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You searched for +publisher:"University of North Carolina" +contributor:("Forest, Gregory"). Showing records 1 – 2 of 2 total matches.

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University of North Carolina

1. HEROY, SAMUEL. Rigidity Percolation in Disordered Fiber Systems: Theory and Applications.

Degree: Mathematics, 2018, University of North Carolina

Nanocomposites, particularly carbon nanocomposites, find many applications spanning an impressive variety of industries on account of their impressive properties and versatility. However, the discrepancy between the performance of individual nanoparticles and that of nanocomposites suggests continued technological development and better theoretical understanding will provide much opportunity for further property enhancement. Study of computational renderings of disordered fiber systems has been successful in various nanocomposite modeling applications, particularly toward the characterization of electrical properties. Motivated by these successes, I develop an explanatory model for `mechanical' or `rheological percolation,' terms used by experimentalists to describe a nonlinear increase in elastic modulus/strength that occurs at particle inclusion volume fractions well above the electrical percolation threshold. Specifically, I formalize a hypothesis given by \citet*{penu}, which states that these dramatic gains result from the formation of a `rigid CNT network.' Idealizing particle interactions as hinges, this amounts to the network property of \emph{rigidity percolation} – the emergence of a giant component (within the inclusion contact network) that is not only connected, but furthermore the inherent contacts are patterned to constrain all internal degrees of freedom in the component. Rigidity percolation has been studied in various systems (particularly the characterization of glasses and proteins) but has never been applied to disordered systems of three-dimensional rod-like particles. With mathematically principled arguments from \emph{rigidity matroid theory}, I develop a scalable algorithm (\emph{Rigid Graph Compression}, or \emph{RGC}), which can be used to detect rigidity percolation in such systems by iteratively compressing provably rigid subgraphs within the rod contact networks. Prior to approaching the 3D system, I confirm the usefulness of \emph{RGC} by using it to accurately approximate the rigidity percolation threshold in disordered systems of 2D fibers – achieving <1% error relative to a previous exact method. Then, I develop an implementation of \emph{RGC} in three dimensions and determine an upper bound for the rigidity percolation threshold in disordered 3D fiber systems. More work is required to show that this approximation is sufficiently accurate – however, this work confirms that rigidity in the inclusion network is a viable explanation for the industrially useful mechanical percolation. Furthermore, I use \emph{RGC} to quantitatively characterize the effects of interphase growth and spatial CNT clustering in a real polymer nanocomposite system of experimental interest. Advisors/Committee Members: HEROY, SAMUEL, MUCHA, PETER, MUCHA, PETER, FOREST, GREGORY, KLOTSA, DAPHNE, DINGEMANS, THEO, Adalsteinsson, David.

Subjects/Keywords: College of Arts and Sciences; Department of Mathematics

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

APA (6th Edition):

HEROY, S. (2018). Rigidity Percolation in Disordered Fiber Systems: Theory and Applications. (Thesis). University of North Carolina. Retrieved from https://cdr.lib.unc.edu/record/uuid:456c1173-d48e-4b39-a6d5-a64b92248b17

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

HEROY, SAMUEL. “Rigidity Percolation in Disordered Fiber Systems: Theory and Applications.” 2018. Thesis, University of North Carolina. Accessed December 01, 2020. https://cdr.lib.unc.edu/record/uuid:456c1173-d48e-4b39-a6d5-a64b92248b17.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

HEROY, SAMUEL. “Rigidity Percolation in Disordered Fiber Systems: Theory and Applications.” 2018. Web. 01 Dec 2020.

Vancouver:

HEROY S. Rigidity Percolation in Disordered Fiber Systems: Theory and Applications. [Internet] [Thesis]. University of North Carolina; 2018. [cited 2020 Dec 01]. Available from: https://cdr.lib.unc.edu/record/uuid:456c1173-d48e-4b39-a6d5-a64b92248b17.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

HEROY S. Rigidity Percolation in Disordered Fiber Systems: Theory and Applications. [Thesis]. University of North Carolina; 2018. Available from: https://cdr.lib.unc.edu/record/uuid:456c1173-d48e-4b39-a6d5-a64b92248b17

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation


University of North Carolina

2. Bernardi, Francesca. Space/Time Evolution in the Passive Tracer Problem.

Degree: Mathematics, 2018, University of North Carolina

This dissertation is concerned with understanding how the behavior of a concentration of tracer undergoing an advection-diffusion process in Poiseuille flows depends on the pipe cross-section. Solutions to the advection-diffusion problem are approached both for the longitudinal moments of the concentration, via exact and asymptotics analysis, and for the entire tracer concentration, via analysis and experiments. The main focus of this work is on the skewness of the distribution, which is the simplest statistic to describe longitudinal asymmetries in the tracer concentration. The results of exact and asymptotic analysis along with experiments and numerical simulations, show that the distribution’s skewness depends significantly on the cross section of the pipe. Advisors/Committee Members: Bernardi, Francesca, Camassa, Roberto, McLaughlin, Richard, Forest, Gregory, Miller, Laura, Newhall, Katherine.

Subjects/Keywords: College of Arts and Sciences; Department of Mathematics

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

APA (6th Edition):

Bernardi, F. (2018). Space/Time Evolution in the Passive Tracer Problem. (Thesis). University of North Carolina. Retrieved from https://cdr.lib.unc.edu/record/uuid:5449c8d0-044c-44a7-ba42-2510b8e50a31

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Bernardi, Francesca. “Space/Time Evolution in the Passive Tracer Problem.” 2018. Thesis, University of North Carolina. Accessed December 01, 2020. https://cdr.lib.unc.edu/record/uuid:5449c8d0-044c-44a7-ba42-2510b8e50a31.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Bernardi, Francesca. “Space/Time Evolution in the Passive Tracer Problem.” 2018. Web. 01 Dec 2020.

Vancouver:

Bernardi F. Space/Time Evolution in the Passive Tracer Problem. [Internet] [Thesis]. University of North Carolina; 2018. [cited 2020 Dec 01]. Available from: https://cdr.lib.unc.edu/record/uuid:5449c8d0-044c-44a7-ba42-2510b8e50a31.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Bernardi F. Space/Time Evolution in the Passive Tracer Problem. [Thesis]. University of North Carolina; 2018. Available from: https://cdr.lib.unc.edu/record/uuid:5449c8d0-044c-44a7-ba42-2510b8e50a31

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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