Geometric partial differential equations: Surface and bulk processes

The workshop brought together experts representing a wide range of topics in geometric partial differential equations ranging from analyis over numerical simulation to real-life applications. The main themes of the conference were the analysis of curvature energies, new developments in pdes on surfaces and the treatment of coupled bulk/surface problems

Simulations of a Neuron Network Model in the Olfactory System

In dieser Arbeit wird ein Modell für das Neuronennetzwerk im olfaktorischen Bulbus entwickelt. Das Modell beinhaltet Mitral- und Körnerzellen, die als Punktneuronen mit “Integrate-and-Fire” Dynamik modelliert werden. Die Aktivität des Netzwerkmodels wird mit so genannten “Equationfree” Techniken simuliert und numerisch analysiert. “Equation-free” Techniken sind Simulationswerkzeuge um das coarse Verhalten von hochdimensionalen Systemen zu untersuchen, ohne dafür geschlossene niederdimensionale Gleichungen herleiten zu müssen. Diese Techniken werden für die Untersuchung des Netzwerkmodels vom olfaktorischen Bulbus weiterentwickelt: “Equation-free” Newton Verfahren, Parameterstudien und Methoden zur Untersuchung von Traveling Waves werden eingeführt. Indem das “Equation-free” Zeitschrittverfahren als Einschrittverfahren interpretiert wird, ist es möglich ein Konvergenztheorem zu beweisen. Punktneuronen sind u.U. nicht ausreichend wenn z.B. Simulationsergebnisse mit Imagingexperimenten verglichen werden sollen. Hier muss die räumliche Ausdehnung der Neuronen berüksichtigt werden. Um die Aktivität einzelner Neuronen zu simulieren wird ein Finite-Elemente Ansatz basierend auf dem Hodgkin-Huxley Mechanismus beschrieben. Bei diesem Ansatz wird adaptive Gittersteuerung in Ort und Zeit benutzt. Dafür werden a-posteriori Fehlerschätzer für passive Signalausbreitung in Nervenzellen entwickelt. Die hier präsentierten Simulations- und Analysewerkzeuge ermöglichen es interessante biologische Fragestellungen zu untersuchen. Der Einfluß des zeitlichen Ablaufs von Neuronendynamik und inhibitorischer Aktivität auf die Nervenzelldynamik im olfaktorischen Bulbus werden untersucht. Mittels der “Equation-free” Simulationsmethodik für das Punktneuronenmodell kann der Einfluß von Netzwerkparametern auf die laterale Inhibition und auf Kontrastverstärkungsverhalten untersucht werden. Für Geruchsunterscheidungsaufgaben können experimentelle Ergebnisse reproduziert und Langzeituntersuchungen durchgeführt werden. Letztere zeigen Hystereseeffekte, die zu einer Stabilisierung des Netzwerkoutputs für kleine Inputstörungen führen. Für diese Untersuchung wird der “Equation-free” Ansatz mit Techniken der numerischen Bifurkationsanalyse kombiniert. Schließlich kann angegeben werden, wann Traveling Waves im diskreten Netzwerkmodel entstehen, und es ist möglich eine Erklärung zu geben, warum Wellen in Experimenten mit Knochenfischen entstehen, nicht aber bei Experimenten mit Säugetieren

Evolution of Negative Streamers in Nitrogen: a Numerical Investigation on Adaptive Grids

