Extension of moment projection method to the fragmentation process

© 2017 Elsevier Inc. The method of moments is a simple but efficient method of solving the population balance equation which describes particle dynamics. Recently, the moment projection method (MPM) was proposed and validated for particle inception, coagulation, growth and, more importantly, shrinkage; here the method is extended to include the fragmentation process. The performance of MPM is tested for 13 different test cases for different fragmentation kernels, fragment distribution functions and initial conditions. Comparisons are made with the quadrature method of moments (QMOM), hybrid method of moments (HMOM) and a high-precision stochastic solution calculated using the established direct simulation algorithm (DSA) and advantages of MPM are drawn

Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate

We are interested in the large time behavior of the solutions to the growth-fragmentation equation. We work in the space of integrable functions weighted with the principal dual eigenfunction of the growth-fragmentation operator. This space is the largest one in which we can expect convergence to the steady size distribution. Although this convergence is known to occur under fairly general conditions on the coefficients of the equation, we prove that it does not happen uniformly with respect to the initial data when the fragmentation rate in bounded. First we get the result for fragmentation kernels which do not form arbitrarily small fragments by taking advantage of the Dyson-Phillips series. Then we extend it to general kernels by using the notion of quasi-compactness and the fact that it is a topological invariant

The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible

Hadron Spin Dynamics

Spin effects in exclusive and inclusive reactions provide an essential new dimension for testing QCD and unraveling hadron structure. Remarkable new experiments from SLAC, HERMES (DESY), and the Jefferson Laboratory present many challenges to theory, including measurements at HERMES and SMC of the single spin asymmetries in pion electroproduction, where the proton is polarized normal to the scattering plane. This type of single spin asymmetry may be due to the effects of rescattering of the outgoing quark on the spectators of the target proton, an effect usually neglected in conventional QCD analyses. Many aspects of spin, such as single-spin asymmetries and baryon magnetic moments are sensitive to the dynamics of hadrons at the amplitude level, rather than probability distributions. I illustrate the novel features of spin dynamics for relativistic systems by examining the explicit form of the light-front wavefunctions for the two-particle Fock state of the electron in QED, thus connecting the Schwinger anomalous magnetic moment to the spin and orbital momentum carried by its Fock state constituents and providing a transparent basis for understanding the structure of relativistic composite systems and their matrix elements in hadronic physics. I also present a survey of outstanding spin puzzles in QCD, particularly the double transverse spin asymmetry A_{NN} in elastic proton-proton scattering, the J/psi to rho-pi puzzle, and J/psi polarization at the Tevatron.Comment: Concluding theory talk presented at SPIN2001, the Third Circum-Pan-Pacific Symposium on High Energy Physics, October, 2001, Beijin

Turbulence induced collisional velocities and density enhancements: large inertial range results from shell models

To understand the earliest stages of planet formation, it is crucial to be able to predict the rate and the outcome of dust grains collisions, be it sticking and growth, bouncing, or fragmentation. The outcome of such collisions depends on the collision speed, so we need a solid understanding of the rate and velocity distribution of turbulence-induced dust grain collisions. The rate of the collisions depends both on the speed of the collisions and the degree of clustering experienced by the dust grains, which is a known outcome of turbulence. We evolve the motion of dust grains in simulated turbulence, an approach that allows a large turbulent inertial range making it possible to investigate the effect of turbulence on meso-scale grains (millimeter and centimeter). We find three populations of dust grains: one highly clustered, cold and collisionless; one warm; and the third "hot". Our results can be fit by a simple formula, and predict both significantly slower typical collisional velocities for a given turbulent strength than previously considered, and modest effective clustering of the collisional populations, easing difficulties associated with bouncing and fragmentation barriers to dust grain growth. Nonetheless, the rate of high velocity collisions falls off merely exponentially with relative velocity so some mid- or high-velocity collisions will still occur, promising some fragmentation.Comment: 14 pages, 8 figures, 4 tables, Accepted, MNRA

Light-Cone Quantization and Hadron Structure

In this talk, I review the use of the light-cone Fock expansion as a tractable and consistent description of relativistic many-body systems and bound states in quantum field theory and as a frame-independent representation of the physics of the QCD parton model. Nonperturbative methods for computing the spectrum and LC wavefunctions are briefly discussed. The light-cone Fock state representation of hadrons also describes quantum fluctuations containing intrinsic gluons, strangeness, and charm, and, in the case of nuclei, "hidden color". Fock state components of hadrons with small transverse size, such as those which dominate hard exclusive reactions, have small color dipole moments and thus diminished hadronic interactions; i.e., "color transparency". The use of light-cone Fock methods to compute loop amplitudes is illustrated by the example of the electron anomalous moment in QED. In other applications, such as the computation of the axial, magnetic, and quadrupole moments of light nuclei, the QCD relativistic Fock state description provides new insights which go well beyond the usual assumptions of traditional hadronic and nuclear physics.Comment: LaTex 36 pages, 3 figures. To obtain a copy, send e-mail to [email protected]