O objetivo desta tese consiste na elaboração de dois estudos empíricos. No primeiro, estuda-se as propriedades da estrutura a termo das taxas de juros e em particular testa-se a validade da hipótese de expectativas a dados brasileiros e americanos. Os melhores resultados foram obtidos para os dados americanos. No segundo estudo pesquisa-se os determinantes da volatilidade dos títulos de dívida soberana de quatro países – Brasil, Argentina, Rússia e México. Os modelos utilizados são multivariados da família GARCH. Avalia-se em que medida as crises financeiras pelas quais passaram os países citados implicaram em algum tipo de contágio aos demais. Há evidência favorável à hipótese de contágio de muitos dos eventos estudados. / The thesis is composed by two empirical studies. In the first it’s analyzed the proprieties of the interest rate term structure and, in particular, it’s investigated whether or not the expectation hypothesis is a good description of Brazilian and American data. The results are better for American data. In the second study it’s investigated the sovereign debt bonds volatility of four countries – Brazil, Mexico, Russia and Argentine. The volatility was analyzed by the estimation of multivariate GARCH models. The existence of financial crises contagion was investigated and tested. There is some evidence in favor of the contagion hypothesis.

Neste trabalho utiliza-se uma formulação do método dos elementos de contorno (MEC) para a análise de pavimentos de edifícios, dando-se particular ênfase à análise de lajes cogumelo feita com a incorporação da não-linearidade física. Nesta formulação são consideradas as tensões normais e cisalhantes possibilitando, assim, a determinação da resistência última da estrutura. A formulação é inicialmente desenvolvida para a análise de flexão de placas utilizando-se a teoria de Reissner. A seguir, a formulação é estendida de modo a considerar a interação da placa com outros elementos, como vigas e pilares. Na interação placa-viga, o enrijecimento produzido é computado através de uma combinação com o método dos elementos finitos. Este modelo permite uma avaliação precisa dos momentos e forças cortantes nas interfaces da placa com os elementos lineares. Admite-se a ocorrência de um campo de momentos iniciais, viabilizando, dentre outros, o estudo de pavimentos com não-linearidade física. Para a análise do comportamento não-linear, implementa-se um algoritmo incremental-iterativo baseado no método da rigidez inicial. Visando-se obter uma melhor representação do comportamento do concreto armado, a integração das tensões ao longo da espessura é feita por um esquema numérico tipo gaussiano; a contribuição da armadura é feita de modo discreto considerada concentrada em seu centro geométrico. Pode-se, assim, avaliar separadamente o processo de danificação do concreto e o escoamento das armaduras. Para o concreto adota-se o modelo de dano de Mazars e para as armaduras longitudinais, um modelo elastoplástico uniaxial com endurecimento isotrópico. Quanto à absorção dos esforços oriundos das tensões cisalhantes, adota-se um modelo semelhante à idealização da treliça clássica de Ritter e Mörsch para vigas de concreto armado. Admite-se ainda que, após o início da fissuração, as tensões cisalhantes sejam absorvidas apenas pelas armaduras transversais. Para estas, adotase comportamento elástico linear. Objetivando-se a comprovação da eficiência da formulação proposta, são analisados alguns exemplos cujos resultados são comparados com resultados experimentais ou resultados de outros métodos de análise / This work deals with a formulation of the boundary element method applied to slab floor analysis with special emphasis concrete flat slabs exhibiting physical non-linearities. In this formulation normal and shear components of the stress tensor are taken into account to capture more accurately the ultimate strength of the structural element. The boundary element formulation in the context of Reissner’s plate bending theory is initially studied. Then, the formulation is extended to deal with combinations of plate elements with other elements such as beams and columns and also to incorporate internal support effects, for which full contact is assumed over small areas. The plate-beam and plate-column interaction model is based on a combination with the finite element method. Thus, this model allows an accurate evaluation of the internal forces along the plate-linear element interfaces and also over its vicinity. The presence of possible initial moment fields is also taken into account, which enables us to consider physical non-linear behaviours. The solution of the nonlinear system of algebraic equations is based on an iterative algorithm with constant matrix. In order to obtain a better modelling