Chaotic transport in reversed shear tokamaks

For tokamak models using simplified geometries and reversed shear plasma profiles, we have numerically investigated how the onset of Lagrangian chaos at the plasma edge may affect the plasma confinement in two distinct but closely related problems. Firstly, we have considered the motion of particles in drift waves in the presence of an equilibrium radial electric field with shear. We have shown that the radial particle transport caused by this motion is selective in phase space, being determined by the resonant drift waves and depending on the parameters of both the resonant waves and the electric field profile. Moreover, we have shown that an additional transport barrier may be created at the plasma edge by increasing the electric field. In the second place, we have studied escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall, when there are resonant modes due to the action of an ergodic magnetic limiter. A non-monotonic safety factor profile has been used in the analysis of field line topology in a region of negative magnetic shear. We have observed that, if internal modes are perturbed, the distributions of field line connection lengths and magnetic footprints exhibit spatially localized escape channels. For typical physical parameters of a fusion plasma, the two Lagrangian chaotic processes considered in this work can be effective in usual conditions so as to influence plasma confinement. The reversed shear effects discussed in this work may also contribute to evaluate the transport barrier relevance in advanced confinement scenarios in future tokamak experiments.

Experimental identification of chaotic fibers

In a 2D parameter space, by using nine experimental time series of a Clitia`s circuit, we characterized three codimension-1 chaotic fibers parallel to a period-3 window. To show the local preservation of the properties of the chaotic attractors in each fiber, we applied the closed return technique and two distinct topological methods. With the first topological method we calculated the linking, numbers in the sets of unstable periodic orbits, and with the second one we obtained the symbolic planes and the topological entropies by applying symbolic dynamic analysis. (C) 2007 Elsevier Ltd. All rights reserved.

Nonlinear Schrodinger equation with chaotic, random, and nonperiodic nonlinearity

In this Letter we deal with a nonlinear Schrodinger equation with chaotic, random, and nonperiodic cubic nonlinearity. Our goal is to study the soliton evolution, with the strength of the nonlinearity perturbed in the space and time coordinates and to check its robustness under these conditions. Here we show that the chaotic perturbation is more effective in destroying the soliton behavior, when compared with random or nonperiodic perturbation. For a real system, the perturbation can be related to, e.g., impurities in crystalline structures, or coupling to a thermal reservoir which, on the average, enhances the nonlinearity. We also discuss the relevance of such random perturbations to the dynamics of Bose-Einstein condensates and their collective excitations and transport. (C) 2010 Elsevier B.V. All rights reserved.

Numerical test of Born-Oppenheimer approximation in chaotic systems

We study the validity of the Born-Oppenheimer approximation in chaotic dynamics. Using numerical solutions of autonomous Fermi accelerators. we show that the general adiabatic conditions can be interpreted as the narrowness of the chaotic region in phase space. (C) 2009 Elsevier B.V. All rights reserved.

How complex a dynamical network can be?

Positive Lyapunov exponents measure the asymptotic exponential divergence of nearby trajectories of a dynamical system. Not only they quantify how chaotic a dynamical system is, but since their sum is an upper bound for the rate of information production, they also provide a convenient way to quantify the complexity of a dynamical network. We conjecture based on numerical evidences that for a large class of dynamical networks composed by equal nodes, the sum of the positive Lyapunov exponents is bounded by the sum of all the positive Lyapunov exponents of both the synchronization manifold and its transversal directions, the last quantity being in principle easier to compute than the latter. As applications of our conjecture we: (i) show that a dynamical network composed of equal nodes and whose nodes are fully linearly connected produces more information than similar networks but whose nodes are connected with any other possible connecting topology; (ii) show how one can calculate upper bounds for the information production of realistic networks whose nodes have parameter mismatches, randomly chosen: (iii) discuss how to predict the behavior of a large dynamical network by knowing the information provided by a system composed of only two coupled nodes. (C) 2011 Elsevier B.V. All rights reserved.

Synchronization versus staggering of price changes in Brazil

Apesar de diversos modelos assumirem que os preços não se ajustam sincronizadamente, tanto a evidência empírica quanto a teórica são ambíguas. Este trabalho tem por objetivo identificar o comportamento dos reajustes de preço, analisando uma extensa base de dados brasileira. Foi encontrada uma evidência de escalonamento, mas quanto mais agregado são os dados, mais perto da sincronização perfeita eles estão. A economia brasileira também mostrou um alto grau de heterogeneidade, tanto na frequência quanto na sincronização dos ajustes de preço entre os produtos, as quais ainda variam com a taxa de inflação.

