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MODELS AND SIMULATIONS OF SPROUTING ANGIOGENESIS
Title
MODELS AND SIMULATIONS OF SPROUTING ANGIOGENESIS
Creator
Langman, Catherine
Date
2016, 2016-05
Description
All living mammalian cells need to consume oxygen and nutrients for cellular processes and need a way to remove waste from those cellular...
Show moreAll living mammalian cells need to consume oxygen and nutrients for cellular processes and need a way to remove waste from those cellular processes. Capillary networks provide places for such exchanges to occur. The process of creating new capillaries from existing blood vessels is called angiogenesis. Understanding angiogenesis is critical to the advancement of knowledge in the life sciences, as well as in medical applications where blood vessels play an important role. Angiogenesis is a complex process composed of many subprocesses which are not yet fully understood and take place over varying temporal and spatial scales. Mathematically modeling and simulating angiogenesis, and evaluating the capillary networks that result from angiogenesis, can help further understanding of angiogenesis and improve therapeutic treatments. This thesis examines mathematical models and simulations of sprouting angiogenesis and proposes two generic models of sprouting angiogenesis based on descriptions found in educational and scientific literature. Future research opportunities for scientific study and educational study using these models as a starting place are discussed.
M.S. in Applied Mathematics, May 2016
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CHAIN BY CHAIN MONTE CARLO SIMULATIONS FOR POLYMERIZATION PROCESSES
Title
CHAIN BY CHAIN MONTE CARLO SIMULATIONS FOR POLYMERIZATION PROCESSES
Creator
Demirel, Derya
Date
2016, 2016-05
Description
Predicting chain microstructure became an important task for polymer scientists. Polydisperse nature of polymer molecules makes it an...
Show morePredicting chain microstructure became an important task for polymer scientists. Polydisperse nature of polymer molecules makes it an interesting research area. In this work, a new method, called “Chain-by-Chain Monte Carlo Method” (CBCMC), is presented for simulating chain microstructures one-by-one or chain-by-chain. To the best of our knowledge, it is a new approach for the simulation of chain microstructures. It is a hybrid deterministic-stochastic method that uses the best of two worlds by obtaining information on the mean-field background environment as concentrations of polymer populations and small molecules (only) from the deterministic solver and using it in the stochastic part of the algorithm. Deterministic solver can employ any method that provides this data and in this work uses method of moments. With this information, stochastic part of the algorithm employs kinetic Monte Carlo algorithm to simulate chains one-by-one. The computational load of simulating the whole ensemble is eliminated by getting the mean-field background information from deterministic solvers as concentrations of polymer populations and small molecules at certain time intervals. CBC-MC is suited for chemistries, or situations in which the chain architecture develops slowly with respect to the background environment such as controlled reversible-deactivation radical polymerizations. This method is applied to two case studies for synthesis of linear gradient copolymers. First case study is a styrene/ methyl methacrylate copolymerization by nitroxide-mediated polymerization with forced gradient techniques and the second one is the synthesis of methyl methacrylate/ methyl acrylate hyberbolic gradient copolymerization by atom-transfer radical polymerization again with forced gradient techniques. Gradient distribution of chain properties is analyzed in all cases since it is relatively more challenging and interesting. Chain properties such as number average chain length, weight average chain length, polydispersity index, cumulative and instanteneous copolymer compositions, full molecular weight distributions and sequence length distributions are obtained and compared to results from method of moments and kinetic Monte Carlo methods for di↵erent sample sizes. Results were in good agreement with wellestablished method of moments and kinetic Monte Carlo methods. Importance of simulating chain microstructure rather than average properties is made clear. Simulation times were reduced by at least a factor of six compared to kinetic Monte Carlo method. Results confirm that if applicable, full information regarding the microstructure of chains can be obtained using this method with reduced simulation times and smaller sample sizes. This method is also applied to non-linear copolymerization of acrylamide/N,N-methylenebis(acrylamide) (AM/BisAM) leading to gelation. The e↵ect of a gradient distribution of pendant double bonds along the primary chains on the simulated portion of gel molecules is investigated with the aim of detecting the macro-heterogeinities. Five cases are studied with di↵erent feeding policies but same total number of comonomers introduced to each of them. Primary chain results are compared with MOM for cumulative and instantaneous BisAM compositions, crosslink and PDB densities and found to be in excellent agreement. Further investigations are done on primary chain microsturctures to better understand multiple phenomena going on in these systems such as the age distribution of crosslinking points and PDBs, density of crosslinking points and PDBs in monomer bins along the primary chains and average segment lengths. It has been found that a gradient in PDB distribution along the primary chains can introduce heterogeneities into the gel molecules in surface-bound type polymerizations where primary chains within gels are aligned in the same direction but these heterogeneities seem to be disappearing in bulk polymerizations where the chain alignments are random.
Ph.D. in Chemical Engineering, May 2016
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