For centuries, scientists have dreamed of creating materials by design. Rather than discovery by accident, bespoke materials could be tailored to fulfill specific technological needs. Quantum theory and computational methods are essentially equal to the task, and computational power is the new bottleneck. Machine learning has the potential to solve that problem by approximating material behavior at multiple length scales. A full end-to-end solution must allow us to approximate the quantum mechanics, microstructure and engineering tasks well enough to be predictive in the real world. In this dissertation, I present algorithms and methodology to address some of these problems at various length scales. In the realm of enumeration, systems with many degrees of freedom such as high-entropy alloys may contain prohibitively many unique possibilities so that enumerating all of them would exhaust available compute memory. One possible way to address this problem is to know in advance how many possibilities there are so that the user can reduce their search space by restricting the occupation of certain lattice sites. Although tools to calculate this number were available, none performed well for very large systems and none could easily be integrated into low-level languages for use in existing scientific codes. I present an algorithm to solve these problems. Testing the robustness of machine-learned models is an essential component in any materials discovery or optimization application. While it is customary to perform a small number of system-specific tests to validate an approach, this may be insufficient in many cases. In particular, for Cluster Expansion models, the expansion may not converge quickly enough to be useful and reliable. Although the method has been used for decades, a rigorous investigation across many systems to determine when CE "breaks" was still lacking. This dissertation includes this investigation along with heuristics that use only a small training database to predict whether a model is worth pursuing in detail. To be useful, computational materials discovery must lead to experimental validation. However, experiments are difficult due to sample purity, environmental effects and a host of other considerations. In many cases, it is difficult to connect theory to experiment because computation is deterministic. By combining advanced group theory with machine learning, we created a new tool that bridges the gap between experiment and theory so that experimental and computed phase diagrams can be harmonized. Grain boundaries in real materials control many important material properties such as corrosion, thermal conductivity, and creep. Because of their high dimensionality, learning the underlying physics to optimizing grain boundaries is extremely complex. By leveraging a mathematically rigorous representation for local atomic environments, machine learning becomes a powerful tool to approximate properties for grain boundaries. But it also goes beyond predicting properties by highlighting those atomic environments that are most important for influencing the boundary properties. This provides an immense dimensionality reduction that empowers grain boundary scientists to know where to look for deeper physical insights.

<p> The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, u_x]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0.</p><p>The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense.</p><p>The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.</p>

A design of anautomatic network capacity markets, oftenreferred to as a bandwidth market, is presented. Three topicsare investigated. First, a network model is proposed. Theproposed model is based upon a trisection of the participantroles into network users, network owners, and market middlemen.The network capacity is defined in a way that allows it to betraded, and to have a well defined price. The network devicesare modeled as core nodes, access nodes, and border nodes.Requirements on these are given. It is shown how theirfunctionalities can be implemented in a network. Second, asimulated capacity market is presented, and a statisticalmethod for estimating the price dynamics in the market isproposed. A method for pricing network services based on sharedcapacity is proposed, in which the price of a service isequivalent to that of a financial derivative contract on anumber of simple capacity shares.Third, protocols for theinteraction between the participants are proposed. The marketparticipants need to commit to contracts with an auditableprotocol with a small overhead. The proposed protocol is basedon a public key infrastructure and on known protocols for multiparty contract signing. The proposed model allows networkcapacity to be traded in a manner that utilizes the networkeciently. A new feature of this market model, compared to othernetwork capacity markets, is that the prices are not controlledby the network owners. It is the end-users who, by middlemen,trade capacity among each-other. Therefore, financial, ratherthan control theoretic, methods are used for the pricing ofcapacity. <b>Keywords:</b>Computer network architecture, bandwidthtrading, inter-domain Quality-of-Service, pricing,combinatorial allocation, financial derivative pricing,stochastic modeling

This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, ux]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0. The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense. The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.

