From Dyck Paths to Standard Young Tableaux

We present nine bijections between classes of Dyck paths and classes of standard Young tableaux (SYT). In particular, we consider SYT of flag and rectangular shapes, we give Dyck path descriptions for certain SYT of height at most 3, and we introduce a special class of labeled Dyck paths of semilength n that is shown to be in bijection with the set of all SYT with n boxes. In addition, we present bijections from certain classes of Motzkin paths to SYT. As a natural framework for some of our bijections, we introduce a class of set partitions which in some sense is dual to the known class of noncrossing partitions

Trapezoidal Diagrams, Upward Triangulations, and Prime Catalan Numbers

The d-dimensional Catalan numbers form a well-known sequence of numbers which count balanced bracket expressions over an alphabet of size d. In this paper, we introduce and study what we call d-dimensional prime Catalan numbers, a sequence of numbers which count only a very specific subset of indecomposable balanced bracket expressions. These numbers were encountered during the investigation of what we call trapezoidal diagrams of geometric graphs, such as triangulations or crossing-free perfect matchings. In essence, such a diagram is obtained by augmenting the geometric graph in question with its trapezoidal decomposition, and then forgetting about the precise coordinates of individual vertices while preserving the vertical visibility relations between vertices and segments. We note that trapezoidal diagrams of triangulations are closely related to abstract upward triangulations. We study the numbers of such diagrams in the cases of (i) perfect matchings and (ii) triangulations. We give bijective proofs which establish relations with 3-dimensional (prime) Catalan numbers. This allows us to determine the corresponding exponential growth rates exactly as (i) 5.196ⁿ and (ii) 23.459ⁿ (bases are rounded to three decimal places). Finally, we give exponential lower bounds for the maximum number of embeddings that a trapezoidal diagram can have on any given point set.ISSN:0179-5376ISSN:1432-044

K-theoretic Schubert calculus and applications

A central result in algebraic combinatorics is the Littlewood-Richardson rule that governs products in the cohomology of Grassmannians. A major theme of the modern Schubert calculus is to extend this rule and its associated combinatorics to richer cohomology theories. This thesis focuses on K-theoretic Schubert calculus. We prove the first Littlewood-Richardson rule in torus-equivariant K-theory. We thereby deduce the conjectural rule of H. Thomas and A. Yong, as well as a mild correction to the conjectural rule of A. Knutson and R. Vakil. Our rule manifests the positivity established geometrically by D. Anderson, S. Griffeth and E. Miller, and moreover in a stronger 'squarefree' form that resolves an issue raised by A. Knutson. Our work is based on the combinatorics of genomic tableaux, which we introduce, and a generalization of M.-P. Schuetzenberger's jeu de taquin. We further apply genomic tableaux to obtain new rules in non-equivariant K-theory for Grassmannians and maximal orthogonal Grassmannians, as well as to make various conjectures relating to Lagrangian Grassmannians. This is joint work with Alexander Yong. Our theory of genomic tableaux is a semistandard analogue of the increasing tableau theory initiated by H. Thomas and A. Yong. These increasing tableaux carry a natural lift of M.-P. Schuetzenberger's promotion operator. We study the orbit structure of this action, generalizing a result of D. White by establishing an instance of the cyclic sieving phenomenon of V. Reiner, D. Stanton and D. White. In joint work with J. Bloom and D. Saracino, we prove a homomesy conjecture of J. Propp and T. Roby for promotion on standard tableaux, which partially generalizes to increasing tableaux. In joint work with K. Dilks and J. Striker, we relate the action of K-promotion on increasing tableaux to the rowmotion operator on plane partitions, yielding progress on a conjecture of P. Cameron and D. Fon-der-Flaass. Building on this relation between increasing tableaux and plane partitions, we apply the K-theoretic jeu de taquin of H. Thomas and A. Yong to give, in joint work with Z. Hamaker, R. Patrias and N. Williams, the first bijective proof of a 1983 theorem of R. Proctor, namely that that plane partitions of height k in a rectangle are equinumerous with plane partitions of height k in a trapezoid

