Peculiar trajectories around the Lagrangian equilateral points

In the present work we analyse the behaviour of a particle under the gravitational influence of two massive bodies and a particular dissipative force. The circular restricted three body problem, which describes the motion of this particle, has five equilibrium points in the frame which rotates with the same angular velocity as the massive bodies: two equilateral stable points (L-4, L-5) and three colinear unstable points (L-1, L-2, L-3). A particular solution for this problem is a stable orbital libration, called a tadpole orbit, around the equilateral points. The inclusion of a particular dissipative force can alter this configuration. We investigated the orbital behaviour of a particle initially located near L4 or L5 under the perturbation of a satellite and the Poynting-Robertson drag. This is an example of breakdown of quasi-periodic motion about an elliptic point of an area-preserving map under the action of dissipation. Our results show that the effect of this dissipative force is more pronounced when the mass of the satellite and/or the size of the particle decrease, leading to chaotic, although confined, orbits. From the maximum Lyapunov Characteristic Exponent a final value of gamma was computed after a time span of 10(6) orbital periods of the satellite. This result enables us to obtain a critical value of log y beyond which the orbit of the particle will be unstable, leaving the tadpole behaviour. For particles initially located near L4, the critical value of log gamma is -4.07 and for those particles located near L-5 the critical value of log gamma is -3.96. (c) 2006 Elsevier B.V. All rights reserved.

Three-body problem, its Lagrangian points and how to exploit them using an alternative transfer to L4 and L5

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

The use of the challenge test to analyse preservative efficiency in non-sterile cosmetic and health products: applications and critical points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimization of Radial Basis Function neural network employed for prediction of surface roughness in hard turning process using Taguchi's orthogonal arrays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fixed points and vacuum energy of dynamically broken gauge theories

We show that if a gauge theory with dynamical symmetry breaking has nontrivial fixed points, they will correspond to extrema of the vacuum energy. This relationship provides a different method to determine fixed points.

Uses of QCD sumrules (QCDSR) from different points of view

We support the idea that the baryon, B with mass MB, couples to its current with a coupling λ2 B ∼ 0.71 M6 B from an analysis of magnetic moment sum rules. And we find a sum rule among the experimental magnetic moments which is independent of the parameters of QCDSR. © 1998 Elsevier Science B.V. All rights reserved.

Turning math attractive to computer science students: an application-to-model approach

This paper describes an innovative approach to develop the understanding about the relevance of mathematics to computer science. The mathematical subjects are introduced through an application-to-model scheme that lead computer science students to a better understanding of why they have to learn math and learn it effectively. Our approach consists of a single one semester course, taught at the first semester of the program, where the students are initially exposed to some typical computer applications. When they recognize the applications' complexity, the instructor gives the mathematical models supporting such applications, even before a formal introduction to the model in a math course. We applied this approach at Unesp (Brazil) and the results include a large reduction in the rate of students that abandon the college and better students in the final years of our program.

Surface amorphization in diamond turning of silicon crystal investigated by transmission electron microscopy

Silicon crystal exhibits a ductile regime during machining prior to the onset of fracture when appropriate cutting conditions are applied. The present study shows that the ductile regime is a result of a phase transformation which is indirectly evidenced by the amorphous phase detected in the machined surface. Transmission electron microscopy (TEM) planar view studies were successfully performed on monocrystalline silicon (1 0 0) single point diamond turned. TEM electron diffraction patterns show that the machined surface presents diffuse rings along with traces of crystalline material. This is attributed to crystalline silicon immersed in an amorphous matrix. Furthermore, only diffuse rings in the diffraction patterns of the ductile chip are detected, indicating that it is totally amorphous. © 2000 Elsevier Science B.V. All rights reserved.

