RELATIVISTIC 3-PARTICLE DYNAMICAL EQUATIONS .1. THEORETICAL DEVELOPMENT

Starting from the two-particle Bethe-Salpeter equation in the ladder approximation and integrating over the time component of momentum, we rederive three-dimensional scattering integral equations satisfying constraints of relativistic unitarity and convariance, first derived by Weinberg and by Blankenbecler and Sugar. These two-particle equations are shown to be related by a transformation of variables. Hence we show how to perform and relate identical dynamical calculation using these two equations. Similarly, starting from the Bethe-Salpeter-Faddeev equation for the three-particle system and integrating over the time component of momentum, we derive several three-dimensional three-particle scattering equations satisfying constraints of relativistic unitarity and convariance. We relate two of these three-particle equations by a transformation of variables as in the two-particle case. The three-particle equations we derive are very practical and suitable for performing relativistic scattering calculations. (C) 1994 Academic Press, Inc.

RELATIVISTIC 3-PARTICLE SCATTERING EQUATIONS

We derive a set of relativistic three-particle scattering equations in the three-particle c.m. frame employing a relativistic three-particle propagator suggested long ago by Ahmadzadeh and Tjon in the c.m. frame of a two-particle subsystem. We make the coordinate transformation of this propagator from the c.m. frame of the two-particle subsystem to the three-particle c.m. frame. We also point out that some numerical applications of the Ahmadzadeh and Tjon propagator to the three-nucleon problem use unnecessary nonrelativistic approximations which do not simplify the computational task, but violate constraints of relativistic unitarity and/or covariance.

System size and energy dependence of near-side dihadron correlations

Two-particle azimuthal (Delta phi) and pseudorapidity (Delta eta) correlations using a trigger particle with large transverse momentum (p(T)) in d+Au, Cu+Cu, and Au+Au collisions at root s(NN) = 62.4 GeV and 200 GeV from the STAR experiment at the Relativistic Heavy Ion Collider are presented. The near-side correlation is separated into a jet-like component, narrow in both Delta phi and Delta eta, and the ridge, narrow in Delta phi but broad in Delta eta. Both components are studied as a function of collision centrality, and the jet-like correlation is studied as a function of the trigger and associated p(T). The behavior of the jet-like component is remarkably consistent for different collision systems, suggesting it is produced by fragmentation. The width of the jet-like correlation is found to increase with the system size. The ridge, previously observed in Au+Au collisions at root s(NN) = 200 GeV, is also found in Cu+Cu collisions and in collisions at root s(NN) = 62.4 GeV, but is found to be substantially smaller at root s(NN) = 62.4 GeV than at root s(NN) = 200 GeV for the same average number of participants (< N-part >). Measurements of the ridge are compared to models.

(18O,16O) Two-neutron transfer reactions for spectroscopic studies.

A systematic study of the response of different nuclei to the (18O, 16O) two-neutron transfer reaction at 84 MeV incident energy was pursued at the INFN-LNS in Catania (Italy). The experiments were performed using several solid targets from light (9Bc, 11 B, 12,13C, 16O, 28Si) to heavier ones (58,64Ni, 120Sn, 208Pb). The 16O ejectiles were detected at forward angles by the MAGNEX magnetic spectrometer and identified without the need of time of flight measurements. Exploiting the large momentum (≈ 25%) and angular (50 msr) acceptance of the spectrometer, energy spectra were obtained with a relevant yield up to about 20 MeV excitation energy. A common feature of the light nuclei spectra is the strong population of states with well known configuration of two-particle over a core and the appearance of unknown resonant structures in the continuum. These latter can reveal the excitation of a collective mode connected with the transfer of a pair. For the heavier nuclei as 66Ni a completely different behaviour is observed indicating the presence of more dissipative processes in the reaction mechanisms that hide the spectroscopic information.

A novel quantitative method for analyzing the distributions of nanoparticles between different tissue and intracellular compartments

