Conceptual models of fluid flow in fractures

This thesis is titled CONCEPTUAL MODELS OF FLOW IN FRACTURES . This thesis study has two parts. In the first part, some conceptual models of fluid flow in fractures will be developed. These models will be used to analyze fluid flow in the near field region of nuclear waste canisters emplaced in fractured rock. Fluid near the canister will evaporate and move into the fractures where it condenses on the walls of the fracture. It is then absorbed by the matrix due to the capillary suction. Then, due to the capillary force, the liquid moves towards the heat source. A region of liquid vapor flow is formed which is called the heat pipe region. The heat pipe phenomenon will be analyzed for different models of fractures. The capillary pressure function and relative permeability function which are functions of the liquid saturation will be developed. In the second part of the study, the functions developed from the conceptual model of the fracture will be incorporated into the TOUGH code and the near field examined. TOUGH is a multi-dimensional, numerical model for simulating the coupled transport of water, vapor, air and heat in porous and fractured media

Resource control and strong normalisation

We introduce the \emph{resource control cube}, a system consisting of eight intuitionistic lambda calculi with either implicit or explicit control of resources and with either natural deduction or sequent calculus. The four calculi of the cube that correspond to natural deduction have been proposed by Kesner and Renaud and the four calculi that correspond to sequent lambda calculi are introduced in this paper. The presentation is parameterized with the set of resources (weakening or contraction), which enables a uniform treatment of the eight calculi of the cube. The simply typed resource control cube, on the one hand, expands the Curry-Howard correspondence to intuitionistic natural deduction and intuitionistic sequent logic with implicit or explicit structural rules and, on the other hand, is related to substructural logics. We propose a general intersection type system for the resource control cube calculi. Our main contribution is a characterisation of strong normalisation of reductions in this cube. First, we prove that typeability implies strong normalisation in the ''natural deduction base" of the cube by adapting the reducibility method. We then prove that typeability implies strong normalisation in the ''sequent base" of the cube by using a combination of well-orders and a suitable embedding in the ''natural deduction base". Finally, we prove that strong normalisation implies typeability in the cube using head subject expansion. All proofs are general and can be made specific to each calculus of the cube by instantiating the set of resources

A journey through resource control lambda calculi and explicit substitution using intersection types (an account)

In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit control of resources due to the presence of weakening and contraction operators. Along this journey, we propose intersection type assignment systems for all three resource control calculi. We recognise the need for three kinds of variables all requiring different kinds of intersection types. Our main contribution is the characterisation of strong normalisation of reductions in all three calculi, using the techniques of reducibility, head subject expansion, a combination of well-orders and suitable embeddings of terms

Comparative Analysis of Stockpile Volume Estimation using UAV and GPS Techniques

Mining operations involve the extraction of minerals of economic value from the earth. In surface mining operations, overburdens need to be stripped in other to reach the ore. Large volumes of waste as well as ore is stripped in the process. Various technologies have been used to aid in stockpile volume estimation. Notable among them are the Total Stations and Global Positioning Systems (GPS). However, labour, safety and time has challenged the use of these technologies. Unmanned Aerial Vehicle (UAV), commonly known as drone is an emerging technology for stockpile volume computations in the Mine. UAV technology for data collection is less labour intensive, safer and faster. Therefore, this study applied the UAV technology in an open pit to estimate stockpile volumes from a Mine. For the purpose of this study, GPS and UAV data were collected for measuring stockpile volumes of materials mined. The actual volumes of stockpiles A, B, C, D (Case 2), produced differences of 0.05% for A, 0.05% for B, 0.08% for C, 0.07% for D and 0.03% for A, -0.03% for B, 0.03% for C and 0.04% for D, for the GPS-based and the UAV-based techniques, respectively. The GPS-based technique generated moderate accuracies for volume estimation, but was time consuming and labour intensive, compared to the UAV-based technique; which was faster and less labour intensive. The UAV-based technique was the most accurate, safest and is capable of mapping large areas rapidly. It is therefore recommended that UAV survey be incorporated in stockpile volume estimation. Keywords: UAV, GPS, Stockpile, Mine, Total Station

