8 resultados para Negative dimensional integration method (NDIM)

em Digital Commons - Michigan Tech


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To estimate a parameter in an elliptic boundary value problem, the method of equation error chooses the value that minimizes the error in the PDE and boundary condition (the solution of the BVP having been replaced by a measurement). The estimated parameter converges to the exact value as the measured data converge to the exact value, provided Tikhonov regularization is used to control the instability inherent in the problem. The error in the estimated solution can be bounded in an appropriate quotient norm; estimates can be derived for both the underlying (infinite-dimensional) problem and a finite-element discretization that can be implemented in a practical algorithm. Numerical experiments demonstrate the efficacy and limitations of the method.

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The objective of this doctoral research is to investigate the internal frost damage due to crystallization pore pressure in porous cement-based materials by developing computational and experimental characterization tools. As an essential component of the U.S. infrastructure system, the durability of concrete has significant impact on maintenance costs. In cold climates, freeze-thaw damage is a major issue affecting the durability of concrete. The deleterious effects of the freeze-thaw cycle depend on the microscale characteristics of concrete such as the pore sizes and the pore distribution, as well as the environmental conditions. Recent theories attribute internal frost damage of concrete is caused by crystallization pore pressure in the cold environment. The pore structures have significant impact on freeze-thaw durability of cement/concrete samples. The scanning electron microscope (SEM) and transmission X-ray microscopy (TXM) techniques were applied to characterize freeze-thaw damage within pore structure. In the microscale pore system, the crystallization pressures at sub-cooling temperatures were calculated using interface energy balance with thermodynamic analysis. The multi-phase Extended Finite Element Modeling (XFEM) and bilinear Cohesive Zone Modeling (CZM) were developed to simulate the internal frost damage of heterogeneous cement-based material samples. The fracture simulation with these two techniques were validated by comparing the predicted fracture behavior with the captured damage from compact tension (CT) and single-edge notched beam (SEB) bending tests. The study applied the developed computational tools to simulate the internal frost damage caused by ice crystallization with the two dimensional (2-D) SEM and three dimensional (3-D) reconstructed SEM and TXM digital samples. The pore pressure calculated from thermodynamic analysis was input for model simulation. The 2-D and 3-D bilinear CZM predicted the crack initiation and propagation within cement paste microstructure. The favorably predicted crack paths in concrete/cement samples indicate the developed bilinear CZM techniques have the ability to capture crack nucleation and propagation in cement-based material samples with multiphase and associated interface. By comparing the computational prediction with the actual damaged samples, it also indicates that the ice crystallization pressure is the main mechanism for the internal frost damage in cementitious materials.

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The numerical solution of the incompressible Navier-Stokes Equations offers an effective alternative to the experimental analysis of Fluid-Structure interaction i.e. dynamical coupling between a fluid and a solid which otherwise is very complex, time consuming and very expensive. To have a method which can accurately model these types of mechanical systems by numerical solutions becomes a great option, since these advantages are even more obvious when considering huge structures like bridges, high rise buildings, or even wind turbine blades with diameters as large as 200 meters. The modeling of such processes, however, involves complex multiphysics problems along with complex geometries. This thesis focuses on a novel vorticity-velocity formulation called the KLE to solve the incompressible Navier-stokes equations for such FSI problems. This scheme allows for the implementation of robust adaptive ODE time integration schemes and thus allows us to tackle the various multiphysics problems as separate modules. The current algorithm for KLE employs a structured or unstructured mesh for spatial discretization and it allows the use of a self-adaptive or fixed time step ODE solver while dealing with unsteady problems. This research deals with the analysis of the effects of the Courant-Friedrichs-Lewy (CFL) condition for KLE when applied to unsteady Stoke’s problem. The objective is to conduct a numerical analysis for stability and, hence, for convergence. Our results confirmthat the time step ∆t is constrained by the CFL-like condition ∆t ≤ const. hα, where h denotes the variable that represents spatial discretization.

