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Transportphänomene treten in biologischen und künstlichen Systemen auf allen Längenskalen auf. In dieser Arbeit untersuchen wir sie für verschiedene Systeme aus einer mesoskopischen Perspektive, in der Fluktuationen physikalischer Größen um ihre Mittelwerte eine wichtige Rolle spielen. Im ersten Teil untersuchen wir die persistente Bewegung aktiver Brownscher Teilchen mit zusätzlichem Drehmoment, wie sie z.B. für Spermien oder Janus Teilchen auftritt. Wird ihre Bewegung auf einen Tunnel variierender Breite beschränkt, so setzt im thermischen Nichtgleichgewicht Transport ein; ungerichtete Fluktuationen des rauschhaften Antriebs werden gleichgerichtet. Hierdurch wird ein neuer Ratschentyp realisiert. Im zweiten Teil untersuchen wir den intrazellulären Cargotransport in den Axonen von Nervenzellen mithilfe molekularer Motoren. Sie werden als asymmetrischer Ausschlussprozess simuliert. Zusätzlich können die Cargos zwischen benachbarten Motoren ausgetauscht werden. Dadurch lassen sich charakteristische Eigenschaften des langsamen axonalen Transports mit einer einzigen Motorspezies reproduzieren. Bewerkstelligt wird dies durch die transiente Anbindung der Cargos an rückwärtslaufende Motorstaus. Im dritten Teil diskutieren wir resistive switching, die nicht volatile Widerstandsänderung eines Dielektrikums durch elektrische Impulse. Es wird für Anwendungen im Computerspeicher ausgenutzt, dem resistive RAM. Wir schlagen ein auf Sauerstoffvakanzen basierendes stochastisches Gitterhüpfmodell vor. Wir definieren binäre logische Zustände mit Hilfe der zugrunde liegenden Vakanzenverteilung und definieren Schreibe- und Leseoperationen durch Spannungsimpulse für ein solches Speicherelement. Überlegungen über die Unterscheidbarkeit dieser Operationen unter Fluktuationen zusammen mit der Deutlichkeit der unterschiedlichen Widerstandszustände selbst ermöglichen es uns, eine optimale Vakanzenzahl vorherzusagen. / Transport phenomena occur in biological and artificial systems at all length scales. In this thesis, we investigate them for various systems from a mesoscopic perspective, in which fluctuations around their average properties play an important role. In the first part, we investigate the persistent diffusive motion of active Brownian particles with an additional torque. It can appear in many real life systems, for example in sperm cells or Janus particles. If their motion is confined to a tunnel of varying width, transport arises out of thermal equilibrium; unbiased fluctuations of the noisy drive are rectified. This way, we have realized a novel kind of ratchet. In the second part, we study intracellular cargo transport in the axons of nerve cells by molecular motors. They are modeled by an asymmetric exclusion process. In a new approach, we add a cargo exchange interaction between the motors. This way, the characteristics of slow axonal transport can be accounted for with a single motor species. It is explained by the transient attachment of cargos to reverse walking motors jams. In the third part, we discuss resistive switching, the non-volatile change of resistance in a dielectric due to electric pulses. It is exploited for applications in computer memory, the resistive random access memory (ReRAM). We propose a stochastic lattice hopping model based on the on oxygen vacancies. We define binary logical states by means of the underlying vacancy distributions, and establish a framework of writing and reading such a memory element with voltage pulses. Considerations about the discriminability of these operations under fluctuations together with the markedness of the resistive switching effect itself enable us to predict an optimal vacancy number.

Cilia and flagella are hair-like appendages of eukaryotic cells. They are actively bending structures that exhibit regular beat patterns and thereby play an important role in many different circumstances where motion on a cellular level is required. Most dramatic is the effect of nodal cilia whose vortical motion leads to a fluid flow that is directly responsible for establishing the left-right axis during embryological development in many vertebrate species, but examples range from the propulsion of single cells, such as the swimming of sperm, to the transport of mucus along epithelial cells, e.g. in the ciliated trachea. Cilia and flagella contain an evolutionary highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of elastic filaments (microtubules). In the presence of a chemical fuel (ATP), molecular motors (dynein) exert shear forces between neighbouring microtubules, leading to a bending of the axoneme through structural constraints. We address the following two questions: How can these organelles generate regular oscillatory beat patterns in the absence of a biochemical signal regulating the activity of the force generating elements? And how can the beat patterns be so different for apparently very similar structures? We present a theoretical description of the axonemal structure as an actively bending elastic cylinder, and show that in such a system bending waves emerge from a non-oscillatory state via a dynamic instability. The corresponding beat patterns are solutions to a set of coupled partial differential equations presented herein.

Cilia and flagella are hair-like appendages of eukaryotic cells. They are actively bending structures that exhibit regular beat patterns and thereby play an important role in many different circumstances where motion on a cellular level is required. Most dramatic is the effect of nodal cilia whose vortical motion leads to a fluid flow that is directly responsible for establishing the left-right axis during embryological development in many vertebrate species, but examples range from the propulsion of single cells, such as the swimming of sperm, to the transport of mucus along epithelial cells, e.g. in the ciliated trachea. Cilia and flagella contain an evolutionary highly conserved structure called the axoneme, whose characteristic architecture is based on a cylindrical arrangement of elastic filaments (microtubules). In the presence of a chemical fuel (ATP), molecular motors (dynein) exert shear forces between neighbouring microtubules, leading to a bending of the axoneme through structural constraints. We address the following two questions: How can these organelles generate regular oscillatory beat patterns in the absence of a biochemical signal regulating the activity of the force generating elements? And how can the beat patterns be so different for apparently very similar structures? We present a theoretical description of the axonemal structure as an actively bending elastic cylinder, and show that in such a system bending waves emerge from a non-oscillatory state via a dynamic instability. The corresponding beat patterns are solutions to a set of coupled partial differential equations presented herein.