Breakup Probability Research Articles

A Monte Carlo calculation of the pionium break-up probability with different sets ofpionium target cross sections

Chiral perturbation theory predicts the lifetime of pionium, a hydrogen-likeπ+π− atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is toobtain and check this value experimentally by measuring the break-up probability ofpionium in a target. In order to accurately measure the lifetime one needs to know therelationship between the break-up probability and the lifetime to 1% accuracy. We haveobtained this dependence by modelling the evolution of pionic atoms in the target usingMonte Carlo methods. The model relies on the computation of the pionium–target-atominteraction cross sections. Three different sets of pionium–target cross sections with varyingdegrees of complexity were used: from the simplest first-order Born approximationinvolving only the electrostatic interaction to a more advanced approach, taking intoaccount multiphoton exchanges and relativistic effects. We conclude that, in order toobtain the pionium lifetime to 1% accuracy from the break-up probability, thepionium–target cross sections must be known with the same accuracy for the lowexcited bound states of the pionic atom. This result has been achieved, for lowZ targets, with the two most precise cross section sets. For largeZ targets only the set accounting for multiphoton exchange satisfies the condition.

A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow

Several models for the daughter bubble/droplet size distribution are reviewed and a detailed discussion is given to get a better understanding of the daughter size distribution. A novel theoretical breakup kernel function for bubbles/droplets in a turbulent flow, based on an eddy-bubble/droplet collision method, is developed. It takes into account the energy distribution of turbulent eddies, effect of capillary pressure and surface energy increase during bubble/droplet breakup. An increase in the mother bubble/droplet size and energy dissipation rate increases the probability of unequal breakup. The model prediction is in good agreement with experimental results and the underlying physical situation.

Drop breakup in the flow through fixed fiber beds: An experimental and computational investigation

Dilute fixed fiber beds provide a model system for studying drop dynamics in disordered flows. Fluctuations about the mean uniform velocity are generated by fiber elements within the media, and the disturbance velocities far from any single fiber (at distances on the order of the pore size) have been predicted to be strong in terms of drop deformation and breakup by Mosler and Shaqfeh [Phys. Fluids 9, 5 (1997)]. In this work, we focus on the importance of near-field interactions, or the flow close to individual fibers. We present experimental observations of drop deformation and breakup during flow through a dilute bed of randomly placed fibers. We found breakup to result from only close interactions with fibers and describe two near-field breakup mechanisms which we term “graze” and “hairpin” processes. In addition, we present the breakup probability through the experimental fiber bed as a function of the appropriate Capillary number Ca. To better understand the near-field interactions, we used the boundary integral method to determine drop shape evolution in the flow around an infinite fiber within a porous medium, and our simulations capture the breakup mechanisms observed during experiments. To compare with experimental breakup probabilities, we have defined a critical offset for breakup during flow past a fiber and assuming straight center-of-mass trajectories, calculated breakup probabilities based on this simple model. These predictions compare well with the experimental measurements for Ca⩾2.

Simulated Reversible Aggregation Processes for Different Interparticle Potentials: The Cluster Aging Phenomenon

The kinetics of reversible 3D aggregation processes was studied for different interparticle potentials by means of simulations. In previous work (Phys. Rev. E 2002, 65, 031405),1 freely diffusing particles were considered that aggregate whenever a collision occurs but disintegrate only with a single given breakup probability. The DLVO theory, however, predicts also interparticle potentials showing two minima of different depths separated by an energetic barrier. Hence, two different kind of bonds, primary and secondary ones, can be formed and should be treated separately. In the present work, this behavior was implemented by considering bonds with different breakup probabilities. The data obtained from simulations were compared with the stochastic solutions of the corresponding master equation. For this purpose, the Brownian kernel was employed together with novel fragmentation kernels. The agreement between the simulations and the kinetic description was found to be quite satisfactory. Moreover, studying the time evolution of the bond population showed that cluster aging appears as a natural consequence of the employed model.