Plasmas are ionized media, occupying 99% of the universe. Common examples of plasmas are the sun, which is a high-temperature plasma, and neon lights, which are low-temperature plasmas. A high-temperature plasma is at thermal equilibrium, and is driven by a high pressure and temperature of the medium. A low-temperature plasma, on the other hand, is far from equilibrium, and the ionization is generated by electric or electromagnetic fields. Streamers are transient, filamentary, low-temperature plasma channels which, under influence of the self-enhanced electric field at their tip, propagate rapidly into a non- or weakly ionized medium. They are widely used in industry, e.g. for the treatment of exhaust gasses, cleaning of polluted water, and in aerospatial engineering. Streamers are also found in nature, where they play a role in creating the path of lightning. Recent observations showed the existence of sprites, which are very large discharge structures in the higher parts of the atmosphere, composed of a multitude of streamers. One distinguishes streamers according to their polarity: in positive or cathode-directed streamers, positive space charges propagate in the direction of the electric field. In negative or anode directed streamers, on the other hand, it is negative net charge that propagates in the direction of the electron drift, i.e. opposite to the electric field. Experiments show that positive streamers emerge more easily from a point or a wire electrode than negative ones, which require a much higher voltage to emerge. Consequently, industrial applications mainly focus on the use of positive streamers. On the other hand, when streamers emerge in free space from ionization avalanches, they can have both a positive and a negative end. Lightning as well as sprite discharges are examples of such kind of double-ended discharges. Up to now, most experimental and theoretical efforts have been devoted to positive streamers in air because of their applications. However, the cross-sections for photoionization, which is required for the propagation of positive streamers, are not well-known. To define a clear physical signature, it is therefore desirable to study a situation rather independent of photoionization: negative streamers in pure gases. High-voltage experiments to obtain such streamers are currently being set up at the Eindhoven University of Technology in collaboration with the research theme "Nonlinear Dynamics and Complex Systems" at the national research institute for Mathematics and Computer Science (CWI) in Amsterdam, where numerical and analytical research is carried out. This thesis was written at CWI and is concerned with a numerical method for the simulation of negative streamers, and also with an analytical criterion for the emergence of such streamers. The simulation of streamers represents a great computational challenge. First, multiple spatial scales are involved: the non-ionized region into which the streamer propagates is orders of magnitude larger than the ionized channel, which in turn is much larger than the small active region at the streamer tip, which again has an inner layered structure. Secondly, the spatial density gradients in the tip of the streamer grow during the propagation, requiring an increasing accuracy of the numerical method. Finally, another specific difficulty comes from the unstable nature of streamers: any ionized perturbation in the non-ionized, high-field region just ahead of the streamer tip will grow. The dynamics of the streamers are set in this unstable region, the leading edge, where the densities are very low and the density gradients therefore small. The ionization front is pulled into the non-ionized region by the leading edge, which is a main reason for the failure of standard refinement strategies to describe accurately the streamer dynamics. We have developed a numerical algorithm that copes in an efficient way with the inherent computational difficulties. It computes the evolution of the streamer in a fluid approximation. The model consists of continuity equations for the charged particles, which, in pure nitrogen, are electrons and positive ions. These continuity equations tell us that the temporal change of the charged particles is set by their drift, diffusion, and ionization sources and sinks. The drift velocity of the particles as well as the ionization rate depend on the local electric field, which has to be determined through the so-called Poisson equation for the electric potential, whose source term is given by the space charge. This model is nonlinear because the particle motion and generation depend on the field while the field depends on the particle densities. For negative streamers in nitrogen, it is admissible to neglect ionization sources like photoionization, and the only source of charged particles is then ionization by impact of sufficiently energetic electrons with neutral particles. These mechanisms - namely the drift and impact ionization in the local electric field, the diffusion and the space charge effects - in a continuum approximation constitute the so-called minimal streamer model, which is analyzed in this thesis. The algorithm is implemented for a three-dimensional system with cylindrical symmetry, which reduces the computations effectively to two spatial dimensions. The algorithm is based on a decoupling of the numerical grids for the continuity equations on the one hand, and that for the Poisson equation on the other hand. The grids are refined, according to error monitors, at each time step, thereby adapting themselves to the solution. The leading edge is explicitly included in the refinement criterion. Successful test are carried out both on planar and curved streamer fronts. This algorithm enables us to explore a new parameter regime. We can now apply large background electric fields, in which spatial gradients become very large, and still resolve the streamer in an accurate manner. It is now also possible to compute the streamer evolution in low fields and large gas gaps. The results of the simulations exhibit some very interesting features in both cases. Following the evolution of streamers emerging from a single electron in a plane-parallel electrode geometry shows that three physical stages are passed. The emergence of a streamer can occur through an electron avalanche, characterized by the absence of space charge effects, and is therefore linear. Once the amount of space charges is sufficiently large to change significantly the background electric field, the phenomenon becomes non-linear, and a streamer emerges. If the distance to the anode is long enough, the streamer eventually becomes unstable and branches. During the avalanche phase, the electrons drift, diffuse and multiply in the uniform background electric field. If the avalanche starts from a single electron and the field