Pore network modelling of wettability effects on waterflood oil recovery from Agbada sandstone formation in the Niger Delta, Nigeria

A thesis Submitted to the School of Chemical and Metallurgical Engineering, Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfillment of the requirements for the degree of Doctor of Philosophy Johannesburg, 2016Wettability of a porous reservoir rock is an important factor that affects oil recovery during waterflooding. It is recognized as being important for multiphase properties. Understanding the variation of these properties in the field, due to wettability trends and different pore structures, is very critical for designing efficient and reliable processes and projects for enhanced hydrocarbon recovery. After primary drainage the reservoir wettability changes: if it was oil-wet initially, it gradually changes to water-wet during waterflooding. This change in reservoir wettability towards water-wet will reduce the residual oil saturation and improve the oil displacement efficiency. However, knowledge of the constitutive relationship between the pore scale descriptors of transport in the porous system is required to adequately describe wettability trend and its impact on oil recovery, particularly during waterflooding. In this work, the petrophysical properties that define fluid flow in the Agbada, Nigeria sandstone reservoir were determined using conventional experimental and x-ray CT scanning methods. Experimentally measured average porosity is 0.28, average permeability is 1699 mD, while the initial and irreducible water saturation is 0.22. Permeability in the x, y and z directions, ranging from 50 to 200 mD, were calculated from the pore network extracted from the Agbada sandstone rock. Results obtained from the Amott-Harvey wettability measurement method indicate that the reservoir is strongly water-wet, with Amott-Harvey index of about 0.9. The cross-over between the water and oil relative permeabilities occurred at saturations of the samples above 0.5, giving an indication of strong water-wetness. The work summarizes the mechanism of wettability alteration and characterizes the performance of the reservoir during waterflooding from injecting water, and relates the residual oil saturation, relative permeability and volumes of water injected to wettability and its effects on oil recovery. Waterflood oil recovery is computed using the Buckley-Leverett method based on the reservoir rock and fluid properties. Computed waterflood oil recovery using this method was about 60% of the oil initially in place. Plots of spontaneous imbibition rate show that the injection rate for optimal oil recovery is 40 bbls of injected water per day. At this rate, both the mobility and shock front mobility ratios are less than 1, leading to a stable flood front and absence of viscous fingering. Waterflooding is by far the most widely applied method of improved oil recovery over the years with good results in conventional and unconventional (tight oil) reservoirs It is relatively simple and cost effective: abundance and availability of water. Waterflood oil recovery factor is affected by internal and external factors. The placement of the injection and production wells, for example, impacts on the effectiveness of the waterflooding process. I considered the placement of the wells in a five-spot pattern as elements of an unbounded double periodic array of wells and assumed the reservoir to be homogeneous, infinite and isotropic, with constant porosity and permeability. Both fluids are treated as having slight but constant compressibility and their flow governed by Darcy’s law. The average pressure in the reservoir satisfies quasi-static flow or diffusion equation. I then assumed piston-like displacement of oil by injected water that takes account of viscosity diffence between both fluids and proposed a model based on the theory of elliptic functions, in particular Weierstrass p-functions functions. Oil-water contact movement, dimensionless time for water breakthrough at the production well, areal sweep and average reservoir pressures were modeled. The model was tested using Wolfram Mathematica 10 software and the results are promising. The thesis has therefore established that the Agbada sandstone reservoir is strongly water-wet and that waterflooding is a viable option for enhanced oil recovery from the reservoir.MT201

CIMODE 2016: 3º Congresso Internacional de Moda e Design: proceedings

O CIMODE 2016 é o terceiro Congresso Internacional de Moda e Design, a decorrer de 9 a 12 de maio de 2016 na cidade de Buenos Aires, subordinado ao tema : EM--‐TRAMAS. A presente edição é organizada pela Faculdade de Arquitetura, Desenho e Urbanismo da Universidade de Buenos Aires, em conjunto com o Departamento de Engenharia Têxtil da Universidade do Minho e com a ABEPEM – Associação Brasileira de Estudos e Pesquisa em Moda.info:eu-repo/semantics/publishedVersio