This thesis studies three models: Multi-type TASEP in discrete time, long-range last- passage percolation on the line and convoy formation in a travelling servers model. All three models are relatively easy to state but they show a very rich and interesting behaviour. The TASEP is a basic model for a one-dimensional interacting particle system with non-reversible dynamics. We study some aspects of the TASEP in discrete time and compare the results to recently obtained results for the TASEP in continuous time. In particular we focus on stationary distributions for multi-type models, speeds of second- class particles, collision probabilities and the speed process. We consider various natural update rules.

The theory of large deviations can help to shed light on systems in non-equilibrium statistical mechanics and, more generically, on non-reversible stochastic processes. For this purpose, we target trajectories in space time rather than static configurations and study time-extensive observables. This suggests that the details of the evolution law such as the presence of time correlations take on a major role. In this thesis, we investigate selected models with stochastic dynamics that incorporate memory by means of different mechanisms, devise a numerical approach for such models, and quantify to what extent the memory affects the large deviation functionals. The results are relevant for real-world situations, where simplified memoryless (Markovian) models may not always be appropriate. After an original introduction to the mathematics of stochastic processes, we explore, analytically and numerically, an open-boundary zero-range process which incorporates memory by means of hidden variables that affect particle congestion. We derive the exact solution for the steady state of the one-site system, as well as a mean-field approximation for larger one-dimensional lattices. Then, we focus on the large deviation properties of the particle current in such a system. This reveals that the time correlations can be apparently absorbed in a memoryless description for the steady state and the small fluctuation regime. However, they can dramatically alter the probability of rare currents. Different regimes are separated by dynamical phase transitions. Subsequently, we address systems in which the memory cannot be encoded in hidden variables or the waiting-time distributions depend on the whole trajectory. Here, the difficulty in obtaining exact analytical results is exacerbated. To tackle these systems, we have proposed a version of the so-called 'cloning' algorithm for the evaluation of large deviations that can be applied consistently for both Markovian and non-Markovian dynamics. The efficacy of this approach is confirmed by numerical results for some of the rare non-Markovian models whose large deviation functions can be obtained exactly. We finally adapt this machinery to a technological problem, specifically the performance evaluation of communication systems, where temporal correlations and large deviations are important.

Piecewise-smooth stochastic systems have attracted a lot of interest in the last decades in engineering science and mathematics. Many investigations have focused only on one-dimensional problems. This thesis deals with simple two-dimensional piecewise-smooth stochastic systems in the absence of detailed balance. We investigate the simplest example of such a system, which is a pure dry friction model subjected to coloured Gaussian noise. The nite correlation time of the noise establishes an additional dimension in the phase space and gives rise to a non-vanishing probability current. Our investigation focuses on stick-slip transitions, which can be related to a critical value of the noise correlation time. Analytical insight is provided by applying the uni ed coloured noise approximation. Afterwards, we extend our previous model by adding viscous friction and a constant force. Then we perform a similar analysis as for the pure dry friction case. With parameter values close to the deterministic stick-slip transition, we observe a non-monotonic behaviour of the probability of sticking by increasing the correlation time of the noise. As the eigenvalue spectrum is not accessible for the systems with coloured noise, we consider the eigenvalue problem of a dry friction model with displacement, velocity and Gaussian white noise. By imposing periodic boundary conditions on the displacement and using a Fourier ansatz, we can derive an eigenvalue equation, which has a similar form in comparison to the known one-dimensional problem for the velocity only. The eigenvalue analysis is done for the case without a constant force and with a constant force separately. Finally, we conclude our ndings and provide an outlook on related open problems.

Anders Lindquist, Sanjoy Mitter, Giorgio Picci. / Bibliography: leaves 14-15. / "October, 1981" "Feedback and Synthesis of Linear and Nonlinear Systems -Proceedings of the Workshop in Bielefeld, West-Germany, June 22-26, 1981, and Rome Italy, June 29-July 3, 1981." / "National Science Foundation Grant ECS-7903731" "Air Force Office of Scientific Research grant AFOSR 78-3519"

Thesis (Ph. D.)--University of Kentucky, 2001. / Title from document title page. Document formatted into pages; contains viii, 89 p. : ill. Includes abstract. Includes bibliographical references (p. 81-86).

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Probabilistic bisimulation is a widely studied equivalence relation for stochastic systems. However, it requires the behavior of the states to match on actions with matching labels. This does not allow bisimulation to capture symmetries in the system. In this thesis we define lax probabilistic bisimulation, in which actions are only required to match within given action equivalence classes. We provide a logical characterization and an algorithm for computing this equivalence relation for finite systems. We also specify a metric on states which assigns distance 0 to lax-bisimilar states. We end by examining the use of lax bisimulation for analyzing Markov Decision Processes (MDPs) and show that it corresponds to the notion of a MDP homomorphism, introduced by Ravindran & Barto. Our metric provides an algorithm for generating an approximate MDP homomorphism and provides bounds on the quality of the best control policy that can be computed using this approximation.

Plasma polymerisation (PP) is an emerging processing technology with immense potential for future industrial applications, which is increasingly being used for the fabrication of functional coatings on polymeric substrates. In this technique, the solid polymeric film is directly deposited onto the substrate surface to create a new surface of very interesting and unique properties. PP utilizes gas phase chemistries in low pressure environment to produce well-defined high quality films in controllable and tunable fashion. A major advantage of this process is that it is an environmental safety technique and strategically superior compared to other thin film deposition techniques such as spin coating and spray coating. In eneral, the quality of the plasma polymer film can be controlled, precisely and reproducible. However, mechanism of the coating under plasma polymerisation is complex and has not yet been completely understood. / Thesis (PhD)--University of South Australia, 1999

U. Shaked, P.R. Kumar. / Bibliography: p. 30. / "May, 1984" / "ECS-8304435" "DAAG29-84-K-0005"