The Liapunov exponent as a tool for exploring phase space

We have used the Liapunov exponent to explore the phase space of a dynamical system. Considering the planar, circular restricted three-body problem for a mass ratio mu = 10(-3) (close to the Jupiter/Sun case), we have integrated similar to 16,000 starting conditions for orbits started interior to that of the perturber and we have estimated the maximum Liapunov characteristic exponent for each starting condition. Despite the fact that the integrations, in general, are for only a few thousand orbital periods of the secondary, a comparative analysis of the Liapunov exponents for various values of the 'cut-off' gives a good overview of the structure of the phase space. It provides information about the diffusion rates of the various chaotic regions, the location of the regular regions associated with primary resonances and even details such as the location of secondary resonances that produce chaotic regions inside the regular regions of primary resonances.

Influence of age on the behavior of dental pulp of dog teeth after capping with an adhesive system or calcium hydroxide

This study evaluated histomorphologically the influence of chronological age of the dog on the dental pulp-healing process after capping with the All Bond 2 system or with calcium hydroxide paste. The animals were divided according to age into young and adult groups. Class 5-type cavities were prepared, and the pulp was submitted to an exposure of a diameter of 0.5 mm. The pulp of the teeth was then protected with the adhesive system or with a calcium hydroxide paste. Sixty days after treatment, the results obtained with the adhesive system in the young group were significantly better than those in the adult group. With calcium hydroxide, the results were similar for both groups. The pulp treated with calcium hydroxide exhibited a complete hard tissue bridge and a pulp without inflammatory reaction, a fact not observed when the adhesive system was used. In conclusion, the chronological age of the pulp influenced the comparative results only for the adhesive system (P = 0.1), and the total results were better with calcium hydroxide than with the All Bond 2 system (P = 0.01).

Polymerization shrinkage: effects of boundary conditions and filling technique of resin composite restorations

Objective: To evaluate the linear polymerization shrinkage (LPS) and the effect of polymerization shrinkage of a resin composite and resin-dentin bond strength under different boundary conditions and filling techniques.Methods: Two cavities (4 x 4 x 2 MM) were prepared in bovine incisors (n = 30). The teeth were divided into three groups, according to boundary conditions: In group TE, the total-etch technique was used. In group EE, only enamel was conditioned, and in group NE, none of the watts of the cavities were conditioned. A two-step adhesive system was applied to all cavities. The resin composite was inserted in one (B) or three increments (1), and tight-cured with 600 mW/cm(2) (80 s). The LPS (%) was measured in the top-bottom direction, by placing a probe in contact with resin composite during curing. Enamel and total mean gap widths were measured (400 x) in three slices obtained after sectioning the restorations. Then, the slices were sectioned again, either to obtain sticks from the adhesive interface from the bottom of the cavity or to obtain resin composite sticks (0.8 mm(2)) to be tested for tensile strength (Kratos machine, 0.5 mm/min). The data was subjected to a two-way repeated measures ANOVA and Tukey's test for comparison of the means (alpha = 0.05).Results: the highest percentage of LPS was found for the TE when bulk fitted, and the lowest percentage of LPS was found in the Hand NE when incrementally fitted. The resin dentin bond strength was higher and the total mean gap width was tower for TE group; no significant effect was detected for the main factor fitting techniques. No difference was detected for the tensile strength of resin composite among the experimental groups.Conclusions: the filling technique is not able to minimize effects of the polymerization shrinkage, and bonding to the cavity watts is necessary to assure reduced mean gap width and high bond strength values. (C) 2004 Elsevier Ltd. All rights reserved.

Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).

Influence from the free volume on the photoinduced birefringence in azocompound-containing polymers

The photoinduced birefringence is analyzed in a guest-host azobenzene-containing polymer in the temperature range from 20 to 330 K. An anomalous behavior arises in the low-temperature range, suggesting strong influence from the free volume for the chromophores in the polymer. This influence is so strong that quenched samples have a photoinduced signal ca. 5 times greater than the annealed ones at room temperature. An extended free volume model is presented based on two assumptions about thermal fluctuations in the cavities and their size distribution. This model, which is an extension of the model by Mita et al., can explain the main features of the photoinduced birefringence as a function of time, temperature, and initial free volume state. To account for the influence of free volume on the photoorientation, the detailed reorientation model by Sekkat's was used. We show that Sekkat's model leads to an exponential behavior at small orientation regimes, which simplifies the mathematical treatment and allows the mean free volume to be obtained from the data fitting.

