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Almost all electronic devices require efficient conversion of electrical power from one form to another. Electrical power is used world wide at the rate of approximately 12 billion kW per hour. The Center for Power Electronics Systems at Virginia Tech was established with a vision to develop an integrated systems approach via integrated power electronic modules (IPEMs) to improve the reliability, cost-effectiveness, and performance of power electronics systems. IPEMs are multi-layered structures based on embedded power technology and offer the advantage of three-dimensional (3D) packaging of electronic components in a small and compact volume, replacing the traditional wire bonding technology. They have the potential to offer reduced time and effort associated with developing and manufacturing power processors. However, placing multiple heat generating chips in a small volume also makes thermal management more challenging. With the steady increase in the heat density of the electronic packages during the last few decades, thermal management is becoming a key enabling technology for the future growth of power electronics. The focus of this work is on using computational analysis tools and experimental techniques to assess fundamental and practical cooling limitations on IPEMs, developing both passive and active integrated thermal management strategies, and creating design guidelines for IPEMs based on both thermal and thermo-mechanical stress considerations. Specifically, a commercially available finite element package is used to create a 3D geometric layout of the electronic module. The baseline finite element numerical model is validated using bench-top wind tunnel experiments. The experimental setup is also employed to characterize the thermal behavior of chips in the multi-chip package and test the applicability of superposition methodology for temperature fields of chips within multi-chip modules. Using numerical models, both passive and active integrated thermal management strategies are investigated. The passive cooling strategies include advanced ceramic materials, copper trace thickness, and structural enhancements. Active cooling strategies include double-sided cooling using traditional heat sinks, and an extension of double-sided cooling concept using microchannels integrated with the module on both sides of embedded chips. The overall result of the work presented here is the better understanding of thermal issues and limitations with IPEM technology, and development of thermal design guidelines for cooling strategies that take into consideration both thermal and thermo-mechanical performance. / Ph. D.

The purpose of this research is to develop an understanding of Multichip Modules, (MCMs), more specific those fabricated with a Low Temperature Co-fireable Ceramic (L TCC) tape systems. The study will consist of designing, processing, and testing two generic MCM test patterns. The effects on signal propagation caused by vias and wire bonds, crosstalk for surface and embedded transmission lines, crosstalk between vias, effects of bends in transmission lines are studied and discussed in this work. Time Domain and Frequency Domain measurements are performed and presented in this thesis work for electrical characterization of MCM structures using L TCC systems / Master of Science

Thesis (MSc)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: It is well known that the ring of integers Z and the ring of polynomials A = Fr[T] over a finite field Fr have many properties in common. It is due to these properties that almost all the famous (multiplicative) number theoretic results over Z have analogues over A. In this thesis, we are devoted to utilising this analogy together with the theory of Carlitz modules. We do this to survey and compare the analogues of cyclotomic polynomials, the size of their coefficients and cyclotomic extensions over the rational function field k = Fr(T). / AFRIKAANSE OPSOMMING: Dit is bekend dat Z, die ring van heelgetalle en A = Fr[T], die ring van polinome oor ’n eindige liggaam baie eienskappe in gemeen het. Dit is as gevolg van hierdie eienskappe dat feitlik al die bekende multiplikative resultate wat vir Z geld, analoë in A het. In hierdie tesis, fokus ons op die gebruik van hierdie analogie saam met die teorie van die Carlitz module. Ons doen dit om ’n oorsig oor die analoë van die siklotomiese polinome, hul koëffisiënte, en siklotomiese uitbreidings oor die rasionele funksie veld k = Fr(T).

