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Beams in a typical steel framed floor design are assumed to have pinned supports for purposes of design. In reality, the connections between the beams and girders in a steel framed floor system are not pinned. The design bending moments and deflections of the attached beam could be reduced if the true rotational restraint provided by the beam-girder connections could be included in the design. The connection rotational restraint is characterized by the moment-rotation behavior. Consequently, a method for approximating the moment-rotation behavior of the beam-girder connection is required before the beneficial effects of the true connection rotational restraint can be considered in design. Experimental and analytical research on the moment-rotation behavior of a specific type of beam-girder connection is presented in this dissertation. The primary objective of this research is to develop a component model of the connection that can be used to approximate the moment-rotation behavior. The component model is based on the hypothesis that the connection behavior can be modeled as a combination of the connection component behaviors. The connection components are the fundamental pieces of the connection such as bolts, shear studs, and welds. In general, the component model can be very computationally intensive. Consequently, a secondary objective of this research is to develop a connection model that is simpler to use. Behavior models for each of the connection components are presented and/or developed. These models are derived from a combination of existing literature, experimental and analytical research, and basic mechanics. Next, a method of combining the component behaviors into a connection model that can be used to approximate the moment-rotation behavior is developed. Results from experimental research on the moment-rotation behavior of the beam-girder connection are then used to verify the model. Finally, a simplified model of the beam-girder connection is developed. This model is based on the same hypothesis as the component model; however, through a combination of assumptions, simplifications, and the results of parametric studies the simplified model becomes far less computationally intensive than the full component model. / Ph. D.

Exponential growth of heat flux densities in commercial and industrial electronics, and compact heat exchangers demand surfaces and heat sinks with high dissipation rate capabilities. Among different technologies proposed to meet these demands, high-porosity metal foams have attracted the attention of many investigators due to their higher surface area densities as well as higher thermal performance due to the turbulence and tortuosity generated in the flow due to their structure. One of the disadvantages of such metal foams, however, is the attendant higher pressure drop or pumping power penalty. This thesis was undertaken to investigate whether channels partially filled with metal foams can reduce the required pumping power with a minimal loss in thermal performance. The thermo-hydraulic (T-H) performance factor J/F<sup>1/3, where J is the Colburn-J factor and F is the friction factor, was used to compare the relative performance of foams for various values of blocking fractions (B), where B is defined as the ratio of the height of the foam to the height of the channel. The metal foam samples considered were 10 PPI (pores per inch) 6101-T6 Aluminum, with porosity of ∼ 94 − 96%, and B of 1/6, 1/3, 2/3, 5/6, and 1. Each of these samples was attached to an aluminum slab embedded in one of the walls, which had a patch heater that acted as a heat source. A modification was made to all B < 1 configurations by attaching an aluminum plate on top, which then separated the foam-free and the foam-filled flows completely. These configurations are denoted by a 'P' in their names (e.g. B = 1/3P is the plated modification of B = 1/3). Experiments were conducted in an in-house designed wind tunnel, with a test section of 45" in length and a cross-section of 3"X3". Reynolds number (based on channel hydraulic diameter and inlet velocity) was varied from 1,000 to 15,000 to capture the flow domains from laminar to turbulent. The data obtained for the three scenarios namely - 1. Controlled-Flow Scenario 2. Pumping Power Variation with Temperature Difference, and 3. Fan-Based System were analyzed for their thermo-hydraulic performance. The extreme low blocking fractions are evaluated and compared against the dimpled/protruded surfaces, and were found to give superior performance, hence displaying potential as good turbulators. The plated configurations were found to perform better in almost all scenarios when compared to their non-plated counterparts. Furthermore, a new simplified analytical model is introduced that considers the flow in the partially-blocked region as two separate 'parallel' flows, one in the foam-free region and the other in the foam-filled region. The comparison between this novel approach and the analytical solution from the literature shows good agreement, suggesting that this simplified model may be appropriate. This model is then used for determining the foam-filled region flow ratios for the performed experiments, and a correlation is presented. / Master of Science / Portable devices, such as laptops, and mobile phones are trending towards miniaturization and simultaneously becoming more power-hungry, leading to ever-increasing heat flux densities. Growing energy and technology demands require high thermal dissipation rates to be achieved in equipment such as