14 resultados para non-uniform scale perturbation finite difference scheme
em Digital Commons - Michigan Tech
Resumo:
An electrospray source has been developed using a novel new fluid that is both magnetic and conductive. Unlike conventional electrospray sources that required microfabricated structures to support the fluid to be electrosprayed, this new electrospray fluid utilizes the Rosensweig instability to create the structures in the magnetic fluid when an external magnetic field was applied. Application of an external electric field caused these magnetic fluid structures to spray. These fluid based structures were found to spray at a lower onset voltage than was predicted for electrospray sources with solid structures of similar geometry. These fluid based structures were also found to be resilient to damage, unlike the solid structures found in traditional electrospray sources. Further, experimental studies of magnetic fluids in non-uniform magnetic fields were conducted. The modes of Rosensweig instabilities have been studied in-depth when created by uniform magnetic fields, but little to no studies have been performed on Rosensweig instabilities formed due to non-uniform magnetic fields. The measured spacing of the cone-like structures of ferrofluid, in a non-uniform magnetic field, were found to agree with a proposed theoretical model.
Resumo:
The maximum principle is an important property of solutions to PDE. Correspondingly, it's of great interest for people to design a high order numerical scheme solving PDE with this property maintained. In this thesis, our particular interest is solving convection-dominated diffusion equation. We first review a nonconventional maximum principle preserving(MPP) high order finite volume(FV) WENO scheme, and then propose a new parametrized MPP high order finite difference(FD) WENO framework, which is generalized from the one solving hyperbolic conservation laws. A formal analysis is presented to show that a third order finite difference scheme with this parametrized MPP flux limiters maintains the third order accuracy without extra CFL constraint when the low order monotone flux is chosen appropriately. Numerical tests in both one and two dimensional cases are performed on the simulation of the incompressible Navier-Stokes equations in vorticity stream-function formulation and several other problems to show the effectiveness of the proposed method.
Resumo:
Heat transfer is considered as one of the most critical issues for design and implement of large-scale microwave heating systems, in which improvement of the microwave absorption of materials and suppression of uneven temperature distribution are the two main objectives. The present work focuses on the analysis of heat transfer in microwave heating for achieving highly efficient microwave assisted steelmaking through the investigations on the following aspects: (1) characterization of microwave dissipation using the derived equations, (2) quantification of magnetic loss, (3) determination of microwave absorption properties of materials, (4) modeling of microwave propagation, (5) simulation of heat transfer, and (6) improvement of microwave absorption and heating uniformity. Microwave heating is attributed to the heat generation in materials, which depends on the microwave dissipation. To theoretically characterize microwave heating, simplified equations for determining the transverse electromagnetic mode (TEM) power penetration depth, microwave field attenuation length, and half-power depth of microwaves in materials having both magnetic and dielectric responses were derived. It was followed by developing a simplified equation for quantifying magnetic loss in materials under microwave irradiation to demonstrate the importance of magnetic loss in microwave heating. The permittivity and permeability measurements of various materials, namely, hematite, magnetite concentrate, wüstite, and coal were performed. Microwave loss calculations for these materials were carried out. It is suggested that magnetic loss can play a major role in the heating of magnetic dielectrics. Microwave propagation in various media was predicted using the finite-difference time-domain method. For lossy magnetic dielectrics, the dissipation of microwaves in the medium is ascribed to the decay of both electric and magnetic fields. The heat transfer process in microwave heating of magnetite, which is a typical magnetic dielectric, was simulated by using an explicit finite-difference approach. It is demonstrated that the heat generation due to microwave irradiation dominates the initial temperature rise in the heating and the heat radiation heavily affects the temperature distribution, giving rise to a hot spot in the predicted temperature profile. Microwave heating at 915 MHz exhibits better heating homogeneity than that at 2450 MHz due to larger microwave penetration depth. To minimize/avoid temperature nonuniformity during microwave heating the optimization of object dimension should be considered. The calculated reflection loss over the temperature range of heating is found to be useful for obtaining a rapid optimization of absorber dimension, which increases microwave absorption and achieves relatively uniform heating. To further improve the heating effectiveness, a function for evaluating absorber impedance matching in microwave heating was proposed. It is found that the maximum absorption is associated with perfect impedance matching, which can be achieved by either selecting a reasonable sample dimension or modifying the microwave parameters of the sample.
