DSpace Repository :: Browsing by Author "Shillor, Meir"

Browsing by Author "Shillor, Meir"

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A Hybridized Discontinuous Galerkin Scheme for the Coupled Stokes-Darcy Flow and Transport
(2022-03-22) Pham, Dinh Dong; Cesmelioglu, Aycil; Cheng, Eddie; Horvath, Tamas; Schmidt, Darrell; Shillor, Meir
The main focus of this thesis is on finding highly accurate and robust numerical methods to solve a complex flow and transport problem governed by the fully-coupled time-dependent Stokes-Darcy-transport equations. This problem has many applications one of which is groundwater contamination by pollutants transported via surface/subsurface flow. It consists of two main ingredients; the time-dependent Stokes-Darcy equations describing the flow, and the time-dependent advection-diffusion equation for the transport of chemicals via this flow. Therefore, the first part of this thesis is dedicated to studying the time-dependent Stokes-Darcy problem that describes the free flow and porous media flow on two different parts of a domain and their interaction at the common interface. We introduce a hybridized discontinuous Galerkin (HDG) method which provides exact mass conservation and pressure robustness and handles the interface conditions via facet unknowns. We prove well-posedness and a priori error estimates in the energy norm, and provide numerical experiments that show optimal convergence and robustness of the method with respect to the problem parameters. The second part deals with the time-dependent advection-diffusion equation where we again use an HDG method for the spatial discretization. We show the existence and uniqueness of the semi-discrete transport problem and prove a priori error estimates in the energy norm. A number of numerical experiments are presented for different boundary conditions and we observe optimal rates of convergence in each case. Combining the two parts by a sequential algorithm, we solve the fully coupled time-dependent Stokes-Darcy-transport problem. The coupling of the flow and transport is introduced by the dependence of the fluid viscosity and source/sink terms on the concentration and by the dependence of the dispersion/diffusion tensor in the porous media domain on the advective fluid velocity. Our sequential algorithm employs a linearizing decoupling strategy based on the backward Euler time-stepping where the Stokes-Darcy and the transport equations are solved sequentially by time-lagging the concentration. The well-posedness results and a priori error estimates for the velocity and the concentration in the energy norm are presented and numerical examples demonstrating optimal convergence and mass conservation are provided.
Dynamic contact of two GAO beams
(2012-11) Ahn, Jeongho; Kuttler, Kenneth; Shillor, Meir
The dynamic contact of two nonlinear Gao beams that are connected with a joint is modeled, analyzed, and numerically simulated. Contact is modeled with either (i) the normal compliance condition, or (ii) the unilateral Signorini condition. The model is in the form of a variational equality in case (i) and a variational inequality in case (ii). The existence of the unique variational solution is established for the problem with normal compliance and the existence of a weak solution is proved in case (ii). The solution in the second case is obtained as a limit of the solutions of the first case when the normal compliance stiffness tends to infinity. A numerical algorithm for the problem is constructed using finite elements and a mixed time discretization. Simulation results, based on the implementation of the algorithm, of the two cases when the horizontal traction vanishes or when it is sufficiently large to cause buckling, are presented. The spectrum of the vibrations, using the FFT, shows a rather noisy system.
Dynamic contact with normal compliance wear and discontinuous friction coefficient
(2002-08) Shillor, Meir
We apply the recent theory of evolution inclusions forset-valued pseudomonotone maps, developed in Kuttler and Shillor[Commun.Contemp.Math.,1(1999),pp.87–123]to the problem of dynamic frictional contact with normal compliance and wear. The friction coefficient is assumed to be slip rate dependent, and may be continuous, or discontinuous in the form of a graph with a vertical segment at the origin, representing the transition from the static to the dynamic value.The wear of the contacting surfaces is modeled by the Archard law.We prove the existence of a weak solution for the problem. We establish the uniqueness of the weak solution in the case when the friction coefficient is continuous. We also show that the problem with prescribed wear depends continuously on the wear.