In vitro antimicrobial activity of different gutta-percha points and calcium hydroxide pastes

The aim of this study was to evaluate the antimicrobial activity of different trademarks and compositions of gutta-percha points and calcium hydroxide pastes used in endodontic therapy. The evaluated material consisted of gutta-percha points containing calcium hydroxide (Roeko™), gutta-percha points containing chlorhexidine (Roeko™), two convencional gutta-percha points (Endo Points™ and Roeko™) and two calcium hydroxide pastes (Calen™ and Calen/PMCC™). Antimicrobial tests included five species of microorganisms: Escherichia coli (ATCC10538), Staphylococcus epidermidis (ATCC12228), Staphylococcus aureus (ATCC6538), Pseudomonas aeruginosa (ATCC27853), and Micrococcus luteus (ATCC9341). The Agar difusion method was employed. The plates were kept at room temperature for 2 h for prediffusion and then incubated at 37°C for 24 h. The triphenyltetrazolium chloride gel was added for optimization and the zones of inhibition were measured. Statistical evaluation was carried out using analysis of variance and Tukey Test. The obtained results showed that all microbial species used in the study were inhibited by the gutta-percha points containing chlorhexidine and by the calcium hydroxide pastes (Calen™ and Calen/ PMCC™), with similar results (p > 0.05). No antimicrobial activity was observed for the other groups. It was concluded that the gutta-percha points containing chlorhexidine presented antimicrobial activity, whereas the gutta-percha points containing calcium hydroxide did not.

Influence of brush type as a carrier of adhesive solutions and paper points as an adhesive-excess remover on the resin bond to root dentin

Purpose: To evaluate the influence of the brush type as a earner of priming adhesive solutions and the use of paper points as a remover of the excess of these solutions on the push-out bond strength of resin cement to bovine root dentin. The null hypotheses were that brush type and the use of paper points do not affect the bond strength. Materials and Methods: The canals of 80 single-root bovine roots (16 mm in length) were prepared at 12 mm using the preparation drill (FRC Postec Plus, Ivoclar). Half of each root was embedded in acrylic resin and the specimens were divided into 8 groups, considering the factors brush type (4 levels) and paper point (2 levels) (n = 10): Gr 1: small microbrush (Cavi-Tip, SDI); Gr 2: Microbrush (Dentsply); Gr 3: Endobrush (Bisco); Gr 4: conventional brush (Bisco); Gr 5: Cavi-Tip (SDI) + paper points; Gr 6: Microbrush (Dentsply) + paper points; Gr 7: Endobrush (Bisco) + paper points; Gr 8: conventional brush (Bisco) + paper points. The root dentin was treated with a multistep total-etch adhesive system (All Bond 2). The adhesive system was applied using each microbrush, with and without using paper points. One fiber post was molded with addition silicon and 80 posts were made of resin cement (Duolink), The resin posts were luted (Duolink resin cement), and the specimens were stored for 24 h in water at 37°C. Each specimen was cut into 4 disk-shaped samples (1.8 mm in thickness), which were submitted to the push-out test. Results: The brush type (p < 0.0001) (small microbrush > microbrush = endobrush = conventional brush) and the use of paper points (p = 0.0001) (with > without) influenced the bond strength significantly (two-way ANOVA). The null hypotheses were rejected. Conclusion: The smallest brush (Cavi-Tip) and the use of paper points significantly improved the resin bond to bovine root dentin.

Evaluation of the performance of α-SiAlON tool when turning Ti-6Al-4V alloy without coolant

Due to their high hardness and wear resistance, Si3N4 based ceramics are one of the most suitable cutting tool materials for machining cast iron, nickel alloys and hardened steels. However, their high degree of brittleness usually leads to inconsistent results and sudden catastrophic failures. This necessitates a process optimization when machining superalloys with Si3N4 based ceramic cutting tools. The tools are expected to withstand the heat and pressure developed when machining at higher cutting conditions because of their high hardness and melting point. This paper evaluates the performance of α-SiAlON tool in turning Ti-6Al-4V alloy at high cutting conditions, up to 250 m min-1, without coolant. Tool wear, failure modes and temperature were monitored to access the performance of the cutting tool. Test results showed that the performance of α-SiAl0N tool, in terms of tool life, at the cutting conditions investigated is relatively poor due probably to rapid notching and excessive chipping of the cutting edge. These facts are associated with adhesion and diffusion wear rate that tends to weaken the bond strength of the cutting tool.

