Cell size error in stochastic particle methods for coagulation equations with advection

The paper studies the approximation error in stochastic particle methods for spatially inhomogeneous population balance equations. The model includes advection, coagulation and inception. Sufficient conditions for second order approximation with respect to the spatial discretization parameter (cell size) are provided. Examples are given, where only first order approximation is observed

Stochastic weighted particle methods for population balance equations

A class of stochastic algorithms for the numerical treatment of population balance equations is introduced. The algorithms are based on systems of weighted particles, in which coagulation events are modelled by a weight transfer that keeps the number of computational particles constant. The weighting mechanisms are designed in such a way that physical processes changing individual particles (such as growth, or other surface reactions) can be conveniently treated by the algorithms. Numerical experiments are performed for complex laminar premixed flame systems. Two members of the class of stochastic weighted particle methods are compared to each other and to a direct simulation algorithm. One weighted algorithm is shown to be consistently better than the other with respect to the statistical noise generated. Finally, run times to achieve fixed error tolerances for a real flame system are measured and the better weighted algorithm is found to be up to three times faster than the direct simulation algorithm

A kinetic equation for the distribution of interaction clusters in rarefied gases

We consider a stochastic particle model governed by an arbitrary binary interaction kernel. A kinetic equation for the distribution of interaction clusters is established. Under some additional assumptions a recursive representation of the solution is found. For particular choices of the interaction kernel (including the Boltzmann case) several explicit formulas are obtained. These formulas are confirmed by numerical experiments. The experiments are also used to illustrate various conjectures and open problems

Equivalent thermo-mechanical parameters for perfect crystals

Thermo-elastic behavior of perfect single crystal is considered. The crystal is represented as a set of interacting particles (atoms). The approach for determination of equivalent continuum values for the discrete system is proposed. Averaging of equations of particles' motion and long wave approximation are used in order to make link between the discrete system and equivalent continuum. Basic balance equations for equivalent continuum are derived from microscopic equations. Macroscopic values such as Piola and Cauchy stress tensors and heat flux are represented via microscopic parameters. Connection between the heat flux and temperature is discussed. Equation of state in Mie-Gruneisen form connecting Cauchy stress tensor with deformation gradient and thermal energy is obtained from microscopic considerations.Comment: To be published in proceedings of IUTAM Simposium on "Vibration Analysis of Structures with Uncertainties", 2009; 14 pages

Determination of the branching ratios Γ(KL→3π0)/Γ(KL→π+π−π0)\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0) and Γ(KL→3π0)/Γ(KL→πeν)\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu )

Improved branching ratios were measured for the $K_L \to 3 \pi^0$ decay in a neutral beam at the CERN SPS with the NA31 detector: $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0) = 1.611 \pm 0.037$ and $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu ) = 0.545 \pm 0.010$. From the first number an upper limit for $\Delta I =5/2$ and $\Delta I = 7/2$ transitions in neutral kaon decay is derived. Using older results for the Ke3/K$\mu$3 fraction, the 3$\pi^0$ branching ratio is found to be $\Gamma (K_L \to 3 \pi^0 )/ \Gamma_{tot} = (0.211 \pm 0.003)$, about a factor three more precise than from previous experiments

Constraints on Dark Matter Annihilation in Clusters of Galaxies with the Fermi Large Area Telescope

Nearby clusters and groups of galaxies are potentially bright sources of high-energy gamma-ray emission resulting from the pair-annihilation of dark matter particles. However, no significant gamma-ray emission has been detected so far from clusters in the first 11 months of observations with the Fermi Large Area Telescope. We interpret this non-detection in terms of constraints on dark matter particle properties. In particular for leptonic annihilation final states and particle masses greater than ~200 GeV, gamma-ray emission from inverse Compton scattering of CMB photons is expected to dominate the dark matter annihilation signal from clusters, and our gamma-ray limits exclude large regions of the parameter space that would give a good fit to the recent anomalous Pamela and Fermi-LAT electron-positron measurements. We also present constraints on the annihilation of more standard dark matter candidates, such as the lightest neutralino of supersymmetric models. The constraints are particularly strong when including the fact that clusters are known to contain substructure at least on galaxy scales, increasing the expected gamma-ray flux by a factor of ~5 over a smooth-halo assumption. We also explore the effect of uncertainties in cluster dark matter density profiles, finding a systematic uncertainty in the constraints of roughly a factor of two, but similar overall conclusions. In this work, we focus on deriving limits on dark matter models; a more general consideration of the Fermi-LAT data on clusters and clusters as gamma-ray sources is forthcoming.Comment: accepted to JCAP, Corresponding authors: T.E. Jeltema and S. Profumo, minor revisions to be consistent with accepted versio

Gluon polarization in the nucleon from quasi-real photoproduction of high-pT hadron pairs

We present a determination of the gluon polarization Delta G/G in the nucleon, based on the helicity asymmetry of quasi-real photoproduction events, Q^2<1(GeV/c)^2, with a pair of large transverse-momentum hadrons in the final state. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarized muon beam scattered on a polarized 6-LiD target. The helicity asymmetry for the selected events is = 0.002 +- 0.019(stat.) +- 0.003(syst.). From this value, we obtain in a leading-order QCD analysis Delta G/G=0.024 +- 0.089(stat.) +- 0.057(syst.) at x_g = 0.095 and mu^2 =~ 3 (GeV}/c)^2.Comment: 10 pages, 3 figure

A new measurement of the Collins and Sivers asymmetries on a transversely polarised deuteron target

New high precision measurements of the Collins and Sivers asymmetries of charged hadrons produced in deep-inelastic scattering of muons on a transversely polarised 6LiD target are presented. The data were taken in 2003 and 2004 with the COMPASS spectrometer using the muon beam of the CERN SPS at 160 GeV/c. Both the Collins and Sivers asymmetries turn out to be compatible with zero, within the present statistical errors, which are more than a factor of 2 smaller than those of the published COMPASS results from the 2002 data. The final results from the 2002, 2003 and 2004 runs are compared with naive expectations and with existing model calculations.Comment: 40 pages, 28 figure