Dokument

Zusammenfassung:
This thesis deals with computer simulations and analytical calculations in simple and complex systems. In the last decades there has been a great interest in the area of complexity, and there are numerous definitions of complexity. In this work the attribute complex will be given based on two criteria. On the one hand we shall call a system “complex” if it is composed of a great number of simple interacting systems. Regarded from this perspective, every system we consider is complex, however on the other hand the classification is different when dealing with fluids. In this case one distingushes between simple and complex fluids using the interaction potentials as a criterion. Fluids with isotropic intermolecular potentials like Lennard-Jones systems are referred to as simple fluids, whereas e.g. liquid crystals belong to the class of complex fluids due to their anisotropic interaction potentials. After explaining some basic notions of statistical mechanics the theory of stochastic processes and molecular dynamics computer simulations, these methods are applied systematically to systems with increasing “complexity” in the next chapters. In Chapters 4 and 5 the discussed problems are of a fundamental nature: The Ehrenfest urn is a model introduced in order to explain the irreversibility of macroscopic thermodynamics as stated by Boltzmann’s H-theorem, although resulting from a time-reversible microscopic dynamics. After reviewing the defintition and derivation of Boltzmann’s state function in Chapter 4, the model of the Ehrenfest urn is studied via MD simulations of a realistic fluid in Chapter 5, and it turns out that the Markov hypothesis lying at the foundations of statistical mechanics is valid even in the liquid phase. In Chapter 6 liquid crystalline systems are studied. After introducing basic notions a discotic system confined in a cylindrical nanopore is simulated. Discotic liquid crystals are interesting from a technical point of view, since, due to their anisotropic conductivity in the columnar phase, they are promising for applications like organic light emiting diodes field effect transistors and solar cells. Finally in Chapter 7 first passage times for a stochastic process relevant for many physical chemical biological and other problems are calculated analytically and simulated numerically.

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