Stein factors for negative binomial approximation in Wasserstein distance

The paper gives the bounds on the solutions to a Stein equation for the negative binomial distribution that are needed for approximation in terms of the Wasserstein metric. The proofs are probabilistic, and follow the approach introduced in Barbour and Xia (Bernoulli 12 (2006) 943-954). The bounds are used to quantify the accuracy of negative binomial approximation to parasite counts in hosts. Since the infectivity of a population can be expected to be proportional to its total parasite burden, the Wasserstein metric is the appropriate choice.Comment: Published at http://dx.doi.org/10.3150/14-BEJ595 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Development of a hybrid multi-scale simulation approach for spray processes

This paper presents a multi-scale approach coupling a Eulerian interface-tracking method and a Lagrangian particle-tracking method to simulate liquid atomisation processes. This method aims to represent the complete spray atomisation process including the primary break-up process and the secondary break-up process, paving the way for high-fidelity simulations of spray atomisation in the dense spray zone and spray combustion in the dilute spray zone. The Eulerian method is based on the coupled level-set and volume-of-fluid method for interface tracking, which can accurately simulate the primary break-up process. For the coupling approach, the Eulerian method describes only large droplet and ligament structures, while small-scale droplet structures are removed from the resolved Eulerian description and transformed into Lagrangian point-source spherical droplets. The Lagrangian method is thus used to track smaller droplets. In this study, two-dimensional simulations of liquid jet atomisation are performed. We analysed Lagrangian droplet formation and motion using the multi-scale approach. The results indicate that the coupling method successfully achieves multi-scale simulations and accurately models droplet motion after the Eulerian–Lagrangian transition. Finally, the reverse Lagrangian–Eulerian transition is also considered to cope with interactions between Eulerian droplets and Lagrangian droplets.This work was supported by the Engineering and Physical Sciences Research Council of the UK (grant number EP/L000199/1)

Observation of the Presuperfluid Regime in a Two-Dimensional Bose Gas

In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of pre-superfluid behavior. As phase-space density $\rho$ increases toward degenerate values, we observe a gradual divergence of the compressibility $\kappa$ from the value predicted by a bare-atom model, $\kappa_{ba}$. $\kappa/\kappa_{ba}$ grows to 1.7 before $\rho$ reaches the value for which we observe the sudden emergence of a spike at $p=0$ in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-meanfield physics in the pre-superfluid but degenerate 2D Bose gas.Comment: Replace with the version appeared in PR

A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with $O(N \log^2 N)$ arithmetic complexity and $O(N \log N)$ memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the $\mathcal{H}$-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $\mathcal{H}$-LU and that it can tackle problems where algebraic multigrid fails to converge

Test of the τ-model of Bose–Einstein correlations and reconstruction of the source function in hadronic Z-boson decay at LEP

Bose–Einstein correlations of pairs of identical charged pions produced in hadronic Z decays are analyzed in terms of various parametrizations. A good description is achieved using a Lévy stable distribution in conjunction with a model where a particle’s momentum is correlated with its space–time point of production, the τ-model. Using this description and the measured rapidity and transverse momentum distributions, the space–time evolution of particle emission in two-jet events is reconstructed. However, the elongation of the particle emission region previously observed is not accommodated in the τ-model, and this is investigated using an ad hoc modification

Charge collective modes in an incommensurately modulated cuprate

We report the first measurement of collective charge modes of insulating Sr14Cu24O41 using inelastic resonant x-ray scattering over the complete Brillouin zone. Our results show that the intense excitation modes at the charge gap edge predominantly originate from the ladder-containing planar substructures. The observed ladder modes (E vs. Q) are found to be dispersive for momentum transfers along the "legs" but nearly localized along the "rungs". Dispersion and peakwidth characteristics are similar to the charge spectrum of 1D Mott insulators, and we show that our results can be understood in the strong coupling limit (U >> t_{ladder}> t_{chain}). The observed behavior is in marked contrast to the charge spectrum seen in most two dimensional cuprates. Quite generally, our results also show that momentum-tunability of inelastic scattering can be used to resolve mode contributions in multi-component incommensurate systems.Comment: 4+ pages, 5 figure

Physics of puffing and microexplosion of emulsion fuel droplets

The physics of water-in-oil emulsion droplet microexplosion/puffing has been investigated using high-fidelity interface-capturing simulation. Varying the dispersed-phase (water) sub-droplet size/location and the initiation location of explosive boiling (bubble formation), the droplet breakup processes have been well revealed. The bubble growth leads to local and partial breakup of the parent oil droplet, i.e., puffing. The water sub-droplet size and location determine the after-puffing dynamics. The boiling surface of the water sub-droplet is unstable and evolves further. Finally, the sub-droplet is wrapped by boiled water vapor and detaches itself from the parent oil droplet. When the water sub-droplet is small, the detachment is quick, and the oil droplet breakup is limited. When it is large and initially located toward the parent droplet center, the droplet breakup is more extensive. For microexplosion triggered by the simultaneous growth of multiple separate bubbles, each explosion is local and independent initially, but their mutual interactions occur at a later stage. The degree of breakup can be larger due to interactions among multiple explosions. These findings suggest that controlling microexplosion/puffing is possible in a fuel spray, if the emulsion-fuel blend and the ambient flow conditions such as heating are properly designed. The current study also gives us an insight into modeling the puffing and microexplosion of emulsion droplets and sprays.This article has been made available through the Brunel Open Access Publishing Fund