Resumo:
Liquid films, evaporating or non-evaporating, are ubiquitous in nature and technology. The dynamics of evaporating liquid films is a study applicable in several industries such as water recovery, heat exchangers, crystal growth, drug design etc. The theory describing the dynamics of liquid films crosses several fields such as engineering, mathematics, material science, biophysics and volcanology to name a few. Interfacial instabilities typically manifest by the undulation of an interface from a presumed flat state or by the onset of a secondary flow state from a primary quiescent state or both. To study the instabilities affecting liquid films, an evaporating/non-evaporating Newtonian liquid film is subject to a perturbation. Numerical analysis is conducted on configurations of such liquid films being heated on solid surfaces in order to examine the various stabilizing and destabilizing mechanisms that can cause the formation of different convective structures. These convective structures have implications towards heat transfer that occurs via this process. Certain aspects of this research topic have not received attention, as will be obvious from the literature review. Static, horizontal liquid films on solid surfaces are examined for their resistance to long wave type instabilities via linear stability analysis, method of normal modes and finite difference methods. The spatiotemporal evolution equation, available in literature, describing the time evolution of a liquid film heated on a solid surface, is utilized to analyze various stabilizing/destabilizing mechanisms affecting evaporating and non-evaporating liquid films. The impact of these mechanisms on the film stability and structure for both buoyant and non-buoyant films will be examined by the variation of mechanical and thermal boundary conditions. Films evaporating in zero gravity are studied using the evolution equation. It is found that films that are stable to long wave type instabilities in terrestrial gravity are prone to destabilization via long wave instabilities in zero gravity.
Resumo:
Biogeochemical processes in the coastal region, including the coastal area of the Great Lakes, are of great importance due to the complex physical, chemical and biological characteristics that differ from those on either the adjoining land or open water systems. Particle-reactive radioisotopes, both naturally occurring (210Pb, 210Po and 7Be) and man-made (137Cs), have proven to be useful tracers for these processes in many systems. However, a systematic isotope study on the northwest coast of the Keweenaw Peninsula in Lake Superior has not yet been performed. In this dissertation research, field sampling, laboratory measurements and numerical modeling were conducted to understand the biogeochemistry of the radioisotope tracers and some particulate-related coastal processes. In the first part of the dissertation, radioisotope activities of 210Po and 210Pb in a variability of samples (dissolved, suspended particle, sediment trap materials, surficial sediment) were measured. A completed picture of the distribution and disequilibrium of this pair of isotopes was drawn. The application of a simple box model utilizing these field observations reveals short isotope residence times in the water column and a significant contribution of sediment resuspension (for both particles and isotopes). The results imply a highly dynamic coastal region. In the second part of this dissertation, this conclusion is examined further. Based on intensive sediment coring, the spatial distribution of isotope inventories (mainly 210Pb, 137Cs and 7Be) in the nearshore region was determined. Isotope-based focusing factors categorized most of the sampling sites as non- or temporary depositional zones. A twodimensional steady-state box-in-series model was developed and applied to individual transects with the 210Pb inventories as model input. The modeling framework included both water column and upper sediments down to the depth of unsupported 210Pb penetration. The model was used to predict isotope residence times and cross-margin fluxes of sediments and isotopes at different locations along each transect. The time scale for sediment focusing from the nearshore to offshore regions of the transect was on the order of 10 years. The possibility of sediment longshore movement was indicated by high inventory ratios of 137Cs: 210Pb. Local deposition of fine particles, including fresh organic carbon, may explain the observed distribution of benthic organisms such as Diporeia. In the last part of this dissertation, isotope tracers, 210Pb and 210Po, were coupled into a hydrodynamic model for Lake Superior. The model was modified from an existing 2-D finite difference physical-biological model which has previously been successfully applied on Lake Superior. Using the field results from part one of this dissertation as initial conditions, the model was used to predict the isotope distribution in the water column; reasonable results were achieved. The modeling experiments demonstrated the potential for using a hydrodynamic model to study radioisotope biogeochemistry in the lake, although further refinements are necessary.
