Statistical properties of a dissipative kicked system: Critical exponents and scaling invariance

A new universal empirical function that depends on a single critical exponent (acceleration exponent) is proposed to describe the scaling behavior in a dissipative kicked rotator. The scaling formalism is used to describe two regimes of dissipation: (i) strong dissipation and (ii) weak dissipation. For case (i) the model exhibits a route to chaos known as period doubling and the Feigenbaum constant along the bifurcations is obtained. When weak dissipation is considered the average action as well as its standard deviation are described using scaling arguments with critical exponents. The universal empirical function describes remarkably well a phase transition from limited to unlimited growth of the average action. (C) 2012 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)

Dynamical properties of a particle in a wave packet: Scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterise the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2. (C) 2011 Elsevier Ltd. All rights reserved.

Recurrence of particles in static and time varying oval billiards

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

Velocity-dependent KAM islands

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

Contadores eletrônicos no laboratório didático: parte I. Montagem e aplicações

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

Determination of a point sufficiently close to the asymptote in nonlinear growth functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Puberty and growth rate in thoroughbred fillies

We measured progesterone and estradiol levels from birth to the beginning of adult life in 10 Thoroughbred fillies from the Equilia Stud Farm in Avare SP, Brasil. The animals were measured and weighed monthly for the determination of body development and of a possible correlation between the rate of weight and height gain and the onset of detectable sex hormone levels. Jugular blood was collected twice a week and stored at -20 degrees C until assay of progesterone by a solid phase RIA with a sensitivity of 0.32 nmol/L and of estradiol by liquid phase RIA adapted to low levels (3.67 pmol/L). The fillies were born with high serum levels of both hormones,which fell to undetectable levels by the first week of life. A variation in growth rate was observed, with the highest levels occuring from birth to the 3rd month of life, followed by a reduction until 15 mo of life, when fast growth was resumed. The monthly weight gain was 1.5% when the fillies reached puberty and 5.4% during the next month, (P<0.05, Friedman test). During this second period of accelerated growth after the beginning of progesterone production at detectable levels (above 0.318 nmol/L), the parameters of skeletal growth did not differ (P>0.05). The month of onset of puberty was the month of lowest weight gain in the life of the fillies, and it coincided with the highest insolation period. In conclusion, horses, like all other developed vertebrates, have a double pattern of development, with the acceleration observed at puberty depending on sex steroids, which in turn coincides with the highest insolation period. Gonadal activity characterized by serum progesterone levels was low from birth to the onset of puberty. After puberty the progesterone cycles were similar to those of adult animals with a mature hypothalamic-gonadal axis. (C) 1997 by Elsevier B.V.

FIBER TYPES DISTRIBUTION IN THE DIGASTRIC MUSCLE OF TUFTED CAPUCHIN MONKEY (CEBUS-APELLA)

Fiber types distribution in the diagastric muscle of tufted capuchin monkey was studied by means of NADH-TR, myosin-ATPase, after alkaline and acid preincubations and SDH histochemical reactions. Three different types of fibers were found presenting an equal distribution. The percentage and types of fibers were as follow: 18.2 % SO (Slow Oxydative), 38.4 % FOG (Fast Oxydative Glycolytic) and 43.4 % FG (Fast Glycolytic). FG fibers revealed the largest area. The relatively high concentration of fast twitch (81.2 %) seems to indicate this muscle is involved with the acceleration and fast speed of jaw movements. Aerobic metabolism represented by SO + FOG fibers (56.6 %) suggests that this muscle possesses an additional role than that related to the lowering of the jaw.

Consolidation and break-up of the South American platform in southeastern Brazil: Tectonothermal and denudation histories

The different tectonic stages that occurred at the end of the Proterozoic and during the Phanerozoic have an important bearing on the tectonothermal history of the South American Platform and its consolidation. Geochronological data (U/Pb monazite, Ar-40/Ar-39 whole rock) and apatite fission-track analysis, from Precambrian rocks of the southeastern Brazilian coastline, permit the modeling of a long-term thermal history of the crust and constrain variable denudation rates.Using these data, a temperature-time diagram reflects a period of accelerated exhumation during the end of the Brasiliano Orogeny, followed by long stability and reactivation of the platform during the Rifting Phase of the South Atlantic Ocean.U/Pb zircon and monazite (blocking temperature of ca. 650degreesC) data from a series of igneous bodies suggest that a tangential and transpressional tectonic regime occurred between 625 and 610 Ma. During the following escape tectonics, between 610 and 590 Ma the exhumation process indicates cooling rates of ca. 12degreesC/Ma. Ar-40/Ar-39 biotite ages between 540 and 510 Ma (ca. 300degreesC) and a corrected fission-track age on apatites (100degreesC) of 480 Ma indicate an exhumation event related to block tectonics with huge vertical displacement along shear zones.A long stabilization phase, with low exhumation, and cooling rate around 0.25degreesC/Ma was recorded from the Cambro/Ordovician to the Mesozoic. At 65 Ma an acceleration of the exhumation through denudation and reworking of the South American surface with cooling rate of 1.5degreesC/Ma is observed.The uplift of the Mantiqueira and Serra do Mar mountain ranges along the southeast Brazilian coastline works as a climatic barrier provoking lateral erosional processes causing long-term scarp retreat, combined with intense, but progressive denudation towards the continent. A denudation of 2.5 to 4 km was calculated for such processes. This lateral retreat of escarpments and flexural response can provide important insights regarding marginal isostatic uplift and the evolution of offshore sedimentary basins of southeast Brazil.

ACCELERATING ITERATIVE ALGORITHMS FOR SYMMETRICAL LINEAR COMPLEMENTARITY-PROBLEMS

We propose a method for accelerating iterative algorithms for solving symmetric linear complementarity problems. The method consists in performing a one-dimensional optimization in the direction generated by a splitting method even for non-descent directions. We give strong convergence proofs and present numerical experiments that justify using this acceleration.

Analytic solutions for the Lambda-FRW model

The high precision attained by cosmological data in the last few years has increased the interest in exact solutions. Analytic expressions for solutions in the Standard Model are presented here for all combinations of Lambda = 0, Lambda not equal 0, kappa = 0, and kappa = 0, in the presence and absence of radiation and nonrelativistic matter. The most complete case (here called the Lambda gamma CDM Model) has Lambda not equal 0, kappa not equal 0, and supposes the presence of radiation and dust. It exhibits clearly the recent onset of acceleration. The treatment includes particular models of interest such as the Lambda CDM Model (which includes the cosmological constant plus cold dark matter as source constituents).

Separation of particles in time-dependent focusing billiards

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

Efeitos da estimulação ultra-sônica sobre o processo de reparo em ferida de extração dental: estudo histológico em ratos.

The effects of ultrasound on the wound healing process after teeth extractions were studied histologically. The right upper incisor was extracted in 56 rats. They were divided into 2 groups, one control (I) and one experimental (II). Group II received ultrasound stimulation that was applied with the frequency of repetition of 1,000 Hz and pulse length of 2,000 us continuously, during five minutes daily since the extraction day until 24 hours before the death. The rats were sacrificed at 3, 6, 9, 12, 15, 18, and 21 postoperative days. The results showed a precocious granulation tissue formation, faster remodeling of osseous ridges, and consequently acceleration of the alveolar wound healing process.