Alumina (Al2O3) is one of the most widely used engineering ceramic. It can be used in a wide range of applications like electrical/thermal insulation, wear resistance, structural refractories, cutting tools, abrasives, catalyst carriers and coatings. A traditional ceramic process has several steps (i.e. powder synthesis and processing, shape forming, drying, organic burnout and densification). Accessing powders with sizes in the range of a couple of micrometers down to several tens of nanometers is considered critical in attaining higher densities in the final ceramic bodies. Besides since significant shrinkage can be observed in the thermal treatment steps due to the excessive use of additives (e.g. binders, solvents and plasticizers) in the powder processing and forming steps, it is important to take remedies that would increase the solids loading in the initial mixtures. In addition, most of the conventional additives and solvents used in these steps are toxic and it is necessary to replace them with the environmentally benign aqueous-based alternatives. Alumoxanes could be used as a benign aqueous-based alternative to be used as a ceramic precursor or an agent. They are a group of compounds that have nano sized boehmite cores encapsulated with the organic groups used in its production steps. In this research work, alumoxane nano particles which can be used as precursors for nano-alumina were developed starting from aluminum trihydroxide. As a preconditioning step, grinding was applied to decrease the aluminum hydroxide particle size (&amp / #8804 / 60 &amp / #956 / m) to submicron sizes. This process was followed by the glycothermal ageing step, and organic derivative of boehmite was obtained. The amorphous particles thus obtained were further treated mechanochemically in a high energy ball mill with organic chemicals like acetic acid, methoxy acetic acid, stearic acid and L-lysine. After this step the observed sizes of the particles were as low as 10-100 nm. The effects of organic molecules used in each step were studied by FTIR spectroscopy and their effectiveness in exfoliation of hydroxide layers were identified with dynamic light scattering from processing solutions dispersed in aqueous medium. Moreover, in each step, structural analyses were carried out by XRD.

The purpose of the study was threefold: (1) to determine the factor structure of mathematical thinking at the within-classroom and at the between-classroom level / (2) to investigate the extent of variation in the relationships among different mathematical thinking constructs at the within- and between-classroom levels / and (3) to examine the cross-level interactions among different types of mathematical thinking. Previous research was extended by investigating the factor structure of mathematical thinking in derivative at the within- and between-classroom levels, and further examining the direct, indirect, and cross-level relations among different types of mathematical thinking. Multilevel analyses of a cross-sectional dataset containing two independent samples of undergraduate students nested within classrooms showed that the within-structure of mathematical thinking includes enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking, whereas the between-structure contains formal-axiomatic, proceptual-symbolic, and conceptual-embodied thinking. Major findings from the two-level mathematical thinking model revealed that: (1) enactive, iconic, algebraic, and axiomatic thinking varied primarily as a function of formal and algorithmic thinking / (2) the strongest direct effect of formal-axiomatic thinking was on proceptual-symbolic thinking / (3) the nature of the relationships was cyclic at the between-classroom level / (4) the within-classroom mathematical thinking constructs significantly moderate the relationships among conceptual-embodied, proceptual-symbolic, and formal-axiomatic thinking / and (5) the between-classroom mathematical thinking constructs moderate the relationships among enactive, iconic, algorithmic, algebraic, formal, and axiomatic thinking. The challenges when using multilevel exploratory factor analysis, multilevel confirmatory factor analysis, and multilevel structural equation modeling with categorical variables are emphasized. Methodological and educational implications of findings are discussed.

In this dissertation, we present new approaches to improve standard designs in adaptive control theory, and novel adaptive control architectures. We first present a novel Kalman filter based approach for approximately enforcing a linear constraint in standard adaptive control design. One application is that this leads to alternative forms for well known modification terms such as e-modification. In addition, it leads to smaller tracking errors without incurring significant oscillations in the system response and without requiring high modification gain. We derive alternative forms of e- and adaptive loop recovery (ALR-) modifications. Next, we show how to use Kalman filter optimization to derive a novel adaptation law. This results in an optimization-based time-varying adaptation gain that reduces the need for adaptation gain tuning. A second major contribution of this dissertation is the development of a novel derivative-free, delayed weight update law for adaptive control. The assumption of constant unknown ideal weights is relaxed to the existence of time-varying weights, such that fast and possibly discontinuous variation in weights are allowed. This approach is particularly advantageous for applications to systems that can undergo a sudden change in dynamics, such as might be due to reconfiguration, deployment of a payload, docking, or structural damage, and for rejection of external disturbance processes. As a third and final contribution, we develop a novel approach for extending all the methods developed in this dissertation to the case of output feedback. The approach is developed only for the case of derivative-free adaptive control, and the extension of the other approaches developed previously for the state feedback case to output feedback is left as a future research topic. The proposed approaches of this dissertation are illustrated in both simulation and flight test.