Dynamic contact with Signorini's condition and slip rate dependent friction
(2004-06) Kuttler, Kenneth; Shillor, Meir
Existence of a weak solution for the problem of dynamic frictional contact between a viscoelastic body and a rigid foundation is established. Contact is modelled with the Signorini condition. Friction is described by a slip rate dependent friction coefficient and a nonlocal and regularized con- tact stress. The existence in the case of a friction coefficient that is a graph, which describes the jump from static to dynamic friction, is established, too. The proofs employ the theory of set-valued pseudomonotone operators applied to approximate problems and a priori estimates.
A frictional contact problem for an electro-viscoelastic body
(2007-12) Lerguet, Zhor; Shillor, Meir; Sofonea, Mircea
A mathematical model which describes the quasistatic frictional contact between a piezoelectric body and a deformable conductive foundation is studied. A nonlinear electro-viscoelastic constitutive law is used to model the piezoelectric material. Contact is described with the normal compliance condition, a version of Coulomb’s law of dry friction, and a regularized electrical conductivity condition. A variational formulation of the model, in the form of a coupled system for the displacements and the electric potential, is derived. The existence of a unique weak solution of the model is established under a smallness assumption on the surface conductance. The proof is based on arguments of evolutionary variational inequalities and fixed points of operators.
Investigations Of Magnetic/Electric Field Control Of Magnetization Of Ferromagnetic And Multiferroics
(2022-11-09) Xiong, Yuzan; Qu, Hongwei; Zhang, Wei; Li, Jia; Yang, Ankun; Shillor, Meir
The shortcomings of contemporary complementary metal oxide semiconductor (CMOS) technologies include increased power consumption, scalability, volatility, and device variability. New materials and novel devices are being investigated in this regard. Spintronic devices, which are normally based on magnetic materials, store and process data based on the modes of electron spins, rather than the presence or absence of charges as in the CMOS, are one possible approach. Numerous potential advantages of spintronic devices include its quick operational speed, low power requirement, and non-volatility. Two ferromagnetic materials suitable for creating spintronic devices are investigated in his dissertation study. Material properties, techniques for regulating the magnetization of materials, with both magnetic and electrical fields, and the development of devices useful for use in frequency modulations are all respectively detailed.The first section of this dissertation studies the magnetically-induced transparence (MIT) effect in Y3Fe5O12 (YIG)/Permalloy (Py) coupled bilayers. The measurement is achieved via a heterodyne detection of the coupled magnetization dynamics using a single wavelength that probes the magneto-optical Kerr and Faraday effects of Py and YIG, respectively. Clear features of the MIT effect are evident from the deeply modulated ferromagnetic resonance of Py due to the perpendicular-standing-spin-wave of YIG. We develop a phenomenological model that nicely represents the experimental results including the induced amplitude and phase evolution caused by the magnon-magnon coupling. This work offers a new route towards studying phase-resolved spin dynamics and hybrid magnonic systems. The second part of this dissertation discusses the research on the hexaferrite material, Zn2Y, and the prospect of controlling its magnetic characteristics by applying a dc voltage, which is akin to a bias electric field. The detection and investigation of the magnetoelectric (ME) effect for in-plane currents orthogonal to the hexagonal axis in single crystal and thin films of Zn2Y grown via liquid phase epitaxy. By applying a dc voltage, tuning of ferromagnetic resonance (FMR) was achieved in the hexaferrites. In addition to the frequency shift caused by the electrical tuning, magnetic properties of the material as a function of the input tuning power was also studied.
Load Distributions in Bolted Single Lap Joints Under Non-Central Tensile Shear Loading
(2021-11-16) Sinthusiri, Chaiwat; Nassar, Sayed; Shillor, Meir; Yang, Xianjie; Wu, Zhijun
This study uses a numerically calibrated beam theory-based model to investigate the bolt load distributions in a preloaded two-bolt single lap joint under non-central tensile shear loading. The linear spring-based modeling is used for the two preloaded bolts and substrates. The bolt stiffnesses were derived from the bolt flexibilities influence by the bending deformation, the shear deformation, the bolt, and plate contact deformations. Due to the non-uniform load distribution along the bolt shank, the 3D finite element analysis was used to determine the correlation factors of each influence factors. Non central loading may be due to geometric tolerances that would cause additional moment loading on the joint. Thus, the load would not be equally distributed among all bolts in the joint. The effect of various joint parameters, bolt preload and off-center location of the tensile shear loading is investigated and discussed.
