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Percolation in correlated systems
Descriptive
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Title
Percolation in correlated systems
Name
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Marinov
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Vesselin
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Vesselin Marinov
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author
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Lebowitz
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Joel
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Advisory Committee
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Joel L Lebowitz
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chair
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Moore
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Gregory
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Advisory Committee
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Gregory W Moore
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internal member
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Coleman
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Piers
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Advisory Committee
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Piers Coleman
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internal member
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Speer
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Eugene
Affiliation
Advisory Committee
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Eugene R Speer
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outside member
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Rutgers University
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degree grantor
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Graduate School - New Brunswick
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Text
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theses
OriginInfo
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2007
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2007
Language
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English
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electronic
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viii, 75 pages
Abstract
In this thesis we study various problems in dependent percolation theory. In the first
part of this thesis we study disordered q-state Potts models as examples of systems in which
there is percolation for an arbitrary low density and no percolation for arbitrary high density of
occupied sites. In the second part of the thesis we study dependent percolation models in which the correlations between the site occupation variables are long range, i.e. decaying as r [superscript -a] for a [less than sign] d, where r is the separation between any two sites and d is the dimension of the model. Scaling analysis suggests that such long range correlated percolation models define a new percolation
universality classes with critical exponents depending on a. We develop a field theoretic description of these models in an attempt to calculate the critical exponents of the transition in an double expansion in terms of epsilon = 6 - d and delta = 4 - a. In the third part we study the percolation transition for two specific long range correlated percolation models on the 3 dimensional integer square lattice. These two percolation models are derived from the Voter model and the Harmonic crystal respectively.
Our simulation results confirm the basic scaling arguments and the field theoretic results.
part of this thesis we study disordered q-state Potts models as examples of systems in which
there is percolation for an arbitrary low density and no percolation for arbitrary high density of
occupied sites. In the second part of the thesis we study dependent percolation models in which the correlations between the site occupation variables are long range, i.e. decaying as r [superscript -a] for a [less than sign] d, where r is the separation between any two sites and d is the dimension of the model. Scaling analysis suggests that such long range correlated percolation models define a new percolation
universality classes with critical exponents depending on a. We develop a field theoretic description of these models in an attempt to calculate the critical exponents of the transition in an double expansion in terms of epsilon = 6 - d and delta = 4 - a. In the third part we study the percolation transition for two specific long range correlated percolation models on the 3 dimensional integer square lattice. These two percolation models are derived from the Voter model and the Harmonic crystal respectively.
Our simulation results confirm the basic scaling arguments and the field theoretic results.
Note
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Ph.D.
Note
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Includes bibliographical references (p. 71-74).
Subject
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Topic
Physics and Astronomy
Subject
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Topic
Percolation (Statistical physics)
Subject
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Topic
Lattice theory
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Title
Graduate School - New Brunswick Electronic Theses and Dissertations
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rucore19991600001
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http://hdl.rutgers.edu/1782.2/rucore10001600001.ETD.16736
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ETD_267
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doi:10.7282/T3ZS2WXB
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ETD doctoral
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Rights
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The author owns the copyright to this work.
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Open
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Name
Vesselin Marinov
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Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
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Non-exclusive ETD license
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Author Agreement License
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I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
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