
A test problem involving a non-linear drift field [Vigelius2012a]. The source code is in Nonlinear.xml and standard analysis can be done by:
$python -m gpgmp.test.nonlinear <output-file>
An implementation of an Ornstein-Uhlenbeck process [Vigelius2012a]. The source code is in OrnsteinUhlenbeck.xml and standard analysis can be done by:
$python -m gpgmp.test.ornstein_uhlenbeck <output-file>
This is a simple system with two species \(A\) and \(B\) and a corresponding reaction \(A+B\xrightarrow{k_1}\emptyset\). Details can be found in [Vigelius2010]. You can analyze it using:
$python -m gpgmp.test.annihilation_2d <output-file>
This example is the same as example A+B Annihilation except that a constant drift field is present. The source code is found in ABAnnihilationDrift.xml. Analysis can be done using:
$python -m gpgmp.test.annihilation_2d_drift <output-file>
In this example, a number of individuals is initialized with random diffusivity and drift, where each individual has a different diffusivity and drift. The source code is found in RandomDrift.xml. Analysis can be done using:
$python -m gpgmp.test.random_drift <output-file>
This example implements an actual biological model used to describe the intracellular distribution of Calcium ions (cf. [Vigelius2012b] for details). The model is found in Calcium.xml and can be analysed using:
$python -m python -m gpgmp.models.calcium <output-file>
This is the Oregonator model of the Belousov-Zhabotinsky reaction which is covered in the tutorial. The model is found in Oregonator.xml. Analysis is covered in the tutorial.
The model of migrating neurons in the brain which is also covered in the tutorial. The model is found in Slit.xml. Analysis is covered in the tutorial.
[Vigelius2010] | (1, 2, 3) Vigelius M, Lane A, Meyer B (2010): Accelerating reaction–diffusion simulations with general-purpose graphics processing units Bioinformatics (2011) 27 (2): 288-290. |
[Vigelius2012a] | (1, 2, 3, 4, 5) Vigelius M, Meyer B (2012a) Multi-Dimensional, Mesoscopic Monte Carlo Simulations of Inhomogeneous Reaction-Drift-Diffusion Systems on Graphics-Processing Units. PLoS ONE 7(4): e33384. doi:10.1371/journal.pone.0033384 |
[Vigelius2012b] | Vigelius M, Meyer B (2012b): Stochastic Simulations of Pattern Formation in Excitable Media. PLoS ONE 7(8): e42508. doi:10.1371/journal.pone.0042508 |