Studies on the Spectrum and the Energy of Graphs

Department of Mathematics, Cochin University of Science and Technology

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.

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

Measuring toughness and the cohesive stress-displacement relationship by the essential work of fracture concept

The complete fracture behaviour of ductile double edge notched tension (DENT) specimen is analysed with an approximate model, which is then used to discuss the essential work of fracture (EWF) concept. The model results are compared with the experimental results for an aluminium alloy 6082-O. The restrictions on the ligament size for valid application of the EWF method are discussed with the aid of the model. The model is used to suggest an improved method of obtaining the cohesive stress-displacement relationship for the fracture process zone (FPZ).

On the available energy of an axisymmetric vortex

A theory of available energy for axisymmetric circulations is presented. The theory is a generalization of the classical theory of available potential energy, in that it accounts for both thermal and angular momentum constraints on the circulation. The generalization relies on the Hamiltonian structure of the (conservative) dynamics, is exact at finite amplitude, and has a local form. Application of the theory is presented for the case of an axisymmetric vortex on an f -plane in the context of the Boussinesq equations.

The Landau free energy of hard ellipses obtained from microscopic simulations

Systems of two-dimensional hard ellipses of varying aspect ratios and packing fractions are studied by Monte Carlo simulations in the generalised canonical ensemble. From this microscopic model, we extract a coarse-grained macroscopic Landau-de Gennes free energy as a function of packing fraction and orientational order parameter. We separate the free energy into the ideal orientational entropy of non-interacting two-dimensional spins and an excess free energy associated with excluded volume interactions. We further explore the isotropic-nematic phase transition using our empirical expression for the free energy and find that the nature of the phase transition is continuous for the aspect ratios we studied.

Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.

Energy of bond defects in quantum spin chains obtained from local approximations and from exact diagonalization

We study the influence of ferromagnetic and antiferromagnetic bond defects on the ground-state energy of antiferromagnetic spin chains. In the absence of translational invariance, the energy spectrum of the full Hamiltonian is obtained numerically, by an iterative modi. cation of the power algorithm. In parallel, approximate analytical energies are obtained from a local-bond approximation, proposed here. This approximation results in significant improvement upon the mean-field approximation, at negligible extra computational effort. (C) 2008 Published by Elsevier B.V.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

Digestibility and metabolizable energy of some carbohydrate sources for dogs

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Digestibility and metabolizable energy of maize gluten feed for dogs as measured by two different techniques

Maize gluten feed (MGF) is a co-product of wet milling of maize, and is composed of structures that remain after most starch, gluten and germ has been extracted from the grain. Although currently used in dog foods, its digestibility and energy values have not been documented. Two techniques were used to determine nutrient digestibility of MGF for dog foods. Both techniques used extruded diets fed to Beagle dogs, with six replicates per diet. The first study used a difference method in which 300 g/kg of a reference diet was replaced by MGF. Based on the difference method, the coefficient of total tract apparent digestibility (CTTAD) of MGF was 0.53 for dry matter (DM), 0.69 for crude protein (CP), 0.74 for fat, 0.99 for starch, and 0.55 for gross energy (GE). The calculated metabolizable energy (ME) of MGF was 7.99 MJ/kg (as-fed). The second study used a regression method and included a basal diet and a basal diet with 70, 140 and 210 g MGF/kg of diet (as a substitute for maize starch). Maize gluten feed inclusion resulted in a linear reduction of CTTAD of DM (R(2)=0.99; P<0.001), CP (R(2)=0.95; P=0.002), fat (R(2)=0.87; P=0.009). starch (R(2)=0.81; P<0.001), and GE (R(2)=0.99; P<0.001). Faecal production increased linearly from 56 g to 107 g/dog/d (R(2)=0.99; P<0.001), with a linear reduction of faecal DM (R(2)=0.99: P<0.001) and a linear increase in faecal lactic acid concentration (P<0.02). Both urine (R(2)=0.77; P=0.029) and faeces (R(2)=0.92: P=0.019) showed a linear reduction in pH. Results of ingredient MAD obtained by the regression and difference methods were close (6% or less of variation) for CP, fat, and starch, and also for ME content (1.4% higher for the difference method), but the two methods disagreed on calculated CTTAD of DM and organic matter. The high dietary fiber content of MGF (382 g/kg) may explain the low digestibility of this ingredient. Maize gluten feed could be a useful ingredient for formulations designed to have low energy or reduce the urine pH of dogs. (C) 2011 Elsevier B.V. All rights reserved.