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Continuous Time Random Walk: Difference between revisions
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→The Master Equation
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In addition, homogeneity in space and time is assumed (i.e., ''p'' and ''ψ'' do not depend on ''x'' and ''t''). However, recently it was shown that a Master Equation can also be derived in the case that ''p'' depends on ''x'' and ''t'', while ''ψ'' depends on ''x'' (but not ''t''). | In addition, homogeneity in space and time is assumed (i.e., ''p'' and ''ψ'' do not depend on ''x'' and ''t''). However, recently it was shown that a Master Equation can also be derived in the case that ''p'' depends on ''x'' and ''t'', while ''ψ'' depends on ''x'' (but not ''t''). | ||
<ref>[http://link.aip.org/link/?PHPAEN/11/2272/1 B.Ph. van Milligen, R. Sánchez, and B.A. Carreras, ''Probabilistic finite-size transport models for fusion: anomalous transport and scaling laws'', Phys. Plasmas '''11''', 5 (2004) 2272]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/11/2272/1 B.Ph. van Milligen, R. Sánchez, and B.A. Carreras, ''Probabilistic finite-size transport models for fusion: anomalous transport and scaling laws'', Phys. Plasmas '''11''', 5 (2004) 2272]</ref> | ||
This significant extension of the standard CTRW model has led to the development of a model with very interesting properties from the point of view of plasma transport (see the cited reference). | This significant extension of the standard CTRW model has led to the development of a model with very interesting properties from the point of view of plasma transport (see the cited reference and <ref>[http://link.aip.org/link/?PHPAEN/11/3787/1 B.Ph. van Milligen, B.A. Carreras, and R. Sánchez, Phys. Plasmas '''11''', 3787 (2004)]</ref>). | ||
The Master Equation can be written in the form | The Master Equation can be written in the form | ||