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The Pacaya volcanic complex is part of the Central American volcanic arc, which is associated with the subduction of the Cocos tectonic plate under the Caribbean plate. Located 30 km south of Guatemala City, Pacaya is situated on the southern rim of the Amatitlan Caldera. It is the largest post-caldera volcano, and has been one of Central America’s most active volcanoes over the last 500 years. Between 400 and 2000 years B.P, the Pacaya volcano had experienced a huge collapse, which resulted in the formation of horseshoe-shaped scarp that is still visible. In the recent years, several smaller collapses have been associated with the activity of the volcano (in 1961 and 2010) affecting its northwestern flanks, which are likely to be induced by the local and regional stress changes. The similar orientation of dry and volcanic fissures and the distribution of new vents would likely explain the reactivation of the pre-existing stress configuration responsible for the old-collapse. This paper presents the first stability analysis of the Pacaya volcanic flank. The inputs for the geological and geotechnical models were defined based on the stratigraphical, lithological, structural data, and material properties obtained from field survey and lab tests. According to the mechanical characteristics, three lithotechnical units were defined: Lava, Lava-Breccia and Breccia-Lava. The Hoek and Brown’s failure criterion was applied for each lithotechnical unit and the rock mass friction angle, apparent cohesion, and strength and deformation characteristics were computed in a specified stress range. Further, the stability of the volcano was evaluated by two-dimensional analysis performed by Limit Equilibrium (LEM, ROCSCIENCE) and Finite Element Method (FEM, PHASE 2 7.0). The stability analysis mainly focused on the modern Pacaya volcano built inside the collapse amphitheatre of “Old Pacaya”. The volcanic instability was assessed based on the variability of safety factor using deterministic, sensitivity, and probabilistic analysis considering the gravitational instability and the effects of external forces such as magma pressure and seismicity as potential triggering mechanisms of lateral collapse. The preliminary results from the analysis provide two insights: first, the least stable sector is on the south-western flank of the volcano; second, the lowest safety factor value suggests that the edifice is stable under gravity alone, and the external triggering mechanism can represent a likely destabilizing factor.

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This study develops an automated analysis tool by combining total internal reflection fluorescence microscopy (TIRFM), an evanescent wave microscopic imaging technique to capture time-sequential images and the corresponding image processing Matlab code to identify movements of single individual particles. The developed code will enable us to examine two dimensional hindered tangential Brownian motion of nanoparticles with a sub-pixel resolution (nanoscale). The measured mean square displacements of nanoparticles are compared with theoretical predictions to estimate particle diameters and fluid viscosity using a nonlinear regression technique. These estimated values will be confirmed by the diameters and viscosities given by manufacturers to validate this analysis tool. Nano-particles used in these experiments are yellow-green polystyrene fluorescent nanospheres (200 nm, 500 nm and 1000 nm in diameter (nominal); 505 nm excitation and 515 nm emission wavelengths). Solutions used in this experiment are de-ionized (DI) water, 10% d-glucose and 10% glycerol. Mean square displacements obtained near the surface shows significant deviation from theoretical predictions which are attributed to DLVO forces in the region but it conforms to theoretical predictions after ~125 nm onwards. The proposed automation analysis tool will be powerfully employed in the bio-application fields needed for examination of single protein (DNA and/or vesicle) tracking, drug delivery, and cyto-toxicity unlike the traditional measurement techniques that require fixing the cells. Furthermore, this tool can be also usefully applied for the microfluidic areas of non-invasive thermometry, particle tracking velocimetry (PTV), and non-invasive viscometry.

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Emerging nanogenerators have attracted the attention of the research community, focusing on energy generation using piezoelectric nanomaterials. Nanogenerators can be utilized for powering NEMS/MEMS devices. Understanding the piezoelectric properties of ZnO one-dimensional materials such as ZnO nanobelts (NBs) and Nanowires (NWs) can have a significant impact on the design of new devices. The goal of this dissertation is to study the piezoelectric properties of one-dimensional ZnO nanostructures both experimentally and theoretically. First, the experimental procedure for producing the ZnO nanostructures is discussed. The produced ZnO nanostructures were characterized using an in-situ atomic force microscope and a piezoelectric force microscope. It is shown that the electrical conductivity of ZnO NBs is a function of applied mechanical force and its crystalline structure. This phenomenon was described in the context of formation of an electric field due to the piezoelectric property of ZnO NBs. In the PFM studies, it was shown that the piezoelectric response of the ZnO NBs depends on their production method and presence of defects in the NB. Second, a model was proposed for making nanocomposite electrical generators based on ZnO nanowires. The proposed model has advantages over the original configuration of nanogenerators which uses an AFM tip for bending the ZnO NWs. Higher stability of the electric source, capability for producing larger electric fields, and lower production costs are advantages of this configuration. Finally, piezoelectric properties of ZnO NBs were simulated using the molecular dynamics (MD) technique. The size-scale effect on piezoelectric properties of ZnO NBs was captured, and it is shown that the piezoelectric coefficient of ZnO NBs decreases by increasing their lateral dimensions. This phenomenon is attributed to the surface charge redistribution and compression of unit cells that are placed on the outer shell of ZnO NBs.