Resumo:
For the past sixty years, waveguide slot radiator arrays have played a critical role in microwave radar and communication systems. They feature a well-characterized antenna element capable of direct integration into a low-loss feed structure with highly developed and inexpensive manufacturing processes. Waveguide slot radiators comprise some of the highest performance—in terms of side-lobe-level, efficiency, etc. — antenna arrays ever constructed. A wealth of information is available in the open literature regarding design procedures for linearly polarized waveguide slots. By contrast, despite their presence in some of the earliest published reports, little has been presented to date on array designs for circularly polarized (CP) waveguide slots. Moreover, that which has been presented features a classic traveling wave, efficiency-reducing beam tilt. This work proposes a unique CP waveguide slot architecture which mitigates these problems and a thorough design procedure employing widely available, modern computational tools. The proposed array topology features simultaneous dual-CP operation with grating-lobe-free, broadside radiation, high aperture efficiency, and good return loss. A traditional X-Slot CP element is employed with the inclusion of a slow wave structure passive phase shifter to ensure broadside radiation without the need for performance-limiting dielectric loading. It is anticipated this technology will be advantageous for upcoming polarimetric radar and Ka-band SatCom systems. The presented design methodology represents a philosophical shift away from traditional waveguide slot radiator design practices. Rather than providing design curves and/or analytical expressions for equivalent circuit models, simple first-order design rules – generated via parametric studies — are presented with the understanding that device optimization and design will be carried out computationally. A unit-cell, S-parameter based approach provides a sufficient reduction of complexity to permit efficient, accurate device design with attention to realistic, application-specific mechanical tolerances. A transparent, start-to-finish example of the design procedure for a linear sub-array at X-Band is presented. Both unit cell and array performance is calculated via finite element method simulations. Results are confirmed via good agreement with finite difference, time domain calculations. Array performance exhibiting grating-lobe-free, broadside-scanned, dual-CP radiation with better than 20 dB return loss and over 75% aperture efficiency is presented.
Resumo:
Light-frame wood buildings are widely built in the United States (U.S.). Natural hazards cause huge losses to light-frame wood construction. This study proposes methodologies and a framework to evaluate the performance and risk of light-frame wood construction. Performance-based engineering (PBE) aims to ensure that a building achieves the desired performance objectives when subjected to hazard loads. In this study, the collapse risk of a typical one-story light-frame wood building is determined using the Incremental Dynamic Analysis method. The collapse risks of buildings at four sites in the Eastern, Western, and Central regions of U.S. are evaluated. Various sources of uncertainties are considered in the collapse risk assessment so that the influence of uncertainties on the collapse risk of lightframe wood construction is evaluated. The collapse risks of the same building subjected to maximum considered earthquakes at different seismic zones are found to be non-uniform. In certain areas in the U.S., the snow accumulation is significant and causes huge economic losses and threatens life safety. Limited study has been performed to investigate the snow hazard when combined with a seismic hazard. A Filtered Poisson Process (FPP) model is developed in this study, overcoming the shortcomings of the typically used Bernoulli model. The FPP model is validated by comparing the simulation results to weather records obtained from the National Climatic Data Center. The FPP model is applied in the proposed framework to assess the risk of a light-frame wood building subjected to combined snow and earthquake loads. The snow accumulation has a significant influence on the seismic losses of the building. The Bernoulli snow model underestimates the seismic loss of buildings in areas with snow accumulation. An object-oriented framework is proposed in this study to performrisk assessment for lightframe wood construction. For home owners and stake holders, risks in terms of economic losses is much easier to understand than engineering parameters (e.g., inter story drift). The proposed framework is used in two applications. One is to assess the loss of the building subjected to mainshock-aftershock sequences. Aftershock and downtime costs are found to be important factors in the assessment of seismic losses. The framework is also applied to a wood building in the state of Washington to assess the loss of the building subjected to combined earthquake and snow loads. The proposed framework is proven to be an appropriate tool for risk assessment of buildings subjected to multiple hazards. Limitations and future works are also identified.