Evaluation of autogenous bone grafts, particulate or collected during osteotomy with implant burs: Histologic and histomorphometric analysis in rabbits

Purpose: the aim of this study was to evaluate bone regeneration in bone cavities filled with particulate autogenous bone either harvest in blocks and subjected to milling procedures or collected during osteotomy with implant burs. Materials and Methods: In 12 rabbits, 3 noncritical unicortical cavities 7 mm in diameter were prepared with a trephine drill on the right tibia. The cavities were filled respectively with particulate autogenous bone achieved with a manual bone crusher ( particulate group), with particulate autogenous bone obtained using bone collector during osteotomy ( collected group), and with blood clot ( control group). Animals were sacrificed at 7, 15, and 30 days after surgery ( 4 animals for each time period). The sections were examined by histologic and histomorphometric analysis. Results: At 7 days, the samples were filled by coagulum, and bone particles were observed only in the collected (24%) and particulate groups (44.75%). At 15 days, there was connective differentiation in all groups, with presence of grafted bone particles and onset of newly formed bone in the collected (38.88%) and particulate groups (46.0%). At 30 days, there was bone fill ( immature trabecular bone) of the cavities in the control (50%), collected (64.63%) and particulate groups (66%). Conclusion: No significant difference was demonstrated between noncritical unicortical bone defects in rabbit tibiae filled with particulate bone harvested as a block and subjected to milling and those filled with bone collected during osteotomy with implant drills when the defects were observed up to 30 days following their creation.

Analysing the new Saturnian rings, R/2004 S1 and R/2004 S2

The Cassini-Huygens arrival into the Saturnian system brought a large amount of data about the satellites and rings. Two diffuse rings were found in the region between the A ring and Prometheus. R/2004 S1 is coorbital to Atlas and R/2004 S2 is close to Prometheus. In this work we analysed the closest approach between Prometheus and both rings. As a result we found that the satellite removes particles from R/2004 S2 ring. Long-term numerical simulations showed that some particles can cross the F ring region . The well known region of the F ring, where small satellites are present and particles are being taking from the ring, gains a new insight with the presence of particles from R/2004 S2 ring. The computation of the Lyapunov Characteristic Exponent reveled that the R/2004 S2 ring lies in a chaotic region while R/2004 S1 ring and Atlas are in a stable region. Atlas is responsible for the formation of three regimes in the R/2004 S1 ring, as expected for a satellite embedded in a ring.

Microleakage of hydrophilic adhesive systems in Class V composite restorations

Purpose: To investigate the microleakage of four hydrophilic adhesive systems: one multiple-bottles (Scotchbond Multi-Purpose Plus); two one-bottle (Single Bond, Stae); and one self-etching (Etch & Prime 3.0). Materials and Methods: 120 bovine incisor teeth were divided into four groups (n = 30) and Class V cavities were prepared at the cemento-enamel junction. The cavities were restored with the adhesive systems and with Z100 composite. The teeth were thermocycled 1,000 times between 5 +/- 2 degreesC and 55 +/- 2 degreesC with a dwell time of 1 min, and then placed in a 2% methylene blue dye (pH 7.0) for 4 hrs, washed and sectioned vertically through the center of the restorations. The qualitative evaluation was made by three examiners who distributed pre-established scores (0-4) for each tooth using a stereomicroscope at x30 magnification. Results: In enamel margins little microleakage was observed and the Kruskal-Wallis analysis did not show differences. In dentin margins the KruskaI-Wallis and multiple comparison analyses were applied: microleakage was significantly greater with Stae (median 3) and Scotchbond MP Plus (median 4). Single Bond (median 1) and Etch & Prime 3.0 (median 2) showed the best results in dentin margins, and the statistical analysis did not demonstrate differences in microleakage among these groups.

Pressure field along the axis of a high-power klystron amplifier

The pressure field in a high-power klystron amplifier is investigated to scale the ionic vacuum pump used to maintain the ultra high-vacuum in the device in order to increase its life-time. The investigation is conducted using an 1.3 GHz, 100 A - 240 keV high-power klystron with five reentrant coaxial cavities, assembled in a cylindrical drift tube 1.2 m long. The diffusion equation is solved to the regime molecular flow to obtain the pressure profile along the axis of the klystron drift tube. The model, solved by both analytical and numerical procedures, is able to determine the pressure values in steady-state case. This work considers the specific conductance and all important gas sources, as in the degassing of the drift tube and cavities walls, cathode, and collector. For the drift tube degassing rate equals to q(deg) = 2x10(-12) (-)mbar.L.s(-1) cm(-2) (degassing rate per unit area), to cavities q(cavity) = 3x10(-13) mbar.L.s(-1)cm(-2), to the cathode q(cathode) = 6x10(-9)_mbar.L.s(-1) and to the collector q(collector) = 6x10(-9) mbar.L.s(-1), it was found that a 10 L.s(-1) ionic vacuum pump connected in the output waveguide wall is suitable. In this case, the pressure obtained in the cathode is p(cathode) = 6.3x10(-9) mbar, in the collector p(collector) = 2.7x10(-9) mbar, and in the output waveguide p = 2.1x10(-9) mbar. Although only the steady-state case is analyzed, some aspects that may be relevant in a transient situation, for instance, when the beam hits the drift tube walls, producing a gas burst, is also commented.

