**Short
Presentations**

A Bidimensional Phase-Field
Model

with Convection for Change Phase of an Alloy

Gabriela Planas

gplanas@ime.unicamp.br

José Luiz Boldrini

Abstract: The article analyzes a two-dimensional phase-field model for a non-stationary process of solidification of a binary alloy with thermal properties. The model allows the occurrence of fluid flow in non-solid regions, which are a priori unknown, and is thus associated to a free boundary value problem for a highly non-linear system of partial differential equations. These equations are the phase-field equation, the heat equation, the concentration equation and a modified Navier-Stokes equations obtained by the addition of a penalization term of Carman-Kozeny type, which accounts for the mushy effects, and also of a Boussinesq term to take care of the effects of variations of temperature and concentration in the flow. A proof of existence of weak solutions for such system is given. The problem is firstly approximated and a sequence of approximate solutions is obtained by Leray-Schauder fixed point theorem. A solution is then found by using compactness argument.

A Direct Finite-Difference Scheme Satisfying an Optimal Condition

José-Gerardo Tinoco-Ruiz

jtinoco@zeus.umich.mx

Adán Cortés-Medina

acme@fismat.umich.mx

Abstract: In solving PDE's, finite-difference schemes (FDS's) have been used extensively because of their simplicity when the physical region is rectangular or can be decomposed in several rectangular regions. However, if the region is irregular, these schemes are not suitable; other methods behave much better. The main problem seems to be an adequate discretization of the domain. When this step is done, some alternatives for discretizing the differential operators can be proposed. The aim of this talk is to introduce a simple FDS applied directly over a discretization of the physical region given by a quadrilateral, logically-rectangular grid. The grid is obtained using the discrete variational approach of grid generation. The FDS is designed to minimize, in certain sense, the discretization error; some simple examples are solved in order to compare with other FDS's.

A General Approach to Conformal Mappings

Used in Numerical Weather Prediction

Andrei Bourchtein

aburstein@uol.com.br

Lioudmila Bourchtein

Elismar da Rosa Oliveira

Abstract: A class of conformal separable variable mappings is introduced to generalize different conformal projections used in numerical weather prediction and cartography for the representation of spherical domains. It is shown that conformal stereographic, conic and cylindrical projections are particular cases of this class of mappings. A second approach based on composition of conformal mappings is used to describe the set of all conformal maps from a sphere to a plane. Under a natural assumption about independence of the map factor from longitude, the theorem of equivalence between the two above classes of conformal mappings is proved. A problem of minimization of map factor variation within a constructed set of mappings is considered. A comparison of map factors of different kinds of mappings (polar and oblique stereographic, conic and cylindrical) is performed based on numerical evaluations. Obliq ue stereographic projection is found to be the best choice of conformal mapping for hydrodynamic modeling in limited spherical domains.

A Genetic Approach to the Determination of Polynomial Zeros

Luiz C. G. Lopes

lopes@math.uma.pt

Department of Mathematics

University of Madeira

Penteada Campus

9000-390 Funchal, Madeira - Portugal

Abstract: Due to the importance of the problem of determining polynomial zeros, many different approaches and algorithms have been proposed for its resolution. In this work, a new approach to solve polynomial equations by using genetic algorithms is presented. Genetic algorithms are a class of randomized parallel search heuristics based on principles from population genetics and evolution theory. These algorithms manipulate a population of possible solutions to the problem under consideration using selection, recombination and mutation procedures in order to generate new candidate solutions. Following the Darwinian principle of survival of the fittest, at each generation of the genetic algorithm the least promising candidates in the population are discarded and replaced by new ones. This process is repeated until a satisfactory solution is found. Two types of genetic algorithms for the determination of polynomial zeros, real-coded and binary-coded, are considered. In both cases, the initial population of potential solutions (vectors of floating-point numbers or binary strings, respectively) is chosen randomly, with the constraint of belonging to the smallest disk (or the smallest possible square which contains that disk) centered at the origin that contains all the zeros of the given polynomial. The results obtained indicate that real-coded genetic algorithms perform better in terms of efficiency and precision than the binary-coded genetic algorithms since they avoid the time consuming conversion into and out of binary representations, and provides higher precision, especially with high degree polynomials whose binary encoding of the zeros would require a prohibitively long representation. The possibility of combining genetic algorithms with traditional iterative methods for the simultaneous approximation of polynomial zeros is also considered in this work. In the proposed hybrid algorithms, the genetic algorithm performs a global adaptive search and the iterative algorithm locally refines the initial estimates provided by the genetic algorithm. The principal advantage of such hybrid approach is to combine the robustness of genetic algorithms with the efficiency of the traditional iterative methods for the determination of real and complex zeros of polynomials.

A Marker-and-Cell Method for Calculating Viscoelastic Free Surface Flows

Murilo F. Tome

murilo@lcad.icmc.sc.usp.br

Depto. de Ciencias Computacao e Estatistica

ICMC - USP de Sao Carlos

Av. Trabalhador Saocarlense, 400 - Caixa Postal 668

Sao Carlos - SP - BRAZIL

CEP - 13560-970

N. Mangiavacchi

J.A. Cuminato

A. Castelo

Abstract: This work is concerned with the development of a numerical method capable of simulating viscoelastic free surface flows of an Oldroyd-B fluid. The basic equations governing the flow of an Oldroyd-B fluid are considered. A novel formulation is developed for the computation of the non-Newtonian extra-stress components on rigid boundaries. The full free surface stress conditions are employed. The resulting governing equations are solved by a finite difference method on a staggered grid, influenced by the ideas of the marker-and-cell (MAC) method. Numerical results demonstrating de capabilities of this new technique are presented for a number of problems involving unsteady free surface flows.

A Mathematical
Analysis of a Phase Field Type Model for Solidification

with Convection: Pure Materials in the Two Dimensional Case

Cristina Lúcia Dias Vaz

cvaz@ufpa.br

José Luiz Boldrini

boldrini@ime.unicamp.br

with Convection: Pure Materials in the Two Dimensional Case

Cristina Lúcia Dias Vaz

cvaz@ufpa.br

José Luiz Boldrini

boldrini@ime.unicamp.br

Abstract: We investigate the existence and regularity of weak solutions of a phase filed type model for pure material solidification in presence of natural convection. We assume that the nonstat ionary solidification process occurs in a bounded domain, which for technical reasons is restricted to be two dimensional. The governing equations of the model are the phase field equation coupled with a nonlinear heat equation and modified Navier-Stokes equations, which include buoyancy forces modeled by Boussinesq approximation and a Carman-Koseny term that models the flow in mushy regions. Since these modified Navier-Stokes equations only hold in a priori unknown non-solid regions, we actually have a free boundary value problem.

A Method of Fundamental Solutions

for Modeling Porous Media Advective Flow

J.M. Guevara-Jordan

jguevara@euler.ciens.ucv.ve

Universidad Central de Venezuela

Apartado Postal 6228 Carmelitas 1010

Caracas, Venezuela.

South America

Abstract: A new application of the Fundamental Solutions Method for modeling advective solute flow problems in groundwater modeling is presented. It combines a modified version of the Image's Method and the Singular Value Decomposition (S.V.D) algorithm to obtain linear semi-analytical multipotential expressions for the reservoir pressure and velocity. They are used to generate a coordinate system based on streamlines and the time of flight concept. The solute concentration is determined by solving an advection-transport equation along each streamline using its time of flight and the method of characteristics. This strategy reduces the multidimensional concentration equation into a finite sequence of one-dimensional problems, which are easily integrated. The new technique is validated by comparison against analytical solutions and applications to reservoirs engineering problems in two dimensions. These studies showed that the main advantages of the new method are the reduction of CPU times in comparison with the boundary element methods, its lack of numerical diffusion in the solute concentration approximations and the freedom of selecting time step sizes without stability restrictions.

A Model for Thermodynamic and Stress Forces Driven Cavity Flow

Obidio Rubio

obidio@math.unitru.edu.pe

Universidad Nacional de Trujillo

Facultad de CCFF y Matematicas

Trujillo, PERU

Luis Lara

Ruth Noriega

Abstract: We present a mathematical model that describes the flow driven by thermodynamic and stress forces at the upper wall of a basin with high aspect ratio, where the horizontal scale is larger than the vertical one; the model is based on the Navier Stokes equations with a Boussinesq approximation. For a 3D basin, we consider the hydrostatic approximation which provides a fundamental equation connecting the pressure and density. Models of this type are an abstraction for the study of the circulation of the tropical Pacific Ocean due to wind and thermodynamic forces in a equatorial region. We develop a velocity-pressure algorithm with a pressure Neumann condition; the pressure-field is updated in a one-step weighted form. Also we make numerical simulations for several Rayleigh numbers using fixed Reynolds and Prandtl numbers.

A Mollification Method for a One-Dimensional Inverse Heat Conduction Problem

Ruben D. Spies

rspies@imalpde.ceride.gov.ar

Abstract: The Aproximate Inverse is used to solve a severely-ill posed inverse heat conduction problem. It is shown how the mollification can be performed a-priory before the data is needed, by creating a reconstruction Kernel which can then be used to reconstruct several different data sets, greatly reducing the costly part of the computation process. Advantages and differences with some standard mollification methods are shown and several numerical results are presented.

