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--- examples:reaction-diffusion [15:37 26.07.2013] – [XML model] Walter
+++ examples:reaction-diffusion [16:17 18.08.2021] (current) – Moved to GitLab Pages Diego Jahn
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-~~NOTOC~~
-===== Reaction-diffusion models =====
-==== 1D reaction-diffusion: Activator-Inhibitor ====
-[{{ :examples:1D-PDE.png?direct&225|Space-time plot of 1D reaction diffusion model.}}]
-{{vimeo>70815567?small}}
-=== Introduction ===
-The first example models a 1D activator-inhibitor model ([[http://www.eb.tuebingen.mpg.de/fileadmin/uploads/pdf/Emeriti/Hans_Meinhardt/kyb.pdf|Meinhardt and Gierer, 1972]]).
-=== Model description ===
-This 1D PDE model uses a ''Lattice'' with ''linear'' structure and periodic boundary conditions.
-The ''PDE'' defined two species called ''Layers'': A (activator) and I (inhibitor) with resp. low and high ''Diffusion'' rates. The reaction part of the equations are defined in the ''System''. Similar to ODE model, the ''System'' defines ''Constants'' and ''DiffEqn''s.
-The results are recorded and visualized using the ''Logger'' and ''SpaceTimeLogger''.
-=== Full model ===
-<code xml |h ActivatorInhibitor_1D.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/PDE/ActivatorInhibitor_1D.xml
-</code>
-\\
-In Morpheus GUI: ''File -> Examples -> PDE -> ActivatorInhibitor_1D.xml''
-----
-==== 2D reaction-diffusion: Activator-Inhibitor ====
-[{{ :examples:activator_inhibitor.png?direct&200|Stripe pattern generated by 2D Gierer-Meinhardt model}}]
-{{vimeo>47171577?small}}
-=== Introduction ===
-A 2D activator-inhibitor model ([[http://www.eb.tuebingen.mpg.de/fileadmin/uploads/pdf/Emeriti/Hans_Meinhardt/kyb.pdf|Meinhardt and Gierer, 1972]]).
-=== Description ===
-This model uses a standard ''Lattice'' with ''square'' structure and periodic boundary conditions.
-The ''PDE'' defined two species or ''Layers'' A (activator) and I (inhibitor) with resp. low and high ''Diffusion'' rates. The reaction part of the equations are defined in the ''System''.
-The results are visualized using the ''Gnuplotter''.
-=== Full model ===
-<code xml |h ActivatorInhibitor_2D.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/PDE/ActivatorInhibitor_2D.xml
-</code>
-\\
-In Morpheus GUI: ''File -> Examples -> PDE -> ActivatorInhibitor_2D.xml''
-=== Things to try ===
-  * Alter the level of saturation of the activator by changing ''kappa'' (for example, using a ''ParamSweep''). By changing this parameter, the model can generate stripes, nets and spots.
-----
-=== Domains: Reaction-diffusion in irregular domains ===
-[{{ :examples:example-domains.png?direct&200|Spot pattern in Gierer-Meinhardt model with irregular domain}}]
-{{vimeo>70395104?small}}
-=== Introduction ===
-A 2D activator-inhibitor model ([[http://www.eb.tuebingen.mpg.de/fileadmin/uploads/pdf/Emeriti/Hans_Meinhardt/kyb.pdf|Meinhardt and Gierer, 1972]]), solved in a irregular domain that is load from file.
-=== Model description ===
-This model uses an irregular ''Domain'' with ''constant'' boundary conditions. The domain is loaded from a TIFF image. See ''Space/Lattice/Domain''.
-=== XML model ===
-<code xml |h ActivatorInhibitor_Domain.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/PDE/ActivatorInhibitor_Domain.xml
-</code>
-\\
-//Note: This model requires the external file [[{{:examples:domain.tif|domain.tif]].//
-\\
-In Morpheus GUI: ''File -> Examples -> PDE -> ActivatorInhibitor_Domain.xml''
-----
-==== Spatial parameter sweep: Turing patterns ====
-[{{ :example-TuringMiyazawa.png?direct&175|Spots and stripes appear under various conditions in linear Turing model}}]
-{{vimeo>47171578?small}}
-=== Introduction ===
-This model shows the pattern formation abilities of Turing's linear activator-inhibitor model ([[http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2982180/|Miyazawa et al., 2010]]). It shows how to vary parameters as a function of space.
-=== Model description ===
-Instead of fixed parameters defined as ''Constant''s, this model uses ''Function''s for two parameters. The parameters C (activator production) and A (rate of auto-activation) as defined as ''Function'' of space and varied over the X- and Y-axes respectively. This requires the definition of a ''SpaceSymbol'' that can be used in expressions.
-The results show the appearance of white spots (left), black spots (right) and labyrinthine patterns (middle).
-=== XML model ===
-<code xml |h TuringPatterns.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/PDE/TuringPatterns.xml
-</code>
-\\
-In Morpheus GUI: ''File -> Examples -> PDE -> TuringPatterns.xml''
-----
-==== 3D reaction-diffusion: Excitable Media ====
-[{{ :example-barkley_3D.png?direct&200|Scroll wave appear in Barkley model of excitable media in 3D}}]
-{{vimeo>47172325? small}}
-=== Introduction ===
-This example uses the [[http://www.scholarpedia.org/article/Barkley_model|Barkley model of excitable media]], similar to the [[http://en.wikipedia.org/wiki/FitzHugh%E2%80%93Nagumo_model|Fitzhugh-Nagumo model]] to show how to model and visualize reaction-diffusion models in 3D.
-=== Model description ===
-This model defines a 3D ''cubic Lattice'' with ''noflux BoundaryConditions''. Two ''Layers'' are defined for the two species: 'u' is the signal, and 'v' the refractoriness. As in the examples above, the ''DiffEqn'' as specified in the ''System'' in ''PDE''. Nothing strange here.
-To visualize the resulting scrolling waves in 3D, the ''TiffPlotter'' is used. This ''Analysis'' plugin writes TIFF image stacks that cam be opened by image analysis software such as [[http://fiji.sc|Fiji/ImageJ]]. To import Morpheus TIFF images into Fiji, macros scripts are available that help you to create 3D (xyz), 4D (xyzt) or even 5D (xyzct) images and movies of your simulations.
-Although unable to plot 3D, the ''GnuPlotter'' can still be helpful to plot a 2D slice. See ''Analysis/Gnuplotter/PDE/slice''.
-=== XML model ===
-<code xml |h ExcitableMedium_3D.xml |h>
-extern>http://imc.zih.tu-dresden.de/morpheus/examples/PDE/ExcitableMedium_3D.xml
-</code>
-\\
-In Morpheus GUI: ''File -> Examples -> PDE -> ExcitableMedium_3D.xml''
-=== Things to try ===
-  * Import resulting sequence of TIFF images in ImageJ or Fiji, and create 4D movie using ImageJ's 3D plugin:
-    - Open ''u_v.tif'' in ImageJ: ''File -> Open''.
-    - Create hyperstack: ''Image -> Hyperstack -> Convert to Hyperstack''. Channels ( c ): 2, Slices (z): 50, Frames (t): 51, Display Mode: Composite.
-    - Display in 4D: ''Plugins -> 3D Viewer''. Use default parameters. Press OK.
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