is homogeneous, the equation for the electrons has an analytical solution, which can be used to derive analytical expressions for the spatial moments of the ions. This allows us to find an analytical approximation for the electric field, and hence determine when the space charge effects have become so strong, that the transition to a streamer takes place. We have thus derived a criterion for the avalanche to streamer transition, which includes the effect of diffusion. The traditional criterion for the transition, Meek's criterion, postulates that, in a specific gas at a specific pressure, the travel time and distance of the electron avalanche before turning into a streamer only depend on the applied background field. The inclusion of diffusion shows that this is not the case and that diffusion can in fact considerably delay the emergence of a streamer. Once the streamer has emerged, the evolution is nonlinear. At this point our grid refinement strategy provides us with a powerful tool to compute the further streamer propagation. The streamer is characterized by the enhanced conductivity of its body, which is therefore partially shielded from the exterior electric field. This shielding requires a space charge layer at the streamer tip, which in turn enhances the electric field ahead of the tip. The streamer extends in this self-enhanced field. We investigate the evolution and branching of streamers in both cases of overvolted and undervolted gaps. These are distinguished by the ability of the background electric field to provide an electron with a sufficient amount of energy to ionize a neutral atom or molecule when colliding with it. In an overvolted gap, the background electric field is sufficiently high for this to happen, and the streamer penetrates a highly unstable state. Its radius continues to grow up to branching, giving it a conical shape. Moreover, the spatial density gradients become very steep, thereby requiring a very high accuracy from the numerical method. In an undervolted gap, the electrons only multiply in the small region ahead of the streamer where the field is sufficiently enhanced, giving the streamer a more filamentary shape. For a sufficient field enhancement, a sufficient amount of charge in the streamer head is required. The accumulation of charge in the head depends both on the initial distribution of ionization and on the boundary conditions on the electrode. We study different cases and eventually, in all cases, the streamer branches provided the gap is sufficiently long. The branching state of the streamer has not been analyzed much up to now, mainly due to a lack of accurate numerical tools which now have become available through the work presented in this thesis. Indeed, the refinement algorithm enables us to reach the branching state with sufficient numerical accuracy within a reasonable computational time, and more importantly, within the limits of the computational memory. First, we here establish that the time of branching converges for identical initial and boundary conditions when using finer and finer numerical grids. Such tests were out of reach up to now. The convergence of branching times allows us now to derive quantitative predictions under given conditions. We find that the branching times converge for sufficiently fine numerical grids both for the underand the overvolted case. An interesting detail is that in the undervolted case, the branched state is always the same while in the overvolted case, different branched states are reached on different grids after a similar evolution time. This suggests that in the second case, several branched states are accessible from the unstable head state. The outcome of such a nonlinear bifurcation process then will depend on minor details (like the numerical grid) as is well known even to the general public as the unpredictability of "chaos theory". Another reason not to analyze the details of the branched state is the assumed cylindrical symmetry in our calculations. Within the present thesis, the streamer splits not into branches but into concentric rings as the space of linear perturbations has been restricted to cylinder symmetrical ones. When a larger space of linear perturbations is admitted, the branching instability can be expected after a similar time of evolution, but to a different state. The physically relevant question that can be answered with the present analysis is: can we characterize a generic unstable state of the streamer head that leads to branching? This indeed seems to be the case: numerical experiments in a fixed external electric field with a variety of initial ionization distributions and boundary conditions on the electrode always seem to evolve to a very similar state of the streamer head immediately before branching. This particular head state would then be an intermediate at tractor of the dynamics that is followed by branching. However, this hypothesis requires further numerical and analytical studies. There is another insight that can be gained from the present numerical studies, namely a verification of a reduced model for well developed streamers that is currently being studied analytically at CWI. Such a model for moving ionization boundaries consists of several building blocks: 1) The ionization front at the streamer tip propagates with a velocity that is a function of the electric field ahead of it. 2) The width of the space charge layer is a decreasing function of the electric field and saturates at high fields. 3) The conductivity in the interior of the streamer is so high that it approaches Lozansky and Firsov's limit of ideal conductivity. For the dependence of front velocity and width on the electric field, analytical predictions have been derived for planar fronts. Their validity for curved fronts can be tested on the numerical results. Furthermore, analytical results show that a planar front is dynamically unstable and will branch due to a Laplacian instability, while the analysis of curved fronts is underway. The limit of a planar front is never reached in the simulations, but a limit of small curvature where the radius of curvature of the streamer head is much larger than the front width does occur. Numerical studies do reveal for which curvature the Laplacian instability sets in and are therefore complementary to the analytical studies. We conclude that the minimal streamer model analyzed in this thesis already exhibits very complex behavior and is better adapted for explorative systematic studies than a model including many more physical features from the start. The predictions of this model should now be tested on experiments on negative streamers in nitrogen while more features like the less well-known photo-ionization should be included to predict the behavior of streamers in air. Also, the step towards fully three-dimensional simulations should be made

