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Abstract: Lévy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how Lévy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of Lévy walks. We show that Lévy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent , which coincides with experimental results. This work provides a means to confirm Lévy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior.
Keywords: Lévy walks, E. coli
Published in DKUM: 19.06.2017; Views: 912; Downloads: 321
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Abstract: A grafted polymer layer can be used to prevent the deposition of colloidal particles on a solid surface. This thesis presents Monte Carlo simulations of hard-sphere colloids pushed to a polymer brush under the influence of external fields (e.g. gravity). For weak fields colloids can not penetrate the brush and the effective potential acting on a single colloid is approximately quadratic. The phase diagram of three-dimensional hard-sphere colloids, that in one dimension are constrained to a plane by a harmonic potential, is presented. Under the influence of sufficiently strong external fields colloids penetrate the brush and form internally ordered, columnar structures that span the polymer layer. The morphology of the patterns that form depends sensitively on the strength of the applied field. We propose a simple phenomenological theory that accounts for the main characteristics of the observed behaviour. The present results suggest a simple experimental method to determine the surface polymer coverage.
Keywords: Soft Matter, Monte Carlo Method, Wang-Landau Algorithm, Free Energy, Polymer Brush, Colloids, Ordering
Published in DKUM: 04.03.2013; Views: 2280; Downloads: 98
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