Browsing by Author "Zhilin Li, Committee Member"

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Advanced Computational Methodology for Full-Core Neutronics Calculations
(2004-08-17) Hiruta, Hikaru; Dmitriy Y. Anistratov, Committee Chair; Paul J. Turinsky, Committee Member; Robin P. Gardner, Committee Member; Zhilin Li, Committee Member
The modern computational methodology for reactor physics calculations is based on single–assembly transport calculations with reflective boundary conditions that generate homogenized few–group data, and core–level coarse-mesh diffusion calculations that evaluate a large-scale behavior of the scalar flux. Recently, an alternative approach has been developed. It is based on the low-order equations of the quasidiffusion (QD) method in order to account accurately for complicated transport effects in full–core calculations. The LOQD equations can capture transport effects to an arbitrary degree of accuracy. This approach is combined with single–assembly transport calculations that use special albedo boundary conditions which enable one to simulate efficiently effects of an unlike neighboring assembly on assembly's group data. In this dissertation, we develop homogenization methodology based on the LOQD equations and spatially consistent coarse–mesh finite element discretization methods for the 2D low–order quasidiffusion equations for the full–core calculations. The coarse–mesh solution generated by this method preserves a number of spatial polynomial moments of the fine–mesh transport solution over coarse cells. The proposed method reproduces accurately the complicated large–scale behavior of the transport solution within assemblies. To demonstrate accuracy of the developed method, we present numerical results of calculations of test problems that simulate interaction of MOX and uranium assemblies. We also develop a splitting method that can efficiently solve coarse-mesh discretized low-order quasidiffusion (LOQD) equations. The presented method splits the LOQD problem into two parts: (i) the $D$-problem that captures a significant part of transport solution in the central parts of assemblies and can be reduced to a diffusion-type equation, and (ii) the $Q$-problem that accounts for the complicated behavior of the transport solution near assembly boundaries. Independent coarse-mesh discretizations are applied: the $D$-problem equations are approximated by means of a finite-element method, whereas the $Q$-problem equations are discretized using a finite-volume method. Numerical results demonstrate the efficiency of the presented methodology. This methodology can be used to modify existing diffusion codes for full-core calculations (which already solve a version of the $D$-problem) to account for transport effects.
An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix
(2007-03-09) Chanchana, Prakash; Carl D. Meyer, Committee Chair; Ernie L. Stitzinger, Committee Member; Zhilin Li, Committee Member; Min Kang, Committee Member
We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz's formula with a special inverse iteration algorithm discussed in [10, Linear Algebra Appl., 15 (1976), pp 235-242]. Numerical experiments demonstrate that our algorithm is able to compute the Perron root accurately and faster than other well known algorithms; in particular, when the size of the matrix is large. The proof of convergence of our algorithm is also presented.
Anisotropic Diffusion in Fluorescence Microscopy
(2004-04-08) Wan, Xiaohai; Sharon R. Lubkin, Committee Chair; Cavell Brownie, Committee Co-Chair; Zhilin Li, Committee Member
Diffusion of tracer molecules in configurations of collagen fibrils may be used to determine anisotropy of fiber distributions in fluorescence microscopy experiments. Mathematical simulations are used to study the feasibility of these kinds of experiments. The anisotropic diffusion phenomenon can be modeled as a random walk process in simulated completely aligned fibers using the Monte Carlo method. We studied the relationships between the diffusion coefficients (either parallel or perpendicular to fiber orientation) and two influencing factors (density of fibers and relative size of fibers and tracer molecules). Using simulations and statistical analysis, we found that for a given fiber density, relatively bigger size tracer molecules are preferred in order to detect certain level of anisotropy of the fibers. If tracer molecules are too small compared with fibers, even high density of fibers can help little to detect any anisotropy.