Adhesive performance of dentin bonding agents applied in vivo and in vitro. Effect of intrapulpal pressure and dentin depth

The purpose of this study was to evaluate the influence of intrapulpal pressure and dentin depth on bond strengths of an etch-and-rinse and a self-etching bonding agent to dentin in vitro and in vivo. Twenty-four pairs of premolars were randomly divided into four groups (n = 6) according to the dentin bonding agent, Single Bond and Clearfil SE Bond, and intrapulpal pressure, null or positive. Each tooth of the pair was further designated to be treated in vivo or in vitro. The intrapulpal pressure was controlled in vivo by the delivery of local anesthetics containing or not a vasoconstrictor, while in vitro, it was achieved by keeping the teeth under hydrostatic pressure. Class I cavities were prepared and the dentin bonding agents were applied followed by incremental resin restoration. For the teeth treated in vitro, the same restorative procedures were performed after a 6 month-storage period. Beams with I mm 2 cross-sectional area were prepared and, microtensile tested. Clearfil SE Bond was not influenced by any of the variables of the study, while bond strengths produced in vitro were significatly higher for Single Bond. Overall, lower bond strengths were produced in deep dentin, which reached statistical significance when Single Bond was applied under physiological or simulated intrapulpal pressure. In conclusion, in vitro bonding may overestimate the immediate adhesive performance of more technique-sensitive dentin bonding systems. The impact of intrapulpal pressure on bond strength seems to be more adhesive dependent than dentin morphological characteristics related to depth. (C) 2007 Wiley Periodicals, Inc.

Evaluation of cutting patterns produced in primary teeth by an air-abrasion system

Objective: the aim of this in vitro study was to assess the effect of tip diameter, nozzle distance, and application time of an air-abrasion system for cavity preparation on the enamel of primary teeth. Method and materials: Forty exfoliated primary teeth were air abraded with a microabrasion machine used with a handpiece with an 80-degree-angle nozzle, 50-mum abrasive particle size, and 80-psi air pressure. The effects of 0.38- or 0.48-mm inner tip diameter, 2- or 5-mm distance from tip to tooth surface, and 15 or 30 seconds of application time on cutting efficiency were evaluated. Cutting width and depth were analyzed and measured from scanning electron micrographs. Results: Statistical analysis revealed that the width of the cuts was significantly greater when the tip distance was increased. Significantly deeper cavities were produced by a tip with a 0.48-mm inner diameter. The application time did not influence the cuts. Conclusion: the cutting patterns found in this study suggest that precise removal of enamel in primary teeth is best accomplished when a tip with a 0.38-mm inner diameter is used at a 2-mm distance.

SEMICLASSICAL THEORY OF MAGNETIZATION FOR A 2-DIMENSIONAL NONINTERACTING ELECTRON-GAS

We compute the semiclassical magnetization and susceptibility of non-interacting electrons, confined by a smooth two-dimensional potential and subjected to a uniform perpendicular magnetic field, in the general case when their classical motion is chaotic. It is demonstrated that the magnetization per particle m(B) is directly related to the staircase function N(E), which counts the single-particle levels up to energy E. Using Gutzwiller's trace formula for N, we derive a semiclassical expression for m. Our results show that the magnetization has a non-zero average, which arises from quantum corrections to the leading-order Weyl approximation to the mean staircase and which is independent of whether the classical motion is chaotic or not. Fluctuations about the average are due to classical periodic orbits and do represent a signature of chaos. This behaviour is confirmed by numerical computations for a specific system.

Polymeric organic-inorganic hybrid material containing iron(III) porphyrin using sol-gel process

Here we describe the preparation of iron(II) porphyrinosilica in a simple one-pot reaction, where the -SO2Cl groups present in the phenyl rings of FeTDCSPP+ react with 3-aminopropyltriethoxysilane and tetraethoxysilane in the presence of a nitrogenous base, leading to iron(III) porphyrinosilica. In this same procedure, molecular cavities containing regularly spaced functional groups are created through the molecular imprinting technique, in which the nitrogenous base coordinated to the iron(III) porphyrin serves as a template. The removal of such template in a Soxhlet extractor leads to a cavity with the same shape and size as the nitrogenous base, enabling the construction of shape-selective catalysts mimicking cytochrome P-450. Five different imprinting molecules have been used: imidazole, 1-methylimidazole, 2-methylbenzimidazole, 4-phenylimidazole and miconazole and ultra-violet/visible absorption spectroscopy, thermogravimetric analysis and electron paramagnetic resonance carried out. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Microleakage and nanoleakage: Influence of laser in cavity preparation and dentin pretreatment

