LOW-ENERGY BEHAVIOR OF FEW-PARTICLE SCATTERING-AMPLITUDES IN 2 DIMENSIONS

A study of the analytic behavior of different few-particle scattering amplitudes at low energies in two space dimensions is presented. Such a study is of use in modeling and understanding different few-particle processes at low energies. A detailed discussion of the energy and the momentum dependence of the partial-wave on-the-energy-shell and off-the-energy-shell two-particle t matrices is given. These t-matrix elements tend to zero as the energy and momentum variables tend to zero. The multiple-scattering series is used to show that the connected three-to-three amplitudes diverge in the low-energy-momentum limit. Unitarity relations are used to show that the connected two-to-three and one-to-three amplitudes have specific logarithmic singularities at the m-particle breakup threshold. The subenergy singularity in the two-to-three amplitudes is also studied, and comments are made on some applications of the present study in different problems of ph cal interest.

Influence of seed particle frequency on the phase formation and on the microstructure of 0.88 PZN-0.07 BT-0.05 PT ceramic

The Pechini method as well as the simultaneous addition of seeds particles and dopant solutions of BaTiO3 (BT) and PbTiO3 (PT) were used to prepare the perovskite phase 0.88 PZN-0.07 BT-0.05 PT. To study the influence of seed particle frequency on the synthesis of the PZN ceramic, two ranges of seed particle size were used: the range from 30 to 100 nm, termed small seed particles (frequency of 10(15) particles/cm(3)); and the range from 100 to 900 nm, termed large seed particles (frequency of 10(13) particles/cm(3)). The crystalline nuclei size influenced the calcining process, the sintering process and the microstructure. Samples prepared with lower seed frequency displayed more amount of pyroclore phase, need higher temperatures for sintering and showed a more heterogeneous microstructure with poor dielectric properties. (C) 2000 Elsevier B.V. Ltd and Techna S.r.l. All rights reserved.

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.

Effect of airborne particle abrasion protocols on surface topography of Y-TZP ceramic

This study aimed to evaluate Y-TZP surface after different airborne particle abrasion protocols. Seventy-six Y-TZP ceramic blocks (5×4×4) mm3 were sintered and polished. Specimens were randomly divided into 19 groups (n=4) according to control group and 3 factors: a) protocol duration (2 and 4 s); b) particle size (30 μm, alumina coated silica particle; 45 μm, alumina particle; and 145 μm, alumina particle) and; c) pressure (1.5, 2.5 and 4.5 bar). Airborne particle abrasion was performed following a strict protocol. For qualitative and quantitative results, topography surfaces were analyzed in a digital optical profilometer (Interference Microscopic), using different roughness parameters (Ra, Rq, Rz, X-crossing, Mr1, Mr2 and Sdr) and 3D images. Surface roughness also was analyzed following the primer and silane applications on Y-TZP surfaces. One-way ANOVA revealed that treatments (application period, particle size and pressure of particle blasting) provided significant difference for all roughness parameters. The Tukey test determined that the significant differences between groups were different among roughness parameters. In qualitative analysis, the bonding agent application reduced roughness, filing the valleys in the surface. The protocols performed in this study verified that application period, particle size and pressure influenced the topographic pattern and amplitude of roughness.

Trapping of a particle in a short-range harmonic potential well

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed. © 2012 Springer Science+Business Media, LLC.

Effect of air-particle abrasion protocols on the biaxial flexural strength, surface characteristics and phase transformation of zirconia after cyclic loading