Atomic Simulation of Nanoparticles and polyethylene-nanodiamond composites
(2009-01-30) Hu, Zushou; Donald W. Brenner, Committee Chair; Maurice Balik, Committee Member; Ron O. Scattergood, Committee Member; Zhilin Li, Committee Member
We examine the size and surface orientation/principal axis dependent stability of nanodiamonds and nanorods. We find that the nanodiamonds and nanorods are thermally stable at nanoscale; however, the (001) surface will tend to form dimers, and the (111) surface will buckify to reduce system energy when diameter is less than 2 nm. We also notice that the octahedra is the most stable morphology in all the carbon particles we studied, and the nanorods with the combination of <001> and (011), <011> and (111), and <011> and (001)/(111) are the stable nanorod structures. The MD simulation on glass transition and elastic properties of polyethylene-nanodiamond composites are also carried out in our studies. The results on glass transition show that the transition is a second order phase transition mainly associated with the change in torsional and non-bond interactions. The results on elastic properties indicate that the effect of nanoparticles on polymer composites is mainly determined by the equivalent time scale movement of nanoparticles and polymer chains, which can be improved by either equivalent size scale of nanoparticles and polymer chains or increasing interface interaction, such as chemical bonds at surface. The addition of nanoparticles usually increases the composite density; however, it doesnâ€™t necessarily increase the density of polymer matrix.
Atomic Structure Optical Properties and Electron Transport in Self-assembled Monolayers on Surfaces
(2007-07-18) Wang, Shuchun; Marco Buongiorno Nardelli, Committee Member; Wenchang Lu, Committee Member; Jerry Bernholc, Committee Chair; Chris Roland, Committee Member; Zhilin Li, Committee Member
Adsorbate-induced modification of semiconductor or metal surfaces creates a nano-scale quantum structure which offers a rich vein of exotic physical phenomena for investigation. Human desire to harness these properties for technological or scientific purposes has led to extensive experimental and theoretical investigations. This dissertation focuses on the ab initio simulations of atomic, electronic, optical, and transport properties of nano-scale systems. The calculated results for indium nanowires on the Si(111) surface identify their atomic structure and reveal a phase transition at low temperature. Transport simulations on the self-assembled monolayer of ferrocenyl-alkanethiolate on Au(111) surface show negative difference resistance, which is in very good agreement with experimental observations. This opens a new opportunity for applications in nanoscale molecular devices.
Batch Sedimentation in an Impulsively Heated System.
(2010-07-22) Joshi, Ameya; Thomas Ward, Committee Chair; Alexei Saveliev, Committee Member; Zhilin Li, Committee Member; Tarek Echekki, Committee Member
Characterization of Stress-Effects in Ferroelectrics with Application to Transducer Design
(2006-08-21) Ball, Brian L; Kazifumi Ito, Committee Member; Zhilin Li, Committee Member; Ralph C Smith, Committee Chair; Stefan Seelecke, Committee Member
The increasing investigation of smart material structures requires a more thorough understanding and characterization of the underlying physics in both the constituent materials and the adaptive structures as a whole. To this end, we focus our efforts on understanding the effects of stress on ferroelectric materials and the transducers which utilize them. This dissertation addresses the development of constitutive models based on homogenized energy principles which characterize the ferroelastic switching mechanisms inherent to ferroelectric materials in a manner suitable for subsequent transducer and control design. Models characterizing the manufactured shape and quantifying the displacements generated in THUNDER (THin layer UNimorph ferroelectric DrivER and sensor) actuators in response to applied voltages for a variety of boundary conditions are developed utilizing the developed ferroelastic switching models. To develop constitutive models, we construct Helmholtz and Gibbs energy relations which quantify the potential and electrostatic energy associated with 90 and 180 degree dipole orientations. Equilibrium relations appropriate for homogeneous materials in the absence or presence of thermal relaxation are respectively determined by minimizing the Gibbs energy or balancing the Gibbs and relative thermal energies using Boltzmann principles. Stochastic homogenization techniques are employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds. Models characterizing the manufactured shape of THUNDER actuators and displacements resulting from applied voltages for fields are constructed using thin shell theory and Newtonian principles. The thermal stresses and strains due to repoling resulting in a prestressing of the PZT layer are also included in the model development. Attributes and limitations of the characterization framework are illustrated through comparison with experimental data.