Reactive Flows in Deformable, Complex Media

Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above

The physics of streamer discharge phenomena

In this review we describe a transient type of gas discharge which is commonly called a streamer discharge, as well as a few related phenomena in pulsed discharges. Streamers are propagating ionization fronts with self-organized field enhancement at their tips that can appear in gases at (or close to) atmospheric pressure. They are the precursors of other discharges like sparks and lightning, but they also occur in for example corona reactors or plasma jets which are used for a variety of plasma chemical purposes. When enough space is available, streamers can also form at much lower pressures, like in the case of sprite discharges high up in the atmosphere. We explain the structure and basic underlying physics of streamer discharges, and how they scale with gas density. We discuss the chemistry and applications of streamers, and describe their two main stages in detail: inception and propagation. We also look at some other topics, like interaction with flow and heat, related pulsed discharges, and electron runaway and high energy radiation. Finally, we discuss streamer simulations and diagnostics in quite some detail. This review is written with two purposes in mind: First, we describe recent results on the physics of streamer discharges, with a focus on the work performed in our groups. We also describe recent developments in diagnostics and simulations of streamers. Second, we provide background information on the above-mentioned aspects of streamers. This review can therefore be used as a tutorial by researchers starting to work in the field of streamer physics.Comment: 89 pages, 29 figure

Robust stabilised finite element solvers for generalised Newtonian fluid flows

Various materials and solid-fluid mixtures of engineering and biomedical interest can be modelled as generalised Newtonian fluids, as their apparent viscosity depends locally on the flow field. Despite the particular features of such models, it is common practice to combine them with numerical techniques originally conceived for Newtonian fluids, which can bring several issues such as spurious pressure boundary layers, unsuitable natural boundary conditions and coupling terms spoiling the efficiency of nonlinear solvers and preconditioners. In this work, we present a finite element framework dealing with such issues while maintaining low computational cost and simple implementation. The building blocks of our algorithm are (i) an equal-order stabilisation method preserving consistency even for lowest-order discretisations, (ii) robust extrapolation of velocities in the time-dependent case to decouple the rheological law from the overall system, (iii) adaptive time step selection and (iv) a fast physics-based preconditioned Krylov subspace solver, to tackle the relevant range of discretisation parameters including highly varying viscosity. Selected numerical experiments are provided demonstrating the potential of our approach in terms of robustness, accuracy and efficiency for problems of practical interest