A New 3D Curvilinear Coordinates Model for Oceanic Flow

Over Arbitrary Bathymetry

Carlos R. Torres

ctorres@sciences.sdsu.edu

Computational Science Research Center

San Diego State University

Jose E. Castillo

castillo@myth.sdsu.edu

Computational Science Research Center

San Diego State University

Abstract: We present a new 3-dimensional curvilinear
fluid flow model in boundary-fitted grids. The model solves the primitive
non-linear Navier-Stokes equations under the Boussinesq approximation. Three-dimensional
simulations are made for a stratified flow over a bell-shaped mountain. Results
for the velocity and density fields are presented and discussed.

A New Dynamic Model
Approach Applied to One Link Flexible Manipulator Robot

Celiane Costa Machado

mmaccm@super.furg.br

UFRGS - Graduate Program in Applied Mathematics

Bento Gonçalves, 9500

90501-900, Porto Alegre - RS, Brazil

Álvaro Luiz de Bortoli

dbortoli@mat.ufrgs.br

Sebastião Cícero Pinheiro Gomes

dmtscpg@super.furg.br

Haar Wavelets With Vanishing Moments

Defined Over a Tetrahedrical Grid

Liliana B. Boscardín

lboscar@uns.edu.ar

Depto.de Matemática

Universidad Nacional del Sur

Liliana R. Castro

lcastro@criba.edu.ar

Silvia M. Castro

uscastro@criba.edu.ar

Identification Structures Using Rational Wavelets: Examples of Application

Liliana R. Castro

lcastro@criba.edu.ar

Depto. de Matemática

Universidad Nacional del Sur

Argentina

Osvaldo E. Agamennoni

ieagamen@criba.edu.ar

Carlos E. D'Attellis

ceda@favaloro.edu.ar

Isothermal Fluid Flow in Fractal Domains

Haroldo Fraga de Campos Velho

haroldo@lac.inpe.br

SurfaceMail: LAC-INPE

P.O. Box 515

Sao Jose dos Campos (SP)

Brasil

Erwin Doescher

erwind@bol.com.br

Fernando Manuel Ramos

fernando@lac.inpe.br

Celiane Costa Machado

mmaccm@super.furg.br

UFRGS - Graduate Program in Applied Mathematics

Bento Gonçalves, 9500

90501-900, Porto Alegre - RS, Brazil

Álvaro Luiz de Bortoli

dbortoli@mat.ufrgs.br

Sebastião Cícero Pinheiro Gomes

dmtscpg@super.furg.br

Abstract: Active control law synthesis for flexible structures is still an open problem. It has been the object of many investigations, mainly starting in the 1980's. In spite of many works dedicated to the dynamic modeling of such structures, these models have no physical variables as state coordinates. For example, the well known assumed modes (modal analytic), consider that the partial differential equations of a flexible problem may be separated in two parts: one spatial and other temporal dependent. This approach generates a dynamic model that has no physical variables (positions and angular velocities) as state variables and, so, difficulties may appear when trying to observe and control the system. Therefore, the aim of the present work is to propose a new approach to model flexible structures, applied to the case of one link flexible robot manipulator. We start showing the theoret ical formulation to identify the vibration modes. After this, we introduce the new formulation, in an algorithm form, that permits to find all matrices of the dynamical system. This new method is based on the lumped mass formalism (concentrated mass), but the model parameters are found through a minimization of the error between the analytical frequency modes and the ones of the dynamic model. The state variables of the new model are the physical angular positions and velocities, having the same frequency modes previously estimated by the theory of material dynamic flexibility. It is also possible to equate the frequencies modes of the model to the experimental ones, if we have the last ones. Obviously, a realistic dynamical model with physical and measured variables is of fundamental importance for the control law development and so, this new model approach is a significant contribution to improve the performance for solving control problems.

A
Trust-Region-Approach for Solving a Parameter Estimation Problem

from the Biotechnology Area

Juan Ignacio Ardenghi

arde nghi@criba.edu.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

María Cristina Maciel

immaciel@criba.edu.ar

Adriana B. Verdiell

averdiel@criba.edu.ar

from the Biotechnology Area

Juan Ignacio Ardenghi

arde nghi@criba.edu.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

María Cristina Maciel

immaciel@criba.edu.ar

Adriana B. Verdiell

averdiel@criba.edu.ar

Abstract: Growth kinetics of microorganisms processes involves a parameter estimation problem, which usually is solved by using simulation techniques. In this contribution a different approach is presented. It is based on a trust-region algorithm for nonlinear least square problems with bounds constraints. One important aspect of the algorithm is that both second order information and the Jacobian matrix can be approximated. This feature makes the algorithm suitable to solve a parameter estimation problem taken from the area of biotechnology, because the functional is only known in some points that arise from the resolution of ordinary differential or differential algebraic systems. In this work, the differential algebraic systems have been solved using the well known code, DASSL developed by Petzold. Numerical results are presented.

Accurate
Numerical Solution of Coupled Time Dependent

Parabolic Initial Value Problems

Lucas Jódar

ljodar@mat.upv.es

Instituto de Matemática Multidisciplinar

Universidad Politécnica de Valencia, Spain

Jorge Iván Castaño

icastano@eafit.edu.co

Jose Albeiro Sánchez

josanche@eafit.edu.co

Edgar Medina

Parabolic Initial Value Problems

Lucas Jódar

ljodar@mat.upv.es

Instituto de Matemática Multidisciplinar

Universidad Politécnica de Valencia, Spain

Jorge Iván Castaño

icastano@eafit.edu.co

Jose Albeiro Sánchez

josanche@eafit.edu.co

Edgar Medina

Abstract: This paper deals with the construction of analytic-numerical solution of initial value problems for coupled time dependent parabolic systems. Firstly an integral expression for the solution is given using Fourier transforms. Then by truncation of the integral expression of the solution and numerical integration, a numerical solution is constructed with the requi red accuracy at any point.

Acoustic
Detector Systems

Serrano Eduardo

eduardo.serrano@unsam.edu.ar

SurfaceMail: Escuela de Ciencia y Tecnología

Universidad Nacional de General San Martín

(1650) Villa Ballester - Provincia de Bs As

Serrano Eduardo

eduardo.serrano@unsam.edu.ar

SurfaceMail: Escuela de Ciencia y Tecnología

Universidad Nacional de General San Martín

(1650) Villa Ballester - Provincia de Bs As

Abstract: We consider N acoustic detectors on a planar surface. Given an instantaneous event at some point in the surface the sound propagates with fixed, known velocity. We measure the arrival times at each one of the sensors and we want to determine the coordinates of the event. We discuss the design of the detector array with regards to the number of elements and geometrical distribution, so that the problem is well conditioned. We also analyze the stability of the numerical method used to solve the problem.

An
Adaptive Collocation Meshless Method

Based on Local Optimal Point Interpolation

Carlos Zuppa

zuppa@unsl.edu.ar

D. de Matemáticas. UNSL

Chcabuco y Pedernera.

5700. San Luis

Argentina

Alberto Cardona

José A. Risso

Based on Local Optimal Point Interpolation

Carlos Zuppa

zuppa@unsl.edu.ar

D. de Matemáticas. UNSL

Chcabuco y Pedernera.

5700. San Luis

Argentina

Alberto Cardona

José A. Risso

Abstract: This paper deals with the use of the Local Point Interpolation Formula (LOPI) for solving partial differential equations (PDEs) with a collocation method. An adaptive scheme is tested in a series of problems involving singularities.

An
Application of Genetic Algorithms to Steam Consumption Optimization

Adrián L. E. Will

adri_will@yahoo.com

SurfaceMail: Departamento de Matemática

Facultad de Ciencias Exactas y Tecnología

Universidad Nacional de Tucumán

Avenida Independencia 1800

CP 4000 - Tucumán

Amber O. López

amberol@yahoo.com

Daniel F. Anderlini

anderlini@arnet.com.ar

Adrián L. E. Will

adri_will@yahoo.com

SurfaceMail: Departamento de Matemática

Facultad de Ciencias Exactas y Tecnología

Universidad Nacional de Tucumán

Avenida Independencia 1800

CP 4000 - Tucumán

Amber O. López

amberol@yahoo.com

Daniel F. Anderlini

anderlini@arnet.com.ar

Abstract: Steam consumption in the sugar
industry comes in part from a discontinous process, and exhibits a really
bad behavior consisting of peaks and valleys that increase the cost of
the production process. The problem is to optimize the process in order
to smooth the function and make it as flat as possible. Unfortunately
this vapor consumption function is not linear, differentiable, or even
convex, so we used Genetic Algorithms to develop a program that simulates
the process and adjusts the variables involved to smooth the peaks and
valleys. The first results obtained from this program using real data
from a sugar factory are encouraging, and they are currently being analyzed.
The program was developed in Matlab, and a GUI was developed in Visual
Basic to make a friendlier interaction for people from the industry.