of the reinforced concrete slabs, the stress integrals along the thickness are performed with an appropriate gauss scheme; the reinforcement contribution is computed by considering concentrated effects at its geometric centre. Thus, the concrete degradation and the steel yielding can be independently evaluated. To represent the concrete behaviour the Mazars’ damage model has been adopted, while the steel material is governed by a uniaxial elastoplastic criterion with isotropic hardening. After the initial cracking of the concrete the shear stresses are properly transferred to the shear reinforcement using the Mörsch truss concept. The accuracy of the proposed formulation is illustrated by the analysing some practical examples. The results obtained are compared with experimental results and other numerical technique solutions

Cette thèse vise à développer une méthode pour la justification des fondations superficielles sous charge sismique dans le cadre du nouveau zonage sismique de la France, entré en vigueur en 2011 et des justifications post Fukushima. Elle s’inscrit dans le cadre d’un contrat de recherche entre l’IFSTTAR et EDF CEIDRE.Un modèle basé sur le concept de macroélément est développé pour étudier l’interaction sol-structure (ISS) en prenant en compte les différentes non linéarités. Sa formulation se base sur la théorie de l’élastoplasticité et s’inspire des normes en vigueur (Eurocodes 7 et 8) et. Les différents paramètres sont définis à partir d’essais au laboratoire ou in situ, ou à partir de simulations numériques en conditions statiques. Les coûts de calcul sont réduits du fait que les non linéarités liées à l’interaction sol-structure sont concentrés en des points particuliers du modèle de calcul. L’avantage du macroélément réside dans une formulation en efforts et déplacements, ce qui facilite son utilisation pour la justification des fondations (capacité portante, glissement, décollement, tassements, translations, distorsions et rotations).Le macroélément est implémenté dans le code par éléments finis CESAR LCPC et permet de simuler le comportement statique et sismique d’une fondation superficielle. Trois approches pour la modélisation de la radiation des ondes sismiques dans le sol sont comparées en considérant des chargements statiques et sismiques.Ensuite, des études paramétriques sont réalisées sur une structure en mettant en jeu plusieurs signaux réels. L’influence des différents paramètres de nocivité sur le comportement de la structure est étudiée.Le comportement statique et sismique d’un ouvrage réel est aussi analysé. Il s’agit d’un bâtiment fondé sur un radier reposant sur un sol stratifié. L’aléa sismique est défini par 5 accélérogrames d’accélération maximale égale à 0.4g. Des justifications normatives sont menées en se basant sur les résultats des différentes simulations réalisées / This PhD work concerns the elaboration of a method to verify the seismic sustainability of shallow foundations considering 2011 seismic zoning of France. It is a part of a research contract between EDF CEIDRE and IFSTTAR.To this end, a macroelement based model is developed in order to assess nonlinear soil structure interaction. The elastoplastic formulation of the macroelement constitutive model is compliant with the classical plasticity theory. The formulations for the plastic mechanisms are inspired from the applied standard (Eurocodes 7 & 8). The rate dependent response and the effects of the embedment and the soil inertia efforts are taken into account. The parameters for the constitutive model are defined from laboratory or field tests, or calibrated from static finite element method simulations. The calculation cost is significantly reduced due to the simplified modelling of the soil and its non linearities. Another advantage is that the macroelement based tool is formulated in terms of generalized variables (forces and displacements): this promotes its application in the verification of the sustainability of shallow foundations (bearing capacity, sliding, overturning, settlements, translations, rotations and distortions).The macroelement is implemented in the Finite Element software CESAR LCPC. It allows to simulate the static and the seismic behaviour of a shallow foundation. Three alternative approaches to assess SSI through this model are possible. These alternative approaches are explained and tested under static and seismic load.Then, it is used to perform parametric studies involving various input motions derived from earthquake recordings. The seismic response of a simple structure is studied with respect to the input motion key parameters.Finally, the static and seismic behaviour of a real structure is analysed. The structure is founded on a large raft foundation laying on a multi-layered soil. The seismic hazard is defined by five 0.4 g-PGA accelerograms. Verification to the applied standards is performed on the base of the simulation results, considering many features of the seismic behaviour

