Exact closed-form solutions of the Dirac equation with a scalar exponential potential

The problem of a fermion subject to a general scalar potential in a two-dimensional world for nonzero eigenenergies is mapped into a Sturm-Liouville problem for the upper component of the Dirac spinor. In the specific circumstance of an exponential potential, we have an effective Morse potential which reveals itself as an essentially relativistic problem. Exact bound solutions are found in closed form for this problem. The behaviour of the upper and lower components of the Dirac spinor is discussed in detail, particularly the existence of zero modes. (c) 2005 Elsevier B.v. All rights reserved.

Extended class of exact twistons and crystalline polyethylene

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Beam Search Algorithms for Minimizing Tool Switches on a Flexible Manufacturing System

In the minimization of tool switches problem we seek a sequence to process a set of jobs so that the number of tool switches required is minimized. In this work different variations of a heuristic based on partial ordered job sequences are implemented and evaluated. All variations adopt a depth first strategy of the enumeration tree. The computational test results indicate that good results can be obtained by a variation which keeps the best three branches at each node of the enumeration tree, and randomly choose, among all active nodes, the next node to branch when backtracking.

Allocation of protective devices in distribution circuits using nonlinear programming models and genetic algorithms

The optimized allocation of protective devices in strategic points of the circuit improves the quality of the energy supply and the system reliability index. This paper presents a nonlinear integer programming (NLIP) model with binary variables, to deal with the problem of protective device allocation in the main feeder and all branches of an overhead distribution circuit, to improve the reliability index and to provide customers with service of high quality and reliability. The constraints considered in the problem take into account technical and economical limitations, such as coordination problems of serial protective devices, available equipment, the importance of the feeder and the circuit topology. The use of genetic algorithms (GAs) is proposed to solve this problem, using a binary representation that does (1) or does not (0) show allocation of protective devices (reclosers, sectionalizers and fuses) in predefined points of the circuit. Results are presented for a real circuit (134 busses), with the possibility of protective device allocation in 29 points. Also the ability of the algorithm in finding good solutions while improving significantly the indicators of reliability is shown. (C) 2003 Elsevier B.V. All rights reserved.

Aplicação do algoritmo de otimização por colônia de formigas sobre o problema do passeio do robô seletivo

This work seeks to propose and evaluate a change to the Ant Colony Optimization based on the results of experiments performed on the problem of Selective Ride Robot (PRS, a new problem, also proposed in this paper. Four metaheuristics are implemented, GRASP, VNS and two versions of Ant Colony Optimization, and their results are analyzed by running the algorithms over 32 instances created during this work. The metaheuristics also have their results compared to an exact approach. The results show that the algorithm implemented using the GRASP metaheuristic show good results. The version of the multicolony ant colony algorithm, proposed and evaluated in this work, shows the best results

Uma investigação de algoritmos exatos e metaheurísticos aplicados ao nonograma

Nonogram is a logical puzzle whose associated decision problem is NP-complete. It has applications in pattern recognition problems and data compression, among others. The puzzle consists in determining an assignment of colors to pixels distributed in a N  M matrix that satisfies line and column constraints. A Nonogram is encoded by a vector whose elements specify the number of pixels in each row and column of a figure without specifying their coordinates. This work presents exact and heuristic approaches to solve Nonograms. The depth first search was one of the chosen exact approaches because it is a typical example of brute search algorithm that is easy to implement. Another implemented exact approach was based on the Las Vegas algorithm, so that we intend to investigate whether the randomness introduce by the Las Vegas-based algorithm would be an advantage over the depth first search. The Nonogram is also transformed into a Constraint Satisfaction Problem. Three heuristics approaches are proposed: a Tabu Search and two memetic algorithms. A new function to calculate the objective function is proposed. The approaches are applied on 234 instances, the size of the instances ranging from 5 x 5 to 100 x 100 size, and including logical and random Nonograms

Using Amino Acid Correlation and Community Detection Algorithms to Identify Functional Determinants in Protein Families

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

Use of genetic algorithms and solvation potential to study peptides structure

In this work, genetic algorithms concepts along with a rotamer library for proteins side chains and implicit solvation potential are used to optimize the tertiary structure of peptides. We starting from the known PDB structure of its backbone which is kept fixed while the side chains allowed adopting the conformations present in the rotamer library. It was used rotamer library independent of backbone and a implicit solvation potential. The structure of Mastoporan-X was predicted using several force fields with a growing complexity; we started it with a field where the only present interaction was Lennard-Jones. We added the Coulombian term and we considered the solvation effects through a term proportional to the solvent accessible area. This paper present good and interesting results obtained using the potential with solvation term and rotamer library. Hence, the algorithm (called YODA) presented here can be a good tool to the prediction problem. (c) 2007 Elsevier B.V. All rights reserved.

On exact boundary controllability for linearly coupled wave equations

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Exact Foldy-Wouthuysen transformation for real spin-0 particle in curved space

Up to now, the only known exact Foldy-Wouthuysen transformation (FWT) in curved space is that concerning Dirac particles coupled to static spacetime metrics. Here we construct the exact FWT related to a real spin-0 particle for the aforementioned spacetimes. This exact transformation exists independently of the value of the coupling between the scalar field and gravity. Moreover, the gravitational Darwin term written for the conformal coupling is one-third of the corresponding term in the fermionic case. There are some arguments in the literature that seem to favor the choice lambda=1/6. We rehearse a number of claims of these works.

Exact renormalization of massless QED(2)

We perform the exact renormalization of two-dimensional massless gauge theories. Using these exact results we discuss the cluster property and confinement in both the anomalous and chiral Schwinger models.

An exact equation for the free surface of a fluid in a porous medium

We study the problem of the evolution of the free surface of a fluid in a saturated porous medium, bounded from below by a. at impermeable bottom, and described by the Laplace equation with moving-boundary conditions. By making use of a convenient conformal transformation, we show that the solution to this problem is equivalent to the solution of the Laplace equation on a fixed domain, with new variable coefficients, the boundary conditions. We use a kernel of the Laplace equation which allows us to write the Dirichlet-to-Neumann operator, and in this way we are able to find an exact differential-integral equation for the evolution of the free surface in one space dimension. Although not amenable to direct analytical solutions, this equation turns out to allow an easy numerical implementation. We give an explicit illustrative case at the end of the article.

Exact static soliton solutions of (3+1)-dimensional integrable theory with nonzero Hopf numbers

In this paper, we explicitly construct an infinite number of Hopfions (static, soliton solutions with nonzero Hopf topological charges) within the recently proposed (3 + 1)-dimensional, integrable, and relativistically invariant field theory. Two integers label the family of Hopfions we have found. Their product is equal to the Hopf charge which provides a lower bound to the soliton's finite energy. The Hopfions are explicitly constructed in terms of the toroidal coordinates and shown to have a form of linked closed vortices.

On the energy transported by exact plane gravitational-wave solutions

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

Kramers equation for a charged Brownian particle: the exact solution

We report the exact fundamental solution for Kramers equation associated to a Brownian gas of charged particles, under the influence of homogeneous (spatially uniform) otherwise arbitrary, external mechanical, electrical and magnetic fields. Some applications are presented, namely the hydrothermodynamical picture for Brownian motion in the long-time regime. (c) 2005 Elsevier B.V. All rights reserved.