Comparative study on turning CI and CGI using silicon nitride cutting tools

There has been a great interest for improving the machining of cast iron materials in the automotive and other industries. Comparative studies for tool used to machine grey cast iron (CI) and compacted graphite iron (CGI) on dry machining were also performed in order to find out why in this case the tool lifetime is not significantly higher. However the machining these materials while considering turning with the traditional high-speed steel and carbide cutting tools present any disadvantages. One of these disadvantages is that all the traditional machining processes involve the cooling fluid to remove the heat generated on workpiece due to friction during cutting. This paper present a new generation of ceramic cutting tool exhibiting improved properties and important advances in machining CI and CGI. The tool performance was analyzed in function of flank wear, temperature and roughness, while can be observed that main effects were found for tool wear, were abrasion to CI and inter-diffusion of constituting elements between tool and CGI, causing crater. However the difference in tool lifetime can be explained by the formation of a MnS layer on the tool surface in the case of grey CI. This layer is missing in the case of CGI.

Turning of compacted graphite iron using commercial tiN coated Si 3N4 under dry machining conditions

Due to their high hardness and wear resistance Si3N4 based ceramics are one of the most suitable cutting tool materials for machining hardened materials. Therefore, their high degree of brittleness usually leads to inconsistent results and sudden catastrophic failures. Improvement of the functional properties these tools and reduction of the ecological threats may be accomplished by employing the technology of putting down hard coatings on tools in the state-of-the-art PVD processes, mostly by improvement of the tribological contact conditions in the cutting zone and by eliminating the cutting fluids. However in this paper was used a Si3N4 based cutting tool commercial with a layer TiN coating. In this investigation, the performance of TiN coating was assessed on turning used to machine an automotive grade compacted graphite iron. As part of the study were used to characterise the performance of cutting tool, flank wear, temperature and roughness. The results showed that the layer TiN coating failed to dry compacted graphite iron under aggressive machining conditions. However, using the measurement of flank wear technique, the average tool life of was increased by VC=160 m/min.The latter was also observed using a toolmakers microscope and scanning electron microscopy (SEM).

Interplanetary natural routes via Moon and Lagrangiam points L1 and L2

Swing-by techniques are extensively used in interplanetary missions to minimize fuel consumption and to raise payloads of spaceships. The effectiveness of this type of maneuver has been proven since the beginning of space exploration. According to this premise, we have explored the existence of a natural and direct links between low Earth orbits and the lunar sphere of influence, to obtain low-energy interplanetary trajectories through swing-bys with the Moon and the Earth. The existence of these links are related to a family of retrograde periodic orbits around the Lagrangian equilibrium point L1 predicted for the circular, planar, restricted three-body Earth-Moon-particle problem. The trajectories in these links are sensitive to small disturbances. This enables them to be conveniently diverted reducing so the cost of the swing-by maneuver. These maneuvers allow us a gain in energy sufficient for the trajectories to escape from the Earth-Moon system and to stabilize in heliocentric orbits between the Earth and Venus or Earth and Mars. On the other hand, still within the Earth sphere of influence, and taking advantage of the sensitivity of the trajectories, is possible to design other swing-bys with the Earth or Moon. This allows the trajectories to have larger reach, until they can reach the orbit of other planets as Venus and Mars.(3σ)Broucke, R.A., Periodic Orbits in the Restricted Three-Body Problem with Earth-Moon Masses, JPL Technical Report 32-1168, 1968.

Cutting performance of diamond coated Si3N4 tool during turning

Silicon nitride cutting tools have been used successfully for machining hard materials, like: cast irons, nickel based alloys, etc. However these cutting tools with diamond coating present little information on dry turning operations of gray cast iron. In the present work, Si3N4 square inserts was developed, characterized and subsequently coated with diamond for dry machining operations on gray cast iron. All experiments were conducted with replica. It was used a 1500, 3000, 4500 m cutting length, feed rate of 0.33 mm/rev and keeping the depth of cut constant and equal to 1 mm. The results show that wear in the tool tips of the Si3N4 inserts, in all cutting conditions, was caused by both mechanical and chemical processes. To understand the tool wear mechanisms, a morphological analysis of the inserts, after experiments, has been performed by SEM and optical microscopy. Diamond coated PVD inserts showed to be capable to reach large cutting lengths when machining gray cast iron. © (2010) Trans Tech Publications.