Mathematical model for outgassing and contamination
(1991-10) Shillor, Meir
A model for the mathematical description of the processes of outgassing and contamination in a vacuum system is proposed. The underlying assumptions are diffusion in the source, convection and diffusion in the cavity, mass transfer across the source-cavity interface, and a generalization of the Langmuir isotherm for the sorption kinetics on the target. Three approximations are considered where the asymptotic behavior of the model for large time is shown as well as the dependence and sensitivity of the model on some of the parameters. Some numerical examples of the full model are then presented together with a proof of the uniqueness of the solution.
Mathematical Models, Analysis and Simulations of the Handy Model with Middle Class
(2021-12-06) Al-Khawaja, Thanaa Ali Kadhim A; Shillor, Meir; Spagnuolo, Anna Maria; Ogunyemi, Theophilus; Andrews, Kevin
This study presents three different mathematical versions of the HANDY (Human And Nature DYnamics) model for the socioeconomic dynamics of a large stratified society. The basic model was introduced in the ground breaking publications of Motesharrei (dissertation 2014) and Motesharrei et. al. (2016). The original model consists of a nonlinear system of four ordinary differential equations (ODEs) which describe the development, in time, of a ’very simple’ society consisting of two populations: the Elite (rich) and Commoners (workers). Included also are the use of natural (renewable and nonrenewable) resources and the accumulation of human wealth. The model’s solutions depict the dynamics of these variables. Motesharrei’s main impetus and interest was to use the model as a tool for evaluating the conditions that contribute to the flourishing, sustainability, or collapse of complex societies. This dissertation expands the basic HANDY model and studies its mathematical properties and those of its three extensions. It establishes the existence of solutions to the models, as well as their uniqueness, boundedness and positivity. Furthermore, it investigates the stability of the systems’ steady states, which describe the long-time behavior of the societies. It also presents a number of qualitatively different computer simulations, providing insights into potential behaviors of the societies described by these models. The main contributions of this work are the mathematical analysis of the basic HANDY model, its three expansions and their analysis, and computer simulations. The first extension, the HANDY-SM model, includes social mobility. Rich individuals may go bankrupt and become workers, and some workers may become rich. It also allows for two different aspects of inequality, through variations in salaries and the wealth structure. The second extension, the HANDY-MC-I model, includes the Middle Class population, making the model more practical when applied to modern societies. It expands the system into five ODEs, and allows for social mobility among the three populations. Finally, in the third extension, HANDY-MC-II, two variables describe the natural resources: the renewable resources (wood, solar and wind energies), and nonrenewable resources (coal, oil, gas). This particular extension makes the model more realistic, but it also adds considerable complexity since it consists of six nonlinear coupled ODEs. The model simulations depict the consequences of having three different populations with different income status, two natural resources, and unequal contributions to wealth structure. Analysis of the models’ steady states shows that the state is stable when the populations and wealth die out but nature (the resources) is at its equilibrium. The model has also asymptotically stable, nonzero steady states to which the populations, the resources and the wealth converge in the long-time limit. The simulations also show the existence of periodic solutions in which the populations, the natural resources and wealth undergo large oscillations, indicating cycles of ‘boom and bust.’ Finally, the simulations demonstrate that the models may have chaotic solutions, pointing to a high level of unpredictability. This dissertation describes three increasingly more complex HANDY models. It paves the way and raises mathematically interesting topics for their further study. In particular, the uniqueness of the solutions, and the questions of the existence of periodic solutions, limit cycles and chaos, remain unresolved, yet. Furthermore, it suggests the possibility of tailoring such models to existing societies, and then using them as tools for evaluation of the potential outcomes of various policy decision
A Model for Chagas Disease with Oral and Congenital Transmission
(2013-06) Coffield, Daniel; Spagnuolo, Anna Maria; Shillor, Meir; Mema, Ensela; Pell, Bruce; Pruzinsky, Amanda; Zetye, Alexandra
This work presents a new mathematical model for the domestic transmission of Chagas disease, a parasitic disease affecting humans and other mammals throughout Central and South America. The model takes into account congenital transmission in both humans and domestic mammals as well as oral transmission in domestic mammals. The model has time-dependent coefficients to account for seasonality and consists of four nonlinear differential equations, one of which has a delay, for the populations of vectors, infected vectors, infected humans, and infected mammals in the domestic setting. Computer simulations show that congenital transmission has a modest effect on infection while oral transmission in domestic mammals substantially contributes to the spread of the disease. In particular, oral transmission provides an alternative to vector biting as an infection route for the domestic mammals, who are key to the infection cycle. This may lead to high infection rates in domestic mammals even when the vectors have a low preference for biting them, and ultimately results in high infection levels in humans.
