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dc.contributor.advisorSeibold, Benjamin
dc.creatorRamadan, Rabie
dc.date.accessioned2020-11-02T14:46:28Z
dc.date.available2020-11-02T14:46:28Z
dc.date.issued2020
dc.identifier.urihttp://hdl.handle.net/20.500.12613/2078
dc.description.abstractEven though first order LWR models have many limitations, they are still widely used in many engineering applications. Second-order models, on the other hand, address many of those limitations. Among second-order models, the inhomogeneous Aw-Rascle-Zhang (ARZ) model is well-received as its structure generates characteristic waves that make physical sense. The ARZ model --- and other $2\times 2$ hyperbolic systems with a relaxation term --- possess a critical phase transition: whenever the sub-characteristic condition (SCC) is violated, uniform traffic flow is unstable, and small perturbations grow into nonlinear traveling waves, called jamitons. The case where the SCC is satisfied has been studied extensively. However, what is essentially unstudied is the question: which jamiton solutions are dynamically stable? To understand which stop-and-go traffic waves can arise through the dynamics of the model, this question is critical. This dissertation first outlines the mathematical foundations of the ARZ model and its solutions, then presents a computational study demonstrating which types of jamitons are dynamically stable, and which are not. After that, a procedure is presented that characterizes the stability of jamitons. The study reveals that a critical component of this analysis is the proper treatment of the perturbations to the shocks, and of the neighborhood of the sonic points. The insight gained from answering the question regarding the dynamical stability of jamitons has many applications. One particular application presented here is deriving an averaged model for the ARZ model. Such a model is as simple to solve (analytically and numerically) as the LWR model, but nevertheless captures the cumulative effects of jamitons regarding fuel consumption, total flow, and braking events.
dc.format.extent156 pages
dc.language.isoeng
dc.publisherTemple University. Libraries
dc.relation.ispartofTheses and Dissertations
dc.rightsIN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available.
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/
dc.subjectMathematics
dc.subjectTransportation
dc.subjectApplied Mathematics
dc.subjectAveraging
dc.subjectFuel Consumption
dc.subjectJamiton
dc.subjectStability
dc.subjectSub-characteristic Condition
dc.subjectTraffic Modeling
dc.titleNon-Equilibrium Dynamics of Second Order Traffic Models
dc.typeText
dc.type.genreThesis/Dissertation
dc.contributor.committeememberQueisser, Gillian
dc.contributor.committeememberKlapper, Isaac
dc.contributor.committeememberRosales, Rodolfo R.
dc.description.departmentMathematics
dc.relation.doihttp://dx.doi.org/10.34944/dspace/2060
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.description.degreePh.D.
refterms.dateFOA2020-11-02T14:46:28Z


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