Objective: the purpose of this study was to verify if the application of the Nd:YAG laser following pretreatment of dentin with adhesive systems that were not light cured in class V cavities and were prepared with Er:YAG laser would promote better sealing of the gingival margins when compared to cavities prepared the conventional way. Background Data: Previous studies had shown that the pretreatment of dentin with laser irradiation after the application of an adhesive system is efficient in achieving higher shear bond and tensile bond strength. Materials and Methods: Er:YAG laser (Kavo-Key, Germany) with 350 mJ, 4 Hz, and 116.7 J/cm(2) was used for cavity preparation. The conventional preparation was made with diamond bur mounted in high-speed turbine. Dentin treatment was accomplished using an Nd:YAG laser (Pulse Master 1000, ADT. USA) at 60 mJ, 10 Hz, and 74.65/cm(2) following application of the adhesive system. The cavities were stored with Single Bond/Z100 and Prime & Bond NT/TPH. Eighty bovine incisors were used, and class V preparations were done at buccal and lingual surfaces divided into eight groups: (1) Er:YAG preparation + Prime & Bond NT + TPH; (2) Er:YAG preparation + Single Bond + Z100; (3) Er:YAG preparation + Single Bond + Nd:YAG + Z100; (4) Er:YAG preparation + Prime & Bond NT + Nd:YAG + TPH; (5) conventional preparation + Prime & Bond NT + TPH; (6) conventional preparation + Single Bond + Z100; (7) conventional preparation + Single Bond + Nd:YAG + Z100; (8) conventional preparation + Prime & Bond NT + Nd:YAG + TPH. All specimens were thermocycled for 300 full cycles between 5 degreesC +/- 2 degreesC and 55 degreesC +/- 2 degreesC (dwell time of 30 sec), and stored in 50% silver nitrate solution for 24 h soaked in photodeveloping solution and exposed to fluorescent light for 6 h. After this procedure, the specimens were sectioned longitudinally in 3 portions and the extension of microleakage at the gingival wall was determined following a criteria ranging from 0 to 4 using scanning electron microscopy (SEM). The medium portion sectioned of each specimen was polished and prepared for nanoleakage avaliation by SEM. Results: Kruskall-Wallis and Miller statistical tests determined that group 3 presented less microleakage and nanoleakage. Conclusion: Application of the Nd:YAG laser following pretreatment of dentin with adhesive Single Bond non-photocured Single Bond adhesive in cavities prepared with Er:YAG promote better sealing of the gingival margins.

The strands of the F ring disturbed by its closest satellites

Some Voyager images showed that the F ring of Saturn is composed of at least four separate, non-intersecting, strands covering about 45 degrees in longitude. According to Murray et al. [Murray, C.D., Gordon, M., Giuliatti Winter, S.M. Unraveling the strands of Saturn's F ring. Icarus 129, 304, 1997.] this structure may be caused by undetected satellites embedded in the gaps.Due to precession, the satellites Prometheus and Pandora and the ring particles can experience periodic close encounters. Giuliatti Winter et al. [Giuliatti Winter, S.M, Murray, C.D., Gordon, M. Perturbations to Saturn's F-ring strands at their closest approach to Prometheus. Plan. Space Sciences, 48, 817, 2000.] analysed the behaviour of these four strands at closest approach with the satellite Prometheus. Their work suggests that Prometheus can induce the ring particles to scatter in the direction of the planet, thus increasing the population of small bodies in this region.In this work we analysed the effects of Prometheus on the radial structure of Saturn's F ring during the Voyager and early Cassini epochs. Our results show that at Voyager epoch Prometheus, and also Pandora, had a negligible influence in the strands. However, during the Cassini encounter Prometheus could affect the strands significantly, scattering particles of the inner strand in the direction of the planet. This process can contribute to the replenishment of material in the region between the F ring and the A ring, where two rings have recently been discovered [Porco, C. et al. Cassini imaging science. Initial results on Saturn's rings and small Satellites. Science, 307, 1226, 2005].We also analyse the behaviour of undetected satellites under the effects of these two satellites by computing the Lyapunov Characteristic Exponent. Our results show that these satellites have a chaotic behaviour which leads to a much more complex scenario. The new satellite S/2004 S6 also presents a chaotic behaviour with can alter the dynamic of the system, since this satellite crosses the orbit of the strands. (C) 2006 COSPAR. Published by Elsevier Ltd. All rights reserved.