Modeling Extreme Insurance Losses Using Transmutation and Copula
(2023-01-01) Addai, Solomon; Ogunyemi, Theophilus; Perla, Subbaiah; Shillor, Meir; Drignei, Dorin; So, Hon Yiu
In this dissertation, we apply transmutation to the theoretical work in insurance. From our extensive literature search, this seems to be a novel piece of work with regards to the transmutation, we particularly focus on the theoretical application of the exponential, Pareto and Weibull distributions. By shedding light on this unexplored area, our findings contribute valuable insights into the broader domain of insurance studies. We also do some exploratory work with regard to future research pursuit on a combined application of copula and transmutation to insurance data.
A one-dimensional spot welding model
(2006-11) Andrews, K.T.; Guessous, L.; Nassar, S.; Putta, S.V.; Shillor, Meir
A one-dimensional model is proposed for the simulations of resistance spot welding, which is a common industrial method used to join metallic plates by electrical heating. The model consists of the Stefan problem, in enthalpy form, coupled with the equation of charge conservation for the electrical potential. The temperature dependence of the density, thermal conductivity, specific heat, and electrical conductivity are taken into ac- count, since the process generally involves a large temperature range, on the order of 1000 K. The model is general enough to allow for the welding of plates of different thicknesses or dissimilar materials and to account for variations in the Joule heating through the material thickness due to the dependence of electrical resistivity on the temperature. A novel feature in the model is the inclusion of the effects of interface resistance between the plates which is also assumed to be temperature dependent. In addition to construct- ing the model, a finite difference scheme for its numerical approximations is described, and representative computer simulations are depicted. These describe welding processes involving different interface resistances, different thicknesses, different materials, and different voltage forms. The differences in the process due to AC or DC currents are depicted as well.
Process Optimization of Autoclave Bonded Light-Weight Material Joints
(2022-04-01) Jagatap, Shraddha Ratnakar; Nassar, Sayed; Shillor, Meir; Yang, LianXiang; Wu, Zhijun
This dissertation research fills a gap in the existing open literature regarding the significance of autoclave cure process variables and their interactions on the static strength of lightweight material single lap joints under tensile-shear loading. Specifically, the research investigates the dependence between the degree of cure of the epoxy adhesive and the mechanical performance of the single lap joint boded with same epoxy adhesive. Lightweight material system includes polycarbonate, Aluminum 6061 and glass reinforced plastics (GFRP) extren 500. A commercially available polyurethane film adhesive PE399 was selected to bond Polycarbonate single lap joints (SLJ) while epoxy film adhesive AF163-2K was selected to bond aluminum and GFRP joints. Studied variables include cure temperature, cure pressure and their respective rates as well as the duration of cure time. Dynamic Mechanical Analysis (DMA) is used to quantify glass transition temperature of AF163-2K cured with different combinations of autoclave process variables. The relative significance of variables and variable combinations are investigated for their effect on the bond strength. Experimental test data shows interaction between autoclave variable cure temperature in combination with cure time, temp ramp rate and pressure ramp rate have significant effect on glass transition temperature, bond strength and failure mode. Changes in joint static load transfer capacity (LTC) was investigated after cyclic temperature profile fluctuates between 20° C and 85° C at a constant relative humidity (RH) level of 85 %.