industrial and commercial electronics, data centers, heat exchangers in automobiles, and power plants - both renewable and non-renewable. One of the best ways to enhance convective heat transfer is by increasing the heat transfer surface area. This is traditionally done using fins. A much higher surface area can be achieved using a metal foam instead, along with improving the turbulent mixing of the fluid. The flow through the metal foam, however, faces a higher pressure drop penalty which is one of the major reasons for a continued preference for fins. In this experimental study, we aim at minimizing this pressure drop penalty of a metal-foam heat-sink along with maintaining a respectable heat transfer performance through 'partial-blocking' (filling) of the channel, where the height of the foam is lower than the total channel height. The ratio of metal foam height to the channel height is named as blocking fraction B. A general comparison of the hydraulic, thermal, and thermo-hydraulic (T-H) performance reveals that the ∼ 83.3% plated configuration is capable of superseding the baseline of full blockage. The 'plating' here denotes a slight modification - a solid plate rests on top of the metal foam, separating the foam-free and foam-filled flow. For applications with Re > 10000, ∼ 33.3% plated configuration is highly recommended. For fan-based systems, ∼ 83.3% plated, ∼ 33.3% plated, and 33.3% non-plated configurations emerge as possible alternatives to the fully-blocked case. Furthermore, while considering partial configurations, it is shown that one should go for lower PPI metal foams to improve the flow ratio inside the metal foam. For pressure-drop critical equipment, ∼ 16.7% configuration is found to perform better than the conventional double-protruded walls and other turbulence-enhancing surface treatments. Finally, this thesis presents a novel and simplified approach for estimating the flow ratios for partially-blocked channels using scaling analysis.

A number of significant challenges confront effective communication in partially distributed conceptual design teams (PDCDTs), mainly due to the ill-defined and open nature of conceptual design tasks and their associated solution spaces. In contrast to co-located team members who interact face-to-face, communication difficulties among PDCDTs can intensify as a result of the physical separation of team members and their heavy reliance on communication technologies to achieve desired outcomes. Despite advances in these technologies, the ability to convey contextual and paralinguistic cues is still more limited between distant partners in comparison to face-to-face interactions. Thus, team members often experience challenges in establishing and maintaining shared understanding. In addition, partially distributed teams are more vulnerable to in-group dynamics than fully distributed or fully co-located teams. There have been substantial theoretical advances in the field of computer-mediated communication (CMC) that seek to address these challenges. Although CMC theories are hypothetically convincing and generally accepted, actual empirical findings are to some extent either unconvincing or contradictory. Moreover, questions remain about whether CMC theories can hold up in the context of non-equivalent communication technologies. The proliferation of various communication devices (e.g., smart phones, tablets, laptops, and desktops)–not to mention the growing corporate use of fully immersive telepresence technologies–means that a variety of combinations of communication devices can be used. To date, however, the majority of CMC studies have focused on the use of equivalent communication technologies (e.g., laptop to laptop). Given these practical challenges and research gaps, the overall objective of this study was to investigate how to improve shared understanding in PDCDTs. The study encompassed four distinct research threads. Study 1 conceptualized shared understanding in PDCDTs. From Study 1, factors associated with shared understanding were identified, and an input-process-output (IPO) model of shared understanding was developed. Study 2 examined the intra- and inter-sub-group communication patterns among PDCDTs. From Study 2, three different analytical approaches for exploring communication patterns were used to elucidate valuable insights into how interactions within and across sub-groups change with design tasks, as well as how individual roles and interpersonal dynamics affect those interactions. Study 3 utilized the outcomes from Study 1 (IPO model of shared understanding) to develop and validate an instrument to measure shared understanding. Lastly, Study 4 examined how different combinations of non-equivalent communication technologies impacted shared understanding in PDCDTs by using the shared understanding instrument developed from Study 3. Specifically, four types of communication technology conditions were utilized: (1) telepresence to telepresence (two different sizes), (2) telepresence to laptops, (3) telepresence to mobile devices, and (4) laptops to mobile devices. The findings revealed significant impacts of communication technologies on co-located and distant shared understanding, as well as differences between co-located and distant shared understanding for each communication technology condition. In addition, the impacts of shared understanding on different communication technology user groups were identified. Based on these findings, a number of communication technology recommendations, as well as managerial intervention strategies to operate successful PDCDTs, were developed. / Ph. D.