The penetration, translocation, and distribution of ultrafine and nanoparticles in tissues and cells are challenging issues in aerosol research. This article describes a set of novel quantitative microscopic methods for evaluating particle distributions within sectional images of tissues and cells by addressing the following questions: (1) is the observed distribution of particles between spatial compartments random? (2) Which compartments are preferentially targeted by particles? and (3) Does the observed particle distribution shift between different experimental groups? Each of these questions can be addressed by testing an appropriate null hypothesis. The methods all require observed particle distributions to be estimated by counting the number of particles associated with each defined compartment. For studying preferential labeling of compartments, the size of each of the compartments must also be estimated by counting the number of points of a randomly superimposed test grid that hit the different compartments. The latter provides information about the particle distribution that would be expected if the particles were randomly distributed, that is, the expected number of particles. From these data, we can calculate a relative deposition index (RDI) by dividing the observed number of particles by the expected number of particles. The RDI indicates whether the observed number of particles corresponds to that predicted solely by compartment size (for which RDI = 1). Within one group, the observed and expected particle distributions are compared by chi-squared analysis. The total chi-squared value indicates whether an observed distribution is random. If not, the partial chi-squared values help to identify those compartments that are preferential targets of the particles (RDI > 1). Particle distributions between different groups can be compared in a similar way by contingency table analysis. We first describe the preconditions and the way to implement these methods, then provide three worked examples, and finally discuss the advantages, pitfalls, and limitations of this method.

Influence of Particle Size of Deproteinized Bovine Bone Mineral on New Bone Formation and Implant Stability after Simultaneous Sinus Floor Elevation: A Histomorphometric Study in Minipigs

BACKGROUND Deproteinized bovine bone mineral (DBBM) is one of the best-documented bone substitute materials for sinus floor elevation (SFE). PURPOSE DBBM is available in two particle sizes. Large particles are believed to facilitate improved neoangiogenesis compared with small ones. However, their impact on the rate of new bone formation, osteoconduction, and DBBM degradation has never been reported. In addition, the implant stability quotient (ISQ) has never been correlated to bone-to-implant contact (BIC) after SFE with simultaneous implant placement. MATERIALS AND METHODS Bilateral SFE with simultaneous implant placement was performed in 10 Göttingen minipigs. The two sides were randomized to receive large or small particle size DBBM. Two groups of 5 minipigs healed for 6 and 12 weeks, respectively. ISQ was recorded immediately after implant placement and at sacrifice. Qualitative histological differences were described and bone formation, DBBM degradation, BIC and bone-to-DBBM contact (osteoconduction) were quantified histomorphometrically. RESULTS DBBM particle size had no qualitative or quantitative impact on the amount of newly formed bone, DBBM degradation, or BIC for either of the healing periods (p > 0.05). Small-size DBBM showed higher osteoconduction after 6 weeks than large-size DBBM (p < 0.001). After 12 weeks this difference was compensated. There was no significant correlation between BIC and ISQ. CONCLUSION Small and large particle sizes were equally predictable when DBBM was used for SFE with simultaneous implant placement.

Measurement with the ATLAS detector of multi-particle azimuthal correlations in p+Pb collisions at sqrtsNN=5.02 TeV

In order to study further the long-range correlations ("ridge") observed recently in p+Pb collisions at sqrt(s_NN) =5.02 TeV, the second-order azimuthal anisotropy parameter of charged particles, v_2, has been measured with the cumulant method using the ATLAS detector at the LHC. In a data sample corresponding to an integrated luminosity of approximately 1 microb^(-1), the parameter v_2 has been obtained using two- and four-particle cumulants over the pseudorapidity range |eta|<2.5. The results are presented as a function of transverse momentum and the event activity, defined in terms of the transverse energy summed over 3.1two-particle correlation methods, and to predictions from hydrodynamic models of p+Pb collisions. Despite the small transverse spatial extent of the p+Pb collision system, the large magnitude of v_2 and its similarity to hydrodynamic predictions provide additional evidence for the importance of final-state effects in p+Pb reactions.

Measurement of distributions sensitive to the underlying event in inclusive Z-boson production in pp collisions at √ s=7 TeV with the ATLAS detector

A measurement of charged-particle distributions sensitive to the properties of the underlying event is presented for an inclusive sample of events containing a Z-boson, decaying to an electron or muon pair. The measurement is based on data collected using the ATLAS detector at the LHC in proton–proton collisions at a centre-of-mass energy of 7 TeV with an integrated luminosity of 4.6fb−1. Distributions of the charged particle multiplicity and of the charged particle transverse momentum are measured in regions of azimuthal angle defined with respect to the Z-boson direction. The measured distributions are compared to similar distributions measured in jet events, and to the predictions of various Monte Carlo generators implementing different underlying event models.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at √sNN = 2.76 TeV are shown using a dataset of approximately 7μb−1 collected at the LHC in 2010. The measurements are performed for charged particles with transversemomenta 0.5 < pT < 20 GeV and in the pseudorapidity range |η| < 2.5. The anisotropy is characterized by the Fourier coefficients, vn, of the charged-particle azimuthal angle distribution for n = 2–4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the vn coefficients are presented. The elliptic flow, v2, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, v3 and v4, are determined with two- and four-particle cumulants. Flow harmonics vn measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to vn measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Modeling the molecular weight distribution of block copolymer formation in a reversible addition-fragmentation chain transfer mediated living radical polymerization

