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You searched for +publisher:"Delft University of Technology" +contributor:("Redig, Frank"). Showing records 1 – 2 of 2 total matches.

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Delft University of Technology

1. van Ginkel, Bart (author). Invariance principle and hydrodynamic limits on Riemannian manifolds.

Degree: 2017, Delft University of Technology

In this report we study Markov processes on compact and connected Riemannian manifolds. We define a random walk on such manifolds and give a direct proof of the invariance principle. This principle says that under some conditions on the jumping distributions (i.e. the distributions of single steps), the random walk converges to Brownian motion when space is scaled by 1/N, time by N2 and N tends to infinity (which has been shown with more general methods by Jorgensen and by Blum). To prove this, we show convergence of the generators on the set of smooth functions and we apply the Trotter-Kurtz theorem (as has been done by Blum, in a rather sketchy way and in a slightly different setting). We also show convergence of the corresponding Dirichlet forms. Then we show that the conditions on the jumping distributions are satisfied if they are compactly supported and have mean 0 and a covariance matrix which is invariant under orthogonal transformations. Next, we define random grids on a Riemannian manifold and we define random walks on them. We show that their Dirichlet forms converge to the Dirichlet form of Brownian motion, using the results above. We also prove a result that is a bit weaker than convergence of the generators in this case. Finally, these grids allow us to define the Symmetric Exclusion Process (SEP) on a manifold. Using the convergence results above, we follow the line of a proof of Seppäläinen to show that the hydrodynamic limit of the SEP satisfies the heat equation. Some details still need to be filled in, but we believe that this method will allow us to study interacting particle systems and their hydrodynamic limits on Riemannian manifolds. Before all of this we start with an introduction to Markov processes, their semigroups and generators. In particular we focus on time-reversible (or symmetric) processes and the Dirichlet form with its properties. We also give an introduction to Riemannian manifolds and related notions. Advisors/Committee Members: Redig, Frank (mentor), van Neerven, Jan (graduation committee), Ruszel, Wioletta (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Riemannian manifold; invariance principle; hydrodynamic limit; geodesic random walk; interacting particle system

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

van Ginkel, B. (. (2017). Invariance principle and hydrodynamic limits on Riemannian manifolds. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694

Chicago Manual of Style (16th Edition):

van Ginkel, Bart (author). “Invariance principle and hydrodynamic limits on Riemannian manifolds.” 2017. Masters Thesis, Delft University of Technology. Accessed November 26, 2020. http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694.

MLA Handbook (7th Edition):

van Ginkel, Bart (author). “Invariance principle and hydrodynamic limits on Riemannian manifolds.” 2017. Web. 26 Nov 2020.

Vancouver:

van Ginkel B(. Invariance principle and hydrodynamic limits on Riemannian manifolds. [Internet] [Masters thesis]. Delft University of Technology; 2017. [cited 2020 Nov 26]. Available from: http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694.

Council of Science Editors:

van Ginkel B(. Invariance principle and hydrodynamic limits on Riemannian manifolds. [Masters Thesis]. Delft University of Technology; 2017. Available from: http://resolver.tudelft.nl/uuid:e6258e4f-9b41-4eb2-9f41-adcbfb689694


Delft University of Technology

2. de Koning, Wouter (author). A simulation based approach to synchromodal container transport.

Degree: 2019, Delft University of Technology

Logistics service providers (LSPs) offering container transport to the hinterland of the Netherlands face the challenge of efficiently using the capacity of the barge in order to minimize cost, while part of the relevant information is still lacking at the moment decisions have to be made. The existing infrastructure and the transportation activities are studied and modeled as an online optimization problem with simultaneously vehicle routing and container-to-mode assignment. A characteristic of great importance in the problem is the uncertainty element that reflects in the requested appointment times that have to be confirmed by another agent in the network. An online optimization approach is proposed, where the input data come in sequentially and decisions have to be made in between, because new information becomes available only after the decision has been made. At each decision moment, the uncertainty element is converted to an offline optimization problem by disregarding the uncertainty or by simulating various potential future scenarios. Subsequently, the problem is modeled as a multi-commodity network design problem on a time-space graph. Four different solution methods are developed in order to solve the online optimization problem. Three confirmation based methods concern a model in which the uncertainty element is partially disregarded, by assuming that each requested appointment time will be scheduled at a specific time relative to the requested one. Alternatively, a much more complex method is developed in which various future scenarios are simulated for the requested appointment times given their probability vector. The simulation based model seeks robust solutions that are resistant to change, i.e., feasible and (sub)optimal for every potential future scenario that has been simulated. Using randomly generated (but realistic) instances, the computational results show that the proposed simulation model surpasses the simpler models both in terms of outcomes, robustness and reliability. However, the practical relevance is somewhat restricted in the sense that the model is built on several assumptions.

CoMet-PS

Advisors/Committee Members: Gijswijt, Dion (mentor), Phillipson, Frank (mentor), Chiscop, Irina (mentor), Aardal, Karen (graduation committee), Redig, Frank (graduation committee), Delft University of Technology (degree granting institution).

Subjects/Keywords: Intermodal transport; Synchromodal transport; Online optimization; Multi-period time window; Simulation algorithm

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

de Koning, W. (. (2019). A simulation based approach to synchromodal container transport. (Masters Thesis). Delft University of Technology. Retrieved from http://resolver.tudelft.nl/uuid:ad4d445e-0e92-4760-9a88-98b50551c6eb

Chicago Manual of Style (16th Edition):

de Koning, Wouter (author). “A simulation based approach to synchromodal container transport.” 2019. Masters Thesis, Delft University of Technology. Accessed November 26, 2020. http://resolver.tudelft.nl/uuid:ad4d445e-0e92-4760-9a88-98b50551c6eb.

MLA Handbook (7th Edition):

de Koning, Wouter (author). “A simulation based approach to synchromodal container transport.” 2019. Web. 26 Nov 2020.

Vancouver:

de Koning W(. A simulation based approach to synchromodal container transport. [Internet] [Masters thesis]. Delft University of Technology; 2019. [cited 2020 Nov 26]. Available from: http://resolver.tudelft.nl/uuid:ad4d445e-0e92-4760-9a88-98b50551c6eb.

Council of Science Editors:

de Koning W(. A simulation based approach to synchromodal container transport. [Masters Thesis]. Delft University of Technology; 2019. Available from: http://resolver.tudelft.nl/uuid:ad4d445e-0e92-4760-9a88-98b50551c6eb

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