Matrix Representation of the Stationary Measure for the Multispecies TASEP

In this work we construct the stationary measure of the N species totally asymmetric simple exclusion process in a matrix product formulation. We make the connection between the matrix product formulation and the queueing theory picture of Ferrari and Martin. In particular, in the standard representation, the matrices act on the space of queue lengths. For N > 2 the matrices in fact become tensor products of elements of quadratic algebras. This enables us to give a purely algebraic proof of the stationary measure which we present for N=3.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

An investigation of worn work roll materials used in the finishing stands of the hot strip mill for steel rolling

The surface failure characteristics of different work roll materials, i.e. High Speed Steel, High Chromium Iron and Indefinite Chill Iron, used in the finishing stands of a hot strip mill have been investigated using stereo microscopy, 3D optical profilometry, scanning electron microscopy and energy dispersive X-ray spectroscopy. The results show that the surface failure mechanisms of work rolls for hot rolling are very complex, involving plastic deformation, abrasive wear, adhesive wear, mechanical and thermal induced cracking, material transfer and oxidation. Despite the differences in chemical composition and microstructure, the tribological response of the different work roll materials was found to be strongly dependent on the material microstructure and especially the presence and distribution of microstructural constituents, such as the different carbide phases and graphite (in the case of Indefinite Chill Iron). Cracking and chipping of the work roll surfaces, both having a negative impact on work roll wear, are strongly influenced by the presence of carbides, carbide networks and graphite in the work roll surface. Consequently, the amount of carbide forming elements as well as the manufacturing process must be controlled in order to obtain an optimised microstructure and a predictable wear rate.

Experimental and computational investigation of the roll forming process

One of the first questions to consider when designing a new roll forming line is the number of forming steps required to produce a profile. The number depends on material properties, the cross-section geometry and tolerance requirements, but the tool designer also wants to minimize the number of forming steps in order to reduce the investment costs for the customer. There are several computer aided engineering systems on the market that can assist the tool designing process. These include more or less simple formulas to predict deformation during forming as well as the number of forming steps. In recent years it has also become possible to use finite element analysis for the design of roll forming processes. The objective of the work presented in this thesis was to answer the following question: How should the roll forming process be designed for complex geometries and/or high strength steels? The work approach included both literature studies as well as experimental and modelling work. The experimental part gave direct insight into the process and was also used to develop and validate models of the process. Starting with simple geometries and standard steels the work progressed to more complex profiles of variable depth and width, made of high strength steels. The results obtained are published in seven papers appended to this thesis. In the first study (see paper 1) a finite element model for investigating the roll forming of a U-profile was built. It was used to investigate the effect on longitudinal peak membrane strain and deformation length when yield strength increases, see paper 2 and 3. The simulations showed that the peak strain decreases whereas the deformation length increases when the yield strength increases. The studies described in paper 4 and 5 measured roll load, roll torque, springback and strain history during the U-profile forming process. The measurement results were used to validate the finite element model in paper 1. The results presented in paper 6 shows that the formability of stainless steel (e.g. AISI 301), that in the cold rolled condition has a large martensite fraction, can be substantially increased by heating the bending zone. The heated area will then become austenitic and ductile before the roll forming. Thanks to the phenomenon of strain induced martensite formation, the steel will regain the martensite content and its strength during the subsequent plastic straining. Finally, a new tooling concept for profiles with variable cross-sections is presented in paper 7. The overall conclusions of the present work are that today, it is possible to successfully develop profiles of complex geometries (3D roll forming) in high strength steels and that finite element simulation can be a useful tool in the design of the roll forming process.

A systematic component of the jump-risk premium in an AJD model

We develop an affine jump diffusion (AJD) model with the jump-risk premium being determined by both idiosyncratic and systematic sources of risk. While we maintain the classical affine setting of the model, we add a finite set of new state variables that affect the paths of the primitive, under both the actual and the risk-neutral measure, by being related to the primitive's jump process. Those new variables are assumed to be commom to all the primitives. We present simulations to ensure that the model generates the volatility smile and compute the "discounted conditional characteristic function'' transform that permits the pricing of a wide range of derivatives.

Dependence of the electrical conductivity and elastomeric properties on sample preparation of blends of polyaniline and natural rubber

Blend films (free-standing) containing 20% in volume of polyaniline (PANI) in 80% of natural rubber (NR) were fabricated by casting in three different ways: (1) adding PANI-EB (emeraldine base) dissolved in N-methyl-2-pyrrolidone (NMP) to the latex (NRL), (2) adding PANI-EB dissolved in in-cresol to NR dissolved in xylol (NRD), (3) overlaying the surface of a pure NR cast film with a PANI layer grown by in situ polymerization (NRO). All the films were immersed into HCl solution to achieve the primary doping (protonation) of PANI before the characterization. The main goal here was to investigate the elastomeric and electrical conductivity properties for each blend, which may be applied as pressure and deformation sensors in the future. The characterization was carried out by optical microscopy, dc conductivity, vibrational spectroscopy (infrared absorption and Raman scattering), thermogravimetry analysis (TGA), differential scanning calorimetry (DSC), dynamic mechanical thermal analysis (DMTA), and tensile stress-strain curves. The results suggest that the NRL blend is the most suitable in terms of mechanical and electrical properties required for applications in pressure and deformation sensors: a gain of conductivity without losing the elastomeric property of the rubber. (c) 2005 Wiley Periodicals, Inc.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Cyclic-loading of the human gracilis and semitendinosus muscle tendons: Study of young adult cadavers