Block copolymers have become an integral part of the preparation of complex architectures through self-assembly. The use of reversible addition-fragmentation chain transfer (RAFT) allows blocks ranging from functional to nonfunctional polymers to be made with predictable molecular weight distributions. This article models block formation by varying many of the kinetic parameters. The simulations provide insight into the overall polydispersities (PDIs) that will be obtained when the chain-transfer constants in the main equilibrium steps are varied from 100 to 0.5. When the first dormant block [polymer-S-C(Z)=S] has a PDI of 1 and the second propagating radical has a low reactivity to the RAFT moiety, the overall PDI will be greater than 1 and dependent on the weight fraction of each block. When the first block has a PDI of 2 and the second propagating radical has a low reactivity to the RAFT moiety, the PDI will decrease to around 1.5 because of random coupling of two broad distributions. It is also shown how we can in principle use only one RAFT agent to obtain block copolymers with any desired molecular weight distribution. We can accomplish this by maintaining the monomer concentration at a constant level in the reactor over the course of the reaction. (c) 2005 Wiley Periodicals, Inc.

Gold nanoparticle induced vasculature damage in radiotherapy: Comparing protons, megavoltage photons, and kilovoltage photons

Purpose: The purpose of this work is to investigate the radiosensitizing effect of gold nanoparticle (GNP) induced vasculature damage for proton, megavoltage (MV) photon, and kilovoltage (kV) photon irradiation. Methods: Monte Carlo simulations were carried out using tool for particle simulation (TOPAS) to obtain the spatial dose distribution in close proximity up to 20 µm from the GNPs. The spatial dose distribution from GNPs was used as an input to calculate the dose deposited to the blood vessels. GNP induced vasculature damage was evaluated for three particle sources (a clinical spread out Bragg peak proton beam, a 6 MV photon beam, and two kV photon beams). For each particle source, various depths in tissue, GNP sizes (2, 10, and 20 nm diameter), and vessel diameters (8, 14, and 20 µm) were investigated. Two GNP distributions in lumen were considered, either homogeneously distributed in the vessel or attached to the inner wall of the vessel. Doses of 30 Gy and 2 Gy were considered, representing typical in vivo enhancement studies and conventional clinical fractionation, respectively. Results: These simulations showed that for 20 Au-mg/g GNP blood concentration homogeneously distributed in the vessel, the additional dose at the inner vascular wall encircling the lumen was 43% of the prescribed dose at the depth of treatment for the 250 kVp photon source, 1% for the 6 MV photon source, and 0.1% for the proton beam. For kV photons, GNPs caused 15% more dose in the vascular wall for 150 kVp source than for 250 kVp. For 6 MV photons, GNPs caused 0.2% more dose in the vascular wall at 20 cm depth in water as compared to at depth of maximum dose (Dmax). For proton therapy, GNPs caused the same dose in the vascular wall for all depths across the spread out Bragg peak with 12.7 cm range and 7 cm modulation. For the same weight of GNPs in the vessel, 2 nm diameter GNPs caused three times more damage to the vessel than 20 nm diameter GNPs. When the GNPs were attached to the inner vascular wall, the damage to the inner vascular wall can be up to 207% of the prescribed dose for the 250 kVp photon source, 4% for the 6 MV photon source, and 2% for the proton beam. Even though the average dose increase from the proton beam and MV photon beam was not large, there were high dose spikes that elevate the local dose of the parts of the blood vessel to be higher than 15 Gy even for 2 Gy prescribed dose, especially when the GNPs can be actively targeted to the endothelial cells. Conclusions: GNPs can potentially be used to enhance radiation therapy by causing vasculature damage through high dose spikes caused by the addition of GNPs especially for hypofractionated treatment. If GNPs are designed to actively accumulate at the tumor vasculature walls, vasculature damage can be increased significantly. The largest enhancement is seen using kilovoltage photons due to the photoelectric effect. Although no significant average dose enhancement was observed for the whole vasculature structure for both MV photons and protons, they can cause high local dose escalation (>15 Gy) to areas of the blood vessel that can potentially contribute to the disruption of the functionality of the blood vessels in the tumor.

