Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
-
Karl K. Sabelfeld
and
Anastasiya Kireeva
Abstract
Exact representations for the probability density of the life time and survival probability for a sphere and a disc are derived for a general drift-diffusion-reaction process. Based on these new formulas, we suggest an extremely efficient stochastic simulation algorithm for solving transient cathodoluminescence (CL) problems without any mesh in space and time. The method can be applied to a broad class of drift-diffusion-reaction problems where the time behavior of the absorbed material is of interest. The important advantage of the method suggested is the ability to incorporate local inclusions like dislocations, point defects and other singular folds and complicated structures. General Robin boundary conditions on the boundary are treated in a probabilistic way. The method is tested against exact solutions for a series of examples with bounded and unbounded domains. An application to the dislocation imaging problem, which includes thousand threading dislocations, is given.
Funding source: Russian Science Foundation
Award Identifier / Grant number: N 14-11-00083
Funding statement: Support of the Russian Science Foundation under Grant N 14-11-00083 is kindly acknowledged.
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Articles in the same Issue
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
Articles in the same Issue
- Frontmatter
- Probability distribution of the life time of a drift-diffusion-reaction process inside a sphere with applications to transient cathodoluminescence imaging
- A quasi-Monte Carlo implementation of the ziggurat method
- On the efficient simulation of the left-tail of the sum of correlated log-normal variates
- Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes
- On the modeling of linear system input stochastic processes with given accuracy and reliability
- Remarks on randomization of quasi-random numbers
- On average dimensions of particle transport estimators
