Title:
Lorentz Lattice Gases on Graphs

dc.contributor.advisor Bunimovich, Leonid
dc.contributor.author Kreslavskiy, Dmitry Michael en_US
dc.contributor.committeeMember Mihai Ciucu
dc.contributor.committeeMember Thomas Morley
dc.contributor.committeeMember Dana Randall
dc.contributor.committeeMember Tetali, Prasad
dc.contributor.department Algorithms, Combinatorics, and Optimization en_US
dc.contributor.department Mathematics
dc.date.accessioned 2005-06-16T20:04:03Z
dc.date.available 2005-06-16T20:04:03Z
dc.date.issued 2003-11-26 en_US
dc.description.abstract The present work consists of three parts. In the first part (chapters III and IV), the dynamics of Lorentz lattice gases (LLG) on graphs is analyzed. We study the fixed scatterer model on finite graphs. A tight bound is established on the size of the orbit for arbitrary graphs, and the model is shown to perform a depth-first search on trees. Rigidity models on trees are also considered, and the size of the resulting orbit is established. In the second part (chapter V), we give a complete description of dynamics for LLG on the one-dimensional integer lattice, with a particular interest in showing that these models are not capable of universal computation. Some statistical properties of these models are also analyzed. In the third part (chapter VI) we attempt to partition a pool of workers into teams that will function as independent TSS lines. Such partitioning may be aimed to make sure that all groups work at approximately the same rate. Alternatively, we may seek to maximize the rate of convergence of the corresponding dynamical systems to their fixed points with optimal production at the fastest rate. The first problem is shown to be NP-hard. For the second problem, a solution for splitting into pairs is given, and it is also shown that this solution is not valid for partitioning into teams composed of more than two workers. en_US
dc.description.degree Ph.D. en_US
dc.format.extent 627499 bytes
dc.format.mimetype application/pdf
dc.identifier.uri http://hdl.handle.net/1853/6423
dc.language.iso en_US en_US
dc.publisher Georgia Institute of Technology en_US
dc.subject Cellular automata en_US
dc.subject Lorentz Lattice gas en_US
dc.subject Logic gates en_US
dc.subject Depth-first search en_US
dc.subject Universal computation en_US
dc.subject Bucket brigades en_US
dc.subject TSS lines en_US
dc.title Lorentz Lattice Gases on Graphs en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.advisor Bunimovich, Leonid
local.contributor.corporatename College of Sciences
local.contributor.corporatename School of Mathematics
relation.isAdvisorOfPublication 8385d52f-b627-4839-8603-2683ea2daa55
relation.isOrgUnitOfPublication 85042be6-2d68-4e07-b384-e1f908fae48a
relation.isOrgUnitOfPublication 84e5d930-8c17-4e24-96cc-63f5ab63da69
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