Phonon spectra and temperature variation of thermodynamic properties of fcc metals via Finnis-Sinclair type many body potentials: Sutton-Chen and improved Sutton-Chen models

Volume(density)-independent pair-potentials cannot describe metallic cohesion adequately as the presence of the free electron gas renders the total energy strongly dependent on the electron density. The embedded atom method (EAM) addresses this issue by replacing part of the total energy with an explicitly density-dependent term called the embedding function. Finnis and Sinclair proposed a model where the embedding function is taken to be proportional to the square root of the electron density. Models of this type are known as Finnis-Sinclair many body potentials. In this work we study a particular parametrization of the Finnis-Sinclair type potential, called the "Sutton-Chen" model, and a later version, called the "Quantum Sutton-Chen" model, to study the phonon spectra and the temperature variation thermodynamic properties of fcc metals. Both models give poor results for thermal expansion, which can be traced to rapid softening of transverse phonon frequencies with increasing lattice parameter. We identify the power law decay of the electron density with distance assumed by the model as the main cause of this behaviour and show that an exponentially decaying form of charge density improves the results significantly. Results for Sutton-Chen and our improved version of Sutton-Chen models are compared for four fcc metals: Cu, Ag, Au and Pt. The calculated properties are the phonon spectra, thermal expansion coefficient, isobaric heat capacity, adiabatic and isothermal bulk moduli, atomic root-mean-square displacement and Gr\"{u}neisen parameter. For the sake of comparison we have also considered two other models where the distance-dependence of the charge density is an exponential multiplied by polynomials. None of these models exhibits the instability against thermal expansion (premature melting) as shown by the Sutton-Chen model. We also present results obtained via pure pair potential models, in order to identify advantages and disadvantages of methods used to obtain the parameters of these potentials.

Extracting Ramachandran torsional angle distributions from 2D NMR data using Tikhonov regularization /

Solid state nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for studying structural and dynamical properties of disordered and partially ordered materials, such as glasses, polymers, liquid crystals, and biological materials. In particular, twodimensional( 2D) NMR methods such as ^^C-^^C correlation spectroscopy under the magicangle- spinning (MAS) conditions have been used to measure structural constraints on the secondary structure of proteins and polypeptides. Amyloid fibrils implicated in a broad class of diseases such as Alzheimer's are known to contain a particular repeating structural motif, called a /5-sheet. However, the details of such structures are poorly understood, primarily because the structural constraints extracted from the 2D NMR data in the form of the so-called Ramachandran (backbone torsion) angle distributions, g{^,'4)), are strongly model-dependent. Inverse theory methods are used to extract Ramachandran angle distributions from a set of 2D MAS and constant-time double-quantum-filtered dipolar recoupling (CTDQFD) data. This is a vastly underdetermined problem, and the stability of the inverse mapping is problematic. Tikhonov regularization is a well-known method of improving the stability of the inverse; in this work it is extended to use a new regularization functional based on the Laplacian rather than on the norm of the function itself. In this way, one makes use of the inherently two-dimensional nature of the underlying Ramachandran maps. In addition, a modification of the existing numerical procedure is performed, as appropriate for an underdetermined inverse problem. Stability of the algorithm with respect to the signal-to-noise (S/N) ratio is examined using a simulated data set. The results show excellent convergence to the true angle distribution function g{(j),ii) for the S/N ratio above 100.

Square Root Finding In Graphs

Abstract: Root and root finding are concepts familiar to most branches of mathematics. In graph theory, H is a square root of G and G is the square of H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Graph square is a basic operation with a number of results about its properties in the literature. We study the characterization and recognition problems of graph powers. There are algorithmic and computational approaches to answer the decision problem of whether a given graph is a certain power of any graph. There are polynomial time algorithms to solve this problem for square of graphs with girth at least six while the NP-completeness is proven for square of graphs with girth at most four. The girth-parameterized problem of root fining has been open in the case of square of graphs with girth five. We settle the conjecture that recognition of square of graphs with girth 5 is NP-complete. This result is providing the complete dichotomy theorem for square root finding problem.

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.

You get what you pay for : independent music and Canadian public policy

The aim of this MA thesis is to demonstrate how corporate concentration within the global music industry specifically affects the Canadian music industry's ability to compete for its own national audience as well as audiences worldwide. Federal public policies, regulatory regimes and subsidies are considered within the context of the structure of the global marketplace which is, in effect, an oligopoly controlled by four major corporations. Through an extensive literature review of political economy theory, Canadian public policies and music studies, as well as personal interviews conducted with Canadian musicians, entrepreneurs and public servants, I will situate my research within the body of political economy theory; present a detailed report of the structure of the global music industry; address the key players within the industry; describe the relationship between the major corporations and the independent companies operating in the industry; discuss how new technologies affect said relationships; consider the effectiveness of Canadian public policies in safeguarding the national music industry; and recommend steps that can be taken to remedy the shortcomings of Federal policies and regulatory regimes.

Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

The Relationship Between Youth Risk-Taking Behaviour and Activity Engagement

Youth have been found to engage in various risk-taking behaviours at higher rates than any other age group. However, there is a lack of research on the division between adaptive and maladaptive risk behaviours among adolescents and emerging adults. Adaptive risk-taking behaviours may present youth with ways to successfully partake in the risk behaviours that they are naturally inclined to engage in. The relationship between activity engagement and positive youth development has been extensively studied and cited as a way to expose youth to positive experiences and promote successful development. However, the relationship between activity engagement and risk behaviours among youth has yetto be studied in depth. This study investigated the potential relationship between various adaptive and maladaptive risk behaviours and activity engagement among youth, through an indirect link through five mediator variables. These potential mediators represented the three systems in Jessor's Problem Behaviour Theory. Participants included 276 youth (M = 19.06 years, SD = 1.60, 89.1 % female) from Brock University. Results revealed that activity engagement significantly predicted greater adaptive social risk behaviours among youth. However, there was no mediating effect through the problem behaviour systems. Correlations revealed that being male was associated with more maladaptive risk behaviours and fewer adaptive risk behaviours than females. Additionally, behavioural engagement specifically related to less maladaptive physical health risks and psychological engagement related to greater adaptive social risks. Overall, these findings suggest that activity engagement may be differentially related to the various types of risk-taking and gender associations may exist between the various types and dimensions of risk behaviours, but future work is needed to understand the variables that may explain such relationships.

Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.

Backbone Colouring of Graphs

Consider an undirected graph G and a subgraph of G, H. A q-backbone k-colouring of (G,H) is a mapping f: V(G) {1, 2, ..., k} such that G is properly coloured and for each edge of H, the colours of its endpoints differ by at least q. The minimum number k for which there is a backbone k-colouring of (G,H) is the backbone chromatic number, BBCq(G,H). It has been proved that backbone k-colouring of (G,T) is at most 4 if G is a connected C4-free planar graph or non-bipartite C5-free planar graph or Cj-free, j∈{6,7,8} planar graph without adjacent triangles. In this thesis we improve the results mentioned above and prove that 2-backbone k-colouring of any connected planar graphs without adjacent triangles is at most 4 by using a discharging method. In the second part of this thesis we further improve these results by proving that for any graph G with χ(G) ≥ 4, BBC(G,T) = χ(G). In fact, we prove the stronger result that a backbone tree T in G exists, such that ∀ uv ∈ T, |f(u)-f(v)|=2 or |f(u)-f(v)| ≥ k-2, k = χ(G). For the case that G is a planar graph, according to Four Colour Theorem, χ(G) = 4; so, BBC(G,T) = 4.