A note on learning chaotic sunspot equilibrium

In this paper we prove convergence to chaotic sunspot equilibrium through two learning rules used in the bounded rationality literature. The rst one shows the convergence of the actual dynamics generated by simple adaptive learning rules to a probability distribution that is close to the stationary measure of the sunspot equilibrium; since this stationary measure is absolutely continuous it results in a robust convergence to the stochastic equilibrium. The second one is based on the E-stability criterion for testing stability of rational expectations equilibrium, we show that the conditional probability distribution de ned by the sunspot equilibrium is expectational stable under a reasonable updating rule of this parameter. We also report some numerical simulations of the processes proposed.

Effect of timing of estradiol benzoate administration upon synchronization of ovulation in suckling Nelore cows (Bos indicus) treated with a progesterone-releasing intravaginal device

The present study investigated how the timing of the administration of estradiol benzoate (EB) impacted the synchronization of ovulation in fixed-time artificial insemination protocols of cattle. To accomplish this, two experiments were conducted, with EB injection occurring at different times: at withdrawal of the progesterone-releasing (N) intravaginal device or 24 h later. The effectiveness of these times was compared by examining ovarian follicular dynamics (Experiment 1, n = 30) and conception rates (Experiment 2, n = 504). In Experiment 1, follicular dynamics was performed in 30 Nelore cows (Bos indicus) allocated into two groups. on a random day of the estrous cycle (Day 0), both groups received 2 mg of EB i.m. and a P4-releasing intravaginal device, which was removed on Day 8, when 400 IU of eCG and 150 mu g of PGF were administered. The control group (G-EB9; n = 15) received 1 mg of EB on Day 9, while Group EB8 (G-EB8; n = 15) received the same dose a day earlier. Ovarian ultrasonographic evaluations were performed every 8 h after device removal until ovulation. The timing of EB administration (Day 8 compared with Day 9) did affect the interval between P4 device removal to ovulation (59.4 +/- 2.0 h compared with 69.3 +/- 1.7 h) and maximum diameter of dominant (1.54 +/- 0.06 a cm compared with 1.71 +/- 0.05 b cm, P = 0.03) and ovulatory (1.46 +/- 0.05 a cm compared with 1.58 +/- 0.04 b cm, P < 0.01) follicles. In Experiment 2,504 suckling cows received the same treatment described in Experiment 1, but insemination was performed as follows: Group EB8-AI48h (G-EB8-AI48h; n = 119) and Group EB8-AI54h (G-EB8-AI54h; n = 134) received 1 mg of EB on Day 8 and FrAI was performed, respectively, 48 or 54 h after P4 device removal. Group EB9-AI48h (G-EB9-AI48h; n = 126) and Group EB9-AI54h (G-EB9-AI54h n = 125) received the same treatments and underwent the same FTAI protocols as G-EB8-AI48h and G-EB8-AI54h, respectively; however, EB was administered on Day 9. Conception rates were greater (P < 0.05) in G-EB9-AI54h 163.2% (79/125) a], G-EB9-AI48h [58.7% (74/126) a] and G-EB8-AI48h [58.8% (70/119) a] than in G-EB8-AI54h [34.3% (46/134) b]. We concluded that when EB administration occurred at device withdrawal (D8), the interval to ovulation shortened and dominant and ovulatory follicle diameters decreased. Furthermore, when EB treatment was performed 24 h after device removal, FTAI conducted at either 48 or 54 h resulted in similar conception rates. However, EB treatment on the same day as device withdrawal resulted in a lesser conception rate when FTAI was conducted 54 h after device removal. (C) 2007 Elsevier B.V. All rights reserved.