Two different sets of problems are addressed in this thesis. The first one is on partially observed semi-Markov Games (POSMG) and the second one is on semi-Markov modulated financial market model. In this thesis we study a partially observable semi-Markov game in the infinite time horizon. The study of a partially observable game (POG) involves three major steps: (i) construct an equivalent completely observable game (COG), (ii) establish the equivalence between POG and COG by showing that if COG admits an equilibrium, POG does so, (iii) study the equilibrium of COG and find the corresponding equilibrium of original partially observable problem. In case of infinite time horizon game problem there are two different payoff criteria. These are discounted payoff criterion and average payoff criterion. At first a partially observable semi-Markov decision process on general state space with discounted cost criterion is studied. An optimal policy is shown to exist by considering a Shapley’s equation for the corresponding completely observable model. Next the discounted payoff problem is studied for two-person zero-sum case. A saddle point equilibrium is shown to exist for this case. Then the variable sum game is investigated. For this case the Nash equilibrium strategy is obtained in Markov class under suitable assumption. Next the POSMG problem on countable state space is addressed for average payoff criterion. It is well known that under this criterion the game problem do not have a solution in general. To ensure a solution one needs some kind of ergodicity of the transition kernel. We find an appropriate ergodicity of partially observed model which in turn induces a geometric ergodicity to the equivalent model. Using this we establish a solution of the corresponding average payoff optimality equation (APOE). Thus the value and a saddle point equilibrium is obtained for the original partially observable model. A value iteration scheme is also developed to find out the average value of the game. Next we study the financial market model whose key parameters are modulated by semi-Markov processes. Two different problems are addressed under this market assumption. In the first one we show that this market is incomplete. In such an incomplete market we find the locally risk minimizing prices of exotic options in the Follmer Schweizer framework. In this model the stock prices are no more Markov. Generally stock price process is modeled as Markov process because otherwise one may not get a pde representation of price of a contingent claim. To overcome this difficulty we find an appropriate Markov process which includes the stock price as a component and then find its infinitesimal generator. Using Feynman-Kac formula we obtain a system of non-local partial differential equations satisfied by the option price functions in the mildsense. .Next this system is shown to have a classical solution for given initial or boundary conditions. Then this solution is used to have a F¨ollmer Schweizer decomposition of option price. Thus we obtain the locally risk minimizing prices of different options. Furthermore we obtain an integral equation satisfied by the unique solution of this system. This enable us to compute the price of a contingent claim and find the risk minimizing hedging strategy numerically. Further we develop an efficient and stable numerical method to compute the prices. Beside this work on derivative pricing, the portfolio optimization problem in semi-Markov modulated market is also studied in the thesis. We find the optimal portfolio selections by optimizing expected utility of terminal wealth. We also obtain the optimal portfolio selections under risk sensitive criterion for both finite and infinite time horizon.