This study evaluated the effect of air-particle abrasion protocols on the biaxial flexural strength, surface characteristics and phase transformation of zirconia after cyclic loading. Disc-shaped zirconia specimens (Ø: 15mm, thickness: 1.2mm) (N=32) were submitted to one of the air-particle abrasion protocols (n=8 per group): (a) 50μm Al2O3 particles, (b) 110μm Al2O3 particles coated with silica (Rocatec Plus), (c) 30μm Al2O3 particles coated with silica (CoJet Sand) for 20s at 2.8bar pressure. Control group received no air-abrasion. All specimens were initially cyclic loaded (×20,000, 50N, 1Hz) in water at 37°C and then subjected to biaxial flexural strength testing where the conditioned surface was under tension. Zirconia surfaces were characterized and roughness was measured with 3D surface profilometer. Phase transformation from tetragonal to monoclinic was determined by Raman spectroscopy. The relative amount of transformed monoclinic zirconia (FM) and transformed zone depth (TZD) were measured using XRD. The data (MPa) were analyzed using ANOVA, Tukey's tests and Weibull modulus (m) were calculated for each group (95% CI). The biaxial flexural strength (MPa) of CoJet treated group (1266.3±158A) was not significantly different than that of Rocatec Plus group (1179±216.4A,B) but was significantly higher than the other groups (Control: 942.3±74.6C; 50μm Al2O3: 915.2±185.7B,C). Weibull modulus was higher for control (m=13.79) than those of other groups (m=4.95, m=5.64, m=9.13 for group a, b and c, respectively). Surface roughness (Ra) was the highest with 50μm Al2O3 (0.261μm) than those of other groups (0.15-0.195μm). After all air-abrasion protocols, FM increased (15.02%-19.25%) compared to control group (11.12%). TZD also showed increase after air-abrasion protocols (0.83-1.07μm) compared to control group (0.59μm). Air-abrasion protocols increased the roughness and monoclinic phase but in turn abrasion with 30μm Al2O3 particles coated with silica has increased the biaxial flexural strength of the tested zirconia. © 2013 Elsevier Ltd.

The Linear Potential Propagator via Wave Function Expansion

ABSTRACT: We evaluate the quantum propagator for the motion of a particle in a linear potential via a recently developped formalism [A.B. Nassar et al., Phys. Rev. E56, 1230, (1997)]. In this formalism, the propagator comes about as a type of expansion of the wave function over the space of the initial velocities.

Determination of reactivity rates of silicate particle-size fractions

The efficiency of sources used for soil acidity correction depends on reactivity rate (RR) and neutralization power (NP), indicated by effective calcium carbonate (ECC). Few studies establish relative efficiency of reactivity (RER) for silicate particle-size fractions, therefore, the RER applied for lime are used. This study aimed to evaluate the reactivity of silicate materials affected by particle size throughout incubation periods in comparison to lime, and to calculate the RER for silicate particle-size fractions. Six correction sources were evaluated: three slags from distinct origins, dolomitic and calcitic lime separated into four particle-size fractions (2, 0.84, 0.30 and <0.30-mm sieves), and wollastonite, as an additional treatment. The treatments were applied to three soils with different texture classes. The dose of neutralizing material (calcium and magnesium oxides) was applied at equal quantities, and the only variation was the particle-size material. After a 90-day incubation period, the RER was calculated for each particle-size fraction, as well as the RR and ECC of each source. The neutralization of soil acidity of the same particle-size fraction for different sources showed distinct solubility and a distinct reaction between silicates and lime. The RER for slag were higher than the limits established by Brazilian legislation, indicating that the method used for limes should not be used for the slags studied here.

Influence of air-particle deposition protocols on the surface topography and adhesion of resin cement to zirconia