Computational Biomechanical Models for the Pericellular Matrix of Articular Cartilage
(2010-04-21) Kim, EunJung; Mansoor A. Haider, Committee Chair; Farshid Guilak, Committee Member; Zhilin Li, Committee Member; Ralph C. Smith, Committee Member
Articular cartilage is a resilient biological soft tissue that serves to support load in diarthrodial joints such as the knee, shoulder and hip. Cartilage can be idealized as a biphasic mixture that is comprised of a solid extracellular matrix (ECM) saturated by interstitial fluid. Cartilage ECM is maintained by a sparse population of cells called chondrocytes, which are surrounded by a narrow layer called the pericellular matrix (PCM). Together, the chondrocyte and its surrounding PCM have been termed the chondron. Since cartilage is avascular and aneural, cell metabolic activity is highly dependent upon the mechanical characteristics of the local extracellular environment. However, the relationships between microscopic and macroscopic biphasic mechanical variables are not well understood. This research is motivated by the need to quantify these relationships. Two computational models were developed pertaining to mechanical interactions between the cells, the PCM and the ECM of articular cartilage. In the first study, a transient finite element model (FEM) was developed for linear biphasic mechanics in the microscopic environment of a single cell within a cartilage layer under cyclic loading in confined compression. The microscopic domain was modeled as a micron-scale cylinder of ECM with a spherical inclusion arising from the presence of a single cell and its encapsulating PCM . Boundary conditions for the three-zone microscale model were generated using an analytic solution for the macroscopic cyclic confined compressive loading of a cartilage layer. To perform these simulations, an axisymmetric displacement-velocity penalty biphasic FEM was implemented as a custom weak formulation in the software package Comsol Multiphysics. Accuracy of the implementation was validated against known analytic solutions for cyclic compressive loading of a biphasic layer, and the dynamic radial deformation of a layered biphasic sphere. The microscale biphasic FEM was employed to analyze the effects of frequency on biphasic mechanical variables in the cellular microenvironment under macroscopic cyclic confined compressive loading at 1% engineering strain, and in the frequency range 0.01-1Hz. The second study consisted of the formulation, implementation and application of a multiscale axisymmetric elastic boundary element method (BEM) for simulating in situ chondron deformation in states of mechanical equilibrium within a cartilage explant under equilibrated unconfined compression. The microscopic domain was modeled as a micron-scale sphere of ECM with an ellipsoidal inclusion, representing the chondron. Boundary conditions for this microscale model were generated using a known analytic solution for unconfined compression of a cartilage layer. Accuracy of the three-zone BEM was evaluated and compared to analytical solutions and finite element solutions. The BEM was then integrated with a nonlinear optimization technique (Nelder-Mead) to determine PCM elastic properties in situ within the ECM of the cartilage explant by solving an inverse problem associated with the experimental data.
Control of Infinite Dimensional Bilinear Systems: Applications to Quantum Control Systems
(2009-08-03) Zhang, Qin; Xiaobiao Lin, Committee Member; Ralph Smith, Committee Member; Zhilin Li, Committee Member; Kazufumi Ito, Committee Chair
In the dissertation, optimal control problem for bilinear systems motivated from quantum control theory are studied. Specifically, problems of quantum feedback control, control of tumor growth dynamics and time optimal control are analyzed for bilinear systems. Feedback synthesis, receding horizon synthesis and semi-smooth Newton method are developed to solve these problems. The contents of the dissertation are outlined as follows: The first problem studied is control of quantum systems described by the linear SchrÃ‚Â¨odinger equation. Control inputs enter through coupling operators and results in a bilinear control system. Feedback control laws with switching term are developed for the orbit tracking and the performance of the feedback control laws is demonstrated by a stable and accurate numerical integration of the closed-loop system. The asymptotic properties of the feedback laws are analyzed by the LaSalle-type invariance principle. The receding horizon control synthesis is applied to improve the performance of the feedback law. The second order accurate numerical integrations via time-splitting and the monotone convergent iterative scheme are combined to solve the optimality system. The switching mechanism in the feedback law can be applied to a wide general class of control systems and feedback synthesis based on the Lyapunov stability. By using this principle, the problem of the tumor treatment, aiming at the reduction of the tumor cells population, is formulated in terms of optimal control theory as a state regulator problem and a feedback law with switching term is designed. Numerical evidence is shown to demonstrate the effectiveness of the feedback law to suppress the tumor growth. A quantum system interacts with its environment. As a consequence, quantum state subject to continuous measurement can be modeled as a nonlinear stochastic differential equation by quantum filtering theory. The problem of stochastic stabilization of quantum spin systems under the noisy environment and continuous measurement via feedback control is studied. New nonlinear control law with switching term is proposed and developed to globally stabilize the quantum spin system to an arbitrary equilibrium state. Nonnegative definite preserving properties of the density matrix to measure the quantum system is very essential and a numerical method is developed to fulfill this. Finally, time optimal and minimum effort control problems for linear and bilinear systems are studied. To overcome the difficulties of nondifferentiability in the bang-bang control, a regularized problem is formulated and the semi-smooth Newton method is applied for solving the regularized optimality system. By integrating the state and costate and variation of them in the optimality system, the nonlinear optimality system is further reduced to a nonlinear equation with some shooting parameters. The reduced Jacobian is computed for the Newton update. The initialization of the Newton method is achieved by solving a related minimum norm problem and using the standard line search strategy. The effectiveness of the proposed method is demonstrated by examples for quantum spin system and parabolic systems.