Les amplificateurs de puissance sont au centre des systèmes actuels de télécommunications. Leur linéarité (pour préserver la qualité des données transmises) et leur rendement énergétique (pour faire des économies d’énergie) sont très importants et constituent les préoccupations majeures des concepteurs. Cependant, ce sont des composants analogiques intrinsèquement non-linéaires et leur utilisation avec des signaux à enveloppes non-constantes génèrent des distorsions à savoir des remontées spectrales hors-bandes et une dégradation du taux d’erreurs. Les signaux OFDM à la base de nombreux standards comme le Wifi, le Wi-Max, la télévision numérique, le LTE, etc. ont de fortes variations de puissance encore appelées PAPR (Peak-to-Average Power Ratio) qui aggravent ces problèmes de non-linéarité de l’amplificateur et réduit son rendement. Le traitement conjoint des non-linéarités et l’amélioration du rendement de l’amplificateur est l’objectif de cette thèse.Pour cela, l’accent est mis sur une approche conjointe de la linéarisation et de la réduction du PAPR. Ces deux méthodes jusqu’à présent abordées séparément dans la littérature sont en fait complémentaires et interdépendantes. Cela a été prouvé grâce à une étude analytique que nous avons menée. Grâce à l’approche conjointe, on peut simplement les associer, on parle dans ce cas d’approche non-collaborative ou leur permettre en plus d’échanger des informations et de s’adapter l’une par rapport à l’autre et/ou vice versa. Ce dernier cas est l’approche collaborative. Nous avons ensuite proposé des algorithmes d’approche conjointe collaborative basés sur les techniques d’ajout de signal. La réduction du PAPR et la prédistorsion (choisie comme méthode de linéarisation) sont fusionnées sous une seule formulation d’ajout de signal. Un signal additionnel conjoint est alors généré pour à la fois compenser les non-linéarités de l’amplificateur de puissance et réduire la dynamique du signal à amplifier. / Power amplifiers are key components of current telecommunications systems. Their linearity (to preserve the quality of the data) and efficiency (for power savings) are the primary concerns of designers. However, they are non-linear analog components in nature that cause spectral leakage, warping and clustering of the constellation. The overall consequences of this are out-of-band interferences and Bit Error Rate (BER) degradation at the receiver.OFDM’s modulation used in many standards such as Wi-Fi, WiMAX, digital TV, LTE, etc. generates temporal signals with high power fluctuations also termed as Peak-to-average Power Ratio (PAPR). High PAPRs aggravate the non-linearity problem of the amplifier and reduce its efficiency. The objective of this thesis is to jointly increase the linearity and the efficiency of the power amplifier.For this, we focus on a joint approach of linearization and PAPR reduction. These two methods so far discussed separately in the literature are complementary and interdependent. This has been proven through an analytical study that we conducted. Through the joint approach, the two methods can be simply associated; in this case we speak of non-collaborative approach, or allowed to exchange some information in order to adapt each other. This latter case is collaborative approach. Then, we proposed algorithms of collaborative approach based on adding signal techniques. PAPR reduction and predistortion (chosen as linearization’s method) are merged into one global adding signal formulation. A joint additional signal is then generated to compensate at the same time the non-linearities introduced by the power amplifier and reduce the dynamic range of the signal to be amplified.

Le travail de recherche présenté dans ce manuscrit contribue à une étude générale de la susceptibilité électromagnétique (EM) d'un transistor MOS (Metal Oxide Semiconductor) dans une gamme de fréquences allant de 10 MHz à 1 GHz. Ce composant est destiné à un usage général pour des applications analogiques et numériques. Le but principal de ce travail est d'apporter une compréhension fine des mécanismes physiques mis en jeu au sein du composant lorsque ce dernier est soumis à une agression EM injectée en mode conduit au niveau de sa grille. Notre étude porte sur l'élaboration d'un modèle physique, essentiellement basé sur les variations de charges au sein du composant électronique. Cette approche permet à la fois de comprendre le fonctionnement nominal du transistor et la modification de son comportement lors d'un dysfonctionnement. En effet, la compréhension des mécanismes physiques mis en jeu