This thesis has two distinguish parts. The first part concerns the study of n-ary algebras. A n-ary algebra is a vector space with a multiplication on n arguments. Classically the multiplications are binary, but the use of ternary multiplication in theoretical physic like for Nambu brackets led mathematicians to investigate these type of algebras. Two classes of n-ary algebras are fundamental: the associative n-ary algebras and the Lie n-ary algebras. We are interested by both classes. Concerning the associative n-ary algebras we are mostly interested in 3-ary partially associative 3-ary algebras, that is, algebras whose multiplication satisfies ((xyz)tu)+(x(yzt)u)+(xy(ztu))=0. This type is interesting because the previous woks on this subject was not distinguish the even and odd cases. We show in this thesis that the case n=3 can not be treated as the even cases. We investigate in detail the free partially associative 3-ary algebra on k generators. This algebra is graded and we compute the dimensions of the 7 first components. In the general case, we give a spanning set such as the sub family of non zero vector is a basis. The main consequences are the free partially associative 3-ary algebra is solvable. In the free commutative partially associative 3-ary algebra any product on 9 elements is trivial. The operad for partially associative 3-ary algebra do not satisfy the Koszul property. Then we study n-ary products on the tensors. The simplest example is given by a internal product of non square matrices. We can define a 3-ary product by taking A . ^tB . C. We show that we have to generalize a bit the definition of partial associativity for n-ary algebras. We then introduce the products -partially associative where  is a permutation of the symmetric group of degree n. Concerning the n-ary algebras, two classes have been defined: Filipov algebras (also called recently Lie-Nambu algebras) and some more general class, the n-Lie algebras. Filipov algebras are very important in the study of the mechanic of Nambu-Poisson, and is a particular case of the other. So to define an approach of Maurer-Cartan type, that is, define a scalar cohomology, we consider in this work Fillipov as n-Lie algebras and develop such a calculus in the n-Lie algebras frame work. We also give some classifications of n-ary nilpotent algebras. The last chapter of this part concerns my work in Master on the Poisson algebras on polynomials. We present link with the Lie algebras is clear. Thus we extend our study to Poisson algebras which associated Lie algebra is rigid and we apply these results to the enveloping algebras of rigid Lie algebras. The second part concerns intervals arithmetic. The interval arithmetic is used in a lot of problems concerning robotic, localization of parameters, and sensibility of inputs. The classical operations of intervals are based of the rule : the result of an operation of interval is the minimal interval containing all the result of this operation on the real elements of the concerned intervals. But these operations imply many problems because the product is not distributive with respect the addition. In particular it is very difficult to translate in the set of intervals an algebraic functions of a real variable. We propose here an original model based on an embedding of the set of intervals on an associative algebra. Working in this algebra, it is easy to see that the problem of non distributivity disappears, and the problem of transferring real function in the set of intervals becomes natural. As application, we study matrices of intervals and we solve the problem of reduction of intervals matrices (diagonalization, eigenvalues, and eigenvectors).

This thesis is concerned with dynamic electrochemistry experiments in which faradaic processes are driven by the application of potential to an electrode immersed in an electrolyte solution. In particular, experimental methods are considered which could be used to study electrochemical systems in a more informative way if the processes occurring at the electrode were better understood. The work develops the theoretical models which describe these experiments, and details the approximations made in each model and the conditions under which they are appropriate. Numerical simulations are reported which demonstrate how the models can be used to infer quantitative details of chemical behaviour from experimentally recorded data. The first system studied in detail is linear sweep voltammetry at a microband electrode array. The diffusional behaviour of an electroactive species is shown to depend on the configuration of the microband array and on the potential scan rate used. Details are given on how experimental conditions can be optimised for the study of electrochemical systems. The next area of work develops the theory of nanoparticle-modified electrodes. Experiments are considered in which an electron transfer reaction is catalysed only at the site of the nanoparticles, whilst the supporting planar electrode remains electrochemically inert. Numerical simulations show how the current measured at these modified electrodes depends on the size and shape of the particles, on the distribution of the particles on the electrode surface, and on the timescale of the experiment. The final theme of work is on electrochemical experiments in poorly conducting solutions. A theoretical model is developed which takes into account the effects of an electric field on the mass transport of electroactive species and on the charge transfer kinetics at the electrode. The model is then used to rationalise the unusual current behaviour that is observed in the anodic stripping of thallium from an amalgam.