Deterministic and Semi-Mechanistic Approaches in Predictive Fermentation Microbiology
(2002-10-10) Dougherty, Daniel Patrick; Marcia L. Gumpertz, Committee Member; Zhilin Li, Committee Member; Frederick Breidt Jr., Committee Co-Chair; Sharon R. Lubkin, Committee Chair
Predictive fermentation microbiology utilizes deterministic and stochastic mathematical models to study the growth dynamics of microorganisms. If the components of such models represent known or hypothesized biological growth processes then these models can be used to refine existing hypotheses or generate new hypotheses about the factors controlling growth. Special techniques must be used when fitting such models to experimental data. Methods are suggested for model re-parameterization and model fitting which improve the estimation of model parameters. Once estimates of model parameters have been made, temporal and multivariate sensitivity analyses can assess important relationships among the model parameters. A deterministic dynamic model of batch growth by a homofermentative lactic acid bacterium growing in a variable temperature environment was derived. This model predicts cell growth as well as changes in the chemical composition of the medium. This model was fit to experimental data. Analysis of the model revealed a quantitative reversal in parameter sensitivities across temperatures. Although mechanistic, this model neglected the effects of pH, organic acid dissociation and ionic strength of the medium. It is shown that these chemical dynamics are important and can be modeled through a convenient semi-mechanistic approach. The ability to model these chemical dynamics appropriately allows for a modeling framework in which the acid tolerance strategies commonly exhibited by bacteria can be studied.
Direct Detection of Microcalcification Pairs in Simulated Digital Mammograms
(2002-10-31) Zeigler, Gary Boyce; R. Eugene Johnston, Committee Member; Kuruvilla Verghese, Committee Chair; Zhilin Li, Committee Member; J. Michael Doster, Committee Member; Douglas E. Peplow, Committee Member
Using the MCMIS (Monte Carlo for Mammography Image Simulation) code, several possible scenarios of microcalcification images were simulated for the Fischer Senoscan™ digital mammography system, which has been approved for clinical use by the F.D.A. The cases simulated included detectors that have 100 μm x 100 μm, 50 μm x 50 μm, and 25 μm x 25 μm pixels in order to determine how much improvement can be obtained through decreased pixel size in the detection of microcalcification clusters in mammograms. Breast thickness was also varied for each modality from 4 to 7 cm in order to determine the effect that reduced breast compression will have on image quality under ideal conditions. The breast phantom used for each simulation included a region of microcalcification pairs of varying size and pair spacing. This microcalcification cluster phantom was designed such that simulated images would indicate the minimum required size and spacing for microcalcification clusters to become distinctly discernable in each of the modalities under scrutiny. Both qualitative and quantitative analyses were performed for each simulated image produced. A decrease in detector pixel size did not show the expected result of significant improvement in cluster detection ability, even under ideal conditions. However, for the range of breast thickness studied, results indicate that decreasing the amount of compression during a mammogram did not significantly affect the image quality in terms of image resolution or contrast for all detector modalities tested. These results suggest that new detector modalities incorporating smaller detector pixel sizes may not show significant improvement over current modalities. However, they also suggest that doctors may be able to make the mammogram process less painful for the patient while maintaining image quality.
