Monte Carlo Modeling
Many particle tracing physics features define expressions that include random numbers. In the Particle Tracing for Fluid Flow interface, the Drag Force and Brownian Force physics features are forces that potentially include components which are random in nature. In addition, some settings for particle-wall interaction and emission of secondary particles depend on random numbers. When these features are included in a model, it can be necessary to solve the problem multiple times and take a statistical average of the results. The seeding of random numbers is controlled by the Arguments for random number generation list in the physics interface Advanced Settings section. The following options are available:
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Generate unique arguments: seed random numbers based on the position of each physics feature in the model tree. This ensures that random numbers generated for different physics features are independent of each other. Use this option to make the results of a study reproducible when running the study multiple times in succession. The random numbers may still differ when running the same study on different architectures or in different versions of the software.
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Generate random arguments: seed random numbers using randomly generated double-precision numbers.
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User defined: When this option is selected, additional text fields appear in the settings windows for all features that use random numbers. The number entered in this text field is used as an additional argument for random number generation. A set of distinct solutions can be obtained by running a Parametric Sweep over several values of this additional argument.
For more information about the available options, see Particle Release and Propagation in The Mathematical Particle Tracing Interface.
In the Brownian Motion tutorial, several different values of the User defined random number seed are used. The results show similar global quantities such as transmission probability, but the paths of individual particles are uncorrelated for each value of the random number seed.
Brownian Motion: Application Library path Particle_Tracing_Module/Tutorials/brownian_motion
All three particle tracing interfaces include a Velocity Reinitialization feature. This allows for general purpose Monte Carlo modeling because the velocity vector can be discretely changed at each time step according to some logical expression. The Charged Particle Tracing interface also includes dedicated features for stochastic modeling of particle collisions with a rarefied background gas.
The Collisions node supports a variety of subnodes, such as Elastic collisions and Ionization reactions, which can be used to model the interactions that can occur when particles collide with atoms or molecules in a rarefied background gas. If a collision should occur, the charged particle has its velocity vector reinitialized by sampling the velocity of the background gas particle at random from a drifting Maxwellian distribution. This provides an accurate description of a charged particle interacting with a background gas.