FUSION OF LIGHT PROTON-RICH EXOTIC NUCLEI AT NEAR-BARRIER ENERGIES

We study, theoretically, the fusion of the light proton-rich exotic nuclei 17 F and 8 B at near-barrier energies in order to investigate the possible role of breakup processes on their fusion cross sections. To this end, coupled channel calculations are performed, considering the couplings to the breakup channels of these projectiles. In case of 17 F , the coupling arising out of the inelastic excitation from the ground state to the bound excited state and its couplings to the continuum have also been taken into consideration. It is found that the inelastic excitation/breakup of 17 F affect the fusion cross sections very nominally even for a heavy target like Pb. On the other hand, calculations for fusion of the one-proton halo nucleus 8 B on a Pb target show a significant suppression of the complete fusion cross section above the Coulomb barrier. This is due to the larger breakup probability of 8 B as compared to that of 17 F . However, even for 8 B , there is little change in the complete fusion cross sections as compared to the no-coupling case at sub-barrier energies.

Constant bond breakup probability model for reversible aggregation processes.

Reversible aggregation processes were simulated for systems of freely diffusing sticky particles. Reversibility was introduced by allowing that all bonds in the system may break with a given probability per time interval. In order to describe the kinetics of such aggregation-fragmentation processes, a fragmentation kernel was developed and then used together with the Brownian aggregation kernel for solving the corresponding kinetic master equation. The deduced fragmentation kernel considers a single characteristic lifetime for all bonds and accounts for the cluster morphology by averaging over all possible configurations for clusters of a given size. It became evident that the simulated cluster-size distributions could be described only when an additional fragmentation effectiveness was considered. Doing so, the stochastic solutions were in good agreement with the simulated data.

Eikonal approximation in heavy-ion fragmentation reactions

Projectile fragmentation reactions are well suited to structure studies of weakly bound nuclei, but an accurate reaction theory is necessary to extract quantitative spectroscopic properties. We examine here the accuracy of the commonly used eikonal approximation for the nuclear-induced breakup of halo nuclei. Comparing to numerical solutions of the full time-dependent Schrodinger equation, we find that the eikonal remains fairly accurate for calculating breakup probabilities of halo nuclei even down to 20 MeV/nucleon, reproducing relative spectroscopic strengths to within a few percent. Absolute reaction probabilities tend to be underpredicted by the eikonal, which would make extracted spectroscopic strengths somewhat too high. We discuss other features that are seen in the full calculation but are missing in the eikonal approximation such as the ‘‘towing’’ mode.

Coherent and incoherent atomic scattering: formalism and application to pionium interacting with matter

The experimental determination of the lifetime of pionium provides avery important test of chiral perturbation theory. This quantity isdetermined in the DIRAC experiment at CERN. In the analysis of thisexperiment, the breakup probabilities of pionium in matter are neededto high accuracy as a theoretical input. We study in detail theinfluence of the target electrons.They contribute through screening and incoherent effects. We useDirac-Hartree-Fock-Slaterwavefunctions in order to determine the corresponding form factors.We find that the inner-shell electrons contribute less thanthe weakly bound outer electrons. Furthermore, we establish a morerigorous estimate for the magnitude of the contribution from thetransverse current (magnetic terms thus far neglected in thecalculations).

SCALING LAWS OF REVERSIBLE AGGREGATION IN COMPACT CLUSTER SYSTEMS

The reversible cluster–cluster aggregation processes in compact cluster systems are studied via a scaling argument and Monte Carlo simulations. To describe the detail effects of fragmentations from tree-like fractal to compact clusters a relative breakup probability [Formula: see text] with an exponent β is introduced. The mean-field rate equation and numerical simulation results indicate that the critical exponent y, which is defined as <s (k, ∞)> ~ k-y, has a value of (α + ξ - β + 2)-1. It is shown that the scaling properties of the cluster size distributions are determined by the selections of the exponents α, β and ξ.

