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--- documentation:tech_specs [11:25 02.08.2013] – [Diffusion] Walter
+++ documentation:tech_specs [22:02 02.08.2013] (current) – [Random numbers] Walter
@@ Line 101: / Line 101: @@
 where $T$ (for 'temperature') modulates the probability of unfavorable updates to be accepted and can be taken to represent local protrusions/retractions of the cell membrane. The parameter $Y$ (for 'yield') is sometimes used to avoid oscillations with energy-neutral updates. This can be said to represent cytoskeletal resistance to membrane fluctuations.
-=== Random number generators (RNG) ===
+===== Random numbers =====
-By default, Morpheus uses the [[http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne Twister 19937]] pseudo-random number generator included in the CPP GNU compiler (TR1). Alternatively, the [[http://www.boost.org/doc/libs/1_53_0/doc/html/boost_random.html|Boost RNG]] can be used (specified in CMake options).
+By default, Morpheus uses the [[http://en.wikipedia.org/wiki/Mersenne_twister|Mersenne Twister 19937]] pseudo-random number generator included in the Cpp GNU compiler (TR1). Alternatively, the [[http://www.boost.org/doc/libs/1_53_0/doc/html/boost_random.html|Boost RNG]] can be used (specified in CMake options).
 **Note**: In multithreaded simulations, each thread gets its own RNG (the random seeds for which are based on the specified seed of the master thread RNG). Therefore, to reproduce simulation results, not only the random seed needs to be specified (''Time/RandomSeed''), but also the same number of threads (''Settings -> Local-> threads'').
-===== Model integration =====
-To be documented.
-==== Symbolic references and spatial mapping ====
-In order to reference variables in mathematical terms in a multi-model environment one requires to identify the respective sub-model a variable is defined in and to perform a mapping between different (spatial) contexts, i.e. determine the corresponding CPM cell from a spatial position to access a cell property.
-This ensemble of a variable definition and contextual meta-data we call a symbol, which can be referenced all over the multi-model environment. (Also allows to iteration over the elements od a symbol context).
-In case of spatial ambiguity Morpheus provides a set of predefined ''Reporters'' to take care for the spatial mapping. For example, a ''PDEReporter'' should be defined to compute the average concentration of a diffusible within the area occupied by a particular cell.
-**Example Autocrine Chemotaxis**
-<IMAGE>
-<code xml |h AutocrineChemotaxis.xml |h>
-extern> http://imc.zih.tu-dresden.de/morpheus/examples/Multiscale/AutocrineChemotaxis.xml
-</code>
-\\
-==== Time scheduling ====
-The time scheduler takes care (i) to evolve numerical schemes in time, (ii) to schedule and execute spatial data mappings, and (iii) to run event-based schemes, i.e. schemes which are run in certain time intervals. In order to combine different schemes in a single scheduler we exploit the method of fractional time steps. The basis is for our automatic scheduling is extensive knowledge of the data dependencies of the schemes and what kind of updated data they provide. This information is represented as a symbolic dependency graph based on the expressions, input and output symbols defined within the schemes.
-We envisage the following criteria for the design of our scheduler implementation.
-  * Time stepping for all schemes shall be automatically adjusted, as far as possible, to the maximum permitted time step.
-  * In addition, time stepping can be overridden from in the MDL, allowing for user guided step sizes.
-  * The order of the specification of the schemes in the MDL shall not matter.
-  * The sequential order of updates within a temporal step shall be determined by the symbolic interdependency graph.
-  * Tightly coupled systems, often bearing circular dependencies, have to be defined in a **System** tag to be updated jointly.
-A robust automatic scheduling methods necessarily needs reliable information about the internal limits of numerical schemes and its external dependencies. External dependencies are extracted as a dependency tree. Internal time step limits are reported by the schemes and can be adoptive in time.
-Solving Reaction-Diffusion Systems, for example, using a finite difference scheme and operator splitting allows us to schedule the diffusion solver depending on the CFL condition and running the reaction part independently.
-=== Schematic Representation of the Time Scheduler ===
-== Initialisation: ==
-  - Adjusting time steps:
-    * Continuous Time Solvers: Ensure numerical stability and .
-    * Mappers: Ensuring updated data is available as needed, but not computed more often than necessary. We let the time step size depend on the time steps of the downstream dependency tree (e.g a spatial Reporter shall run as often as it's output is needed by another scheme), and on stability criteria of the numerical schemes (e.g. CFL for Diffusion).
-  - Sorting of schemes to be updated sequentially: The order is determined by the dependency tree. Circular dependencies cannot be sorted unambiguously and thus are rejected.
-  - Initialisation of initial time state (e.g. mappings)
-== Main Loop: 3 Phase Time Stepper: ==
-  - ''Phase I:'' Synchronous Time Evolution Schemes. The schemes are executed sequentially or in parallel, but the results are buffered as intermediates and only applied at the very end of that phase, such that any scheme exclusively depends on the previous time step solutions. Tightly coupled systems, defined in a **System** tag, are evolved by a system solver.
-  - Time Step Progression
-  - ''Phase II:'' Sequentially Updated Schemes (Mappers, Events),  depending on data that has already been updated.
-  - ''Phase III:'' Output generation in Analysis plug-ins. Can be performed in any order, just because there is nor interdependency.
-  - Checkpointing of simulation state.