Dynamic Game Theoretic Models in Marketing and Finance
(2008-07-15) Wan, Wei; Negash Medhin, Committee Chair; Zhilin Li, Committee Member; Tao Pang, Committee Member; Ivan T. Kandilov, Committee Member
Fast Numerical Methods for Evolving Interfaces
(2006-07-10) Kuster, Christopher M.; Stephen L. Campbell, Committee Member; Pierre A. Gremaud, Committee Chair; Zhilin Li, Committee Member; Carl T. Kelley, Committee Member
Free and/or moving boundary problems occur in a wide range of applications. These boundaries can obey either local or global conditions. In this dissertation, new numerical techniques for solving some of these problems are developed, analyzed, implemented and tested. The new techniques for free and moving boundary problems are 1) a second order method for solving moving boundary problems and 2) a hybrid level set/boundary element method for solving some free boundary problems. The main tool used in both is the Fast Marching method, a fast algorithm for solving the eikonal equation. An application using Fast Marching to solve a model for sand pile formation in domains with obstacles is shown. A new, second order Fast Marching scheme for domains with obstacles is introduced. We look at the stability and accuracy of discretizations commonly used with Fast Marching. The performance of Fast Marching is compared that of Fast Sweeping, another eikonal solver. The second order method for solving moving boundary problems is applied to some simple examples. Finally, a globally defined free boundary problem inspired by fluid dynamics, the Bernoulli problem, is solved using the hybrid method.
First Principles Studies of Interface Dielectric Properties of Polymer/metal-oxide Nanocomposites}
(2009-07-29) Yu, Liping; Wenchang Lu, Committee Member; Zhilin Li, Committee Member; Marco Buongiorno Nardelli, Committee Member; Jerry Bernholc, Committee Chair
This thesis is devoted to studying interface dielectric properties of polymer nanocomposites from first principles. We aim to understand at atomic scale the role of interface effects and the dielectric finite size effects of nanoparticles in determining the effective dielectric properties of polymer nanocomposites. To study surface effects from first principles, we first investigate the two common methods, namely dipole correction and Coulomb cutoff, used to eliminate the artificial effects introduced by using the supercell approximation. We implement Coulomb cutoff technique in a plane-wave-based density functional theory code and compare it with dipole correction for the same system under the same conditions. By comparison, both methods are shown to be equivalent and able to remove the artificial effects of periodic images very accurately. We also find that a combination of these two methods offers an easy way to distinguish the localized bound states of interest from highly delocalized unoccupied states while using a relatively small supercell, and to ascertain the convergence of the results with respect to supercell size. To understand the dielectric properties at the atomic scale, we develop a new nanoscale averaging model to connect the macroscopic quantities to the corresponding microscopic ones. This model allows us to compute the spatially resolved local dielectric permittivity, including the critically important ionic contributions, for interfaces and other complex structures. In this model, a simple way of evaluating real-space decay length of the nonlocal dielectric functions is also proposed. By using the dipole correction and our averaging model in supercells, we calculate the optical and static local dielectric permittivity profiles for polymer (polypropylene) / metal-oxide (PbTiO$_3$ and alumina) nanocomposites. Our {em ab-initio} results show that metal-oxide/polymer interface effects are very localized and are mostly confined to the metal-oxide surface side, and that nanoscale metal-oxide slabs can on average retain the macroscopic value of bulk dielectric permittivity. These findings suggest that classical mixing laws associated with macroscopic composites can be applied to model the overall dielectric constant of a real polymer/metal-oxide nanocomposite system.