Nuclear forward glory,σRandfN(0°)in the scattering of6Heby carbon

Using the generalized optical theorem for charged particles, the total reaction cross section ${\ensuremath{\sigma}}_{R}$ and the nuclear scattering amplitude ${f}_{N}$ at $0\ifmmode^\circ\else\textdegree\fi{}$ have been determined model independently for the first time in the ${}^{6}\mathrm{He}{+}^{12}\mathrm{C}$ system. A large fraction of ${\ensuremath{\sigma}}_{R}$ is accounted for by ${f}_{N}(0\ifmmode^\circ\else\textdegree\fi{})$ --- a manifestation of the nuclear forward glory effect. A comparison with the ${}^{6}\mathrm{Li}{+}^{12}\mathrm{C}$ system supports the prediction that the high break-up probability of ${}^{6}\mathrm{He}$ reduces the fraction of the total reaction cross section accounted for by the nuclear scattering amplitude at $0\ifmmode^\circ\else\textdegree\fi{}.$

Influence of wear particle interaction in the sliding interface on friction of metals

The role of wear particles at the sliding interface on the frictional behavior of metals was investigated with respect to size and agglomeration characteristics using both pin-on-disk and pin-on-reciprocator tribotesters. The wear particle interaction at the sliding interface was monitored using a CCD camera. It was found that the friction coefficient significantly rises once a wear particle is produced and trapped at the interface. Wear particles of soft, ductile metal pairs go through a cycle of agglomeration and breakup, while wear particles of hard material pairs are less likely to agglomerate. The wear particles were smaller for the bidirectional sliding motion compared with those in the unidirectional sliding motion, which resulted in lower friction and wear characteristics. This difference is attributed to the higher probability of particle breakup in bidirectional sliding motion. The frictional behavior was also investigated when metal particles are introduced into the interface of Cu–Cu sliding pair. The friction coefficient increased with the introduction of Ni powder whereas it decreased with the introduction of Al powder. It is concluded from these results that frictional behavior could be altered at will by inserting appropriate particles into the sliding interface.

Optimization of production process design in small- and medium bath production

The conditions of production process design in contemporary market economies is presented in this paper. The methods used in choosing optimal solutions for planning courses are described. Costs, time of planning, and probability of project activity break-up are taken into consideration making this choice. The problems presented in this paper are illustrated using an example. The example illustrated is concerned with production process design for general purpose gear.

Development of giant drops and high-reflectivity cores in Hawaiian clouds: numerical simulations using a kinematic model with detailed microphysics

Cores of high radar reflectivity (>50 dBZ) and raindrops larger than 4 mm in diameter were occasionally reported in warm clouds, offshore from Hawaii. A kinematic numerical model with detailed microphysics was used to study the formation of these cores and the development of the giant drops. The role of collisional and spontaneous breakup of drops was evaluated. Our results show that spontaneous breakup of raindrops restricts the formation of giant drops ( D>4 mm). This could be a result of the poor parameterization of the fragment size distribution, and the probabilities of the spontaneous breakup. The inclusion of only binary breakup mechanism explained the observed radar echoes and the drop spectra. These results corroborate the hypothesis that the updrafts in the Hawaiian clouds sort out different size drops in such a way that millimeter size drops are allowed to fall in an environment deficient of smaller raindrops. In this way, the large raindrops continue to grow by collection of small cloud droplets, but have a smaller chance for collisional breakup (the efficiency for this type of breakup is small for collisions with cloud droplets). The collisional breakup of big raindrops was also found to play a significant role in the formation of giant drops. Such drops are formed following collision–breakup of large raindrops in which one of the fragments is larger than the original drops.

The Microphysical Structure and Evolution of Hawaiian Rainband Clouds. Part II: Aircraft Measurements within Rainbands Containing High Reflectivity Cores

Abstract The microphysical structure of high reflectivity cores and surrounding weaker echo regions in Hawaiian rainbands is documented using aircraft data. These data show that high reflectivity cores are associated with giant raindrops (D > 4 mm) present in narrow (∼500 m wide) columns coincident with the core updraft. Updrafts were found to be strong enough to suspend 1–2-mm raindrops near cloud top. As these raindrops subsequently fall through the updraft core, they are exposed to high liquid water content, allowing them to grow to large sizes, provided that updrafts are not significantly sheared. The data indicate that size sorting due to differential terminal velocities of the larger and smaller raindrops occurs initially in the updraft. As a result, the larger raindrops fall through an environment in which there is a low concentration of smaller raindrops, decreasing the probability of breakup. Calculations of raindrop growth rates and breakup probabilities are used to demonstrate that high reflect...