Process Optimization of Autoclave Bonded Light-Weight Material Joints
(2022-01-01) Jagatap, Shraddha Ratnakar; Nassar, Sayed; Shillor, Meir; Yang, LianXiang; Wu, Zhijun
This dissertation research fills a gap in the existing open literature regarding the significance of autoclave cure process variables and their interactions on the static strength of lightweight material single lap joints under tensile-shear loading. Specifically, the research investigates the dependence between the degree of cure of the epoxy adhesive and the mechanical performance of the single lap joint boded with same epoxy adhesive. Lightweight material system includes polycarbonate, Aluminum 6061 and glass reinforced plastics (GFRP) extren 500. A commercially available polyurethane film adhesive PE399 was selected to bond Polycarbonate single lap joints (SLJ) while epoxy film adhesive AF163-2K was selected to bond aluminum and GFRP joints. Studied variables include cure temperature, cure pressure and their respective rates as well as the duration of cure time. Dynamic Mechanical Analysis (DMA) is used to quantify glass transition temperature of AF163-2K cured with different combinations of autoclave process variables. The relative significance of variables and variable combinations are investigated for their effect on the bond strength. Experimental test data shows interaction between autoclave variable cure temperature in combination with cure time, temp ramp rate and pressure ramp rate have significant effect on glass transition temperature, bond strength and failure mode. Changes in joint static load transfer capacity (LTC) was investigated after cyclic temperature profile fluctuates between 20 C and 85 C at a constant relative humidity (RH) level of 85 .
Product measurability with applications to a stochastic contact problem with friction
(2014-12) Kuttler, Kenneth; Shillor, Meir
A new product measurability result for evolution equations with random inputs, when there is no uniqueness of the ω-wise problem, is established using results on measurable selection theorems for measurable multi- functions. The abstract result is applied to a general stochastic system of ODEs with delays and to a frictional contact problem in which the gap be- tween a viscoelastic body and the foundation and the motion of the foundation are random processes. The existence and uniqueness of a measurable solution for the problem with Lipschitz friction coefficient, and just existence for a discontinuous one, is obtained by using a sequence of approximate problems and then passing to the limit. The new result shows that the limit exists and is measurable. This new result opens the way to establish the existence of measurable solutions for various problems with random inputs in which the uniqueness of the solution is not known, which is the case in many problems involving frictional contact.
Regularity result for the problem of vibrations of a nonlinear beam
(2008-02) M'Bengue, M.F.; Shillor, Meir
A model for the dynamics of the Gaonon linear beam, which allows for buckling, is studied. Existence and uniqueness of the local weak solution was established in Andrews et al. (2008). In this work the further regularity in time of the weak solution is shown using recent results for evolution problems. Moreover, the weak solution is shown to be global, existing on each finite time interval.
Transportation Related Algorithm Design and Application
(2024-01-01) Kulick, Anthony James; Cheng, Eddie; Kruk, Serge; Shillor, Meir; Liptak, Laszlo
In this thesis several algorithms are proposed and developed to solve a variety of transportation related problems. First we considered, a dynamic programming approach to create an exact solver to minimize distance in a vehicle routing problemwith time windows (VRPTW) variant. Several new tests are developed to reduce the size of the state space and ultimately reduce the number of state transitions.
Ultrasonic Parameters as a Function of Absolute Hydrostatic Pressure. II. Mathematical Models of the Speed of Sound in Organic Liquids
(2003-09) Oakley, B; Hanna, D; Shillor, Meir; Barber, G
Polynomial expressions for the speed of sound as a function of pressure for 68 different organic liquids are presented in tabular form. The liquids form a subset of those discussed in the companion paper: Ultrasonic parameters as a function of absolute hydrostatic pressure. I. A review of the data for organic liquids. The polynomial expressions are based upon the experimental results reported by many different researchers. For some common liquids, such as benzene, hexane, ethanol, and carbon tetrachloride, the results of as many as five different researchers are reported. These results sometimes vary widely—far more than would be expected from calculated experimental uncertainties. An analysis is presented of how well pressure-dependent polynomials fit the experimental data when the number of coefficients is increased. The error in the polynomial fit is also explored when both pressure and temperature dependencies are present. Finally, differences between ultrasonic and Brillouin scattering experimental results are discussed.

Browsing by Author "Shillor, Meir"

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