Intra-nodal Study for the Mixed LEU-MOX Cores
(2004-07-08) Jiang, Qunlei; Dmitriy Y. Anistratov, Committee Co-Chair; Paul J. Turinsky, Committee Chair; Zhilin Li, Committee Member
One favored method being considered for the disposal of surplus weapons grade plutonium (WGPu) is to burn the WGPu as mixed oxide (MOX) fuel in commercial existing Light Water Reactors (LWRs). Duke Power Company intends to irradiate MOX fuel assemblies in their four Westinghouse pressurized water reactors (PWR). The introduction of MOX fuel into LWRs poses several challenges for the reactor physics analysis. The difference in properties of uranium and plutonium induces neutron energy spectrum difference between the MOX and LEU assemblies, which creates a large thermal flux gradient at the interface between these assemblies. Current methods for predicting the intra-nodal flux distribution have difficulty to model this gradient. This study is focused on improving the fidelity of the core simulator utilized in FORMOSA-P to model mixed LEU-MOX cores. In particular, the nature of challenge in regard to accurately model the LEU-MOX interfaces due to both strong spatial variations of the thermal flux and energy spectra, the later impacting the two-group cross section values, will be assessed. The specific focus is on pin-wise power reconstruction; however, issues related to the nodal solution will also be assessed. To complete the work on pin-wise power reconstruction, there are three ways to improve the prediction accuracy, those being to improve the prediction accuracy of the intra-nodal flux shape, improve the prediction accuracy of the intra-nodal kappa-sigma-fission shape, and to introduce group power form factors. However, since the intra-nodal flux and kappa-sigma-fission both are predicted using results obtained from the nodal solution, the prediction accuracy of the nodal solution for mixed LEU-MOX cores enters. This study is completed by using HELIOS, a transport theory based lattice physics code, and NESTLE, a diffusion theory core simulator. The single assembly (SA) calculation is done by HELIOS to generate the homogenized cross sections, discontinuity factors (DFs) at corner points and surfaces, and power form factors using infinite-medium spectra. Homogenized cross sections and surface average DFs are generally used in diffusion calculations. Obviously, they are not that accurate because the effect from neighbors is ignored in SA calculations, hence introduce errors in diffusion calculations. The colorset (CS) calculation done by HELIOS is to generate the same information but now accounting for LEU-MOX interface effects, where a colorset denotes an LEU-MOX assembly infinite checkerboard loading. The intra-nodal flux distribution is obtained by a SA NESTLE calculation using the finite difference method with a very fine spatial mesh. The surface current boundary condition imposed is obtained from the CS HELIOS calculation, with the NESTLE calculation completed using SA HELIOS determined homogenized cross sections or CS HELIOS determined intra-nodal cross sections. The shape of intra-nodal cross section shows that the thermal group 'flat' cross section can not represent the interfacial effect. This assumption no longer works for mixed LEU-MOX cores. The group dependent 'flat' cross sections contribute errors to the , intra-nodal fluxes and powers. Comparing the cross sections, DFs, and power form factors from SA lattice physics, CS lattice physics, and diffusion theory calculations, we can evaluate the errors induced by the MOX and LEU spectrum interactions on these values. Contrasting SA lattice physics and diffusion theory (using intra-nodal cross sections) predictions, for the SA lattice physics predictions about a 1.5% relative error in the LEU fuel assembly and 2.2% relative error in the MOX fuel assembly are observed in the thermal group surface averaged DFs. The relative errors in the fast group ADF ratios are small. However about a 2.7% relative error is observed in the thermal group ADFs' ratios at BOL. Likewise, about a 3% relative error in the LEU fuel assembly and 4.4% relative error in the MOX fuel assembly are observed in the thermal group corner point DFs at BOL. Also about a 1% relative error is observed in in both the LEU and MOX fuel assemblies at a higher level burnup (20 GWD/THM). With regard to the intra-nodal cross sections, stronger spatial dependences are noted for the down-scattering, thermal transport, fast and thermal absorption, and fast and thermal fission cross sections. A steep spatial gradient is noted for the intra-nodal flux due to interfacial effects. The resulting flux shape presents a difficulty problem to accurately functionalize. The study on the effect of ADF's and cross sections shows that errors in the cross sections, i.e. the energy and spatial spectrum used for generating the cross sections, are the main error contributors to the , node averaged fluxes and intra-nodal fluxes. ADFs do not greatly effect the value and node averaged fluxes. The results of the study imply that the accuracy of the SA lattice physics calculation to obtain cross sections, DFs and form factors are poor for the mixed LEU-MOX core simulations, in other words, the rehomogenization of cross sections is necessary during the nodal (diffusion theory) calculation for mixed LEU-MOX core simulations. Also, the employment of intra-nodal cross section is effective in improving the accuracy of diffusion calculation.
