Asymptotic theory of hydrodynamic interactions between slender filaments

This book relies on maximum likelihood (ML) estimation of parameters. Asymptotic theory assumes regularity conditions hold when the ML estimator is consistent. Typically an additional third derivative condition is assumed to ensure that the ML estimator is also asymptotically normally distributed. Standard asymptotic results that then hold are summarized in this chapter; for example, the asymptotic variance of the ML estimator is then given by the Fisher information formula, and the log-likelihood ratio, the Wald and the score statistics for testing the statistical significance of parameter estimates are all asymptotically equivalent. Also, the useful profile log-likelihood then behaves exactly as a standard log-likelihood only in a parameter space of just one dimension. Further, the model can be reparametrized to make it locally orthogonal in the neighbourhood of the true parameter value. The large exponential family of models is briefly reviewed where a unified set of regular conditions can be obtained.

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Asymptotic theory for the correlated gamma-frailty model

10.1214/aos/1030563982 ◽

1998 ◽

Vol 26 (1) ◽

pp. 183-214 ◽

Cited By ~ 157

Author(s):

Erik Parner

Keyword(s):

Asymptotic Theory ◽

Frailty Model ◽

Gamma Frailty

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Hydrodynamics can determine the optimal route for microswimmer navigation

Communications Physics ◽

10.1038/s42005-021-00522-6 ◽

2021 ◽

Vol 4 (1) ◽

Author(s):

Abdallah Daddi-Moussa-Ider ◽

Hartmut Löwen ◽

Benno Liebchen

Keyword(s):

Flow Field ◽

Hydrodynamic Interactions ◽

Optimal Trajectories ◽

Optimal Route ◽

Active Particles ◽

Navigation Strategy ◽

Navigation Strategies

AbstractAs compared to the well explored problem of how to steer a macroscopic agent, like an airplane or a moon lander, to optimally reach a target, optimal navigation strategies for microswimmers experiencing hydrodynamic interactions with walls and obstacles are far-less understood. Here, we systematically explore this problem and show that the characteristic microswimmer-flow-field crucially influences the navigation strategy required to reach a target in the fastest way. The resulting optimal trajectories can have remarkable and non-intuitive shapes, which qualitatively differ from those of dry active particles or motile macroagents. Our results provide insights into the role of hydrodynamics and fluctuations on optimal navigation at the microscale, and suggest that microorganisms might have survival advantages when strategically controlling their distance to remote walls.

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