Large deviations in Taylor dispersion
We establish a link between three different fields of research.
The first one deals with Taylor dispersion, describing in its original setting the dispersion of particles in a flow. From a more general perspective, this phenomenon is also relevant to issues such as sedimentation of non-spherical particles, line broadening in NMR, phase decoherence, and residence time problems [1]. It encompasses a huge literature in a variety of journals and fields.
The second is the theory of large deviations, dealing with the asymptotic behaviour of probability distributions when a parameter (in the present instance the time) becomes large. This theory has a strong mathematical component, but also plays a fundamental though less acknowledged role in statistical mechanics (the large parameter being typically the system size) [2].
Finally, the empirical distribution is a central concept in statistics [3].
We show that there is a close connection between Taylor dispersion and empirical distributions. With the aid of the theory of large deviations, which was extensively developed for empirical distributions, we derive an alternative and much more precise description of Taylor dispersion [4].
Refs.
[1] Christian Van den Broeck, "Taylor Di ffusion Revisited", Physica A168, 677(1990).
[2] Hugo Touchette, Physics Reports 478, 1 (2009).
[3] Aad van der Vaart, "Asymptotic statistics”, Cambridge University Press (1998)
[4] Marcel Kahlen, Andreas Engel, and Christian Van den Broeck, "Large deviations
The first one deals with Taylor dispersion, describing in its original setting the dispersion of particles in a flow. From a more general perspective, this phenomenon is also relevant to issues such as sedimentation of non-spherical particles, line broadening in NMR, phase decoherence, and residence time problems [1]. It encompasses a huge literature in a variety of journals and fields.
The second is the theory of large deviations, dealing with the asymptotic behaviour of probability distributions when a parameter (in the present instance the time) becomes large. This theory has a strong mathematical component, but also plays a fundamental though less acknowledged role in statistical mechanics (the large parameter being typically the system size) [2].
Finally, the empirical distribution is a central concept in statistics [3].
We show that there is a close connection between Taylor dispersion and empirical distributions. With the aid of the theory of large deviations, which was extensively developed for empirical distributions, we derive an alternative and much more precise description of Taylor dispersion [4].
Refs.
[1] Christian Van den Broeck, "Taylor Di ffusion Revisited", Physica A168, 677(1990).
[2] Hugo Touchette, Physics Reports 478, 1 (2009).
[3] Aad van der Vaart, "Asymptotic statistics”, Cambridge University Press (1998)
[4] Marcel Kahlen, Andreas Engel, and Christian Van den Broeck, "Large deviations
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