An
Efficient and Robust Algorithm for 2D Stratified Fluid Flow

German Larrazabal

glarraza@uc.edu.ve

Universidad de Carabobo

Facultad de Ciencias y Tecnologia (FACYT)

Departamento de Computacion

Valencia, Estado Carabobo, Venezuela

Carlos Torres

ctorres@sciences.sdsu.edu

Jose Castillo

castillo@myth.sdsu.edu

German Larrazabal

glarraza@uc.edu.ve

Universidad de Carabobo

Facultad de Ciencias y Tecnologia (FACYT)

Departamento de Computacion

Valencia, Estado Carabobo, Venezuela

Carlos Torres

ctorres@sciences.sdsu.edu

Jose Castillo

castillo@myth.sdsu.edu

Abstract: An efficient and robust algorithm for the numerical simulation of 2D stratified flow past an object is presented. In this study we use the GMRES method preconditionated with an ILUT to solve the Poisson equation for the pressure. This algorithm reaches high accuracy in few iterations and permits to study strong stratified fluids for a wide range of Reynolds numbers. The algorithm has been tested with a simple problem consisting of a descending infinite flat plate in a stratified diffusive fluid. Finally, the numerical and analytical solutions are compared.

Analysis
and Simulation for a System of Chemical Reaction Equations with a Vortex
Formulation

Ulices Zavaleta Calderón

ulices@math.unitru.edu.pe

Universidad Nacional de Trujillo,

Departamento de Matemáticas - FCFYM

Álvaro L de Bortoli

dbortoli@mat.ufrgs.br

Mark Thompson

thompson@mat.ufrgs.br

Ulices Zavaleta Calderón

ulices@math.unitru.edu.pe

Universidad Nacional de Trujillo,

Departamento de Matemáticas - FCFYM

Álvaro L de Bortoli

dbortoli@mat.ufrgs.br

Mark Thompson

thompson@mat.ufrgs.br

Abstract: This work presents results for the simulation of two dimensional molecular mixing and chemical reaction processes using a vortex formulation. The particular model studied here is the single-step, irreversible, exothermic Arrhenius type reaction c_A + c_B --> c_P, for an incompressible fluid in a box under Neumann boundary conditions. A second order accurate spatial finite difference scheme is used with a second order accurate Runge-Kutta method for the time step. The behavior of the concentrations c_A, c_B, the temperature, the reaction rate, and product concentration, c_P, is obtained over a wide range of Reynolds and Damköhler numbers.

Applications
of NURBS Surface Interrogation to the Automotive Industry

Flabio Gutierrez Segura

flabio@terra.com

National University of Piura - PERU

Andres Iglesias, Akemi Galvez, Jaime Puig Pey

{iglesias, galveza, puigpeyj}@unican.es

Cantabria University - SPAIN

Flabio Gutierrez Segura

flabio@terra.com

National University of Piura - PERU

Andres Iglesias, Akemi Galvez, Jaime Puig Pey

{iglesias, galveza, puigpeyj}@unican.es

Cantabria University - SPAIN

Abstract: An important topic in CAGD (Computer-Aided Geometric Design) is the interrogation of the designed geometric entities (curves, surfaces). In this paper we describe some methods of interrogation of the NURBS (Non-Uniform Rational B-splines) surfaces, by far, the most commonly used surfaces in the automotive industry. These methods have been successfully applied by the authors to evaluate the 'quality' of the different parts of a car body.

Asymptotic
Behavior of a Heat Conduction Problem

with a Perfect Contact Boundary Condition

Andres Barrea

abarrea@mate.uncor.edu

Cristina Turner

turner@mate.uncor.edu

with a Perfect Contact Boundary Condition

Andres Barrea

abarrea@mate.uncor.edu

Cristina Turner

turner@mate.uncor.edu

Abstract: In this paper, we consider a slab represented by the interval 0<x<1, at the initial temperature u(x,0)=M>0 having a positive constant heat flux q on the left face and a contact perfect condition, ux(1,t)+\gamma ut(1,t)=0 on the right face x=1. We analize asymptotic behavior of the problem when \gamma tends to infinity. Numerical calculations are also given presented.

Bounds
for the Zeros of Polynomials: A Computational Comparison

Luiz C. G. Lopes

lopes@math.uma.pt

Department of Mathematics

University of Madeira

Penteada Campus

9000-390 Funchal, Madeira, Portugal

Luiz C. G. Lopes

lopes@math.uma.pt

Department of Mathematics

University of Madeira

Penteada Campus

9000-390 Funchal, Madeira, Portugal

Abstract: In solving polynomial equations it is usually desirable or necessary to find a circular (or ring-shaped) region centered at the origin of the complex plane containing all the zeros of a given polynomial. It is interesting to note here that often may be more convenient to take for initial region the smallest possible square which contains that circle. There are many results concerning the determination of bounds for the absolute values of the zeros of a polynomial with real or complex coefficients, from the classical ones, such as those due to Cauchy and Gerschgorin, up to more recent contributions. However, probably because of the difficulty or impossibility in comparing directly various of these results, relatively little has been done in order to get an evaluation of the practical applicability of these methods for the location of zeros of polynomials and the quality of their estimates. Moreover, examples in the literature may give a distorted picture of the efficacy of these procedures. In this work, a computational analysis of several methods for calculating upper and lower bounds for the moduli of the zeros of a polynomial was performed, in order to determine which are the best ones in terms of sharpness of the supplied bounds and computational efficiency. More than two dozen of bounds were implemented in Fortran 90, including results by Cauchy, Gauss, Kuniyeda, Carmichael, Williams, Walsh, Dieudonné, Gerschgorin, Marden, Schafarewitsch, Joyal, Datt, Sluis, Kojima, Westerfield, Kieseweter, Guggenheimer and Jain. All these procedures were tested with a set of more than 250 polynomials. Four distinct evaluation criteria were used to compare the relative merits of the different bounds.

Consolidation
on Saturated Clays

with Finite Element Method

Daniel Vazquez Borges

dvborges@yahoo.com.mx

Universidad Autónoma de Querétaro, Mexico

Facultad de Ingeniería

División de Estudios de Posgrado

with Finite Element Method

Daniel Vazquez Borges

dvborges@yahoo.com.mx

Universidad Autónoma de Querétaro, Mexico

Facultad de Ingeniería

División de Estudios de Posgrado

Abstract: This work presents the proccess to find the magnitude of unidimensional consolidation on a saturated clay. The methods to find this parameter on a soil were developed at the middle of last century, and they need to make many manual operations and graphics to get an approximate value of the consolidation. My work developes a method from physic model, obtained from the basic concepts of a continous model; with variational model is possible to make the analysis and it is from where can be applied th Finite Element schemmes.

The principal purpose of my work is to have a tool able to predict the value of consolidation on a saturated clay, using modern techniques of approximation methods, to make more easy and fast the proccess. On a soil laboratory, the time to get consolidation value is about 3 weeks, with a good tool, this time can be reduced to 3 ó 4 days, because the parameters to find for work with a numericall model are easiers and fasters to get.

For building and investigation the consolidation is a very important parameter, and that’s the reason to I’ve decided to do this work. It is also important the fact of we have the technology and tool to make a better Engineering.

Constructive
Solution of Strongly Coupled Hyperbolic Mixed Problems

Lucas Jódar Sánchez

ljodar@mat.upv.es

Instituto de Matemática Multidisciplinar

Universidad Politécnica de Valencia

Valencia (SPAIN)

E.Navarro

entorres@mat.upv.es

M.C.Casabán

macabar@mat.upv.es

A.Posso

possoa@andromeda.utp.edu.co

Lucas Jódar Sánchez

ljodar@mat.upv.es

Instituto de Matemática Multidisciplinar

Universidad Politécnica de Valencia

Valencia (SPAIN)

E.Navarro

entorres@mat.upv.es

M.C.Casabán

macabar@mat.upv.es

A.Posso

possoa@andromeda.utp.edu.co

Abstract: This paper deals with the construction
of exact series solutions of mixed hyperbolic partial differential systems
with matrix coupling in both the partial differential equation and in the
boundary value conditions. Algebraic methods are used to study the underlying
vector Sturm-Liouville problem then a matrix separation of variables method
is used to construct a series solution.

Decomposition
of Forced Responses for Damped Vibrating Systems

Julio R. Claeyssen

julio@mat.ufrgs.br

Rosemaira Dalcin Copetti

rmaira@oslo.ccne.ufsm.br

Inês Ferreira Moraes

inesferr@ig.com.br

Julio R. Claeyssen

julio@mat.ufrgs.br

Rosemaira Dalcin Copetti

rmaira@oslo.ccne.ufsm.br

Inês Ferreira Moraes

inesferr@ig.com.br

Abstract: This work uses a direct time domain formulation for damped systems in terms of the impulse response that allows to decompose the forced response into free and permanent responses. The spatial domain can be discrete or continuous. When computing the forced response through convolution, a free response term might arise. With the dynamical basis, generated by the impulse response, it is possible to determine this free contribution in terms of the initia l values of the permanent response. This process can be considered as a feedback into the system. Numerical simulations are considered with damped matrix systems and with a fixed-free Euler-Bernoulli beam subject to material and viscous damping. The mentioned feedback effects are illustrated with oscillating and piece-wise inputs.