Resumo:
Four papers, written in collaboration with the author’s graduate school advisor, are presented. In the first paper, uniform and non-uniform Berry-Esseen (BE) bounds on the convergence to normality of a general class of nonlinear statistics are provided; novel applications to specific statistics, including the non-central Student’s, Pearson’s, and the non-central Hotelling’s, are also stated. In the second paper, a BE bound on the rate of convergence of the F-statistic used in testing hypotheses from a general linear model is given. The third paper considers the asymptotic relative efficiency (ARE) between the Pearson, Spearman, and Kendall correlation statistics; conditions sufficient to ensure that the Spearman and Kendall statistics are equally (asymptotically) efficient are provided, and several models are considered which illustrate the use of such conditions. Lastly, the fourth paper proves that, in the bivariate normal model, the ARE between any of these correlation statistics possesses certain monotonicity properties; quadratic lower and upper bounds on the ARE are stated as direct applications of such monotonicity patterns.
Resumo:
Skeletal muscle force evaluation is difficult to implement in a clinical setting. Muscle force is typically assessed through either manual muscle testing, isokinetic/isometric dynamometry, or electromyography (EMG). Manual muscle testing is a subjective evaluation of a patient’s ability to move voluntarily against gravity and to resist force applied by an examiner. Muscle testing using dynamometers adds accuracy by quantifying functional mechanical output of a limb. However, like manual muscle testing, dynamometry only provides estimates of the joint moment. EMG quantifies neuromuscular activation signals of individual muscles, and is used to infer muscle function. Despite the abundance of work performed to determine the degree to which EMG signals and muscle forces are related, the basic problem remains that EMG cannot provide a quantitative measurement of muscle force. Intramuscular pressure (IMP), the pressure applied by muscle fibers on interstitial fluid, has been considered as a correlate for muscle force. Numerous studies have shown that an approximately linear relationship exists between IMP and muscle force. A microsensor has recently been developed that is accurate, biocompatible, and appropriately sized for clinical use. While muscle force and pressure have been shown to be correlates, IMP has been shown to be non-uniform within the muscle. As it would not be practicable to experimentally evaluate how IMP is distributed, computational modeling may provide the means to fully evaluate IMP generation in muscles of various shapes and operating conditions. The work presented in this dissertation focuses on the development and validation of computational models of passive skeletal muscle and the evaluation of their performance for prediction of IMP. A transversly isotropic, hyperelastic, and nearly incompressible model will be evaluated along with a poroelastic model.
Resumo:
Mobile Mesh Network based In-Transit Visibility (MMN-ITV) system facilitates global real-time tracking capability for the logistics system. In-transit containers form a multi-hop mesh network to forward the tracking information to the nearby sinks, which further deliver the information to the remote control center via satellite. The fundamental challenge to the MMN-ITV system is the energy constraint of the battery-operated containers. Coupled with the unique mobility pattern, cross-MMN behavior, and the large-spanned area, it is necessary to investigate the energy-efficient communication of the MMN-ITV system thoroughly. First of all, this dissertation models the energy-efficient routing under the unique pattern of the cross-MMN behavior. A new modeling approach, pseudo-dynamic modeling approach, is proposed to measure the energy-efficiency of the routing methods in the presence of the cross-MMN behavior. With this approach, it could be identified that the shortest-path routing and the load-balanced routing is energy-efficient in mobile networks and static networks respectively. For the MMN-ITV system with both mobile and static MMNs, an energy-efficient routing method, energy-threshold routing, is proposed to achieve the best tradeoff between them. Secondly, due to the cross-MMN behavior, neighbor discovery is executed frequently to help the new containers join the MMN, hence, consumes similar amount of energy as that of the data communication. By exploiting the unique pattern of the cross-MMN behavior, this dissertation proposes energy-efficient neighbor discovery wakeup schedules to save up to 60% of the energy for neighbor discovery. Vehicular Ad Hoc Networks (VANETs)-based inter-vehicle communications is by now growingly believed to enhance traffic safety and transportation management with low cost. The end-to-end delay is critical for the time-sensitive safety applications in VANETs, and can be a decisive performance metric for VANETs. This dissertation presents a complete analytical model to evaluate the end-to-end delay against the transmission range and the packet arrival rate. This model illustrates a significant end-to-end delay increase from non-saturated networks to saturated networks. It hence suggests that the distributed power control and admission control protocols for VANETs should aim at improving the real-time capacity (the maximum packet generation rate without causing saturation), instead of the delay itself. Based on the above model, it could be determined that adopting uniform transmission range for every vehicle may hinder the delay performance improvement, since it does not allow the coexistence of the short path length and the low interference. Clusters are proposed to configure non-uniform transmission range for the vehicles. Analysis and simulation confirm that such configuration can enhance the real-time capacity. In addition, it provides an improved trade off between the end-to-end delay and the network capacity. A distributed clustering protocol with minimum message overhead is proposed, which achieves low convergence time.