est la base de la compréhension de la susceptibilité EM. Pour mettre en œuvre ce type d'approche, nous avons choisi d'étudier un type de susceptibilité correspondant à la modification de son point de fonctionnement sous agression EM. Cette modification du point de fonctionnement peut induire un dysfonctionnement du circuit dans lequel est implanté le transistor. Le phénomène physique à l'origine duquel les signaux parasites EM modifient le point de fonctionnement d'un composant électronique est le phénomène de redressement. Ce phénomène apparaît lorsqu'une distorsion est créée au sein du composant. C'est aussi pourquoi les non-linéarités du dispositif sont directement responsables de son observation. Ainsi, pour comprendre finement et physiquement l'effet induit par une agression EM, il est nécessaire de mettre en place une méthode d'étude. Celle-ci est basée sur une mesure des formes d'onde des courants à tous les accès du transistor. En effet, la visualisation de ces courants renseigne sur l'évolution des charges au sein de la structure. De plus, une telle mesure donne accès à une large palette d'observables (valeurs moyennes des courants, distorsions des courants, valeurs crêtes des courants, etc..). Dans un premier temps, les différentes mesures des formes d'onde des courants ont été réalisées lorsqu'une impulsion de tension était appliquée sur la grille du composant avec des temps de montée variables et choisis par rapport au temps de réponse du transistor. Cela nous a permis d'approfondir la compréhension du fonctionnement transitoire fort signal du MOSFET. Dans un second temps, nous avons mesuré les courants lors de l'application d'un signal EM à la grille du composant. En support à ces mesures nous avons utilisé deux outils de calcul : analytique et numérique. La méthode analytique permet la prédiction et l'identification des grandeurs du composant mises en jeu dans le mécanisme de la modification du comportement du transistor. La méthode numérique par simulation électrique permet, quant à elle, de prédire les effets de l'agression EM. Une étape de caractérisation statique et dynamique du composant a également été nécessaire pour enrichir la compréhension des phénomènes observés et fournir les entrées au modèle. / The research work presented here contributes to an overall study of the electromagnetic (EM) susceptibility of Metal Oxide Semiconductor Field Effect Transistors (MOSFET's), in a frequency range from 10 MHz to 1 GHz. This device is used for general purpose: analog and digital applications. The main aim of this study is to provide a detailed understanding of the physical mechanisms involved in the device when the Radio-Frequency (RF) interference is superimposed on the gate terminal. Our study focuses on the development of a physical model, based essentially on the charge variations within the electronic device. This approach allows to understand its behavior with and without the RF interference. Indeed, the knowledge of the involved physical mechanisms is the basic understanding of EM susceptibility. When RF interference is superimposed on the MOSFET terminals, various susceptibility effects take place depending on RF power level, frequency and the transistor operation region. Due to the nonlinearity of the MOS current-voltage characteristics, RF excitations cause distorted drain current waveform which leads to a bias point shift. This modification of the average drain current is called rectification effect. So we developed a method to clearly understand the effect induced by the EM interference. This method is based on the measurement of the currents waveforms to all of the transistor access. In fact, these currents waveforms measurements give us information on the charge variations within the electronic device. Moreover, such a measurement provides access to a wide range of current information (average values, distortion, peak values, etc.). Initially, the different currents waveforms measurements were made when a voltage ramp was applied to the device gate with variable rise time in respect to the transistor response time. This allowed us to understand the large signal transient response of the MOSFET. Secondly, we measured the currents waveforms when an EM interference was injected to the gate terminal. In support of these measurements we used two computation tools: analytical and numerical. The analytical method allows prediction and identification of the quantities of the device involved in the modification of transistor's behavior. The numerical method allows electrical simulation to predict the effects of EM aggression. A static and dynamic characterization of the component was also necessary to understand the observed phenomenon and provide data to the electrical model.

No description available.