Dependence
of the stability of Semi-Implicit Atmospheric Models

on Reference Temperature Profile

Andrei Bourchtein

aburstein@uol.com.br

Maxim Naumov

mnaoumo1@purdue.edu

on Reference Temperature Profile

Andrei Bourchtein

aburstein@uol.com.br

Maxim Naumov

mnaoumo1@purdue.edu

Abstract: The linear stability of three-time-level finite-difference semi-implicit schemes for hydrostatic atmospheric models with viscosity terms is studied. The principal objective is the investigation of a stability dependence on choice of reference temperature profile. A characteristic equation for the scheme amplification factor is derived in the case of a simplified baroclinic atmospheric numerical model, keeping the implicit approximation for the basic temperature profile and explicit approximation for its deviations. Analytical solutions for the amplification factor are found in some special cases and computational experiments are performed for different values of model parameters, such as vertical discretization, temperature profile (basic and actual), and time step. The influence of the viscosity terms on scheme stability is also studied. The performed analysis confirms two principal results obtained numerically in other models: instability generated by inappropriate determination of temperature profile is absolute and computational stability can be recovered if the basic reference profile is chosen to be warmer than the actual one.

Discrete
Grid Generation : A Robust Approach

Pablo Barrera

pablo@athena.fciencias.unam.mx

FOVISSTE A. P. R. Mexico D.F.

MEXICO C.P. 04800

Guilmer F. Gonzalez Flores

gfgf@hp.fciencias.unam.mx

Francisco J.Dominguez-Mota

dmota@zeus.ccu.umich.mx

Pablo Barrera

pablo@athena.fciencias.unam.mx

FOVISSTE A. P. R. Mexico D.F.

MEXICO C.P. 04800

Guilmer F. Gonzalez Flores

gfgf@hp.fciencias.unam.mx

Francisco J.Dominguez-Mota

dmota@zeus.ccu.umich.mx

Abstract: Discrete grid generation on plane regions has been our interest since the late 80's. Our group, UNAMALLA, has developed methods that are effective even on quite irregular regions. Although the techniques have a sound theoretical basis, when we were trying to apply these ideas to orthogonal grid generation we found that something was missing. We think that we have now developed robust automatic grid generators, smooth or orthogonal, that are very efficient and we will pr esent their theoretical formulation and implementation within the grid package UNAMALLA.

Electrocardiogram
Classification by Means of a Multifractal Formalism

Based in the Wavelet Transform Modulus Maxima

Lisandro Javier Fermín

lfermin@euler.ciens.ucv.ve

Departamento de Matemática

Escuela de Matemática

Facultad de Ciencias

Universidad Central de Venezuela

Wilfredo Urbina

wurbina@euler.ciens.ucv.ve

Abstract: The Multifractal Formalism is
a tool to characterize the fractal nature of signals. This method was
established to quantify statistical properties of singular signals behaviour
in function of the scale. In this work we explore the potential of the
Multifractal Formalism, based in the Wavelet Transform Modulus Maxima
method, to the characterization and classification of electrocardiograms
corresponding to patients with diverse cardiopatic diseases. The main
goal is to define parameters in the context of the multifractal algorithm
that allow to quantify the intermittency in the electrocardiograms.
From those parameters the multifractal plane is defined and it is shown
that a useful classification tool is obtained by the projection of the
electrocardiograms on the plane. This tool allows to distinguish patients
with different diseases.

Estimation
of 2D Parametric Motion Models from Image Sequences

Sebastian Horacio Guevara

sguevara@fi.uba.ar

Bruno Cernuschi Frias

bcf@ieee.org

Sebastian Horacio Guevara

sguevara@fi.uba.ar

Bruno Cernuschi Frias

bcf@ieee.org

Abstract: Motion Analysis and Estimation is a very important application of image processing to the study of physical phenomena. This paper describes a probabilistic and iterative Bayes based algorithm for the estimation of an affine motion model from a sequence of two images. Horn-Shunck's equation is modified by adding random terms to compensate the inherent uncertainties derived from the image derivative calculations. Advantages and drawbacks of the algorithm are discussed and future refinements are proposed. Simulations with both synthetic and real images are shown to support the technique described.

Finite
Element Methods for Water Magnetic Treatment

Jorge Luis Mirez Tarrillo

jorgemirez2002@yahoo.es

Facultad de Ingenieria Mecanica Electrica

Universidad Nacional Pedro Ruiz Gallo

Lambayeque, Peru

Jose Joaquin Trista Moncada

trista@jjtm.uo.edu.cu

Abstract: The application of the Finite Elements Method (FEM) to Water Magnetic Treatment (WMT) process physics is used in the improvement of the transmission of heat for the elimination inlays in hardwares heat transfer whose operating liquid is the water, also that it reduces the use considerably chemical products that contaminate the environment. Initially we will detail the theory necessary physical-math to validate the use the MEF, then is described the use of the software "Finite Element Method Magnetics 3.1(FEMM 3.1)", with which the necessary magnetic densities are simulated for the construction of hardwares that TMA carries out. Finally, we will formulate some summations to the application of the MEF to the TMA with the purpose to motivate the theoretical investigation this topic.

Formation
Process of Free Biological Base Pairs Studied by a Monte Carlo Method,
Based on Geometrical and Energetic Probabilistic Principles

Sani de Carvalho Rutz da Silva

sani@mat.ufrgs.br

UFRGS - Graduate Program in Applied Mathematics

Bento Goncalves, 9500

90501-900, Porto Alegre - RS, Brazil

Dimitrios Samios

dsamios@iq.ufrgs.br

Álvaro Luiz de Bortoli

dbortoli@mat.ufrgs.br

Sani de Carvalho Rutz da Silva

sani@mat.ufrgs.br

UFRGS - Graduate Program in Applied Mathematics

Bento Goncalves, 9500

90501-900, Porto Alegre - RS, Brazil

Dimitrios Samios

dsamios@iq.ufrgs.br

Álvaro Luiz de Bortoli

dbortoli@mat.ufrgs.br

Abstract: In this work we analyze a geometrical model of base pairing of DNA bases Adenine, Thymine, Guanine, and Cytosine, through a probabilistic method (Monte Carlo) using homogeneous transformation matrices to define each base; distances among them are evaluated using metrics and the molecules are stochastically moved in a two-dimensional space. The atomic coordinates of all bases and the homogeneous transformation matrices are stored in a structural graph which can be visualized using Rasmol software. The goal is to investigate, among all possible hydrogen bond (H-bonds) patterns, the possibility of each pair formation, based on geometrical and energetic principles. For a given base pair (A-T), a list of all possible H-bonding L=L(A,T) is considered. This list contains all set types that involve two or three H-bonds defined in the literature, and also all that involve only one H-bond. The possibilities of pair formation is first based on the analysis of the geometric probability (distance and orientation of molecules), followed by the analysis of the probability related to the energetic principles. The energetic probability factor P is proportional to the Boltzmann factor, e, where P is the binding energy evaluated using SPARTAN, for each base pair. The decision is based on the following procedure: a) Obtain a random number R in [0,1]; b) If the factor probability P < R, the algorithm will accept the new configuration, else it will be rejected. Numerical results taking into account the geometric probability principles are encouraging and show us that formation at heteropairs counts with a higher probability than the homopairs ones. Such behavior wa s found to follow results in the literature for the case of structures and energy of hydrogen-bonded DNA base pairs. Such analysis can help us understand some commonly occurring mutations and also this kind of biological phenomena.

Game
Theory in Resolution of Problems of Optimization of Crop Residues and Available
Energy in the Plantation of Sugar-Cane

Helenice de Oliveira Florentino

helenice@ibb.unesp.br

Depto de Bioestatística, IB, Unesp,

Rubião Júnior S/N

Botucatu SP

CEP: 18618-000

Brasil

Maria Márcia Pereira Satori

msartori@ibb.unesp.br

Helenice de Oliveira Florentino

helenice@ibb.unesp.br

Depto de Bioestatística, IB, Unesp,

Rubião Júnior S/N

Botucatu SP

CEP: 18618-000

Brasil

Maria Márcia Pereira Satori

msartori@ibb.unesp.br

Abstract: Currently, researchers have suggest for plantation the varieties of sugar-cane that present a reduced amount of crop residue and that demonstrate a good production and adaptation to the soil. Such conduct is to decrease problems of order environmental, agronomic and economic in this culture. On the other hand, with the current crisis of energy, the use of this residual biomassa has been proposed for generation of energy for use in system of production of the mill. The present work proposes the formulation of an optimization problem, that determines the type and the amount of the variety to be planted so that it minimizes the crop residue and maximize the production of energy generated from that residue, using as restrictions the available area for the plantation and the demand of the mill. This problem presents two objective conflicting, that can be resolved using methodologies of theory of games. Such techniques presented satisfactory results for this approach.

G2-Cubic
Contours

Francisco Tovar

ftovar@euler.ciens.ucv.ve

SurfaceMail: Universidad Central de Venezuela

Facultad de Ciencias

Centro de Computacion Grafica y

Geometria Aplicada.

Figueroa Giovanni

giofigue@hotmail.com

Abstract: Let b0, b2 , …, b2n be the
vertex sequence of a convex polygon and through each b2j take a line
L2j which does not cut the polygon, such that any two consecutive lines
meet at b2j+1 in the halfplane external to the polygon. For any choice
d2j+1 of internal point in each point triangle b2j b2j+1 b2j+2 we construct
G2-cubic algebraic splines which interpolate the vertices b0, b2, …,
b2n and the interior points d2j+1. The splines are tangent to L2j at
b2j and are contained in the union of the triangles b2j b2j+1 b2j+2.
For any j = 0, 1, …, n, we show how the choice of d2j+1 limits
the range of variation of the curvatures at the vertices b2j and b2j+2.
We study the conditions for the curvatures at the specific vertices
to vary arbitrarily, hence allowing for the construction of G2-interpolating
cubic splines which are as flat or as sharp, as desired at these vertices.A
generalization for non convex data set sequences is given breaking the
polygon into convex subsets.

