On the Ewald method and the quartic Helmholtz free energy of an anharmonic metallic crystal

Thesis (M. Sc.) - Brock University, 1978.

Variational Monte Carlo estimation of the dissociation energy of CuH using correlated sampling

A new approach to treating large Z systems by quantum Monte Carlo has been developed. It naturally leads to notion of the 'valence energy'. Possibilities of the new approach has been explored by optimizing the wave function for CuH and Cu and computing dissociation energy and dipole moment of CuH using variational Monte Carlo. The dissociation energy obtained is about 40% smaller than the experimental value; the method is comparable with SCF and simple pseudopotential calculations. The dipole moment differs from the best theoretical estimate by about 50% what is again comparable with other methods (Complete Active Space SCF and pseudopotential methods).

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.

Clique Irreducibility of Some Iterative Classes of Graphs

In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations of line graph, the Gallai graphs, the anti-Gallai graphs and its iterations to be clique irreducible and clique vertex irreducible are also obtained.

The (t) property of some classes of graphs

In this note,the (t) properties of five class are studied. We proved that the classes of cographs and clique perfect graphs without isolated vertices satisfy the (2) property and the (3) property, but do not satisfy the (t) property for tis greater than equal to 4. The (t) properties of the planar graphs and the perfect graphss are also studied . we obtain a necessary and suffieient conditions for the trestled graph of index K to satisfy the (2) property

Clique Irreducibility and Clique Vertex Irreducibility of Graphs

A graphs G is clique irreducible if every clique in G of size at least two,has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irreducibility and clique irreducibility of graphs which are non-complete extended p-sums (NEPS) of two graphs are studied. We prove that if G(c) has at least two non-trivial components then G is clique vertex reducible and if it has at least three non-trivial components then G is clique reducible. The cographs and the distance hereditary graphs which are clique vertex irreducible and clique irreducible are also recursively characterized.

Average ground-state energy of finite Fermi systems

Semiclassical theories such as the Thomas-Fermi and Wigner-Kirkwood methods give a good description of the smooth average part of the total energy of a Fermi gas in some external potential when the chemical potential is varied. However, in systems with a fixed number of particles N, these methods overbind the actual average of the quantum energy as N is varied. We describe a theory that accounts for this effect. Numerical illustrations are discussed for fermions trapped in a harmonic oscillator potential and in a hard-wall cavity, and for self-consistent calculations of atomic nuclei. In the latter case, the influence of deformations on the average behavior of the energy is also considered.

Simultaneous Embeddings Of Graphs As Median And Antimedian Subgraphs

The distance DG(v) of a vertex v in an undirected graph G is the sum of the distances between v and all other vertices of G. The set of vertices in G with maximum (minimum) distance is the antimedian (median) set of a graph G. It is proved that for arbitrary graphs G and J and a positive integer r 2, there exists a connected graph H such that G is the antimedian and J the median subgraphs of H, respectively, and that dH(G, J) = r. When both G and J are connected, G and J can in addition be made convex subgraphs of H.

Betweenness Centrality in Some Classes of Graphs

There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest path between them. In this paper we present betweenness centrality of some important classes of graphs.

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

Ground state correlation energy of the Be-sequence for Z = 4-20 in MCDF approximation

The ground state (J = 0) electronic correlation energy of the 4-electron Be-sequence is calculated in the Multi-Configuration Dirac-Fock approximation for Z = 4-20. The 4 electrons were distributed over the configurations arising from the 1s, 2s, 2p, 3s, 3p and 3d orbitals. Theoretical values obtained here are in good agreement with experimental correlation energies.

On the total energy of two-electron atoms

Using the Multi-Configuration Dirac-Fock (MCDF) method we calculate with 9 configuration state functions the correlation energy as well as the total energy of the lowest J = 0 ground state of all two-electron systems from H- to Thorium (Z = 90). A comparison with experimental data, which are available only in the low Z region, shows a very good agreement.

Energy of the future.

Este título pertenece a una serie que examina el calentamiento global y sus posibles consecuencias para la vida en la Tierra. Contiene la estructura y características adecuadas para que los estudiantes aprendan a desarrollar habilidades en la lectura de textos no ficción enseñándoles cómo utilizar la tabla de contenidos, índices, epígrafes, glosario, gráficos, mapas y diagramas a fin de garantizar, en un futuro aprendizaje, un uso adecuado de materiales de referencia. Describe cómo la forma de generar electricidad contribuye al calentamiento global. Analiza las distintas tecnología s que se están desarrollando para producir electricidad sin quemar combustibles fósiles, y muestra cómo cada uno puede ayudar ahora consumiendo menos electricidad. Incluye estudios de casos que permite a los estudiantes aplicar sus conocimientos a situaciones de la vida real y sugerir cambios en su propia vida para aumentar su comprensión de la responsabilidad personal. Tiene glosario, índice y sitios web.

Determination of the direct band-gap energy of InAlAs matched to InP by photoluminescence excitation spectroscopy

A series of InxAl1-xAs samples (0.51≪x≪0.55)coherently grown on InP was studied in order to measure the band-gap energy of the lattice matched composition. As the substrate is opaque to the relevant photon energies, a method is developed to calculate the optical absorption coefficient from the photoluminescence excitation spectra. The effect of strain on the band-gap energy has been taken into account. For x=0.532, at 14 K we have obtained Eg0=1549±6 meV

Quantification of the bond-angle dispersion by Raman spectroscopy and the strain energy of amorphous silicon

A thorough critical analysis of the theoretical relationships between the bond-angle dispersion in a-Si, Δθ, and the width of the transverse optical Raman peak, Γ, is presented. It is shown that the discrepancies between them are drastically reduced when unified definitions for Δθ and Γ are used. This reduced dispersion in the predicted values of Δθ together with the broad agreement with the scarce direct determinations of Δθ is then used to analyze the strain energy in partially relaxed pure a-Si. It is concluded that defect annihilation does not contribute appreciably to the reduction of the a-Si energy during structural relaxation. In contrast, it can account for half of the crystallization energy, which can be as low as 7 kJ/mol in defect-free a-Si