Preface
Spreadability, Vulnerability and Protector Control
In this work, we present some concepts recently introduced in the analysis and control of distributed parameter systems: , and . These concepts permit to describe many biogeographical phenomena, as those of pollution, desertification or epidemics, which are characterized by a spatio-temporal evolution
Block Factorization of Hankel Matrices and Euclidean Algorithm
It is shown that a real Hankel matrix admits an approximate block diagonalization in which the successive transformation matrices are upper triangular Toeplitz matrices. The structure of this factorization was first fully discussed in [1]. This approach is extended to obtain the quotients and the remainders appearing in the Euclidean algorithm applied to two polynomials () and () of degree and , respectively, whith < ...
Influence of Vibrations on Convective Instability of Reaction Fronts in Liquids
Propagation of polymerization fronts with liquid monomer and liquid polymer is considered and the influence of vibrations on critical conditions of convective instability is studied. The model includes the heat equation, the equation for the concentration and the Navier-Stokes equations considered under the Boussinesq approximation. Linear stability analysis of the problem is fulfilled, and the convective instability boundary is found depending on...
RBF Based Meshless Method for Large Scale Shallow Water Simulations: Experimental Validation
2D shallow water equations with depth-averaged − model is considered. A meshless method based on multiquadric radial basis functions is described. This methods is based on the collocation formulation and does not require the generation of a grid and any integral evaluation. The application of this method to a flow in horizontal channel, taken as an experimental device, is presented. The results of computations are compared with experimental data...
Roe Scheme for Two-layer Shallow Water Equations: Application to the Strait of Gibraltar
The flow trough the Strait of Gibraltar could be analyzed as a problem of two-layer hydraulic exchange between the Atlantic ocean and the Mediterranean sea. The shallow water equations in both layers coupled together are an important tool to simulate this phenomenon. In this paper we perform an upwind schemes for hyperbolic equations based on the Roe approximate Riemann solver, to study the resulting model. The main goal assigned was to predict the location of the interface between the two layers....
A SOR Acceleration of Self-Adjoint and m-Accretive Splitting Iterative Solver for 2-D Neutron Transport Equation
We present an iterative method based on an infinite dimensional adaptation of the successive overrelaxation (SOR) algorithm for solving the 2-D neutron transport equation. In a wide range of application, the neutron transport operator admits a Self-Adjoint and m-Accretive Splitting (SAS). This splitting leads to an ADI-like iterative method which converges unconditionally and is equivalent to a fixed point problem where the operator is a 2 by 2 matrix...
Bilevel Approach of a Decomposed Topology Optimization Problem
In topology optimization problems, we are often forced to deal with large-scale numerical problems, so that the domain decomposition method occurs naturally. Consider a typical topology optimization problem, the minimum compliance problem of a linear isotropic elastic continuum structure, in which the constraints are the partial differential equations of linear elasticity. We subdivide the partial differential equations into two subproblems posed...
On the Optimal Control of a Class of Time-Delay System
In this work we study the optimal control problem for a class of nonlinear time-delay systems via paratingent equation with delayed argument. We use an equivalence theorem between solutions of differential inclusions with time-delay and solutions of paratingent equations with delayed argument. We study the problem of optimal control which minimizes a certain cost function. To show the existence of optimal control, we use the main topological properties...
Quasi-Optimal Triangulations for Gradient Nonconforming Interpolates of Piecewise Regular Functions
Anisotropic adaptive methods based on a metric related to the Hessian of the solution are considered. We propose a metric targeted to the minimization of interpolation error gradient for a nonconforming linear finite element approximation of a given piecewise regular function on a polyhedral domain of , ≥ 2. We also present an algorithm generating a sequence of asymptotically quasi-optimal meshes relative to such a...
Hybrid Particle Swarm and Neural Network Approach for Streamflow Forecasting
In this paper, an artificial neural network (ANN) based on hybrid algorithm combining particle swarm optimization (PSO) with back-propagation (BP) is proposed to forecast the daily streamflows in a catchment located in a semi-arid region in Morocco. The PSO algorithm has a rapid convergence during the initial stages of a global search, while the BP algorithm can achieve faster convergent speed around the global optimum. By combining the PSO with...
Particle Dynamics Modelling of Cell Populations
Evolution of cell populations can be described with dissipative particle dynamics, where each cell moves according to the balance of forces acting on it, or with partial differential equations, where cell population is considered as a continuous medium. We compare these two approaches for some model examples
Split of an Optimization Variable in Game Theory
In the present paper, a general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables
Variational Reduction for the Transport Equation in a Multiple Branching Plants Growth Model
Plant growth depends essentially on nutrients coming from the roots and metabolites produced by the plant. Appearance of new branches is determined by concentrations of certain plant hormones. The most important of them are Auxin and Cytokinin. Auxin is produced in the growing, Cytokinin in either roots or in growing parts. Many dynamical models of this phenomena have been studied in [1]. In [5], the authors deal with one branch model. In this work,...
Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers
We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre...
Meshless Polyharmonic Div-Curl Reconstruction
In this paper, we will discuss the meshless polyharmonic reconstruction of vector fields from scattered data, possibly, contaminated by noise. We give an explicit solution of the problem. After some theoretical framework, we discuss some numerical aspect arising in the problems related to the reconstruction of vector fields
Edge-based a Posteriori Error Estimators for Generating Quasi-optimal Simplicial Meshes
We present a new method for generating a -dimensional simplicial mesh that minimizes the -norm, > 0, of the interpolation error or its gradient. The method uses edge-based error estimates to build a tensor metric. We describe and analyze the basic steps of our method
Integer Programming Formulation of the Bilevel Knapsack Problem
The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions of parametric Knapsack Problem. In this paper, we propose two stages exact method for solving the BKP. In the first stage, a dynamic programming algorithm is used to compute the set of reactions of the follower. The second stage consists in solving an integer program reformulation of BKP. We show that the...
A Global Stochastic Optimization Method for Large Scale Problems
In this paper, a new hybrid simulated annealing algorithm for constrained global optimization is proposed. We have developed a stochastic algorithm called ASAPSPSA that uses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to the basic simulated annealing algorithm (SA) that gives the region containing the global solution of an objective function. In addition, Simultaneous Perturbation Stochastic Approximation (SPSA)...
Mesh Refinement For Stabilized Convection Diffusion Equations
We derive a residual a posteriori error estimates for the subscales stabilization of convection diffusion equation. The estimator yields upper bound on the error which is global and lower bound that is local
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