Haar Wavelets With Vanishing Moments

Defined Over a Tetrahedrical Grid

Liliana B. Boscardín

lboscar@uns.edu.ar

Depto.de Matemática

Universidad Nacional del Sur

Liliana R. Castro

lcastro@criba.edu.ar

Silvia M. Castro

uscastro@criba.edu.ar

Abstract: It is well known that multiresolution analysis (MRA) provides a mathematical tool that allows a hierarchical decomposition of functions. Due to this property, it has been widely used to solve different problems in co mputer graphics, since most algorithms involving MRA are of linear order, an important issue due to the high amount of numerical computation and speed involved in this kind of applications.

When it is necessary to have a hierarchical decomposition
of a function, the basis functions cannot always be derived from a single
function. This has been done traditionally, where wavelets are introduced
as translations and dilations of the unique function, its mother wavelet,
giving the so called first generation wavelets. As this kind of wavelets cannot
be defined on arbitrary topological domains other wavelets, known as second
generation wavelets, have been defined using a more general theory but still
enjoying all the powerful

properties of first generation wavelets.

Within this context, Lounsbery built wavelets on arbitrary topological domains on R2, and using the idea of refinability he extended the MRA for functions defined on surfaces. This approach was a posteriori generalized by Sweldens, who recognized that the lifting scheme he proposed was a generalization of Lounsbery's method. Schröeder and Sweldens continued their work and proved that subdivision and lifting provided an efficient methodology for custom-design construction of wavelets. A posteriori, Nielson et al. also defined wavelets over a sphere that are biorthogonal but have an advantage over those defined by Schröeder and Sweldens: on planar surfaces of uniform area they converge to orthogonal wavelets. Both constructions are defined over triangular domains and use the subdivision as a technique for generating surfaces and for building nested spaces such as those required in MRA. So, beginning with a triangular net and using the subdivision as a construction tool, it is possible to generate wavelets on arbitrary topological bidimensional domains. We are interested on modeling volumes, what means that we have to consider the e xtension of the 2D methods to 3D.

One alternative for modeling volumes is to represent
them by simpler volume constructs, such as tetrahedra, analog to triangles
for surfaces. Maubach showed a refinement method of bisection type, which
is applicable to grids of n-dimensional simplices, independent of the dimension
n. Using this subdivision method it is possible to construct wavelets on arbitrary
topological domains. For doing this, it is necessary to define wavelets on
a tetrahedron and the collection of tetrahedra that are obtained by subdividing
the given

tetrahedron. In this work we recall the Haar wavelets defined on the tetrahedra
that form an inconditional basis for Lp(T,s,µ),p>1, whereµ
is the Lebesgue measure and s the s-algebra of all tetrahedra generated by
the chosen subdivision method. We also present an example of the representation
of a density function defined on a tetrahedon using this basis. As these wavelets
are not continuous, we propose to apply the lifting scheme in order to obtain
wavelets with more vanishing moments.

Identification Structures Using Rational Wavelets: Examples of Application

Liliana R. Castro

lcastro@criba.edu.ar

Depto. de Matemática

Universidad Nacional del Sur

Argentina

Osvaldo E. Agamennoni

ieagamen@criba.edu.ar

Carlos E. D'Attellis

ceda@favaloro.edu.ar

Abstract: Wavelets have been proved to be a power ful mathematical tool for many different applications. Also, the construction of different kind of wavelet frames has been a source of work for mathematicians and engineers. One of these constructions, called rational wavelets and the wavelets system transfer functions derived from them, has been used in identification of linear dynamic systems and also as activation functions of neural networks for the identification of nonlinear dynamic systems. In this context, we have proposed to use them on a Wiener-like approximation scheme using rational wavelets for the linear dynamical structure. For approximating the nonlinear static part we use a feedforward Neural Network (abbreviated as NN), and a basis of high level canonical piecewise linear functions (HLCPWL, in short), that can or can not be an orthonormal basis. This class of structures allow approximating nonlinear dynamic systems with fading memory and has two main advantages: time location of the dynam ical components of the system is possible and so is the inclusion of a priori knowledge of those components in the model.

As the proposed model depends only on the input-output values and the wavelets are selected taking into account the linear dynamics of the system, it can be viewed as a black box model with semi-physical regressors. In this paper we present three different examples that show the potential applications of this methodology to the identification of nonlinear dynamic systems with fading memory.

Isothermal Fluid Flow in Fractal Domains

Haroldo Fraga de Campos Velho

haroldo@lac.inpe.br

SurfaceMail: LAC-INPE

P.O. Box 515

Sao Jose dos Campos (SP)

Brasil

Erwin Doescher

erwind@bol.com.br

Fernando Manuel Ramos

fernando@lac.inpe.br

Abstract: A study of isothermal flow in a fractal domain is presented. The domain is a cavity where the boundaries are pre-fractals of the square Koch curve. Simulations are carried out considering pre-fractals of order 0 (square-cavity), 1 and 2. The fluid flow equations are solved by the finite volume method, using a structured staggered grid. Al l simulations are performed considering an isothermal system.

Local Refinement
Techniques in Global Finite-Difference Weather Models

Claudia Ines Garcia

claudiag@ime.usp.br

Instituto de Matematica e Estatistica - USP

Departamento de Matematica Aplicada

R. do Matao, 1010

05508-090 S. Paulo, Brasil

Claudia Ines Garcia

claudiag@ime.usp.br

Instituto de Matematica e Estatistica - USP

Departamento de Matematica Aplicada

R. do Matao, 1010

05508-090 S. Paulo, Brasil

Abstract: We describe a global semi-Lagrangian semi-implicit shallow water model which includes local refinement techniques. We present results showing that this is a very interesting alternative for obtaining high resolution in an area of interest in an efficient way, without having to deal with artificial boundaries as in local models. We will also discuss our ongoing work towards the extention of this approach to a global finite-difference model, based on the primitive equations. We give details about the semi-implicit discretization, which includes the use of non-linear multigrid methods in the solution of elliptic equations.

Lower and
Upper Bounds for Eigenvalues by Finite Element Methods

María Gabriela Armentano

garmenta@dm.uba.ar

Departamento de Matemática

Facultad de Ciencias Exactas y Naturales

Universidad de Buenos Aires, Argentina

Ricardo G. Durán

rduran@dm.uba.ar

María Gabriela Armentano

garmenta@dm.uba.ar

Departamento de Matemática

Facultad de Ciencias Exactas y Naturales

Universidad de Buenos Aires, Argentina

Ricardo G. Durán

rduran@dm.uba.ar

Abstract: The goal is to obtain lower and upper bounds for the eigenvalues of second order elliptic operators. It is known that standard finite element approximations provide upper bounds for eigenvalues. For singular eigenfunctions we prove that, if the mesh size is small enough, a better upper bound can be obtained using the mass-lumping approach and lower bounds can be obtained by a non-conforming finite element method. On the other hand, when the eigenfunctions are regular, several examples suggest that the eigenvalue computed with mass-lumping is below the exact one if the mesh is not too coarse.

Method
of Straight Lines for an Unidimensional Bingham Problem

Germán Ariel Torres

torres@mate.uncor.edu

Cristina Turner

turner@mate.uncor.edu

Germán Ariel Torres

torres@mate.uncor.edu

Cristina Turner

turner@mate.uncor.edu

Abstract: In this work a method of straight lines for an unidimensional Bingham problem is developed. A Bingham fluid has viscosity properties that produce a separation into two regions, a rigid zone and a viscous zone. A method of straight lines is proposed, where we discretize the time variable. The following is proved: well definition of the method; the behaviour of the numerical solution is as that of the theoretical solution; properties about signs of the solution and their derivatives; a monotone property and a convergence theorem. Numerical experiments are also presented.

Álvaro Luiz de Bortoli

dbortoli@mat.ufrgs.br

UFRGS - Department of Pure and Applied Mathematics

Bento Gonçalves, 9500

90501-900, Porto Alegre - RS, Brazil

Abstract: The aim of this work is to study the numerical simulation of mixing and reaction flows inside square cavities. The flow field underlying the diffusion and chemical reaction processes that are analysed, satisfies the two-dimensional time-dependent Navier-Stokes equations when considering an overall, single-step, binary, irreversible reaction between two species A and B to yield P. The overall reaction is taken to be of first order which respect to each of the reactants, and the specific reaction rate constant is controlled by time-dependent Arrhenius kinetics. Density and all transport property variations are considered to be sufficiently small. Numerical results are obtained by solving the governing equations by the finite differences explicit Runge-Kutta three-stage scheme for second order time as well as space approximations. Tests are realized for Schmidt and Prandtl numbers of order 1, and Zel'dovich and heat release parameters of order 10, which are typical gaseous hydrocarbon chemistry values. Reynolds and Damköhler parameters are varied up to 5000 and 300, respectively. The model shows ability to produce accurate mixing and reaction processes, including nonlinear phenomena, such as the local extinction for large Zel'dovich numbers. This model builds upon earlier ones, which were addressed to the mixing and reaction processes, but not to the flow field itself.