Thesis (MSc)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Major works done in Function Field Arithmetic show a strong analogy between the ring of integers Z and the ring of polynomials over a nite eld Fq[T]. While an algorithm has been discovered to factor integers using elliptic curves, the discovery of Drinfeld modules, which are analogous to elliptic curves, made it possible to exhibit an algorithm for factorising polynomials in the ring Fq[T]. In this thesis, we introduce the notion of Drinfeld modules, then we demonstrate the analogy between Drinfeld modules and Elliptic curves. Finally, we present an algorithm for factoring polynomials over a nite eld using Drinfeld modules. / AFRIKAANSE OPSOMMING: 'n Groot deel van die werk wat reeds in funksieliggaam rekenkunde voltooi is toon 'n sterk verband tussen die ring van heelgetalle, Z; en die ring van polinome oor 'n eindige liggaam, F[T]: Terwyl daar alreeds 'n algoritme, wat gebruik maak van elliptiese kurwes, ontwerp is om heelgetalle te faktoriseer, het die ontdekking van Drinfeld modules, wat analoog is aan elliptiese kurwes, dit moontlik gemaak om 'n algoritme te konstrueer om polinome in die ring F[T] te faktoriseer. In hierdie tesis maak ons die konsep van Drinfeld modules bekend deur sekere aspekte daarvan te bestudeer. Ons gaan voort deur 'n voorbeeld te voorsien wat die analoog tussen Drinfeld modules en elliptiese kurwes illustreer. Uiteindelik, deur gebruik te maak van Drinfeld modules, bevestig ons hierdie analoog deur die algoritme vir die faktorisering van polinome oor eindige liggame te veskaf.

Let k be a perfect field of characteristic p > 2 and K a totally ramified extension of K₀ = Frac W(k) with uniformizer π. Let F ⊆ K be a subfield with ϖ, ring of integers O, and residue field k(F) ⊆ k with |k(F)| = q. Let W(F) = O⊗(W(k(F))) W(k) and consider the ring 𝔖 = W(F)⟦u⟧ with an endomorphism φ that lifts the q-power Frobenius of k on W(F) and satisfies φ(u) ≡ u^q mod ϖ and φ(u) ≡ 0 mod u. In this dissertation, we use O-divided powers to define the analogue of Breuil-Kisin modules over the rings 𝔖 and S, where S is an O-divided power envelope of the surjection 𝔖 ↠ O(K) sending u to π. We prove that these two module categories are equivalent, generalizing the case when F = Q(p) and ϖ - p. As an application of our theory, we generalize the results of Kisin [17] and Cais-Lau [8] to relate the Faltings Dieudonné crystal of a ϖ-divisible O-module, which gives a Breuil module over S in our sense, to the modules of Kisin-Ren, providing a geometric interpretation to the latter.

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Rank 2 Drinfeld modular forms have been studied for more than 30 years, and while it is known that a higher rank theory could be possible, higher rank Drinfeld modular forms have only recently been de ned. In 1988 Gekeler published [Ge2] in which he studies the coe cients of rank 2 Drinfeld modular forms. The goal of this thesis is to perform a similar study of the coe cients of higher rank Drinfeld modular forms. The main results are that the coe cients themselves are (weak) Drinfeld modular forms, a product formula for the discriminant function, the rationality of certain naturally de ned modular forms, and the computation of some Hecke eigenforms and their eigenvalues. / AFRIKAANSE OPSOMMING: Drinfeld modulêre vorme van rang 2 word al vir meer as 30 jaar bestudeer en alhoewel dit lankal bekend is dat daar Drinfeld modulêre vorme van hoër rang moet bestaan, is die de nisie eers onlangs vasgepen. In 1988 het Gekeler die artikel [Ge2] gepubliseer waarin hy die koeffisiënte van Fourier reekse van rang 2 Drinfeld modulêre vorme bestudeer. Die doel van hierdie proefskrif is om dieselfde studie vir Drinfeld modulêre vorme van hoër rang uit te voer. Die hoofresultate is dat die koeffi siënte self (swak) Drinfeld modulêre vorme is, `n produk formule vir die diskriminant funksie, die feit dat sekere natuurlik gede finiëerde modulêre vorme rasionaal is, en die vasstelling van Hecke eievorme en hul eiewaardes.

Neste trabalho estudamos os módulos de Gelfand-Tsetlin 1-singulares para gl(n). Em particular, descrevemos bases explícitas para certos subquocientes dos mesmos e estabelecemos um critério que garante a sua irredutibilidade. / In this work we study the Gelfand-Tsetlin 1-singular modules for gl(n). In particular, we describe explicit bases for certain subquotients of the same and establish a criterion that guarantees its irreducibility.