Mathematical Modeling of Laminar and Turbulent Single-phase and Two-phase Flows in Straight and Helical Ducts
(2004-11-05) Cheng, Liping; Kevin M. Lyons, Committee Member; Zhilin Li, Committee Member; William L. Roberts, Committee Member; K. P. Sandeep, Committee Member; Andrey V. Kuznetsov, Committee Chair
The purpose of this research is to investigate numerically the dynamics and heat transfer of laminar or turbulent flows in different media and complicated geometries, including the flow in a composite domain whose central portion is occupied by a clear fluid (turbulent flow) and whose peripheral portion is occupied by a fluid saturated porous medium (laminar flow); a laminar flow of a non-Newtonian fluid in a helical pipe; a laminar flow in a helical pipe filled with a fluid saturated porous medium; a two-phase laminar flow (non-Newtonian carrying fluid and solid particles) in a helical pipe. To model forced convection in a composite porous/fluid domain, the Brinkma-Forchheimer-extended Darcy equation is utilized for the porous region and a two-layer algebraic turbulence model is utilized for the flow in the central region. The effects of turbulence on velocity and temperature distributions as well as on the Nusselt number are analyzed. To investigate a fully developed laminar flow of a non-Newtonian fluid in a helical pipe, an orthogonal helical coordinate system is utilized and the Navier-Stokes and energy equations for the non-Newtonian fluid in this coordinate system are derived. The effects of the curvature and torsion of a helical pipe, the Dean number and Germano number on the velocities, secondary flow and heat transfer are presented. A full momentum equation for the flow in porous media that accounts for the Brinkman and Forchheimer extensions of the Darcy law as well as for the flow inertia is adopted to study the fully developed laminar flow in a helical pipe filled with a fluid saturated porous medium. The effects of the geometry of the helical pipe and the physical properties of the porous medium are investigated. Accounting for the flow inertia is shown to be important for predicting the secondary flow in a helical pipe. For 3D modeling of two-phase laminar flow in a helical pipe, the Eulerian approach is utilized for fluid flow and the Lagrangian approach is utilized for tracking particles. The interaction between the solid particles and the fluid that carries them is accounted for by a source term in the momentum equation for the fluid. The influence of inter-particle and particle-wall collisions is also taken into account.
Microstructure Generation of Asphalt Concrete and Lattice Modeling of Its Cracking Behavior under Low Temperature
(2004-03-10) Zhang, Pu; Roy Borden, Committee Member; Murthy Guddati, Committee Co-Chair; Richard Y. Kim, Committee Chair; Zhilin Li, Committee Member
Fatigue cracking has been pointed out as a major distress in asphalt concrete (AC) pavements. It is well known that cracking performance in AC mainly depends on the mechanical properties of its constituent materials, namely asphalt binder and aggregates. Study of such dependence is the key to effective characterization of the mechanical behavior of AC. Previous studies predicted AC behavior from the mixture properties using extensive physical experiments. As an alternative approach to physical experiments, micromechanical modeling, which is composed of microstructure generation and numerical modeling, is introduced in this study. Digital imaging processing (DIP) of physical specimens to generate microstructures is first investigated, followed by virtual fabrication, which makes use of the mix properties to virtually fabricate the specimen (or the cross section of specimen for 2D analysis), so that the appearance and mechanical behavior of the actual specimen can be simulated. The resulting microstructure is then processed to obtain a lattice network that is expected to mimic the mechanical behavior of the AC specimen. Lattice modeling approximates a continuum by using a lattice, with each link representing an intact bond that can be broken at any time to create a microcrack. The cracking process is simulated by successive removal of failed links. Due to the unrealistic computational cost of direct simulation, the multi-scale approach is adopted to perform microstructural analysis, which considers the effect of different-sized aggregates at different length scales. Such an approach reduces the computational cost significantly, while capturing the mechanical phenomena at various length scales. The effectiveness of the proposed multi-scale modeling approach is then illustrated by modeling the cracking behavior of the uniaxial tension tests under -10°C. In the end, the effects of surface energy are studied.