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This technical report discusses the application of Lattice Boltzmann Method (LBM) in the fluid flow simulation through porous filter-wall of disordered media. The diesel particulate filter (DPF) is an example of disordered media. DPF is developed as a cutting edge technology to reduce harmful particulate matter in the engine exhaust. Porous filter-wall of DPF traps these soot particles in the after-treatment of the exhaust gas. To examine the phenomena inside the DPF, researchers are looking forward to use the Lattice Boltzmann Method as a promising alternative simulation tool. The lattice Boltzmann method is comparatively a newer numerical scheme and can be used to simulate fluid flow for single-component single-phase, single-component multi-phase. It is also an excellent method for modelling flow through disordered media. The current work focuses on a single-phase fluid flow simulation inside the porous micro-structure using LBM. Firstly, the theory concerning the development of LBM is discussed. LBM evolution is always related to Lattice gas Cellular Automata (LGCA), but it is also shown that this method is a special discretized form of the continuous Boltzmann equation. Since all the simulations are conducted in two-dimensions, the equations developed are in reference with D2Q9 (two-dimensional 9-velocity) model. The artificially created porous micro-structure is used in this study. The flow simulations are conducted by considering air and CO2 gas as fluids. The numerical model used in this study is explained with a flowchart and the coding steps. The numerical code is constructed in MATLAB. Different types of boundary conditions and their importance is discussed separately. Also the equations specific to boundary conditions are derived. The pressure and velocity contours over the porous domain are studied and recorded. The results are compared with the published work. The permeability values obtained in this study can be fitted to the relation proposed by Nabovati [8], and the results are in excellent agreement within porosity range of 0.4 to 0.8.

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Graphene, which is a two-dimensional carbon material, exhibits unique properties that promise its potential applications in photovoltaic devices. Dye-sensitized solar cell (DSSC) is a representative of the third generation photovoltaic devices. Therefore, it is important to synthesize graphene with special structures, which possess excellent properties for dye-sensitized solar cells. This dissertation research was focused on (1) the effect of oxygen content on the structure of graphite oxide, (2) the stability of graphene oxide solution, (3) the application of graphene precipitate from graphene oxide solution as counter electrode for DSSCs, (4) the development of a novel synthesis method for the three-dimensional graphene with honeycomb-like structure, and (5) the exploration of honeycomb structured graphene (HSG) as counter electrodes for DSSCs. Graphite oxide is a crucial precursor to synthesize graphene sheets via chemical exfoliation method. The relationship between the oxygen content and the structures of graphite oxides was still not explored. In this research, the oxygen content of graphite oxide is tuned by changing the oxidation time and the effect of oxygen content on the structure of graphite oxide was evaluated. It has been found that the saturated ratio of oxygen to carbon is 0.47. The types of functional groups in graphite oxides, which are epoxy, hydroxyl, and carboxylgroups, are independent of oxygen content. However, the interplanar space and BET surface area of graphite oxide linearly increases with increasing O/C ratio. Graphene oxide (GO) can easily dissolve in water to form a stable homogeneous solution, which can be used to fabricate graphene films and graphene based composites. This work is the first research to evaluate the stability of graphene oxide solution. It has been found that the introduction of strong electrolytes (HCl, LiOH, LiCl) into GO solution can cause GO precipitation. This indicates that the electrostatic repulsion plays a critical role in stabilizing aqueous GO solution. Furthermore, the HCl-induced GO precipitation is a feasible approach to deposit GO sheets on a substrate as a Pt-free counter electrode for a dye-sensitized solar cell (DSSC), which exhibited 1.65% of power conversion efficiency. To explore broad and practical applications, large-scale synthesis with controllable integration of individual graphene sheets is essential. A novel strategy for the synthesis of graphene sheets with three-dimensional (3D) Honeycomb-like structure has been invented in this project based on a simple and novel chemical reaction (Li2O and CO to graphene and Li2CO3). The simultaneous formation of Li2CO3 with graphene not only can isolate graphene sheets from each other to prevent graphite formation during the process, but also determine the locally curved shape of graphene sheets. After removing Li2CO3, 3D graphene sheets with a honeycomb-like structure were obtained. This would be the first approach to synthesize 3D graphene sheets with a controllable shape. Furthermore, it has been demonstrated that the 3D Honeycomb-Structured Graphene (HSG) possesses excellent electrical conductivity and high catalytic activity. As a result, DSSCs with HSG counter electrodes exhibit energy conversion efficiency as high as 7.8%, which is comparable to that of an expensive noble Pt electrode.