Development of a model to predict the life of pneumatic conveyor bends subject to erosive wear

The erosion processes resulting from flow of fluids (gas-solid or liquid-solid) are encountered in nature and many industrial processes. The common feature of these erosion processes is the interaction of the fluid (particle) with its boundary thus resulting in the loss of material from the surface. This type of erosion in detrimental to the equipment used in pneumatic conveying systems. The puncture of pneumatic conveyor bends in industry causes several problems. Some of which are: (1) Escape of the conveyed product causing health and dust hazard; (2) Repairing and cleaning up after punctures necessitates shutting down conveyors, which will affect the operation of the plant, thus reducing profitability. The most common occurrence of process failure in pneumatic conveying systems is when pipe sections at the bends wear away and puncture. The reason for this is particles of varying speed, shape, size and material properties strike the bend wall with greater intensity than in straight sections of the pipe. Currently available models for predicting the lifetime of bends are inaccurate (over predict by 80%. The provision of an accurate predictive method would lead to improvements in the structure of the planned maintenance programmes of processes, thus reducing unplanned shutdowns and ultimately the downtime costs associated with these unplanned shutdowns. This is the main motivation behind the current research. The paper reports on two aspects of the first phases of the study-undertaken for the current project. These are (1) Development and implementation; and (2) Testing of the modelling environment. The model framework encompasses Computational Fluid Dynamics (CFD) related engineering tools, based on Eulerian (gas) and Lagrangian (particle) approaches to represent the two distinct conveyed phases, to predict the lifetime of conveyor bends. The method attempts to account for the effect of erosion on the pipe wall via particle impacts, taking into account the angle of attack, impact velocity, shape/size and material properties of the wall and conveyed material, within a CFD framework. Only a handful of researchers use CFD as the basis of predicting the particle motion, see for example [1-4] . It is hoped that this would lead to more realistic predictions of the wear profile. Results, for two, three-dimensional test cases using the commercially available CFD PHOENICS are presented. These are reported in relation to the impact intensity and sensitivity to the inlet particle distributions.

Azimuthal correlations of electrons from heavy-flavor decay with hadrons in p plus p and Au plus Au collisions at root s(NN)=200 GeV

Measurements of electrons from the decay of open-heavy-flavor mesons have shown that the yields are suppressed in Au+Au collisions compared to expectations from binary-scaled p+p collisions. These measurements indicate that charm and bottom quarks interact with the hot dense matter produced in heavy-ion collisions much more than expected. Here we extend these studies to two-particle correlations where one particle is an electron from the decay of a heavy-flavor meson and the other is a charged hadron from either the decay of the heavy meson or from jet fragmentation. These measurements provide more detailed information about the interactions between heavy quarks and the matter, such as whether the modification of the away-side-jet shape seen in hadron-hadron correlations is present when the trigger particle is from heavy-meson decay and whether the overall level of away-side-jet suppression is consistent. We statistically subtract correlations of electrons arising from background sources from the inclusive electron-hadron correlations and obtain two-particle azimuthal correlations at root s(NN) = 200 GeV between electrons from heavy-flavor decay with charged hadrons in p+p and also first results in Au+Au collisions. We find the away-side-jet shape and yield to be modified in Au+Au collisions compared to p+p collisions.

Photon-hadron jet correlations in p plus p and Au plus Au collisions at s(NN)=200 GeV

We report the observation at the Relativistic Heavy Ion Collider of suppression of back-to-back correlations in the direct photon+jet channel in Au+Au relative to p+p collisions. Two-particle correlations of direct photon triggers with associated hadrons are obtained by statistical subtraction of the decay photon-hadron (gamma-h) background. The initial momentum of the away-side parton is tightly constrained, because the parton-photon pair exactly balance in momentum at leading order in perturbative quantum chromodynamics, making such correlations a powerful probe of the in-medium parton energy loss. The away-side nuclear suppression factor, I(AA), in central Au+Au collisions, is 0.32 +/- 0.12(stat)+/- 0.09(syst) for hadrons of 3 < p(T)(h)< 5 in coincidence with photons of 5 < p(T)(gamma)< 15 GeV/c. The suppression is comparable to that observed for high-p(T) single hadrons and dihadrons. The direct photon associated yields in p+p collisions scale approximately with the momentum balance, z(T)equivalent to p(T)(h)/p(T)(gamma), as expected for a measurement of the away-side parton fragmentation function. We compare to Au+Au collisions for which the momentum balance dependence of the nuclear modification should be sensitive to the path-length dependence of parton energy loss.