Models for Intelligent Transportations Systems

Jose A. Rodriguez Melquiades

University National of Trujillo-PERU

Department Mathematic-School Informatic

jarm@math.unitru.edu.pe

jarm7@latinmail.com

Abstract: In the current scenario, characterized by worldwide economic crisis, solutions that minimize costs assume a fundamental role in the delivering services context. In the big cities, the continuous population growth requires urgency in defining more efficient solutions for goods and individual transportation services. This continuous growth results in many problems related to the traffic and services offered to the community, turning them precarious and unsatisfactory. In this context, Intelligent Transportations Systems have become one of the main tools for resolution of transportation problems, providing efficient solutions. Such systems incorporate Geographic Information Systems and Operations Research approaches during their decision process. The goal of this work is explore the potential of this kind of system through the conception of a generic and flexible environment. Solutions approach and models are analyzed for shortest path, routing and distributions problems.

Multispectral Reconstruction of Bioluminescence Term in Natural Waters

Haroldo Fraga de Campos Velho

haroldo@lac.inpe.br

SurfaceMail: LAC-INPE

P.O. Box 515

Sao Jose dos Campos (SP)

Brasil

Ezzat Salim Chalhoub

ezzat@lac.inpe.br

Abstract: An inverse analysis for the multispectral estimation of internal sources in natural waters, from the knowledge of the exit radiation at the water surface, is presented. The analysis involves a forward model that utilizes an analytical discrete-ordinates method for solving the radiative transfer equation, and an inverse model which contains an algorithm for least-squares estimation that is iteratively solved for retrieving the desired property by using the Levenberg-Marquardt optimizer. The experimental data are simulated with synthetic data corrupted with noise. The results show that the internal sources can be recovered with good accuracy.

New Algorithmic
Developments in CPTEC's Global Spectral Model

Saulo R. M. Barros

saulo@ime.usp.br

SurfaceMail: Instituto de Matematica e Estatistica - USP

R. do Matao, 1010

05508-090 S. Paulo

Brasil

Norms Associated to the Quadrature Formula in the Analysis of the Approximations in Transport Theory

Rubén Panta Pazos

rpp@pucrs.br

SurfaceMail: Av Ipiranga, 6681, Predio 15, PUCRS

CEP 90619-900, Porto Alegre - RS - Brazil

Marco Túllio de Vilhena

vilhena@mat.ufrgs.br

Saulo R. M. Barros

saulo@ime.usp.br

SurfaceMail: Instituto de Matematica e Estatistica - USP

R. do Matao, 1010

05508-090 S. Paulo

Brasil

Abstract: We will give a brief overview of the ongoing activities towards the reformulation of CPTEC's global spectral model. These reformulations include a different treatment of the sytem of equations, more adequated to the incorporation of a semi-Lagrangian scheme. The new model also will include the possibility of using a reduced and a linear grid. The model is being completely rewritten in Fortran90, and it has been designed to accomodate efficient parallelizations, in shared or distributed memory environments.

Norms Associated to the Quadrature Formula in the Analysis of the Approximations in Transport Theory

Rubén Panta Pazos

rpp@pucrs.br

SurfaceMail: Av Ipiranga, 6681, Predio 15, PUCRS

CEP 90619-900, Porto Alegre - RS - Brazil

Marco Túllio de Vilhena

vilhena@mat.ufrgs.br

Abstract: In this work we consider approximations obtained in transport problems when we employ quadrature schemes, such as in discrete ordinates approximation, to solve the linear Boltzmann equation [2]. We define a norm associated to the quadrature formula in order to analyze the error bounds in some problems, i.e., one-dimensional steady-state transport problem for the slab geometry, one-dimensional time-dependent transport problem, two-dimensional steady-state transport problem (spectral [3] and nodal [4] methods). Keller [1] have introduced for the first time this procedure to establish the convergence of the 1D steady-state SN approximations. The relation between the error in the approximated flux and the truncation error in the quadrature formula is the first step in order to obtain the convergence of a class of approximations. Then, if the chosen directions are roots of p(m), where p is an element of a system of orthogonal polynomials with respect to the positive weight w on the velocity space, we use the results of the interpolation polynomial f associated with p . The functional framework gives a unified context for approximations of different quadratures schemes. We give some results for the above mentioned methods.

[1] Keller, H., Approximate Solutions of Transport
Problems, II. Convergence and Applications of the Discrete Ordinate Method,
J.SIAM, vol.8, 1 (1960).

[2] Mokhtar-Kharroubi M., Mathematical Topics in Neutron
Transport Theory, World Scientific, (1997).

[3] Panta Pazos, R. and Vilhena, M.T., Spectral Approximations
for some Linear Transport Problems, Proceedings of ICONE 8, 8 th International
Conference on Nuclear Engineering, 8636, Baltimore, MD, USA (2000)

[4] Panta Pazos, R., Vilhena, M.T. and Hauser, E.B.,
Solution and Study of the Two-dimensional Nodal Neutron Transport Equation,
Proceedings of ICONE 10, 10 th International Conference on Nuclear Engineering,
22611, Arlington, VA, USA (2002)

Numerical
Method for Solving Axisymmetric

Non-newtonian Fre Surface Fluid Flow Problems

Jose Alberto Cuminato

Email1: jacumina@icmc.sc.usp.br

SurfaceMail: Instituto de Ciencias Matematicas e de Computacao

Universidade de Sao Paulo - Campus de Sao Carlos

Av. do Trabalhador Saocarlense,400

Caixa Postal 668

13560-970 Sao Carlos - SP

Brazil

Valdemir Garcia Ferreira

pvgf@icmc.sc usp.br

Norberto Mangiavacchi

norberto@icmc.sc.usp.br

Non-newtonian Fre Surface Fluid Flow Problems

Jose Alberto Cuminato

Email1: jacumina@icmc.sc.usp.br

SurfaceMail: Instituto de Ciencias Matematicas e de Computacao

Universidade de Sao Paulo - Campus de Sao Carlos

Av. do Trabalhador Saocarlense,400

Caixa Postal 668

13560-970 Sao Carlos - SP

Brazil

Valdemir Garcia Ferreira

pvgf@icmc.sc usp.br

Norberto Mangiavacchi

norberto@icmc.sc.usp.br

Abstract: A finite-diference numerical method for computing axisymmetric non-newtonian free-surface fluid flow problems is presented. The methodology employed to solve the unsteady Navier-Stokes and continuity equations is an extension of the two-dimensional GENSMAC: a finite-difference markel-and-cell method for numerical solution of incompressible newtonian free-surface flows using a velocity-pressure formulation. The fluid is represented by marker particles that provide the location and visualization of the free-surface. The capabilities of the numerical solution procedure are demonstrated by application to vario us physical problems.

Numerical
Simulation of the Time-Dependent

Reacting Flows in Pulse Facilities

José P. Tamagno

jtamagno@com.uncor.edu

Sergio A. Elaskar

selaskar@com.uncor.edu

José P. Tamagno+, Sergio A. Elaskar+ and Gustavo Ríos*

+ Departamento de Aeronáutica, Universidad Nacional de Córdoba

Av. Velez Sarfield 1601, Córdoba (5000), Argentina

* Instituto Universitario Aeronáutico

Ruta 20, km 5.5, Córdoba (5022), Argentina

Reacting Flows in Pulse Facilities

José P. Tamagno

jtamagno@com.uncor.edu

Sergio A. Elaskar

selaskar@com.uncor.edu

José P. Tamagno+, Sergio A. Elaskar+ and Gustavo Ríos*

+ Departamento de Aeronáutica, Universidad Nacional de Córdoba

Av. Velez Sarfield 1601, Córdoba (5000), Argentina

* Instituto Universitario Aeronáutico

Ruta 20, km 5.5, Córdoba (5022), Argentina

Abstract: A numerical methodology for simulating the time-dependent reacting flow inside several types of pulse facilities is outlined in this paper. The numerical approach uses a finite-volume Harten-Yee TVD scheme for the quasi-one-dimensional Euler equations coupled with finite rate chemistry. A Riemann solver is included to track gas interfaces and in order to reduce the number of nodes without smearing the interfaces, a moving mesh is used. The source terms representing the finite-rate chemical kinetics and vibrational relaxation are often large and make the algorithm too stiff to be advanced explicitly. To avoid this stiffness, an implicit treatment of these source terms is implemented. The numerical program can work with 13 chemical reacting species and 32 different reactions of a hydrogen-air combustion mechanism, each of which may proceed forward or backward. Since helium is often used in pulse facilities it is also included, although, it is considered as an inert species. Numerical simulations showing the potential of the computer code for the prediction of fluid mechanic properties and the chemical composition of the flow inside pulse facilities are presented.

Numerical Simulation of Two-Species Biofilms

Benito Chen

bchen@uwyo.edu

Department of Mathematics

University of Wyoming

Laramie, WY 82071

Hristo Kojouharov

hristo@uta.edu

Abstract: There are bacteria that form biofilms in porous media. The biofilms can be used as biobarriers to restrict the flow of pollutants. If a second species of bacteria that can actually react with the contaminants is added to the biobarrier, the result is a much more effective way of controlling the pollutants. Here we propose a mathematical model for the formation of these biobarriers. Nonstandard methods will be used to numerically solve the resulting equations for the flow, transport and reactions. Comparisons with some experimental results will be given.