In the past few years a new class of layered piezoceramic and piezoceramic-composite actuators, known as RAINBOW and GRAPHBOW, respectively, that are capable of achieving 100 times greater out-of-plane displacements than previously available has been developed. Prior to the development of RAINBOW and GRAPHBOW, large stacks of piezoelectric actuators, requiring complicated electronic drive circuits, were necessary to achieve the displacement now possible through the use of a single RAINBOW actuator. The major issues with both RAINBOW and GRAPHBOW are the prediction of their room-temperature shapes after processing, and their deformation response under application of electric field. In this research, a methodology for predicting the manufactured shapes of rectangular and disk-style RAINBOW and GRAPHBOW is developed. All of the predictive analyses developed are based on finding approximate displacement responses that minimize the total potential energy of the devices through the use of variational methods and the Rayleigh-Ritz technique. These analyses are based on classical layered plate theory and assumed the various layers exhibited linear elastic, temperature-independent behavior. Geometric nonlinearities are important and are included in the strain-displacement relations. Stability of the predicted shapes is determined by examining the second variation of the total potential energy. These models are easily modified to account for the deformations induced by actuation of the piezoceramic. The results indicate that for a given set of material properties, rectangular RAINBOW can have critical values of sidelength-to-thickness ratio (Lx/H or Ly/H) below which RAINBOW exhibits unique, or single-valued, spherical or domed shapes when cooled from the processing temperature to room temperature. For values of sidelength-to-thickness ratio greater than the critical value, RAINBOW exhibits multiple room-temperature shapes. Two of the shapes are stable and are, in general, near-cylindrical. The third shape is spherical and is unstable. Similarly, disk-style RAINBOW can have critical values of radius-to-thickness ratios (R/H) below which RAINBOW exhibits axisymmetric room-temperature shapes. For values of R/H greater than the critical value, disk-style RAINBOW exhibits two stable near-cylindrical shapes and one unstable axisymmetric shape. Moreover, it is found that for the set of material properties used in this study, the optimal reduced layer thickness would be at 55%, since the maximum change in curvature is achieved under the application of an electric field, while the relationship between the change in curvatures and the electric field is kept very close to being linear. In general, good agreement is found for comparisons between the predicted and manufactured shapes of RAINBOW. A multi-step thermoelastic analysis is developed to model the addition of the fiber-reinforced composite layer to RAINBOW to make GRAPHBOW. Results obtained for rectangular RAINBOW indicate that if the bifurcation temperature in the temperature-curvature relation is lower than the composite cure temperature, then a unique stable GRAPHBOW shape can be obtained. If the RAINBOW bifurcation temperature is above the composite cure temperature, multiple room-temperature GRAPHBOW shapes are obtained and saddle-node bifurcations can be encountered during the cooling to room temperature of [0°/RAINBOW], [RAINBOW/0o], and [0o2/RAINBOW]. Rectangular [RAINBOW/0o/90o] seems to be less likely to encounter saddle-node bifurcations. Furthermore, the unstable spherical RAINBOW configuration is converted to a stable near-cylindrical configuration. For the case considered of disk-style GRAPHBOW, three stable room-temperature shapes are obtained and the unstable axisymmetric RAINBOW configuration is also converted to a stable near-cylindrical configuration. For both rectangular and disk-style GRAPHBOW, the relationship between the major curvature and the electric field is shown to be very close to being linear. This characteristic would aid any dynamic analysis of RAINBOW or GRAPHBOW. / Ph. D.

This research discusses the mechanical characteristics of laminated piezoelectric actuators that are manufactured at an elevated temperature, to cure the adhesive bonding the layers together, or to cure the layers made of polymeric composite material, and then cooled to a service temperature. Mainly discussed are actuators that are composed of layers of passive materials and a layer of piezoelectric material. THUNDER (THin layer UNimorph ferroelectric DrivER and sensor) and LIPCA (LIghtweight Piezo-composite Curved Actuator) actuators, which consist of layers of metal, adhesive and piezoelectric material, and carbon-epoxy, glass-epoxy and piezoelectric material, respectively, are studied and investigated in detail to understand the thermal effects due to the elevated manufacturing temperature. Owing to the large out-of-plane deformations of the THUNDER actuators as a result of cooling to the service temperature, inclusion of geometric nonlinearities in the kinematic relations is taken into consideration for prediction of the thermally-induced deformations and residual stresses. The deformations and residual stresses are predicted by using a 23-term Rayleigh-Ritz approach and more rigorous, time-consuming, finite-element analyses performed with ABAQUS. The thermally-induced deformations of THUNDER actuators can result in multiple room-temperature manufactured shapes, whereas those of LIPCA actuators (LIPCA-C1 and LIPCA-C2) exhibit single room-temperature manufactured shape. Actuation responses of these actuators caused by a quasi-static electric field applied to the piezoelectric layer are also studied with the Rayleigh-Ritz approach. It is shown that geometrical nonlinearities play an important role in the actuation responses, and these nonlinearities can be controlled by the choice of actuator geometry and the materials in the passive layers. In addition, blocking forces representing load-carrying capability of THUNDER and LIPCA actuators are determined. Support conditions and again geometrical nonlinearities are vital factor in load-resisting performances. Amongst the actuators considered, the actuated deflection and blocking forces are compared. Finally, based on the outcome of this study, new criteria for designing a new type of laminated piezoelectric actuators with improvement of performance characteristics are proposed. / Ph. D.