During knee ligament reconstruction, the tendon graft is tensioned to prevent the occurrence of excessive graft elongation during the postoperative period. Tensioning may be achieved by applying a cyclic or static load to the graft during fixation. Although this procedure is part of the surgery, there is no consensus in international literature regarding ideal tension levels to be used in this procedure. This study was conducted on 10 tendons of the human gracilis muscle and 10 tendons of semitendinosus muscle removed from five male cadavers whose mean age was 20.8 years. These tendons underwent 10 in vitro strain cycles at three levels of deformation (2.5, 3, and 4%) and the value of the deforming load used for each cycle was recorded. The statistical analysis demonstrated that in order to attain the same level of deformation during the 10 cycles there was a reduction in the value of strain applied to the graft, observed at the three levels of deformation. It was concluded that the semitendinosus tendon presents a more uniform mechanical behavior and that there is a need for new graft tensioning protocols that consider the force associated with deformation.

On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

Teleparallel origin of the Fierz picture for spin-2 particle

A new approach to the description of a spin-2 particle in flat and curved spacetime is developed on the basis of the teleparallel gravity theory. We show that such an approach is in fact a true and natural framework for the Fierz representation proposed recently by Novello and Neves. More specifically, we demonstrate how the teleparallel theory fixes uniquely the structure of the Fierz tensor, discover the transparent origin of the gauge symmetry of the spin-2 model, and derive the linearized Einstein operator from the fundamental identity of the teleparallel gravity. In order to cope with the consistency problem on the curved spacetime, similarly to the usual Riemannian approach, one needs to include the nonminimal (torsion dependent) coupling terms.

Nonabelian Toda theories from parafermionic reductions of the WZW model

We investigate a class of conformal nonabelian-Toda models representing noncompact SL(2, R)/U(1) parafermions (PF) interacting with specific abelian Toda theories and having a global U(1) symmetry. A systematic derivation of the conserved currents, their algebras, and the exact solution of these models are presented. An important property of this class of models is the affine SL(2, R)(q) algebra spanned by charges of the chiral and antichiral nonlocal currents and the U(1) charge. The classical (Poisson brackets) algebras of symmetries VG(n), of these models appear to be of mixed PF-WG(n) type. They contain together with the local quadratic terms specific for the W-n-algebras the nonlocal terms similar to the ones of the classical PF-algebra. The renormalization of the spins of the nonlocal currents is the main new feature of the quantum VA(n)-algebras. The quantum VA(2)-algebra and its degenerate representations are studied in detail. (C) 1999 Academic Press.

q-Analog of the gap equation for cuprates

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Towards a Realization of the Condensed-Matter-Gravity Correspondence in String Theory via Consistent Abelian Truncation of the Aharony-Bergman-Jafferis-Maldacena Model

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Geochronology of the lpanema layered mafic-ultramafic complex, Minas gerais, Brazil: Evidence of extension at the meso-neoproterozoic time boundary

The mafic/ultramafic Ipanema Layered Complex (ILC), Minas Gerais Brazil, consists of seven individual bodies. These units crosscut polyphase orthogneisses and interlayered paragneisses of the Paleoproterozoic Juiz de Fora Complex. Intrusive granitoids tectonically related to [lie Neoproterozoie Aracuai orogen are also present in the study area.A Sm-Nd whole-rock linear array for seven samples metapyoxenites, metaperidotiles, metagabbro. and meta-anorthosite) from the Santa Cruz massif, the largest body of the ILC. suggest that it was emplaced at 1104 +/- 78 Ma the original magma was derived from a depleted mantle source (epsilon(Ndt)= +3.8). U-Pb single-grain zircon stud of a meta-anorthosite yields all upper intercept age of 1719 +/- 4 Ma, which is interpreted to represent inheritance. The lower intercept at 630+/-3 Ma indicates (hat a Neoproterozoic tectonothermal episode overprinted the ILC, this event occurred under upper-amphiolite-, to granulite-facies conditions. The 630 Ma episode is consistent with the timing of regional metamorphism and deformation of the adjacent Aracuai orogen (Brasiliano collage). Emplacement of the ILC and other coeval metamafies and meta-ultramafics (of alkaline affinity) in the re, oil is attributed to early extension tectonics, accompanying accretion of the Rodinia super- continent during the Mesoproterozoic-Neoproterozoic time boundary.