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field

Efficient computational mesoscale modeling of concrete under cyclic loading

Tesi amb diferents seccions retallades per drets de l'editor.Concrete is a complex material and can be modeled on various spatial and temporal scales. While simulations on coarse scales are practical for engineering applications, a deeper understanding of the material is gained on finer scales. This is at the cost of an increased numerical effort that can be reduced by the three methods developed and used in this work, each corresponding to one publication. The coarse spatial scale is related to fully homogenized models. The material is described in a phenomenological approach and the numerous parameters sometimes lack a physical meaning. Resolving the three-phase mesoscopic structure consisting of aggregates, the mortar matrix and the interfaces between them allow to describe similar effects with simpler models. This work addresses two computational challenges related to mesoscale modeling. First, aggregate particles take up a high volume fraction and an efficient particle-packing algorithm is required to generate non-overlapping, random esostructures. Enforcing an additional distance between the aggregates is essential to obtain undistorted meshes for finite element simulations, but further complicates the packing problem. An event-driven molecular-dynamics algorithm is applied to this problem that, in contrast to traditional methods, allows movement and a dense arrangement of the aggregates. This allows creating concrete mesostructures with realistic aggregate volume fractions. The second challenge concerns stability problems in mesoscale simulations of concrete fracture. The geometric complexity and the combination of three material laws for each of the phases leads to numerical instabilities, even for regularized material models. This requires tiny time steps and numerous iterations per time step when integrated with a classic backward Euler scheme. The implicit–explicit (IMPL-EX) integration extrapolates internal variables that account for the nonlinear behavior. This linearizes the equations, provides additional robustness and a computational speedup. In combination with a novel time step control method, a three-dimensional mesoscale compression test is accelerated by a factor of 40, compared to an adaptive backward Euler algorithm. The life time of concrete under cyclic loads is commonly predicted with empirical Wöhler lines. They relate the number of endured cycles with the applied load amplitude and can be included in constitutive formulations. They can, however, hardly be generalized to geometries and load configurations other than the ones tested. On a finer temporal scale, fatigue failure is modeled by the accumulation of damage within each loading cycle. This resolves the whole process of failure, includes stress redistributions and size effects and can easily be extended to multiphysics phenomena. The third computational challenge solved here is the efficient temporal integration that would not be feasible in a naive cycle-by-cycle integration of thousands or millions of cycles. The cost of evaluating a single cycle is reduced by reformulating the problem in the frequency space. It is sufficient to equilibrate the structure once for each Fourier coefficient which significantly speeds up this evaluation. The accumulated damage of one cycle is integrated in time using an adaptive cycle jump concept. For a two dimensional void test structure, the combination of both techniques leads to a 25 times faster simulation compared to the full integration. These three main contributions decrease the numerical cost of mesoscale simulations, allow larger and more detailed models and are a basis to deepen the understanding of the complex failure patterns in concrete.El hormigón es un material complejo y puede ser modelado en varias escalas espaciales y temporales. Mientras que las simulaciones en escalas gruesas son prácticas para aplicaciones de ingeniería, se obtiene una comprensión más profunda del material en escalas más finas. Esto es a costa de un mayor esfuerzo numérico que puede ser reducido por los tres métodos desarrollados y utilizados en este trabajo, cada uno de los cuales corresponde a una publicación. La escala espacial gruesa está relacionada con modelos totalmente homogeneizados. El material se describe con un enfoque fenomenológico y los numerosos parámetros a veces carecen de significado físico. La resolución de la estructura mesoscópica trifásica formada por los áridos, la matriz de mortero y las interfaces entre ellos permite describir efectos similares con modelos más sencillos. Este trabajo aborda dos retos computacionales relacionados con el modelado a mesoescala. En primer lugar, las partículas agregadas absorben una fracción de gran volumen y se requiere un algoritmo eficiente de empaquetamiento de partículas para generar mesoestructuras aleatorias que no se solapen. Hacer cumplir una distancia adicional entre los agregados es esencial para obtener mallas no distorsionadas para simulaciones de elementos finitos, pero complica aún más el problema de empaquetado. A este problema se le aplica un algoritmo de dinámica molecular impulsado por eventos que, a diferencia de los métodos tradicionales, permite el movimiento y una disposición densa de los agregados. Esto permite crear mesoestructuras de hormigón con fracciones de volumen de agregado realistas. El segundo reto se refiere a los problemas de estabilidad en las simulaciones mesoescalares de fracturas de hormigón. La complejidad geométrica y la combinación de tres leyes materiales para cada una de las fases conduce a inestabilidades numéricas, incluso para modelos materiales regularizados. Esto requiere pequeños pasos de tiempo y numerosas iteraciones por paso de tiempo cuando se integra con un esquema clásico de Euler hacia atrás. La integración implícita- explícita (IMPL-EX) extrapola variables internas que dan cuenta del comportamiento no lineal. Esto linealiza las ecuaciones, proporciona robustez adicional y una aceleración computacional. En combinación con un nuevo método de control de paso en el tiempo, una prueba de compresión tridimensional de mesoescala es acelerada por un factor de 40, en comparación con un algoritmo adaptativo de Euler hacia atrás. La vida útil del hormigón bajo cargas cíclicas se predice comúnmente con las líneas empíricas de Wöhler. Relacionan el número de ciclos soportados con la amplitud de carga aplicada y pueden ser incluidos en formulaciones constitutivas. Sin embargo, difícilmente pueden generalizarse a geometrías y configuraciones de carga distintas a las probadas. En una escala temporal más fina, la falla por fatiga es modelada por la acumulación de daño dentro de cada ciclo de carga. Esto resuelve todo el proceso de fracaso, incluye redistribuciones de estrés y efectos de tamaño, y puede extenderse fácilmente a fenómenos multifísicos. El tercer reto computacional resuelto aquí es la integración temporal eficiente que no sería factible en una integración costosa de miles o millones de ciclos ciclo a ciclo. El costo de evaluar un solo ciclo se reduce reformulando el problema en el espacio de frecuencias. Es suficiente equilibrar la estructura una vez para cada coeficiente de Fourier, lo que acelera significativamente esta evaluación. El daño acumulado de un ciclo se integra en el tiempo utilizando un concepto de salto de ciclo adaptativo. Para una estructura de prueba de vacío bidimensional, la combinación de ambas técnicas conduce a una simulación 25 veces más rápida en comparación con la integración completa.Postprint (published version

