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Koot, Kees (author)In this thesis the behaviour of a Bose Einstein condensate is explored that consists of bosons that annihilate. In order to do this a system where bose einstein condensation occurs is modeled as a Zero Range process which is a special case of a Markov process.<br/>First we made a single slow site Zero range process with uniform rates and see how...bachelor thesis 2022
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van Tol, Berend (author)In this thesis we study criticality in the context of the dissipative Abelian sandpile model. The model is linked to a simple trapped random walk, giving a practical method to determine criticality for certain landscapes of dissipative sites. The main results concern the lifetime of the random walk, especially the divergence of its first moment...bachelor thesis 2021
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Holtrop, Sven (author)In this thesis, the diffusive limit of active particle motion in R<sup>d</sup> is studied via a technique based on homogenisation. Thereafter, this study is extended to active particle motion on a Riemannian manifold. <br/><br/>Furthermore, as an application of active particle motion, a connection is made with the Dirac equation. On the basis of...bachelor thesis 2021
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Fokker, Floris (author)In this thesis, the hydrodynamic limit (HDL) for two trapping models is studied, the Random Waiting Time Model (RWTM) and the fractional kinetics process (FKP), on a discrete lattice Zd . The RWTM is studied for dimension d ≥ 1 and E[wi ],∞where wi denotes the waiting time at position i . On the other hand, the FKP is studied for d ≥ 3 and a...bachelor thesis 2023
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Westdorp, Rik (author)In this thesis we introduce a variation on the quantum random walk to discuss shifts in an arbitrary range. The concept of Hadamard coin was therefore generalised to a higher order. By a Fourier transform method and a tensor product decomposition of the evolution matrix the long-range quantum random walk was found to converge in distribution to...bachelor thesis 2018
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van Kempen, Matt (author)In this paper we started by explaining what a Markov chain is. After this we defined some key concepts such as stationarity, reversibility and ergodicity which were used throughout the rest of the paper. Next, the classical central limit theorem was stated in order to refresh the reader of this theorem and to show that, because of the dependence...bachelor thesis 2022
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Maassen van den Brink, Mitchell (author)In this thesis, research was done in the area of interacting particle systems. Especially, the symmetric exclusion process with local perturbations was investigated. These perturbations, were in the form of sinks and sources, which add or take away particles at certain rates. Moreover, simulations were done for the asymmetric exclusion process....bachelor thesis 2023
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Leenders, Mats (author)In this paper a two agent wealth distribution model for a closed economic system developed in [2] is presented and extended. We first extend the model by randomly distributing the propensity to save of the agents. We derive a closed form of the stationary relative wealth measure of an agent. We also see that if we take both the propensity to...bachelor thesis 2019
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van Roessel, Milan (author)In this thesis, wealth distribution in a closed economic system is examined by studying the simple inclusion process (SIP). The simple inclusion process is a model coming from statistical physics that models the jumping of particles in a graph. In the model particles have attraction among each other and each site also has a characteristic...bachelor thesis 2023
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Van Ginkel, G.J. (author)Dualiteit is een handige manier om Markovprocessen te bestuderen. Hierbij wordt een in zekere zin moeilijk proces op een bepaalde manier met een eenvoudiger proces verbonden. Deze techniek zal in dit verslag worden toegelicht en zal toegepast worden op het Immediate Exchange Model, een welvaartverdelingsmodel waarin handelaren telkens na een...bachelor thesis 2015
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Zaat, Justin (author)The Abelian sandpile model was first introduced by Bak, Tang and Wiesenfeld in 1987. Since then, a lot of researchers have studied this model and similar models, all related by the concept of self-organized criticality. In this thesis, we study a variant on the classical model where dissipative and anti-dissipative vertices are incorporated in...bachelor thesis 2019
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Hoogendijk, Jochem (author)This project aims to describe crude models that work towards a mathematical model for transcription and translation. Transcription refers to the conversion of genetic code to a readable format for the cell, while translation refers to the conversion of this code into polypeptide chains using ribosomes. The main proposal for such a model is the...bachelor thesis 2019
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Benjert, Zylan (author)We consider the problem of random walks moving around on a lattice Zd with an initial Poisson distribution of traps. We consider both static and moving traps. In the static case, we prove that the survival time has a decay of e−c t d /d +2 based on a heuristic argument. In the moving case we aim to prove the sub-exponential...bachelor thesis 2023
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Verberne, S. (author)Markov processes are interesting stochastic proceses with a wide range of applications. In this report we study Markov processes with two time scales where the difference between the time speed of the scales is asymptotically large. In such a situation the behaviour of the process can be estimated by substituting the "faster" process by its...bachelor thesis 2015
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Meskers, Marthe (author)In this thesis, we study the asymptotic behaviour and the dynamics of a one-dimensional active particle model with excluded volume interactions. The model is a version of run-and-tumble motion, where a particle performs both symmetric random walks and active transport. The direction and the speed of the transport are governed by an internal...bachelor thesis 2021
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Jongbloed, H. (author)The Abelian Sandpile model was originally introduced by Bak, Tang and Wiesenfeld in 1987 as a paradigm for self-organized criticality. In this thesis, we study a variant of this model, both from the point of view of mathematics, as well as from the point of view of physics. The effect of dissipation and creation of mass is investigated. By...bachelor thesis 2016
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Zegers, Samuel (author)In several experiments, enzymes have shown an in increase in diffusivity in the presence of their substrate. The enhancement in diffusivity ranged from as low as 28% for urease to 80% in the case of alkaline phosphatase. There are two main competing theories. One asserts that catalytically driven boosts propel the enzyme forward in ‘leaps’,...bachelor thesis 2022
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Versendaal, R. (author)Deze scriptie bespreekt voldoende voorwaarden opdat een random deelverzameling van de natuurlijke getallen willekeurig lange arithmetische progressies bevat. Deze random deelverzameling maken we door een random kleuring van de natuurlijke getallen te definiëren. Bij de resultaten onderscheiden we in een zwakke wet van de grote aantallen en een...bachelor thesis 2014
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Sol, M.K. (author)We introduce a polymer measure to describe a polymer that is attracted to the origin and repelled by the negative half-plane. We work out a direct expression for the partition function and look at properties of the free energy. We look at the model when repellance becomes attraction and when the repellance occurs in a random fashion. We prove...master thesis 2012
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van Tol, Berend (author)In this thesis, we study stochastic duality under hydrodynamic scaling in the context of interacting particles on a grid. The approach is inspired and motivated by the relation between duality and local equilibria. We identify duality relations in terms of the expectation of the density field for which the hydrodynamic limit is recovered. This...master thesis 2023
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