Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Solution of the Hartree-Fock-Slater equations for diatomic molecules by the finite-element method

We present the finite-element method in its application to solving quantum-mechanical problems for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations for molecules like N_2 and CO are presented. The accuracy achieved with fewer than 5000 grid points for the total energies of these systems is 10^-8 a.u., which is about two orders of magnitude better than the accuracy of any other available method.

Solution of the time dependent Dirac-Fock-Slater equation for many-electron collisions systems using a time window method

We present a new scheme to solve the time dependent Dirac-Fock-Slater equation (TDDFS) for heavy many electron ion-atom collision systems. Up to now time independent self consistent molecular orbitals have been used to expand the time dependent wavefunction and rather complicated potential coupling matrix elements have been neglected. Our idea is to minimize the potential coupling by using the time dependent electronic density to generate molecular basis functions. We present the first results for 16 MeV S{^16+} on Ar.

Efficient tree construction for the multicast problem

A new heuristic for the Steiner Minimal Tree problem is presented here. The method described is based on the detection of particular sets of nodes in networks, the “Hot Spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used CIS comparison terms in the experimental analysis which demonstrates the goodness of the heuristic discussed in this paper.

Efficient tree construction for the multicast problem

A new heuristic for the Steiner minimal tree problem is presented. The method described is based on the detection of particular sets of nodes in networks, the “hot spot” sets, which are used to obtain better approximations of the optimal solutions. An algorithm is also proposed which is capable of improving the solutions obtained by classical heuristics, by means of a stirring process of the nodes in solution trees. Classical heuristics and an enumerative method are used as comparison terms in the experimental analysis which demonstrates the capability of the heuristic discussed

A moving-mesh finite element method and its application to the numerical solution of phase-change problems

A distributed Lagrangian moving-mesh finite element method is applied to problems involving changes of phase. The algorithm uses a distributed conservation principle to determine nodal mesh velocities, which are then used to move the nodes. The nodal values are obtained from an ALE (Arbitrary Lagrangian-Eulerian) equation, which represents a generalization of the original algorithm presented in Applied Numerical Mathematics, 54:450--469 (2005). Having described the details of the generalized algorithm it is validated on two test cases from the original paper and is then applied to one-phase and, for the first time, two-phase Stefan problems in one and two space dimensions, paying particular attention to the implementation of the interface boundary conditions. Results are presented to demonstrate the accuracy and the effectiveness of the method, including comparisons against analytical solutions where available.

A NEW METHOD TO OBTAIN GOOD ANATOMICAL SLIDES OF HETEROGENEOUS PLANT PARTS

A new method is presented to prepare anatomical slides of plant materials including a combination of soft and hard tissues, such as stems with cambial variants, arboreal monocotyledons, and tree bark The method integrates previous techniques aimed at softening the samples and making them thereby more homogeneous, with the use of anti-tearing polystyrene foam solution In addition, we suggest two other alternatives to protect the sections from tearing adhesive tape and/or Mayer`s albumin adhesive, both combined with the polystyrene foam solution This solution is cheap and easy to make by dissolving any packaging polystyrene m butyl acetate It is applied before each section is cut on a sliding microtome and ensures that all the tissues in the section will hold together This novel microtechnical procedure will facilitate the study of heterogeneous plant portions, as shown in some illustrated examples

Fast heuristics for the Steiner tree problem with revenues, budget and hop constraints

This article describes and compares three heuristics for a variant of the Steiner tree problem with revenues, which includes budget and hop constraints. First, a greedy method which obtains good approximations in short computational times is proposed. This initial solution is then improved by means of a destroy-and-repair method or a tabu search algorithm. Computational results compare the three methods in terms of accuracy and speed. (C) 2007 Elsevier B.V. All rights reserved.

A contractive method for computing the stationary solution of the euler equation

A contractive method for computing stationary solutions of intertemporal equilibrium models is provide. The method is is implemented using a contraction mapping derived from the first-order conditions. The deterministic dynamic programming problem is used to illustrate the method. Some numerical examples are performed.

A study of a numerical solution of the steady two dimensions Navier-Stokes equations in a constricted channel problem by a compact fourth order method

We present a numerical solution for the steady 2D Navier-Stokes equations using a fourth order compact-type method. The geometry of the problem is a constricted symmetric channel, where the boundary can be varied, via a parameter, from a smooth constriction to one possessing a very sharp but smooth corner allowing us to analyse the behaviour of the errors when the solution is smooth or near singular. The set of non-linear equations is solved by the Newton method. Results have been obtained for Reynolds number up to 500. Estimates of the errors incurred have shown that the results are accurate and better than those of the corresponding second order method. (C) 2002 Elsevier B.V. All rights reserved.

Influence of the solution pH on the morphological, structural and electrical properties of Bi3.50La0.50Ti3O12 thin films obtained by the polymeric precursor method

Lanthanum-doped Bi4Ti3O12 thin films (BLT) were deposited on Pt/Ti/SiO2/Si substrates using a polymeric precursor solution. The spin-coated films were specular, crack-free and crystalline after annealing at 700 degrees C for 2 h. Crystallinity and morphological evaluation were examined by X ray diffraction (YRD) and atomic force microscopy (AFM). The stability of the formed complex is of extreme importance for the formation of the perovskite phase. Films obtained from acid pH solution present elongated grains around 200 ran in size, whereas films obtained from basic solution present a dense microstructure with spherical grains (100 nm). The dielectric and ferroelectric properties of the BLT films are strongly affected by the solution pH. The hysteresis loops are fully saturated with a remnant polarization and coercive voltage of P-r=20.2 mu C/cm(2) and V-c = 1.35 V and P-r= 15 mu C/cm(2) and V-c = 1.69 V for the films obtained from basic and acid solutions, respectively. (C) 2005 Elsevier B.V. All rights reserved.

Influence of the concentration of Sb2O3 and the viscosity of the precursor solution on the electrical and optical properties of SnO2 thin films produced by the Pechini method

SnO2:Sb multi-layer coatings were prepared by the Pechini method. An investigation was made of the influence of the concentration of Sb2O3 and the viscosity of the precursor solution on the electrical and optical properties of SnO2 thin films. The use of a multi-layer system as an alternative form of increasing the packing and. thus. decreasing porosity proved to be efficient, decreasing the system's resistivity without altering its optical properties. (C) 2002 Elsevier B.V. B.V. All rights reserved.

A new approach to the solution of the optimal power flow problem based on the modified Newton's method associated to an augmented Lagrangian function

This paper presents a new algorithm for optimal power flow problem. The algorithm is based on Newton's method which it works with an Augmented Lagrangian function associated with the original problem. The function aggregates all the equality and inequality constraints and is solved using the modified-Newton method. The test results have shown the effectiveness of the approach using the IEEE 30 and 638 bus systems.