Model Development and Control Design for Atomic Force Microscopy
(2004-09-09) Hatch, Andrew Graydon; Ralph C. Smith, Committee Chair; Kazufumi Ito, Committee Member; Zhilin Li, Committee Member; Hien T. Tran, Committee Member
The development of energy-based models and model-based control designs necessary to achieve present and projected applications involving atomic force microscopy is investigated. Applications include real-time product diagnostics or monitoring of biological processes, nanoelectromechanical systems (NEMS) and employment of atomic force microscope (AFM) technology for spintronics. A crucial component in the AFM design is the piezoceramic (PZT)-based stage used to position the sample. Whereas PZT actuators provide the broadband and extremely high set point capabilities required by the AFM stages, they also exhibit frequency-dependent hysteresis and constitutive nonlinearities. To characterize the field-polarization relation in PZT, low-order macroscopic models are constructed based on a combination of energy analysis at the mesoscopic level along with stochastic homogenization techniques. To account for nonuniformity and inhomogeneities in the material, local coercive field values are assumed to be distributed. Due to interactions among the dipoles, the effective field is also assumed to be distributed. Previous work has employed specific functions to describe these distributions. However, the fact that these choices are not based on energy considerations, motivates the use of general densities. The dynamics of the actuator must be incorporated as well. A rod model is suitable for a stacked actuator whose cross-section is small compared to the length. The equation of motion for the rod can be derived using force balancing with boundary conditions determined from the fact that the rod is fixed at one end and pushes against the stage at the other. At low frequencies, the hysteresis and constitutive nonlinearities inherent in PZT can be accommodated through PID or robust control designs. However, at the higher frequencies required by the previously outlined applications, increasing noise-to-data ratios and diminishing high-pass characteristics of control filters preclude a sole reliance on feedback laws to eliminate hysteresis. This motivates the development of control designs that incorporate and approximately compensate for hysteresis through model inverses employed as filters to linearize transducer responses for linear robust control design and PID control design. The inverse models are also tested in an open loop control experiment on a PZT stacked actuator.
Nonlinear image denoising methodologies
(2003-06-24) Bao, Yufang; Alexandra Duel-Hallen, Committee Member; Robert Cohen, Committee Member; Zhilin Li, Committee Member; Hamid Krim, Committee Chair; Arne A. Nilsson, Committee Member; Alexandra Duel-Hallen, Committee Member; Arne A. Nilsson, Committee Member; Hamid Krim, Committee Chair; Zhilin Li, Committee Member; Robert Cohen, Committee Member; Alexandra Duel-Hallen, Committee Member; Arne A. Nilsson, Committee Member; Hamid Krim, Committee Chair; Zhilin Li, Committee Member; Robert Cohen, Committee Member; Alexandra Duel-Hallen, Committee Member; Arne A. Nilsson, Committee Member; Hamid Krim, Committee Chair; Zhilin Li, Committee Member; Robert Cohen, Committee Member
In this thesis, we propose a theoretical as well as practical framework to combine geometric prior information to a statistical/probabilitstic methodology in the investigation of a denoising problem in its generic form together with its various applications in signal/image analysis. We are able in the process, to investigate, understand and mitigate existing limitations of so-called nonlinear diffusion techniques (such as the Perona-Malik equation) from a probabilistic view point, and propose a new nonlinear denoising method that is based on a random walk whose transition probabilities are selected by the information of a two-sided gradient. This results in a piecewise constant filtered image and lifts the long-standing problem of an unknown evolution stopping time. Our second contribution is in establishing a direct link between multi-resolution analysis techniques and so-called scale space analysis methods, which we in turn utilize to improve the performance of segmentation-optimized image analysis techniques. This is accomplished by using wavelets of higher order vanishing moments, specifically, we achieve a reduction in the typical "blocky" artifacts and a better preservation of texture information. Our third and final contribution is to propose a drastically different approach by isolating statistically independent components in a signal, which we later use as a basis for discrimination against noise, or potentially as plain features. This is related to the well known independent component analysis ( ICA ), for which we first propose Jensen-Rényi divergence as an information- theoretic criterion. In addition, we propose a Rényi mutual divergence as a better criterion to separate mixed signals along with a non-parametric estimation technique for such a measure for 1-D problems. A particle system simulation method is on our future plan of work and is currently ongoing to further investigate the stochastic properties of our diffusion framework.
Nonlinear Weighted Flux Methods for Solving Multidimensional Transport Problems.
(2008-01-24) Roberts, Loren Patrick; Zhilin Li, Committee Member; Robin P. Gardner, Committee Member; Paul J. Turinsky, Committee Member; Dmitriy Y. Anistratov, Committee Chair