Complete and incomplete fusion of two-cluster nuclei

We study the influence of the break-up process on the complete and incomplete fusion cross sections. This is done through the introduction of break-up and survival probabilities, which are evaluated with the help of an appropriate polarization potential. For incomplete fusion, we use a spectator model. As examples, we consider several light - heavy-ion collisions, where threshold effects play an interesting role.

Effects of the(α−3He) breakup on the optical model for elastic scattering of 172 MeV α particles on62Ni

The contribution to the optical potential from the breakup reaction $(\ensuremath{\alpha}{\ensuremath{-}}^{3}$He) in the elastic scattering of 172 MeV $\ensuremath{\alpha}$ particles from ${}^{62}$Ni is investigated in a phenomenological fashion. A breakup part of the optical potential is introduced and the partial wave amplitudes of this part are compared with published values of the breakup probabilities for this reaction.

Percolation simulation of the network degradation during ultrasonic devulcanization

The percolation model of network degradation during rubber devulcanization is presented. The model is based on a random crosslink scission and molecular chain breakup. The obtained results indicate that the primary model parameter characterizing the network degradation is the ratio of the probabilities of backbone breakup to crosslink scission. The predicted dependences of the gel fraction of devulcanized rubber on crosslink density are in excellent agreement with experimental data for styrene-butadiene rubber and ground rubber tire. The estimated critical exponents indicate that the process of devulcanization for the vulcanizate without filler appears to belong to the universality class of standard 3D bond percolation while devulcanization for the vulcanizate with filler appears to belong to its own new universality class. © 1996 John Wiley & Sons, Inc.

Bustup Takeovers of Value‐Destroying Diversified Firms

ABSTRACTWe examine whether the value loss from diversification affects takeover and breakup probabilities. We estimate diversification's value effect by imputing stand‐alone values for individual business segments and find that firms with greater value losses are more likely to be taken over. Moreover, those acquired firms whose losses are greatest are most likely to be bought by LBO associations, which frequently break up their targets. For a subsample of large diversified targets: (1) higher value losses increase the extent of post‐takeover bustup; and (2) post‐takeover bustup generally results in divested divisions being operated as part of a focused, stand‐alone firm.

An experiment on the breakup of impinging droplets on a hot surface

Breakup characteristics of liquid droplets impinging on a hot surface are investigated experimentally with the wall temperatures in the Leidenfrost temperature range of 220–330°C for n-decane fuel. Factors influencing droplet breakup are wall temperature, impinging velocity, droplet diameter and impinging angle. The 50% breakup probability shows that the impinging velocity decreases linearly with the droplet diameter increase and there exists an optimum impinging angle near 80° having the minimum value in the impinging velocity for given wall temperature and droplet size. Near the wall temperature of 250°C corresponding to the Leidenfrost temperature, a peculiar nonlinear behavior in the breakup probability is observed.

Coulomb- and nuclear-induced break-up of halo nuclei at bombarding energies around the Coulomb barrier

Abstract We investigate the relative importance of the Coulomb and nuclear fields to induce the break-up of neutron-rich nuclei such as 11 Li at energies close to the Coulomb barrier. We assume that the mechanism that leads to the separation is the excitation of a low-lying dipole mode in which the weakly-bound neutron halo performs a collective oscillation against the residual nuclear core. To this end we exploit semiclassical prescriptions that are adequate to calculate not only the average break-up probabilities but also to estimate the size of fluctuations about the quantal expectation values. Possible outcomes are explored as a function of both bombarding energy and impact parameter. Consequences of the couplings for elastic scattering and fusion processes are also discussed.