Minimum energy path for the nucleation of misfit dislocations in Ge/Si(001) heteroepitaxy

A possible mechanism for the formation of a 90{\deg} misfit dislocation at the Ge/Si(001) interface through homogeneous nucleation is identified from atomic scale calculations where a minimum energy path connecting the coherent epitaxial state and a final state with a 90{\deg} misfit dislocation is found using the nudged elastic band method. The initial path is generated using a repulsive bias activation procedure in a model system including 75000 atoms. The energy along the path exhibits two maxima in the energy. The first maximum occurs as a 60{\deg} dislocation nucleates. The intermediate minimum corresponds to an extended 60{\deg} dislocation. The subsequent energy maximum occurs as a second 60{\deg} dislocation nucleates in a complementary, mirror glide plane, simultaneously starting from the surface and from the first 60{\deg} dislocation. The activation energy of the nucleation of the second dislocation is 30% lower than that of the first one showing that the formation of the second 60{\deg} dislocation is aided by the presence of the first one. The simulations represent a step towards unraveling the formation mechanism of 90{\deg} dislocations, an important issue in the design of growth procedures for strain released Ge overlayers on Si(100) surfaces, and more generally illustrate an approach that can be used to gain insight into the mechanism of complex nucleation paths of extended defects in solids

Spectral Aspects of Cocliques in Graphs

This thesis considers spectral approaches to finding maximum cocliques in graphs. We focus on the relation between the eigenspaces of a graph and the size and location of its maximum cocliques. Our main result concerns the computational problem of finding the size of a maximum coclique in a graph. This problem is known to be NP-Hard for general graphs. Recently, Codenotti et al. showed that computing the size of a maximum coclique is still NP-Hard if we restrict to the class of circulant graphs. We take an alternative approach to this result using quotient graphs and coding theory. We apply our method to show that computing the size of a maximum coclique is NP-Hard for the class of Cayley graphs for the groups $\mathbb{Z}_p^n$ where $p$ is any fixed prime. Cocliques are closely related to equitable partitions of a graph, and to parallel faces of the eigenpolytopes of a graph. We develop this connection and give a relation between the existence of quadratic polynomials that vanish on the vertices of an eigenpolytope of a graph, and the existence of elements in the null space of the Veronese matrix. This gives a us a tool for finding equitable partitions of a graph, and proving the non-existence of equitable partitions. For distance-regular graphs we exploit the algebraic structure of association schemes to derive an explicit formula for the rank of the Veronese matrix. We apply this machinery to show that there are strongly regular graphs whose $\tau$-eigenpolytopes are not prismoids. We also present several partial results on cocliques and graph spectra. We develop a linear programming approach to the problem of finding weightings of the adjacency matrix of a graph that meets the inertia bound with equality, and apply our technique to various families of Cayley graphs. Towards characterizing the maximum cocliques of the folded-cube graphs, we find a class of large facets of the least eigenpolytope of a folded cube, and show how they correspond to the structure of the graph. Finally, we consider equitable partitions with additional structural constraints, namely that both parts are convex subgraphs. We show that Latin square graphs cannot be partitioned into a coclique and a convex subgraph

Resource control and intersection types: an intrinsic connection

In this paper we investigate the $\lambda$ -calculus, a $\lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and con-traction rules in the type assignment system. We introduce directly the class of $\lambda$ -terms and we provide a new treatment of substitution by its decompo-sition into atomic steps. We propose an intersection type assignment system for $\lambda$ -calculus which makes a clear correspondence between three roles of variables and three kinds of intersection types. Finally, we provide the characterisation of strong normalisation in $\lambda$ -calculus by means of an in-tersection type assignment system. This process uses typeability of normal forms, redex subject expansion and reducibility method.Comment: arXiv admin note: substantial text overlap with arXiv:1306.228