Self-consistent equilibrium calculation through a direct variational technique in tokamak plasmas

A self-consistent equilibrium calculation, valid for arbitrary aspect ratio tokamaks, is obtained through a direct variational technique that reduces the equilibrium solution, in general obtained from the 2D Grad-Shafranov equation, to a 1D problem in the radial flux coordinate rho. The plasma current profile is supposed to have contributions of the diamagnetic, Pfirsch-Schluter and the neoclassical ohmic and bootstrap currents. An iterative procedure is introduced into our code until the flux surface averaged toroidal current density (J(T)), converges to within a specified tolerance for a given pressure profile and prescribed boundary conditions. The convergence criterion is applied between the (J(T)) profile used to calculate the equilibrium through the variational procedure and the one that results from the equilibrium and given by the sum of all current components. The ohmic contribution is calculated from the neoclassical conductivity and from the self-consistently determined loop voltage in order to give the prescribed value of the total plasma current. The bootstrap current is estimated through the full matrix Hirshman-Sigmar model with the viscosity coefficients as proposed by Shaing, which are valid in all plasma collisionality regimes and arbitrary aspect ratios. The results of the self-consistent calculation are presented for the low aspect ratio tokamak Experimento Tokamak Esferico. A comparison among different models for the bootstrap current estimate is also performed and their possible Limitations to the self-consistent calculation is analysed.

Hybrid methods for lot sizing on parallel machines

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

Boron adsorption in lowland soils from Parana State, Brazil

Boron adsorption by soil is the main phenomenon that affects its availability to plants. This, the present study investigated the effect of liming on B adsorption by lowland soils of Parana State, and to correlate these values with the physical and chemical properties of the soils. Surface samples of three lowland soils [Gleissolo Haplico (GX), Plintossolo Haplico (FX) and Cambissolo Haplico (CX)], with different origin material and physicochemical properties were used. Samples with or without liming application were incubated during 60 days. Boron adsorption was accomplished by shaking 4.0g soil samples, for 24 h, with 20 mL of 0.01 mol L-1 CaCl2 solution containing different concentrations of B (0, 1, 2, 4, 8 and 16 mg L-1). Sorption was fitted to non-linear form of the Langmuir adsorption isotherm. The adsorption isotherms indicated that the B adsorption increased with its increasing concentration in the equilibrium solution. Maximum adsorption capacity of B ranged from 3.0 to 13.9 mg kg(-1) (without liming) and 14.7 to 35.7 mg kg(-1) (with liming). Liming increased the amount of adsorbed B in Gleissolo Haplico and Plintossolo Haplico soils, although the bonding energy has decreased. The amount of adsorbed B by Cambissolo Haplico soil was not affected by liming application. The most important soil properties affecting the B adsorption in lowland soils were pH, clay content, exchangeable aluminum and iron oxide contents.

Inferência fuzzy para o problema de corte de estoque com sobras aproveitáveis de material

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solução do problema de corte bidimensional de peças retângulares tipo não-guilhotinado usando simulated annealing

Pós-graduação em Engenharia Elétrica - FEIS

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Contribuições para o problema de corte de estoque bidimensional na indústria moveleira

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelagem matemática e aplicações do problema de coloração em grafos

Pós-graduação em Matemática - IBILCE

Adsorção e disponibilidade de fósforo para o crescimento inicial de mamoneira em solos com diferentes classes texturais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Mathematical modeling and analysis of the flocculation process in chambers in series

In this study, the flocculation process in continuous systems with chambers in series was analyzed using the classical kinetic model of aggregation and break-up proposed by Argaman and Kaufman, which incorporates two main parameters: K (a) and K (b). Typical values for these parameters were used, i. e., K (a) = 3.68 x 10(-5)-1.83 x 10(-4) and K (b) = 1.83 x 10(-7)-2.30 x 10(-7) s(-1). The analysis consisted of performing simulations of system behavior under different operating conditions, including variations in the number of chambers used and the utilization of fixed or scaled velocity gradients in the units. The response variable analyzed in all simulations was the total retention time necessary to achieve a given flocculation efficiency, which was determined by means of conventional solution methods of nonlinear algebraic equations, corresponding to the material balances on the system. Values for the number of chambers ranging from 1 to 5, velocity gradients of 20-60 s(-1) and flocculation efficiencies of 50-90 % were adopted.

A genetic algorithm/mathematical programming approach to solve a two-level soft drink production problem

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Modelos Matemáticos e Métodos de Solução para Problemas de Dimensionamento de Lotes

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

NASH game and mixed H2/H∞ control

In this work a Nonzero-Sum NASH game related to the H2 and H∞ control problems is formulated in the context of convex optimization theory. The variables of the game are limiting bounds for the H2 and H∞ norms, and the final controller is obtained as an equilibrium solution, which minimizes the `sensitivity of each norm' with respect to the other. The state feedback problem is considered and illustrated by numerical examples.

Métodos híbridos de pontos interiores/exteriores e de aproximantes de funções em problemas multiobjetivo de despacho econômico e ambiental

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.