Stochastic transport in complex environments : applications in cell biology

Living organisms would not be functional without active processes. This general statement is valid down to the cellular level. Transport processes are necessary to create, maintain and support cellular structures. In this thesis, intracellular transport processes, driven by concentration gradients and active matter, as well as the dynamics of migrating cells are studied. Many studies deal with diffusive intracellular transport in the complex environment of neuronal dendrites, however, focusing on a few spines. In this thesis, a model was developed for diffusive transport in a full dendritic tree. A link was established between complex structural changes by diseases and transport characteristics. Furthermore, recent experimental studies of search processes in migration of dendritic cells show a link between speed and persistence. In this thesis, a correlation between them was included in a stochastic model, which lead to increased search efficiency. Finally, this thesis deals with the question of how active, bidirectional transport by molecular motors in axons can be efficient. Generically, traffic jams are expected in confined environments. Limitations of bypassing mechanisms are discussed with a bidirectional non-Markovian exclusion process, developed in this thesis. Experimental findings of cooperative effects and microtubule modifications have been incorporated in a stochastic model, leading to self-organized lane-formation and thus, efficient bidirectional transport.Ohne aktive Prozesse wären lebendige Organismen nicht funktionsfähig. Dies gilt bis herab zur Zellebene. Transportprozesse sind notwendig um zelluläre Strukturen aufzubauen und zu erhalten. In dieser Arbeit werden intrazelluläre Transportprozesse, getrieben von Konzentrationsgradienten und aktiver Materie, sowie die Dynamik in Zellmigration untersucht. Viele Studien beschäftigen sich mit passivem Transport in der komplexen Umgebung von neuronalen Dendriten, vorwiegend jedoch mit einzelnen Dornvortsätzen (spines). In dieser Arbeit wurde ein Modell zu Diffusion in einer vollständigen Dendritenstruktur entwickelt und eine Relation zwischen Krankheitsverläufen und neuronalen Funktionen gefunden. Die Migration von dendritischen Zellen zeigen einen Zusammenhang zwischen ihrer Geschwindigkeit und Persistenz. Dieser wurde in ein stochastisches Modell übernommen welches zeigte, dass die Sucheffizienz der Zellen damit gesteigert werden kann. Außerdem geht es um die Frage wie aktiver, bidirektionaler Transport durch molekulare Motoren in Axonen effizient sein kann. In einem so begrenzten Raum sind Verkehrsstaus zu erwarten. In dieser Arbeit wurden lokale Austauschmechanismen anhand des entwickelten Nicht-Markovschen, bidirektionalen Exklusionsprozess diskutiert. Experimentell entdeckte kooperative Effekte und Mikrotubulimodifikationen wurde in ein stochastisches Modell übernommen, was zu selbstorganisierter Spurbildung und damit zu effizientem bidirektionalem Transport führte