Objectives: This study evaluated the influence of air-particle abrasion protocols on the surface roughness (SR) of zirconia and the shear bond strength (SBS) of dual-polymerized resin cement to this ceramic. Materials and methods. Sintered zirconia blocks (n = 115) (Lava, 3M ESPE) were embedded in acrylic resin and polished. The specimens were divided according to the 'particle type' (Al: 110 mu m Al2O3; Si: 110 mu m SiO2) and 'pressure' factors (2.5 or 3.5 bar) (n = 3 per group): (a) Control (no air-abrasion); (b) Al2.5; (c) Si2.5; (d) Al3.5; (e) Si3.5. SR (Ra) was measured 3-times from each specimen after 20 s of air-abrasion (distance: 10 mm) using a digital optical profilometer. Surface topography was evaluated under SEM analyses. For the SBS test, 'particle type', 'pressure' and 'thermocycling' (TC) factors were considered (n = 10; n = 10 per group): Control (no air-abrasion); Al2.5; Si2.5; Al3.5; Si3.5; Control(TC); Al2.5(TC); Si2.5(TC); Al3.5(TC); Si3.5(TC). After silane application, resin cement (Panavia F2.0) was bonded and polymerized. Specimens were thermocycled (6.000 cycles, 5-55 degrees C) and subjected to SBS (1 mm/min). Data were analyzed using ANOVA, Tukey's and Dunnett tests (5%). Results. 'Particle' (p = 0.0001) and 'pressure' (p = 0.0001) factors significantly affected the SR. All protocols significantly increased the SR (Al2.5: 0.45 +/- 0.02; Si2.5: 0.39 +/- 0.01; Al3.5: 0.80 +/- 0.01; Si3.5: 0.64 +/- 0.01 mu m) compared to the control group (0.16 +/- 0.01 mu m). For SBS, only 'particle' factor significantly affected the results (p = 0.015). The SiO2 groups presented significantly higher SBS results than Al2O3 (Al2.5: 4.78 +/- 1.86; Si2.5: 7.17 +/- 2.62; Al3.5: 4.97 +/- 3.74; Si3.5: 9.14 +/- 4.09 MPa) and the control group (3.67 +/- 3.0 MPa). All TC specimens presented spontaneous debondings. SEM analysis showed that Al2O3 created damage in zirconia in the form of grooves, different from those observed with SiO2 groups. Conclusions. Air-abrasion with 110 mu m Al2O3 resulted in higher roughness, but air-abrasion protocols with SiO2 promoted better adhesion.

Instrumentação eletrônica para experimentação do modelo Bouncer Ball dissipativo

In our experiments, we studied the classical dynamic of a particle in vertical motion subject to a constant gravitational field and the partial shock with an elastic wall with oscillatory motion located below the particle. The motion of the particle was confined to the vertical direction by a glass guide tube, which was initially evacuated, allowing viscous drag forces to be disregarded. The time between impacts, as well as the time between the reference phase of the movement of the base and the moment of impact and the period of oscillation of the base will be acquired by a hardware and software to obtain the phases space to be compared later with the description of the system through mapping discrete variables via the 'particle velocity immediately after shock 'and' phase of the movement of the base at the instant of shock 'obtained by computer simulation. This requires developing an electronic analog system followed by Digital implemented in reconfigurable logic, more specifically a sequential machine able to discriminate the impact with the metal base from the impacts of the glass guide tube, based on the frequency spectrum of the response of the microphone to these different impacts

Effect of the particle size of maize, rice, and sorghum in extruded diets for dogs on starch gelatinization, digestibility, and the fecal concentration of fermentation products

The influence of rice, maize, and sorghum raw material particle size in extruded dry dog food on the digestibility of nutrients and energy and the fecal concentration of fermentation products was investigated. Three diets with similar nutrient compositions were formulated, each with 1 starch source. Before incorporation into diets, the cereals were ground into 3 different particle sizes (approximately 300, 450, and 600 mu m); therefore, a total of 9 diets were in a 3 x 3 factorial arrangement (3 cereals and 3 particle sizes). Fifty-four beagle dogs (12.0 +/- 0.1 kg BW) were randomly assigned to the diets, with 6 dogs per diet. The digestibility was measured with the chromium oxide method. The data were evaluated with ANOVA considering the carbohydrate source, grinding effect, and interactions. The means were compared with the Tukey test and polynomial contrasts (P < 0.05). With the same grinding procedure, rice was reduced to smaller particles than other cereals. The cereal mean geometric diameter (MGD) was directly related to starch gelatini-zation (SG) during extrusion. For rice diets, the MGD and SG did not change nutrient digestibility (P > 0.05); only GE digestibility was reduced at the largest MGD (P < 0.01). For maize and sorghum diets, the total tract apparent nutrient digestibility was reduced for foods with greater MGD and less SG (P < 0.01). A linear reduction in nutrient digestibility according to cereal particle size was observed for sorghum (r(2) < 0.72; P < 0.01). Higher concentrations of fecal total shortchain fatty acids (SCFA) were observed for sorghum diets (P < 0.05) than for other diets. The rice diets led to the production of feces with less lactate (P < 0.05). The increase in raw material MGD did not influence fecal SCFA for rice diets, but for the dogs fed maize and sorghum foods, an increase in propionate and butyrate concentrations were observed as MGD increased (P < 0.05). In conclusion, for dogs fed different particle sizes of the cereal starches in the extruded diets, the digestibility and fecal characteristics were affected, and this effect was ingredient dependent.