The nonlinear beam deflection (BD) technique is used to directly measure and time-resolve the nonlinearly-induced phase shift in a variety of materials. In this technique, a weak probe beam is spatially overlapped, while slightly displaced, with a strong excitation beam while the temporal delay is scanned. The excitation-induced index gradient, which for 3rd-order nonlinearities is proportional to the nonlinear refractive index 16 n2"> of the medium, deflects the weak probe beam. This deflection is determined using a position sensitive segmented detector after propagation to the far field. In this dissertation, we expand our previous work on BD theory to include the effects of the Gaussian spatial beam profile of the excitation, as opposed to a constant index gradient. We also explore the BD signal as we allow the spatial size and relative position of the probe with respect to the excitation beam, r, at the sample to vary to maximize the calculated signal. While the analysis requires numerical solutions, we find a simple empirical fitting function for the BD signal that allows determination of the nonlinear phase shift and thus the nonlinear refraction. We performed BD experiments at near-degenerate photon energies for various spot size ratios which resulted in very good agreement with our simulation results. In order to examine our empirical function the BD signal for various r (0.2-0.6) is measured while keeping the phase shift relatively constant. This helped us isolate the effect of spot size ratio on the BD signal. Our results showed the correct trend for the growth of BD signal as r increases, which is what is expected from our model. We also studied nondegenerate two-photon absorption (ND-2PA) in bulk silicon. We present the results of spectroscopic pump-probe measurements of ND-2PA in silicon across the indirect-gap (1.12 eV). We observed enhancement of the 2PA coefficient as the degree of degeneracy of pump and probe photon energies increased, and the dispersion compares favorably with our recently-developed semi-empirical theoretical model for the dispersion of indirect ND-2PA in silicon. Additionally, we experimentally investigated WTe2 which is a Weyl semimetal. Here, we prepared very thin flakes (10s of microns thick) of WTe2 and investigated the possibility of observing circular dichroism (CD) in pump-probe measurements, pumping at near IR and probing at mid-IR. Although we did not observe any CD, we believe this is because our pump photon energy is far from Weyl nodes and that we need to pump at mid-IR range.

Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still encumbered by lengthy processing times. Accurate models can be produced quickly by utilizing projection Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated into a ROM. Additional sources of nonlinearities such as radiation boundary conditions, temperature dependent source heating terms, and complex geometry were also integrated. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model. / Ph. D. / Heat transfer systems contain many sources of nonlinearity including temperature dependent material properties, radiation boundary conditions, and internal source terms. Despite progress in numerical simulations, producing accurate models that can predict these complex behaviors are still limited by the time it takes to compute meaningful results. Accurate models can be produced quickly by utilizing some mathematical techniques whereby the original problem is projected into a smaller sub-space and solved with fewer variables. The full space results are then determined by undoing the projection on the results. This is one approach from a larger knowledge base called Reduced Order Modeling (ROM) techniques. For discretized systems, the Singular Value Decomposition technique is the preferred approach but has had limited success on treating nonlinearities. In this research, the treatment of nonlinear temperature dependent material properties was incorporated using the projection approach, tailored to treat the specific material property nonlinearity as well as radiation boundary conditions, temperature dependent source heating terms, and complex geometry. While the approach presented here is specific to the heat transfer application, other problems of a similar form can be handled in the same manner. From the results, low conductivity, highly nonlinear material properties were predicted by the ROM within 1% of full order models, and additional nonlinearities were predicted within 8%. A study was then done to identify initial snapshots for use in developing a ROM that can accurately predict results across a wide range of inputs. From this, a step function was identified as being the most accurate and computationally efficient. The ROM was further investigated by a discretization study to assess computational gains in both 1D and 3D models as a function of mesh density. The lower mesh densities in the 1D and 3D ROMs resulted in moderate computational times (up to 40 times faster). However, highly discretized systems such as 5000 nodes in 1D and 125000 nodes in 3D resulted in computational gains on the order of 2000 to 3000 times faster than the full order model.