Resumo:
Nanoparticles are fascinating where physical and optical properties are related to size. Highly controllable synthesis methods and nanoparticle assembly are essential [6] for highly innovative technological applications. Among nanoparticles, nonhomogeneous core-shell nanoparticles (CSnp) have new properties that arise when varying the relative dimensions of the core and the shell. This CSnp structure enables various optical resonances, and engineered energy barriers, in addition to the high charge to surface ratio. Assembly of homogeneous nanoparticles into functional structures has become ubiquitous in biosensors (i.e. optical labeling) [7, 8], nanocoatings [9-13], and electrical circuits [14, 15]. Limited nonhomogenous nanoparticle assembly has only been explored. Many conventional nanoparticle assembly methods exist, but this work explores dielectrophoresis (DEP) as a new method. DEP is particle polarization via non-uniform electric fields while suspended in conductive fluids. Most prior DEP efforts involve microscale particles. Prior work on core-shell nanoparticle assemblies and separately, nanoparticle characterizations with dielectrophoresis and electrorotation [2-5], did not systematically explore particle size, dielectric properties (permittivity and electrical conductivity), shell thickness, particle concentration, medium conductivity, and frequency. This work is the first, to the best of our knowledge, to systematically examine these dielectrophoretic properties for core-shell nanoparticles. Further, we conduct a parametric fitting to traditional core-shell models. These biocompatible core-shell nanoparticles were studied to fill a knowledge gap in the DEP field. Experimental results (chapter 5) first examine medium conductivity, size and shell material dependencies of dielectrophoretic behaviors of spherical CSnp into 2D and 3D particle-assemblies. Chitosan (amino sugar) and poly-L-lysine (amino acid, PLL) CSnp shell materials were custom synthesized around a hollow (gas) core by utilizing a phospholipid micelle around a volatile fluid templating for the shell material; this approach proves to be novel and distinct from conventional core-shell models wherein a conductive core is coated with an insulative shell. Experiments were conducted within a 100 nl chamber housing 100 um wide Ti/Au quadrapole electrodes spaced 25 um apart. Frequencies from 100kHz to 80MHz at fixed local field of 5Vpp were tested with 10-5 and 10-3 S/m medium conductivities for 25 seconds. Dielectrophoretic responses of ~220 and 340(or ~400) nm chitosan or PLL CSnp were compiled as a function of medium conductivity, size and shell material.
Resumo:
The particulate matter distribution (PM) trends that exist in catalyzed particulate filters (CPFs) after loading, passive oxidation, active regeneration, and post loading conditions are not clearly understood. These data are required to optimize the operation of CPFs, prevent damage to the CPFs caused by non-uniform distributions, and develop accurate CPF models. To develop an understanding of PM distribution trends, multiple tests were conducted and the PM distribution was measured in three dimensions using a terahertz wave scanner. The results of this work indicate that loading, passive oxidation, active regeneration, and post loading can all cause non-uniform PM distributions. The density of the PM in the substrate after loading and the amount of PM that is oxidized during passive oxidations and active regenerations affect the uniformity of the distribution. Post loading that occurs after active regenerations result in distributions that are less uniform than post loading that occurs after passive oxidations.