<p>A design of anautomatic network capacity markets, oftenreferred to as a bandwidth market, is presented. Three topicsare investigated. First, a network model is proposed. Theproposed model is based upon a trisection of the participantroles into network users, network owners, and market middlemen.The network capacity is defined in a way that allows it to betraded, and to have a well defined price. The network devicesare modeled as core nodes, access nodes, and border nodes.Requirements on these are given. It is shown how theirfunctionalities can be implemented in a network. Second, asimulated capacity market is presented, and a statisticalmethod for estimating the price dynamics in the market isproposed. A method for pricing network services based on sharedcapacity is proposed, in which the price of a service isequivalent to that of a financial derivative contract on anumber of simple capacity shares.Third, protocols for theinteraction between the participants are proposed. The marketparticipants need to commit to contracts with an auditableprotocol with a small overhead. The proposed protocol is basedon a public key infrastructure and on known protocols for multiparty contract signing. The proposed model allows networkcapacity to be traded in a manner that utilizes the networkeciently. A new feature of this market model, compared to othernetwork capacity markets, is that the prices are not controlledby the network owners. It is the end-users who, by middlemen,trade capacity among each-other. Therefore, financial, ratherthan control theoretic, methods are used for the pricing ofcapacity.</p><p><b>Keywords:</b>Computer network architecture, bandwidthtrading, inter-domain Quality-of-Service, pricing,combinatorial allocation, financial derivative pricing,stochastic modeling</p>

<p>This work aims at enhancing the understanding and to provideimproved models of the dynamic behavior of rubber vibrationisolators which are widely used in mechanical systems.Initially, a time domainmodel relating compressions tocomponent forces accounting for preload effects, frequency anddynamic amplitude dependence is presented. The problem ofsimultaneously modelling the elastic, viscoelastic and frictionforces are removed by additively splitting them, where theelastic force response is modelled either by a fully linear ora nonlinear shape factor based approach, displaying resultsthat agree with those of a neo-Hookean hyperelastic isolatorunder a long term precompression. The viscoelastic force ismodelled by a fractional derivative element, while the frictionforce governs from a generalized friction element displaying asmoothed Coulomb force. This is a versatile one-dimensionalcomponent model effectively using a small number of parameterswhile exhibiting a good resemblance to measured isolatorcharacteristics. Additionally, the nonlinear excitationeffects on dynamic stiffness and damping of a filled rubberisolator are investigated through measurements. It is shownthat the well-known Payne effect - where stiffness is high forsmall excitation amplitudes and low for large amplitudes whiledamping displays a maximum at intermediate amplitudes -evaluated at a certain frequency, is to a large extentinfluenced by the existence of additional frequency componentsin the signal. Finally, a frequency, temperature and preloaddependent dynamic stiffness model is presented covering theranges from 20 to 20 000 Hz, -50 to +50 °C at 0 to 20 %precompression. A nearly incompressible, thermo-rheologicallysimple material model is adopted displaying viscoelasticitythrough a time - strain separable relaxation tensor with asingle Mittag-Leffler function embodying its time dependence.This fractional derivative based function successfully fitsmaterial properties throughout the whole audible frequencyrange. An extended neo-Hookean strain energy function, beingdirectly proportional to the temperature and density, isapplied for the finite deformation response with componentproperties solved by a nonlinear finite element procedure. Thepresented work is thus believed to enlighten workingconditions’impact on the dynamic properties of rubbervibration isolators, while additionally taking some of thesemost important features into account in the presentedmodels.</p>