As contribuições de Chaim Samuel Hönig para o desenvolvimento da matemática brasileira

Pós-graduação em Educação Matemática - IGCE

Modelo de Lotka-Volterra com inclusão de termos perturbativos e capacitivos

Our purpose is to show the effects in the predator-prey trajectories due to parameter temporal perturbations and/or inclusion of capacitive terms in the Lotka Volterra Model. An introduction to the Lotka Volterra Model (chapter 2) required a brief review of nonlinear differential equations and stability analysis (chapter 1) , for a better understanding of our work. In the following chapters we display in sequence our results and discussion for the randomic pertubation case (chapter 3); periodic perturbation (chapter 4) and inclusion of capacitive terms (chapter 5). Finally (chapter 6) we synthesize our result

Existência de soluções para equações integrodiferenciais em epaços de Banach

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Piecewise Bounded Quadratic Systems in the Plane

In this paper we study the sliding mode of piecewise bounded quadratic systems in the plane given by a non-smooth vector field Z=(X,Y). Analyzing the singular, crossing and sliding sets, we get the conditions which ensure that any solution, including the sliding one, is bounded.

On the properness of an impulsive control extension of dynamic optimization problems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On Properness of Impulsive Extension

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Modelling the dynamics of dengue real epidemics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.