Resumo:
The intent of the work presented in this thesis is to show that relativistic perturbations should be considered in the same manner as well known perturbations currently taken into account in planet-satellite systems. It is also the aim of this research to show that relativistic perturbations are comparable to standard perturbations in speciffc force magnitude and effects. This work would have been regarded as little more then a curiosity to most engineers until recent advancements in space propulsion methods { e.g. the creation of a artiffcial neutron stars, light sails, and continuous propulsion techniques. These cutting-edge technologies have the potential to thrust the human race into interstellar, and hopefully intergalactic, travel in the not so distant future. The relativistic perturbations were simulated on two orbit cases: (1) a general orbit and (2) a Molniya type orbit. The simulations were completed using Matlab's ODE45 integration scheme. The methods used to organize, execute, and analyze these simulations are explained in detail. The results of the simulations are presented in graphical and statistical form. The simulation data reveals that the speciffc forces that arise from the relativistic perturbations do manifest as variations in the classical orbital elements. It is also apparent from the simulated data that the speciffc forces do exhibit similar magnitudes and effects that materialize from commonly considered perturbations that are used in trajectory design, optimization, and maintenance. Due to the similarities in behavior of relativistic versus non-relativistic perturbations, a case is made for the development of a fully relativistic formulation for the trajectory design and trajectory optimization problems. This new framework would afford the possibility of illuminating new more optimal solutions to the aforementioned problems that do not arise in current formulations. This type of reformulation has already showed promise when the previously unknown Space Superhighways arose as a optimal solution when classical astrodynamics was reformulated using geometric mechanics.
Resumo:
Wind energy has been one of the most growing sectors of the nation’s renewable energy portfolio for the past decade, and the same tendency is being projected for the upcoming years given the aggressive governmental policies for the reduction of fossil fuel dependency. Great technological expectation and outstanding commercial penetration has shown the so called Horizontal Axis Wind Turbines (HAWT) technologies. Given its great acceptance, size evolution of wind turbines over time has increased exponentially. However, safety and economical concerns have emerged as a result of the newly design tendencies for massive scale wind turbine structures presenting high slenderness ratios and complex shapes, typically located in remote areas (e.g. offshore wind farms). In this regard, safety operation requires not only having first-hand information regarding actual structural dynamic conditions under aerodynamic action, but also a deep understanding of the environmental factors in which these multibody rotating structures operate. Given the cyclo-stochastic patterns of the wind loading exerting pressure on a HAWT, a probabilistic framework is appropriate to characterize the risk of failure in terms of resistance and serviceability conditions, at any given time. Furthermore, sources of uncertainty such as material imperfections, buffeting and flutter, aeroelastic damping, gyroscopic effects, turbulence, among others, have pleaded for the use of a more sophisticated mathematical framework that could properly handle all these sources of indetermination. The attainable modeling complexity that arises as a result of these characterizations demands a data-driven experimental validation methodology to calibrate and corroborate the model. For this aim, System Identification (SI) techniques offer a spectrum of well-established numerical methods appropriated for stationary, deterministic, and data-driven numerical schemes, capable of predicting actual dynamic states (eigenrealizations) of traditional time-invariant dynamic systems. As a consequence, it is proposed a modified data-driven SI metric based on the so called Subspace Realization Theory, now adapted for stochastic non-stationary and timevarying systems, as is the case of HAWT’s complex aerodynamics. Simultaneously, this investigation explores the characterization of the turbine loading and response envelopes for critical failure modes of the structural components the wind turbine is made of. In the long run, both aerodynamic framework (theoretical model) and system identification (experimental model) will be merged in a numerical engine formulated as a search algorithm for model updating, also known as Adaptive Simulated Annealing (ASA) process. This iterative engine is based on a set of function minimizations computed by a metric called Modal Assurance Criterion (MAC). In summary, the Thesis is composed of four major parts: (1) development of an analytical aerodynamic framework that predicts interacted wind-structure stochastic loads on wind turbine components; (2) development of a novel tapered-swept-corved Spinning Finite Element (SFE) that includes dampedgyroscopic effects and axial-flexural-torsional coupling; (3) a novel data-driven structural health monitoring (SHM) algorithm via stochastic subspace identification methods; and (4) a numerical search (optimization) engine based on ASA and MAC capable of updating the SFE aerodynamic model.