QSpace Community:
http://hdl.handle.net/1974/769
2014-10-02T16:37:00ZParameter Inference and Estimability Analysis for Nonlinear Multi-Response Systems by Means of Profiling
http://hdl.handle.net/1974/12552
Title: Parameter Inference and Estimability Analysis for Nonlinear Multi-Response Systems by Means of Profiling
Authors: Golfar, Bahareh
Abstract: Determining the inference bounds for parameter estimates in multi-response models is a challenge for research and industry since potential co-dependencies among responses add to the complexity of the problem. Statistical profiling is a valuable method in such situations that provides insight into model nonlinearity and co-dependencies among parameter estimates by studying the behavior of the likelihood function.
This thesis focuses on extending the application of profiling for parameter inference and estimability analysis to nonlinear multi-response models with unknown noise covariance terms. Profiling is explored based on Generalized Least Squares (GLS) and Determinant Criterion (DC). One issue is finding the distribution and the corresponding degrees of freedom of the profile likelihood function, which depends on the process of estimation of the noise covariance matrix in multi-response models. A method for estimating this matrix and performing profiling is proposed. This research proves that for multi-response models with m responses, p parameters and n experimental runs, the GLS-based profile likelihood function has a χ_1^2 or an F_(1,nm-p) distribution for cases with known or unknown noise covariance matrices respectively. Similarly, the DC-based profile likelihood is shown to have an F_(1,nm-p) distribution. The GLS-based and DC-based profiling approaches are compared theoretically and in practice, suggesting that the GLS-based method is overall more advantageous for small datasets and a combination of DC for parameter estimation and GLS for profiling generally produces reliable results when certain issues are avoided.
Furthermore, application of profiling for parameter estimability analysis is explored and a profile-based exploratory analysis is proposed which studies the GLS-based profile likelihood plots and profile traces to reveal inestimability issues. This method links parameter estimability analysis to parameter inference and brings the two objectives of this thesis together. All the proposed methods are examined by means of several examples, the results of which validate the defined approaches.
Description: Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2014-10-01 14:50:13.4652014-10-01T04:00:00ZThe Application of Monte Carlo Combined Methods For Modeling of Polymerization Kinetics
http://hdl.handle.net/1974/12530
Title: The Application of Monte Carlo Combined Methods For Modeling of Polymerization Kinetics
Authors: Parsa, Mohammad Ali
Abstract: The advantages and disadvantages of the two major categories of numerical methods, deterministic and stochastic approaches, in polymer reaction engineering are discussed. Combinations of methods are suggested in order to take advantage of both techniques. A hybrid deterministic/stochastic approach and a combined stochastic/stochastic method are developed to represent two polymerization systems of interest.
The distribution of functional groups in polymer chains produced in radical copolymerization by starved-feed semibatch operation is simulated using three different methodologies. A deterministic model is formulated to separately track the homopolymer chains that are produced without the desired functionality, a Monte Carlo (MC) model is written to represent the system, and a hybrid deterministic/MC approach is taken using new capabilities within the software package PREDICI.
Two Monte Carlo algorithms (dynamic and static) are combined in order to model and simulate the branch distribution and topology of polymer chains synthesized in hyper-branched polymerization of polyethylene with Pd-diimine catalysts. A sensitivity analysis is conducted in order to investigate the impact of kinetic and stochastic parameters on the branch distribution as well as average chain length. Simulated results show excellent agreement with experimental observations.
Description: Thesis (Master, Chemical Engineering) -- Queen's University, 2014-09-29 12:23:27.6762014-09-30T04:00:00ZOrientation in Large-Amplitude Oscillatory Shear
http://hdl.handle.net/1974/12525
Title: Orientation in Large-Amplitude Oscillatory Shear
Authors: Schmalzer, Andrew M.; Giacomin, A. Jeffrey
Abstract: We examine the simplest relevant molecular model for large-amplitude oscillatory shear flow of a polymeric liquid: the dilute suspension of rigid dumbbells in a Newtonian solvent. We find explicit analytical expressions for the orientation distribution function, and specifically for test conditions of frequency and shear rate amplitude that generate higher harmonics in the shear stress and normal stress difference responses. Our analysis employs the general method of Bird and Armstrong (1972) for analyzing the orientation of the rigid dumbbells in suspension in any unsteady shear flow. We have solved the diffusion equation analytically to explore the orientations of the molecules induced by the oscillatory shear flow. We see that the orientation distribution function is neither even nor odd. We find zeroth, first, second, third and fourth harmonics of the orientation distribution function, and we have derived explicit analytical expressions for these. We use our analytical solution to examine the detailed shape of the orientation distribution function. We provide a clear visualization of the orientation distribution function in
large-amplitude oscillatory shear flow in spherical coordinates all the way around
one full alternant cycle (at ωt = 0, π4
, π2,…,2π ). Our analysis supplements our
previous results for the shear stress [Bird et al., JCP, 140, 074904 (2014)] and normal
stress differences [Schmalzer et al., PRG Report No. 002, Queen’s University (April
2014)] for a suspension of rigid dumbbells in large-amplitude oscillatory shear flow.
This exploration includes the Newtonian, the linear viscoelastic and nonlinear
viscoelastic regimes. We find the orientation distribution for Newtonian behavior to be nearly isotropic (spherical), for the linearly viscoelastic behavior, only slightly anisotropic (only a slight ellipsoidal departure from spherical), and for the nonlinear viscoelastic regime, we find the orientation distribution function for the dumbbells to be highly anisotropic (and even peanut or dumbbell shaped, which we call lemniscoidal).2014-09-30T04:00:00ZLarge-Amplitude Oscillatory Shear: Comparing Parallel-Disk with Cone-Plate Flow
http://hdl.handle.net/1974/12523
Title: Large-Amplitude Oscillatory Shear: Comparing Parallel-Disk with Cone-Plate Flow
Authors: Giacomin, A. Jeffrey; Gilbert, Peter H.; Merger, Dimitri; Wilhelm, Manfred
Abstract: We compare the ratio of the amplitudes of the third to the first harmonic of the torque, T 3 T 1 , measured in rotational parallel-disk flow, with the ratio of the
corresponding harmonics of the shear stress,
τ 3 τ 1 , that would be observed in
sliding-plate or cone-plate flow. In other words, we seek a correction factor with
which T 3 T 1 must be multiplied, to get the quantity τ 3 τ 1 , where τ 3 τ 1 is
obtained from any simple shearing flow geometry. In this paper, we explore
theoretically, the disagreement between
T 3 T 1 and τ 3 τ 1 using the simplest
continuum model relevant to large-amplitude oscillatory shear flow: the single
relaxation time corotational Maxwell model. We focus on the region where the harmonic amplitudes and thus, their ratios, can be fully described with power laws. This gives the expression for T 3 T 1 , by integrating the explicit analytical solution for the shear stress. In the power law region, we find that, for low Weissenberg numbers, for the third harmonics T 3 T 1 = 2/3 τ 3 τ 1 , and for the fifth harmonics, T 5 T 1 = 1
2 τ 5 τ 1 . We verify these results experimentally. In other words, the heterogeneous flow field of the parallel-disk geometry significantly attenuates the higher harmonics, when compared with the homogeneous, sliding-plate flow. This is because only the outermost part of the sample is subject to the high shear rate amplitude. Further, our expression for the torque in large-amplitude oscillatory parallel-disk flow is also useful for the simplest design of viscous torsional dampers, that is, those incorporating a viscoelastic liquid between two disks.2014-09-30T04:00:00Z