The objects of study in this thesis are automorphism groups of free and right-angled Artin groups. Right-angled Artin groups are defined by a presentation where the only relations are commutators of the generating elements. When there are no relations the right-angled-Artin group is a free group and if we take all possible relations we have a free abelian group. We show that if no finite index subgroup of a group $G$ contains a normal subgroup that maps onto $mathbb{Z}$, then every homomorphism from $G$ to the outer automorphism group of a free group has finite image. The above criterion is satisfied by SL$_m(mathbb{Z})$ for $m geq 3$ and, more generally, all irreducible lattices in higher-rank, semisimple Lie groups with finite centre. Given a right-angled Artin group $A_Gamma$ we find an integer $n$, which may be easily read off from the presentation of $A_G$, such that if $m geq 3$ then SL$_m(mathbb{Z})$ is a subgroup of the outer automorphism group of $A_Gamma$ if and only if $m leq n$. More generally, we find criteria to prevent a group from having a homomorphism to the outer automorphism group of $A_Gamma$ with infinite image, and apply this to a large number of irreducible lattices as above. We study the subgroup $IA(A_Gamma)$ of $Aut(A_Gamma)$ that acts trivially on the abelianisation of $A_Gamma$. We show that $IA(A_Gamma)$ is residually torsion-free nilpotent and describe its abelianisation. This is complemented by a survey of previous results concerning the lower central series of $A_Gamma$. One of the commonly used generating sets of $Aut(F_n)$ is the set of Whitehead automorphisms. We describe a geometric method for decomposing an element of $Aut(F_n)$ as a product of Whitehead automorphisms via Stallings' folds. We finish with a brief discussion of the action of $Out(F_n)$ on Culler and Vogtmann's Outer Space. In particular we describe translation lengths of elements with regards to the `non-symmetric Lipschitz metric' on Outer Space.

A labeled embedding of a planar graph G is a pair (G, g) consisting of a planar drawing G of G and a function g assigning labels (colors) to the faces of G. We study the problem of Embedding Restriction Satisfiability (ERS) that investi- gates whether a given graph has a labeled embedding satisfying a provided set of conditions. ERS is a relatively new problem, so not much is known about it. Nevertheless, it has great potential. It generalizes several problems looking for a particular drawing of a planar graph, such as the problem of Partially Embedded Planarity. Therefore, ERS may become a focal point in the area of graph draw- ing. In this thesis, we examine the computational complexity of ERS. We show that ERS is NP-complete. After that, we look at the complexity of some specific classes of its instances. We try to locate the boundary between the NP-complete and the polynomial variants of the problem. 1

Este trabalho trata das medidas de máxima entropia para certos difeomorfismos em nilvariedades. Considere um difeomorfismo parcialmente hiperbólico f definido em T3, dinamicamente coerente com folheação central compacta. Suponha ainda que a aplicação induzida por f no espaço das folhas centrais é um homeomorfismo de Anosov transitivo em T2. Mostramos que o conjunto das medidas ergódicas hiperbólicas de máxima entropia é enumerável. Usando o princípio de invariância, mostramos que se o primeiro retorno de f à alguma folha periódica tem número de rotação irracional, então, f tem no máximo duas medidas ergódicas de máxima entropia e ter apenas uma medida de máxima entropia equivale a ser extensão de rotação. Se a aplicação de primeiro retorno à alguma folha central periódica é Morse-Smale, então existe um su-toro periódico, ou temos uma cota superior para o número de medidas ergódicas de máxima entropia que depende do número de atratores da dinâmica nessa folha. Além disso, estudamos a topologia da bacia das medidas ergódicas de máxima entropia para uma outra classe de difeomorfismos especiais que são genéricos no espaço dos difeomorfismos absolutamente parcialmente hiperbólicos e denotada por SPH1(M). / This work is about maximal entropy measures for certain diffeomorphisms on nilmanifolds. Consider a partially hyperbolic diffeomorphism f on T3 , C2 , dinamically coherent with compact center foliation which is a circle bundle. Assume that the map induced by f on the space of center leaves is a transitive Anosov homeomorphism. We show that the set of hyperbolic ergodic maximal entropy measures of f is countable. Using the invariance principle, we show that if the first return map to some periodic leaf has irrational rotation number then f has at most two ergodic maximal entropy measures and, in this case, if f has only one maximal entropy measure then f is a rotation extension. If the first return map to some periodic leaf is Morse-Smale then either there exists some periodic su-torus or an upper bound for the number of ergodic maximal entropy measure depending on the number of the attractors of the dynamics in this leaf. Moreover, we study the topology of basin of ergodic maximal entropy measures of another set of special diffeomorphisms that are generic in the space of absolutely partially hyperbolic systems and denoted by SPH1(M).