Numerical Simulation
of Waves

in Poroviscoelastic Solids Saturated by Immiscible Fluids

Juan Enrique Santos

santos@math.purdue.edu

Observatorio Astronomico, UNLP

Paseo del Bosque S/N

La Plata, (1900), Argentina

Abstract: An iterative algorithm formulated in the space--frequency domain to simulate the propagation of waves in a bounded poro-viscoelastic rock saturated by a two--phase fluid is presented. The Biot-type model takes into account capillary forces and viscous and mass coupling interaction coefficients between the fluid phases under variable saturation and pore fluid pressure conditions. The model predicts the existence of three compressional waves or Type-I, Type-II and Type-III waves and one shear or S-wave. The Type-III mode is a new mode not present in the classical Biot theory for single--phase fluids. The differential

The numerical procedure is an iterative non-overlapping domain decomposition method that employs an absorbing boundary condition in order to minimize spurious reflections from the artificial boundaries. The Type III--mode has been observed for the first time at ultrasonic frequencies. This result constitutes a significant departure from the single-phase fluid case. The experiments use a clay--free sandstone saturated with gas and water, a reference fluid pressure Pw = 30 MPa and gas saturation of 10 %. For these conditions, the Type-III wave at 500 KHz has a phase velocity of 418 m/s.

**Abstract:** The Earth-to-Mars flight path
is set up in a computer simulation with the planets in two body motion and
the spacecraft (s/c) in motion about a central body, perturbed by the other
two. The trajectory is continuously integrated, accurate to 14 significant
digits throughout. The simulation provides for a mid-course correction, approximately
at conjunction; plus several variations in the Earth escape and Mars capture
geometries. There are five possible flight path corrections (fifteen degrees
of freedom - magnitude of each of five thrusts and where, in 2D space), similar
to a typical NASA Mars mission flight plan. Given an input of magnitude and
direction of the mid course thrust, the trajectory is then optimized for total
energy usage and transit time for all the other parameters. The complete analysis
takes less than 30 seconds on a 300 mHz PC. The optimization is done without
benefit of any traditional nonlinear programming methods, so the code is compact
and the results are obtained quickly - without loss of accuracy. The program
is able to do this because it takes maximum advantage of the geometry of the
problem, the underlying principles of orbital mechanics, and it uses the variable
step integrator to help determine where the best neighboring optimal paths
lie.

Polynomial Factorization in GF(q): Cantor-Zassenhaus and Rabin Algorithms

Ruth Noriega

Departamento de Matematicas

Universidad Nacional de Trujillo

Peru

Abstract: Using topics of algebra, we studied and described algebraic algorithms for finding polynomial roots and factors in Galois fields GF(q), with q=p^n, where p is the characteristic of the field, which can be arbitrarialy large, Deterministics and probabilistics algorithms are developed to compute polynomials roots and polynomial factorizations in GF(q). Finally we implement the Cantor-Zassenhaus and Rabin Algorithms for square free polynomials in a MAPLE package.

Poultry Farm Nutritional Planning with Fuzzy Linear Programming

Edmundo Vergara Moreno

vergara@math.unitru.edu.pe

Jose Luis Verdegay Galdeano

verdegay@ugr.es

Abstract: This work prposes a system support
decision (SSD) using some methods of fuzzy linear programming (FLP) for diet
planning in a poultry farm, taking into account that the free market in product
prices and nutritional requeriments for birds are not fixed.

q-Columns
Inverse-Updating Methods

for Solving Nonlinear Systems of Equations

Vera Luica Rocha Lopes

vlopes@ime.unicamp.br

Luziane Ferreira-Mendonça

luziane@ime.unicamp.br

for Solving Nonlinear Systems of Equations

Vera Luica Rocha Lopes

vlopes@ime.unicamp.br

Luziane Ferreira-Mendonça

luziane@ime.unicamp.br

José Mario Martínez

martinez@ime.unicamp.br

Abstract: In this work it is introduced new quasi-Newton
methods for solving large-scale nonlinear systems of equations. In these methods
q (>1) columns of the approximation of the inverse Jacobian matrix are
updated, in such a way that the q last secant equations are satisfied (when
it is possible) at every iteration. The new methods obtained are called a
q-Columns Inverse-Updating Method. It is also shown an optimal maximum value
for q, that makes the method competitive. It is proposed a right implementation
from the point of view of linear algebra and numerical stability. It is presented
a local convergence analysis for the case n=2 and several numerical comparative
tests with other quasi Newton methods, in particular the ICUM (Inverse Column
Updating Method) are presented.

Recent
Applications and Numerical Implementation

of quasi-Newton Methods for Solving Nonlinear Systems of Equations

Rosana Pérez

rosana@atenea.ucauca.edu.co

Véra Lucia Rocha Lopes

vlopes@ime.unicamp.br

of quasi-Newton Methods for Solving Nonlinear Systems of Equations

Rosana Pérez

rosana@atenea.ucauca.edu.co

Véra Lucia Rocha Lopes

vlopes@ime.unicamp.br

Abstract: In this work we present a survey on recent applications of quasi-Newton methods to solve nonlinear systems of equations which appear in applied areas such as Physics, Biology, Engineering, Geophysics, Chemistry and Industry. We also present a comparative analysis of the performance of the ICUM (Inverse Column Updating Method) and Broyden´s method when applied to some of the problems mentioned above.

Stochastic
Algorithms in Seismic Tomography

Ana Karina Fermín Rodriguez

afermin@euler.ciens.ucv.ve

Departamento de Matemática

Escuela de Matemática

Facultad de Ciencias

Universidad Central de Venezuela

Av. Los Ilustres, Los Chaguaramos, A.P.: 20513, Caracas 1020 A.

Carenne Ludeña

cludena@cauchy.ivic.ve

Ana Karina Fermín Rodriguez

afermin@euler.ciens.ucv.ve

Departamento de Matemática

Escuela de Matemática

Facultad de Ciencias

Universidad Central de Venezuela

Av. Los Ilustres, Los Chaguaramos, A.P.: 20513, Caracas 1020 A.

Carenne Ludeña

cludena@cauchy.ivic.ve

Abstract: As is well known, seismic reflection tomography is a nonlinear ill posed inverse problem. Usually reconstruction methods for a given set of travel times involve parametrization of the unknown velocity field and solving for succesive linear approximations to the original nonlinear problem. However, generally, the associated linear systems are ill conditioned and require some kind of smoothing or regularization, thus yielding results hard to interpret. In our work we address the minimization problem using stochastic algorithms, i.e., simulated annealing together with a "good" guess for the starting point. This approach allows for an interpretation of the smoothing parameters in terms of prior distributions. We apply the algorithm to heterogeneous velocity fields with unknown depths for the reflectors. Synthetic travel times are generated to test the quality of approximations as well as to obtain execution times.

Study of Stationary Solutions of Two Coupled Models of Reaction-Diffusion Equations

Edgardo A. Moyano

emoyano@cnea.gov.ar

Alberto Scarpettini

ascarpet@cnea.gov.ar

Abstract: This short presentation is concerned
with numerical solutions of two weakly coupled systems of differential equations
by the finite difference method. In certain reaction-diffusion systems, with
concentrations or elements interacting, the effect of diffusion is negligible.
Each coupled system is reduced to a partial differential equation and an ordinary
differential equation. A monotone iteration process for the finite difference
system is generated. The iterations are shown to converge monotonically to
a unique solution of each system. The fundamental question is whether a time
dependent solution of the reaction-diffusion problem converges to an equilibrium
solution as time approaches infinity (Lyapunov stability). The first model
we consider corresponds to a simulation of isothermal fission gas release
during irradiation of uranium dioxide fuel, as proposed by M. V. Speight.
The second one is a simplified version of the study of the excitation of the
nerve axon, proposed by Hodgkin and Huxley, and simplified by FitzHugh and
Nagumo.

Surface
Diffusion: Weak Formulation, Finite Element Discretization,
and Numerical Experiments

Pedro Morin

pmorin@math.unl.edu.ar

Eberhard Bänsch

baensch@wias-berlin.de

Ricardo H. Nochetto

rhn@math.umd.edu

Pedro Morin

pmorin@math.unl.edu.ar

Eberhard Bänsch

baensch@wias-berlin.de

Ricardo H. Nochetto

rhn@math.umd.edu

Abstract: We consider the evolution of a 1- or 2-dimensional surface by surface diffusion. That is, the normal velocity of the surface is given by the Surface Laplacian of the Mean Curvature.We introduce a weak formulation of the 4th order equation, based on a mixed approach, which converts the system into two lower order linear PDEs. We propose a finite element discretization, show stability and conservation properties, and present several numerical experiments.

The
Spectral Gradient Method and Unconstrained Optimal Control Problems

Juan Ignacio Ardenghi

ardenghi@criba.edi.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

Tatiana Inés Gibelli

tgibelli@uns.edu.ar

Juan Ignacio Ardenghi

ardenghi@criba.edi.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

Tatiana Inés Gibelli

tgibelli@uns.edu.ar

Abstract: Optimal control problems and their discretized form can be viewed as optimization problems. Kelley and Sachs have already solved the discretized problem by using quasi-Newton methods. In this contribution the problem is solved by a low cost algorithm such as the spectral gradient method. The convergence behavior of the method for finite-dimensional approximation is analyzed. Numerical examples are given and the results are compared with those obtained by Kelley and Sach.