Mathematical modeling and analysis of the particle interactions in the direct filtration using the colloidal theory

This work used the colloidal theory to describe forces and energy interactions of colloidal complexes in the water and those formed during filtration run in direct filtration. Many interactions of particle energy profiles between colloidal surfaces for three geometries are presented here in: spherical, plate and cylindrical; and four surface interactions arrangements: two cylinders, two spheres, two plates and a sphere and a plate. Two different situations were analyzed, before and after electrostatic destabilization by action of the alum sulfate as coagulant in water studies samples prepared with kaolin. In the case were used mathematical modeling by extended DLVO theory (from the names: Derjarguin-Landau-Verwey-Overbeek) or XDLVO, which include traditional approach of the electric double layer (EDL), surfaces attraction forces or London-van der Waals (LvdW), esteric forces and hydrophobic forces, additionally considering another forces in colloidal system, like molecular repulsion or Born Repulsion and Acid-Base (AB) chemical function forces from Lewis.

Effects of the particle sizes and concentrations on the X-ray absorption by CuO compounds

This work presents a study on the effects of the particle size, material concentration and radiation energy on the X-ray absorption. CuO nanoparticles and microparticles were incorporated separately into a polymeric resin in concentrations of 5%, 10% and 30% relative to the resin mass. X-ray absorption by these materials was analyzed with a CdTe detector. The X-ray absorption is higher for the nanostructured material compared to the microstructured one for low energy X-ray beams for all CuO concentrations. (c) 2011 Elsevier Ltd. All rights reserved.

On the diurnal cycle of urban aerosols, black carbon and the occurrence of new particle formation events in springtime Sao Paulo, Brazil

Large conurbations are a significant source of the anthropogenic pollution and demographic differences between cities that result in a different pollution burden. The metropolitan area of Sao Paulo (MASP, population 20 million) accounts for one fifth of the Brazilian vehicular fleet. A feature of MASP is the amount of ethanol used by the vehicular fleet, known to exacerbate air quality. The study describes the diurnal behaviour of the submicron aerosol and relies on total particle number concentration, particle number size distribution, light scattering and light absorption measurements. Modelled planetary boundary layer (PBL) depth and air mass movement data were used to aid the interpretation. During morning rush-hour, stagnant air and a shallow PBL height favour the accumulation of aerosol pollution. During clear-sky conditions, there was a wind shift towards the edge of the city indicating a heat island effect with implications on particulate pollution levels at the site. The median total particle number concentration for the submicron aerosol typically varied in the range 1.6 x 10(4)-3.2 x 10(4) cm(-3) frequently exceeding 4 x 10(4) cm-3 during the day. During weekdays, nucleation-mode particles are responsible for most of the particles by numbers. The highest concentrations of total particle number concentrations and black carbon (BC) were observed on Fridays. Median diurnal values for light absorption and light scattering (at 637 nm wavelength) varied in the range 12-33 Mm(-1) and 21-64 Mm(-1), respectively. The former one is equal to 1.8-5.0 mu g m(-3) of BC. The growth of the PBL, from the morning rush-hour until noon, is consistent with the diurnal cycle of BC mass concentrations. Weekday hourly median single-scattering albedo (omega(0)) varied in the range 0.59-0.76. Overall, this suggests a top of atmosphere (TOA) warming effect. However, considering the low surface reflectance of urban areas, for the given range of omega(0), the TOA radiative forcing can be either positive or negative for the sources within the MASP. On the average, weekend omega(0) values were 0.074 higher than during weekdays. During 11% of the days, new particle formation (NPF) events occurred. The analysed events growth rates ranged between 9 and 25 nm h(-1). Sulphuric acid proxy concentrations calculated for the site were less than 5% of the concentration needed to explain the observed growth. Thus, other vapours are likely contributors to the observed growth.