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Chaotic diffusion caused by close encounters with several massive asteroids The (4) Vesta case

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Progesterone-based estrous synchronization protocols in non-suckled and suckled primiparous Bos indicus beef cows

In Experiment 1, effects of an intravaginal progesterone insert (CIDR) for synchronization of estrus in non-suckled cycling primiparous Bos indicus beef cows were evaluated. Cows received either no treatment (Control), prostaglandin F(2 alpha) (PGF), or CIDR (6 d)+prostaglandin F(2 alpha) (CIDR+PGF). There were greater (P<0.05) percentages of cows inseminated and pregnant in 4 d of breeding season in CIDR+PGF (81.6%; 48.7%) than in PGF (53.8%; 32.5%) and Control cows (14.6%; 8.5%). In Experiment 2, efficacy of a treatment with CIDR (6 d)+prostaglandin F(2 alpha)+48 h temporary weaning (CIDR+PGF+TW) associated or not with equine chorionic gonadotropin (eCG) for synchronization of estrus in suckled primiparous B. indicus beef cows was evaluated. Cows were assigned to receive either no treatment (Control), CIDR+PGF+TW, CIDR+PGF+TW+200 IU of eCG, or CIDR+PGF+IW+400 IU of eCG. There were greater (P<0.05) percentages of insemination and pregnancy in 4 d of breeding season in treatment groups (47.0%; 27.5%) than in Control cows(4.5%; 3.0%) and in cows treated with eCG (50.9%; 29.4%) than in cows treated only with CIDR+PGF+TW (39.4%: 23.7%). No effects of eCG dosage were detected. The percentage of cows inseminated and pregnant in a 30 d breeding season were greater (P<0.05) in cows assigned to synchronization treatments (53.3%; 37.2%) than in Control cows (35.3%; 21.4%). In the beginning of the BS, non-suckled primiparous cows treated with CIDR+PGF with estrous cycles having been initiated following calving had greater estrous detection and pregnancy rates than PGF and Control cows, and suckled primiparous cows had improved estrous detection and pregnancy rates when eCG was associated with CIDR+PGF+TW. (C) 2009 Elsevier B.V. All rights reserved.

Development of estrous synchronization protocols using melengestrol acetate in Bos indicus cattle

Five experiments were conducted on commercial farms in Brazil designed to develop the basis for an estrus synchronization protocol using melengestrol acetate (MGA) in Bos indicus cattle. These studies resulted in the development of the following protocol: 0.5 mg.d(-1) of MGA between d -14 and -1; 2.0 mg i.m. injection of estradiol cypionate on d -9; 48 h temporary weaning between d 0 and 2; and natural service beginning on d 0. The basis of this protocol was to induce estrous cyclicity before postpartum loss of body condition, prevent premature luteolysis, eliminate the need for labor required to detect estrus, and consequently increase the likelihood of pregnancy early during the postpartum period. This treatment effectively induced estrous cyclicity among anestrous cows, synchronized estrus activity, and prevented premature luteolysis with no negative effect on pregnancy.

Ovarian response of Suffolk ewes to estrous synchronization using short-term protocol

The efficacy of estrus synchronization using short-term protocol was evaluated by ultrasound exams in Suffolk ewes during the pre-breeding season. The control Group (n = 12) was synchronized by treatment for 12 days with vaginal sponges impregnated with medroxyprogesterone acetate, and 400 IU eCG at sponge withdrawal. Experimental groups I, II and III kept the sponge in place for 4 days, and 100 µg of PGF2a was administered at sponge withdrawal. Additionally, Group I (n = 12) had 0.1 mg of estradiol benzoate (EB) administered during sponge placement and 50 µg of GnRH 48 hours after sponge removal. Group II (n = 6) had 35 mg of progesterone (P4) injected, and 0.1 mg of EB administered during sponge placement, 400 IU eCG at withdrawal and 48 hours after, 50 µg GnRH were administrated. Group III (n = 12) had 35 mg of P4 and 0.2 mg of EB administered at sponge placement, 400 IU eCG at withdrawal, and 50 µg of GnRH was administrated after 56 hours. Ovaries were monitored through ultrasound scanning. Concerning the first wave, no difference was detected between the control group and the experimental groups. However, the characteristics of ovulatory wave were significantly different between the groups. The duration of the follicular wave was shorter for Group III than for Group II. The follicle in Group I reached its maximum diameter before the Group II. The diameter of the follicle at the sponge withdrawal in the control group was larger than in Group I. After sponge withdrawal, the follicular growth rate was smaller in the control group than in Group III. The maximum diameter of the follicle in Group II was larger than in the other groups. The short-term protocol in which estrogen was used did not synchronize the emergence of the wave of follicular development.