Generalization of the Hamilton-Jacobi approach for higher-order singular systems

We generalize the Hamilton-Jacobi formulation for higher-order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraints structure present in such systems.

Hamilton-Jacobi approach to Berezinian singular systems

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed For singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the Hamilton-Jacobi equation for such systems, analyzing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared. (C) 1998 Academic Press.

First-order formalism for dark energy and dust

This work deals with a first-order formalism for dark energy and dust in standard cosmology, for models described by a real scalar field in the presence of dust in spatially flat space. The field dynamics may be standard or tachyonic, and we show how the equations of motion can be solved by first-order differential equations. We investigate a model to illustrate how the dustlike matter may affect the cosmic evolution using this framework.

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Permutability of Backlund transformations for N=2 supersymmetric sine-Gordon

The permutability of two Backlund transformations is employed to construct a nonlinear superposition formula and to generate a class of solutions for the N=2 super sine-Gordon model. We present explicitly the one and two soliton solutions.

Negative Even Grade mKdV Hierarchy and its Soliton Solutions

In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra (s) over capl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method based on non zero vacua. The sub-hierarchies admiting such class of solutions are classified.

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.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

Dissipative area-preserving one-dimensional Fermi accelerator model

The influence of dissipation on the simplified Fermi-Ulam accelerator model (SFUM) is investigated. The model is described in terms of a two-dimensional nonlinear mapping obtained from differential equations. It is shown that a dissipative SFUM possesses regions of phase space characterized by the property of area preservation.

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper The mathematical model of the system is represented by coupled non-linear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation. [DOI: 10.1115/1.3124783]

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)

On a nonlinear and chaotic non-ideal vibrating system with shape memory alloy (SMA)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The dynamics of a one-dimensional parabolic problem versus the dynamics of its discretization

In this paper we prove that the spatial discretization of a one dimensional system of parabolic equations. with suitably small step size, contains exactly the same asymptotic dynamics as the continuous problem. (C) 2000 Academic Press.

PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

We consider the family of singularly nonautonomous plate equation with structural dampingu(tt) + a(t, x)u(t) - Delta u(t) + (-Delta)(2)(u) + lambda u = f(u),in a bounded domain Omega subset of R(n), with Navier boundary conditions. When the nonlinearity f is dissipative we show that this problem is globally well posed in H(0)(2)(Omega) x L(2)(Omega) and has a family of pullback attractors which is upper-semicontinuous under small perturbations of the damping a.

LOWER SEMICONTINUITY of PULLBACK ATTRACTORS FOR A SINGULARLY NONAUTONOMOUS PLATE EQUATION

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