The
Spectral Gradient Method on Hilbert Spaces

Susana Orofino

sorofino@criba.edu.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

María Cristina Maciel

immaciel@criba.edu.ar

Susana Orofino

sorofino@criba.edu.ar

Departamento de Matemática

Universidad Nacional del Sur

Argentina

María Cristina Maciel

immaciel@criba.edu.ar

Abstract: The spectral gradient method for unconstrained minimization of a quadratic function has been proved to work quite well in the finite dimensional case. In this contribution the behavior of the method in infinite-dimensional real Hilbert spaces is analyzed. The self-adjoint and compact operator cases are studied and convergence results are established.

Three-Dimensional Visualization of the Density Field Around

the Seamount Alarcón Entrance to the Gulf of California

Aaron Linsdau

Email1: alinsdau@yahoo.com

Carlos Torres

ctorres@sciences.sdsu.edu

Jose Castillo

castillo@myth.sdsu.edu

Abstract: The density structure around the Seamount
Alarcón is numerically simulated with a high-resolution three-dimensional
curvilinear ocean model. The flow is assumed to be uniform and linearly stratified.
Visualizations are made for the time evolution of the density surfaces for
various cases of stratification.

Traffic
Assignment: Models, Algorithms and a Scilab Toolbox

Pablo Lotito

pablo.lotito@inria.fr

Mancinelli Elina

elina.man cinelli@inria.fr

Pablo Lotito

pablo.lotito@inria.fr

Mancinelli Elina

elina.man cinelli@inria.fr

Abstract: We present the traffic assingnment problem that consists in the determination of a multiflow over a network that satisfies given demands and verifies certain criteria. Among these criteria we consider the Wardrop equilibrium and the algorithms for finding it. In certain cases (separability and symmetry), the problem is solved as a nonlinear convex program, but when many classes or modes of transport are considered we have to solve a variational inequation. We don't know a convergent algorithm in this case.We present our advances in this area together with a toolbox for Scilab with our implementation of some algorithms.

Understanding
Infrared Pyrometry in Galvanising Lines

Etcheverry Javier Ignacio

sidjae@sid erca.com

Siderca/CINI Correo 44

Simini 250

2804 - Campana

Buenos Aires

Etcheverry Javier Ignacio

sidjae@sid erca.com

Siderca/CINI Correo 44

Simini 250

2804 - Campana

Buenos Aires

Abstract: Infrared pyrometers are one of the most widely used tools to obtain non-contact temperature measurements in industrial settings. However, there are several factors that must be taken into account in order to obtain reliable readings. A key aspect is the choice of the right instrument for the application (monochromatic, two-wavelength, operating wavelength range, etc.). Mathematical models can be very useful to evaluate competing alternatives for the given application, and, as often there are no trouble-free choices, they can be used to correct the instrument reading, or to identify the most troublesome situations.

In this work we discuss the mathematical modelin g of the use of infrared pyrometers to measure the steel strip temperature inside the furnaces in continuous galvanising lines. In this application the main complicating factors are the high temperature of the walls of the furnace (much higher than the strip temperature that one is trying to measure), the strong infrared emission of the combustion gases, the fact that the strip is somewhat specular, and the poor knowledge of strip emissivity. As many of these issues are typical of the measurement of the load temperature inside furnaces, the present analysis has a wide application range.

Hierarchical Clustering in the Distribution of Traffic Policemen in Trujillo City

Julio. C. Peralta Castañeda

jperal@math.unitru.edu.pe

Department of Mathematics

Faculty of Physical Sciences and Mathematics

National University of Trujillo-Peru

Abstract Due to the deficiencies in the municipal administration, transport sector, in the city of Trujillo, it is important to optimize the distribution of traffic policemen in the civic center of the city. With the purpose of applying a hierarchical clustering theory, we consider statistical information of the following data: spatial coordinates of each intersection among streets and/or avenues, vehicular flow in each intersection during different hours of the day, and the importance function dp(imp). With these data we obtain: the flow function z(t) using cubic splines interpolation; the test function m(z(t)); and the weight function w(t)=m(z(t) )dp(imp). The weight function will allow us to calculate the Similarity (S) or Dissimilarity (D) among intersections. With the calculation of S or D, we apply the general agglomerative scheme clustering all intersections, where each cluster will represent the presence of a traffic policeman, and in this way will get a better distribution of traffic policemen.

Good Quality Point Sets and Error Estimates for Moving Least Square Approximations

Carlos Zuppa

zuppa@unsl.edu.ar

Departamento de Matemáticas

Universidad Nacional de San Luis

Chacabuco y Pedernera. 5700. San Luis , Argentina

Abstract: One goal of this paper is to study the relation of the condition number of the star of nodes in normal equations for error estimates of Moving Least Square approximations in Sobolev spaces. The condition numbers are closely related to the good quality of the set of nodes and the approximating power of the method.

Results About of Cantor Zassenhaus and Rabin Algorithms to Compute Polynomial Factorization in GF(p)

Ruth Noriega S.

ruth@math.unitru.edu.pe

Abstract: This work describes algebraic algorithms for computing in Galois Fields GF(p), where p is the characteristic of the field which can be arbitrarialy large. In order to justify this work, we have developed a program to compute polynomial factorizations using the Cantor-Zassenhaus and Rabin Algorithms, both implemented in MAPLE.

Galerkin Methods for the Shallow Water Equations

Omar Roberto Faure

ofaure@frcu.utn.edu.ar

Ruben D. Spies

rspies@imalpde.ceride.gov.ar

Abstract: A nonlinear Galerkin method for the Shallow Water equations in periodic domains is presented. The method consists of decomposing the space of solutions in two subspaces of low and high modes, respectively. The Courant-Friedrichs-Levy (CFL) stability condition is analised and comparisons are made with a linear Galerkin method. Numerical results are shown.

Discretization of the Phase-Field Equations

Cristina Lúcia Dias Vaz

cvaz@ufpa.br

Abstract: In this paper, a phase-field model
is considered. Analysis of a time discretization for an initial-boundary value
problem for this phase-field model is presented. Convergence is proved and
existence, uniqueness and regularity results are derived.

An Elementary Relationship Between the Riesz Fractional Integration Operator and d-dimensional 1/f Processes.

Bruno Cernuschi Frias

Juan Miguel Medina

jmedina@fi.uba.ar

Facultad de Ingenieria UBA, ARGENTINA

Abstract: In this work we provide an almost sure convergent expansion of a process with power law of fractional order by means of some known theorems from harmonic analysis and rather simple probability theory results. This construction is appropriate for numerical simulations, it also provides a relation between these processes and certain type of linear operators which act on Lp spaces: This result is very important on its own, because it enables us to construct a d-dimensional process with 1/f behavior without using the more complicated theory of Ito integration.

Numerical Stability of the Nonlinear Schrodinger Equation

J. P. Borgna, M. C. Mariani, D. F.
Rial

UBA, ARGENTINA

On a cut subroutine for the
maximum weight stable set problem

Graciela L. Nasini

Dpto. de Matemáticas, FCEIA,

Universidad Nacional de Rosario, Argentina

Mathematical Tool For The Study
of The Cost of Residual Biomass

Maria Márcia Pereira Sartori, Helenice
de Oliveira Florentino

Dept. of Bio-statistics, Inst. of Bio-Sciences,

UNESP, Rubião Junior , Campus of Botucatu,

P.O. Box 510, CEP 18618-000, Botucatu,

São Paulo, Brazil

The sugarcane is one of the cultures more cultivated in the State of São Paulo occupying an area of approximately 2,5 million hectares. That culture presents a great number species, that are chosen for the plantation in function of its adaptation to the soil type, influence to plagues and diseases and the agricultural productivity and of sucrose. Studies have been showing the change need in the crop system, in way to provide the pollution reduction generated for the it burns of the cane before in the crop. That change implies in the destiny of the residual biomassa of crop. The mathematical model can aid in the choice of the species that provides the smallest cost of collection of the residual biomass. Therefore, the objective of this work is to develop an optimization model with the purpose of choosing the plantation varieties, after the usual selection, to aiming at minimize the collection cost and of transport for the recovery and use of the biomassa, evaluating the influence of the density of that material and assisting restrictions of production demand and plantation area. The results show the viability of the model for choice of varieties, that provides the reduction of the cost with the collection of the residual biomassa.

On Differential Games with Maximum cost and Infinite Horizon

Silvia Di Marco(*) and Alain Rapaport(+)

(*)Dpto. de Matematica, FCEIA,

Universidad Nacional de Rosario, Argentina

(+)LASB-INRA, Montpellier, France

We consider an integral form of the Isaacs equations associated
to differential games with L criterion, for the characterization of their
value functions. We prove that upper and lower values are the lowest super-solution
and the largest element of a special set of sub-solutions, of the dynamic
programming equation. This is an alternative to the viscosity solutions approach,
without requiring any regularity assumption on the value functions. For nite
horizon approximations, we propose a scheme in terms of an innitesimal operator
dened over the set of Lipschitz continuous functions. The images of this
operator can be characterized

classically in terms of viscosity solutions.

We illustrate these results on a example, which values functions can be determined
analytically.