Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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.

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

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

Suppressing Fermi acceleration in a two-dimensional non-integrable time-dependent oval-shaped billiard with inelastic collisions

Some dynamical properties of a classical particle confined inside a closed region with an oval-shaped boundary are studied. We have considered both the static and time-dependent boundaries. For the static case, the condition that destroys the invariant spanning curves in the phase space was obtained. For the time-dependent perturbation, two situations were considered: (i) non-dissipative and (ii) dissipative. For the non-dissipative case, our results show that Fermi acceleration is observed. When dissipation, via inelastic collisions, is introduced Fermi acceleration is suppressed. The behaviour of the average velocity for both the dissipative as well as the non-dissipative dynamics is described using the scaling approach. (C) 2009 Elsevier B.V. All rights reserved.

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards. (C) 2010 Elsevier B.V. All rights reserved.

Fermi acceleration and its suppression in a time-dependent Lorentz gas

Some dynamical properties for a Lorentz gas were studied considering both static and time-dependent boundaries. For the static case, it was confirmed that the system has a chaotic component characterized with a positive Lyapunov exponent. For the time-dependent perturbation, the model was described using a four-dimensional nonlinear map. The behaviour of the average velocity is considered in two different situations: (i) non-dissipative and (ii) dissipative dynamics. Our results confirm that unlimited energy growth is observed for the non-dissipative case. However, and totally new for this model, when dissipation via inelastic collisions is introduced, the scenario changes and the unlimited energy growth is suppressed, thus leading to a phase transition from unlimited to limited energy growth. The behaviour of the average velocity is described using scaling arguments. (C) 2010 Elsevier B.V. All rights reserved.

A peculiar Maxwell's Demon observed in a time-dependent stadium-like billiard

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

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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)

Scaling investigation for the dynamics of charged particles in an electric field accelerator

Some dynamical properties of an ensemble of trajectories of individual (non-interacting) classical particles of mass m and charge q interacting with a time-dependent electric field and suffering the action of a constant magnetic field are studied. Depending on both the amplitude of oscillation of the electric field and the intensity of the magnetic field, the phase space of the model can either exhibit: (i) regular behavior or (ii) a mixed structure, with periodic islands of regular motion, chaotic seas characterized by positive Lyapunov exponents, and invariant Kolmogorov-Arnold-Moser curves preventing the particle to reach unbounded energy. We define an escape window in the chaotic sea and study the transport properties for chaotic orbits along the phase space by the use of scaling formalism. Our results show that the escape distribution and the survival probability obey homogeneous functions characterized by critical exponents and present universal behavior under appropriate scaling transformations. We show the survival probability decays exponentially for small iterations changing to a slower power law decay for large time, therefore, characterizing clearly the effects of stickiness of the islands and invariant tori. For the range of parameters used, our results show that the crossover from fast to slow decay obeys a power law and the behavior of survival orbits is scaling invariant. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4772997]

Electron Transport in Dye-Sensitized Solar Cells Based on ZnO Nanotubes: Evidence for Highly Efficient Charge Collection and Exceptionally Rapid Dynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Temporal dynamics of stomatal conductance of plants under water deficit: can homeostasis be improved by more complex dynamics?

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

Morphogenetic and tillering dynamics in Tanzania grass fertilized and non-fertilized with nitrogen according to season

The objectives of this study were to evaluate morphogenetic characteristics and tillering dynamics in Tanzania grass fertilized and non-fertilized with nitrogen, under intermittent grazing, in the spring and the summer. The main plots were composed of four nitrogen rates (0, 100, 200 and 300 kg/ha) and the subplots were growth seasons: spring (October, November and December) and summer (January, February and March). The experimental design was of randomized block with plots subdivided by time (seasons of the year) and four replications. Urea was used as nitrogen supply and was divided into two applications: one in the spring and another in the summer. The experimental units fertilized with N rates of 200 and 300 kg/ha showed six cycles of pasture, with an average of 27 days of pasture interval, while the treatments with no fertilization and 100 kg/ha of N showed only four and five cycles of pasture, respectively. Leaf elongation rate (LER) and the leaf appearance rate (LAR) increased linearly with increasing of N rates. The greatest population density occurred in summer with the higher nitrogen rates. The treatment without N fertilization showed the lowest growth of tiller population, while the other treatments exhibited growth rates above 50% when compared with non-fertilized samples. Nitrogen rates significantly affect the leaf appearance rate and the leaf elongation rate, as well as the number of live leaves in plants of Tanzania grass in both spring and summer.

Tillering dynamics in Guinea grass pastures subjected to management strategies under rotational grazing

This study was carried out to analyze the tillering profile of Guinea grass (Panicum maximum cv. Tanzania) pastures subjected to two grazing frequencies (time necessary to intercept 90 and 95% of the incoming light) and two post-grazing heights (30 and 50 cm) in the period from November 2005 to October 2006. The experimental design was of completely randomized blocks with three replications, in a 2 × 2 factorial arrangement. At the end of the spring, pastures managed with 90% light interception showed greater tiller appearance rates in relation to pastures managed with 95%, regardless of post-grazing height. In the summer and fall, pastures managed with post-grazing height of 30 cm showed higher tiller appearance rates in comparison with pastures managed at 50 cm, regardless of grazing frequency. Concerning the tiller mortality rates, in the summer, higher values were found for pastures managed at 90/50 and 95/30 (interception/height), intermediate values at 90/30 and lower values in those managed at 95/50. Pastures managed at 90/30, 95/30 and 95/50 in the fall presented greater tiller mortality rates than those managed at 90/50. These differences do not occur in the winter/beginning of spring. The stability index remained above 1 all through the experimental period. All management strategies evaluated are adequate for Guinea grass.

Real-time optical monitoring of the dip coating process

A significant part of film production by the coating industry is based on wet bench processes, where better understanding of their temporal dynamics could facilitate control and optimization. In this work, in situ laser interferometry is applied to study properties of flowing liquids and quantitatively monitor the dip coating batch process. Two oil standards Newtonian, non-volatile, with constant refractive indices and distinct flow properties - were measured under several withdrawing speeds. The dynamics of film physical thickness then depends on time as t(-1/2), and flow characterization becomes possible with high precision (linear slope uncertainty of +/-0.04%). Resulting kinematic viscosities for OP60 and OP400 are 1,17 +/- 0,03. St and 9,9 +/- 0,2 St, respectively. These results agree with nominal values, as provided by the manufacturer. For more complex films (a multi-component sol-gel Zirconyl Chloride aqueous solution) with a varying refractive index, through a direct polarimetric measurement, allowing also determination of the temporal evolution of physical thickness (uncertainty of +/- 0,007 microns) is also determined during dip coating.