Abstract
The acquisition of charge by aerosol particles is well-known to be stochastic in nature. We review the principles of charging using the conceptually and computationally clear language of continuous time Markov processes. A novel numeric approach is presented that can be used to calculate the time evolution of various particle charging processes. Its modular character makes it easy to implement and allows for quick adaptation to specific problems. We conclude with the application of ergodicity for finite state-space Markov processes in order to determine stationary charge distributions in case of bipolar charging.
Highlights
Allows for universal statements in aerosol charging, such as the existence and uniqueness of steady-state distributions
Let Xt be a family of random variables, parameterized by t ∈ [0, ∞) and taking values in a countable set E
Before doing so we will look at variations of the formalism to treat other situations and investigate the steady state behaviour of bipolar charging
Summary
Time continuous Markov processes are among the most studied stochastic processes and are widely used in many fields as diverse as probability theory, statistical mechanics and economy They describe parameterized families of events (random variables) whose future only depends on their current state. Once the state space and generator are identified, various probability distributions of the process are calculated using the solution to the Kolmogorov equations. A very basic example of a continuous time Markov process is the Poisson process, which we define and review in the terminology of Markov processes This is the starting point for generalizations and applications to aerosol charging . Let E be a finite state space and G an irreducible generator of a continuous Markov process and Πt(i, j) = etG(i, j). In case of an irreducible generator theorem 2.1 guarantees the existence of a steady state distribution and gives a simple recipe to calculate it
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