Kinematic and Dynamic Collision Statistics of Cloud Droplets From High-Resolution Simulations

We study the dynamic and kinematic collision statistics of cloud droplets for a range of flow Taylor microscale Reynolds numbers (up to 500), using a highly scalable hybrid direct numerical simulation approach. Accurate results of radial relative velocity (RRV) and radial distribution function (RDF) at contact have been obtained by taking advantage of their power-law scaling at short separation distances. Three specific but inter-related questions have been addressed in a systematic manner for geometric collisions of same-size droplets (of radius from 10 to 60 μm) in a typical cloud turbulence (dissipation rate at 400 cm2 s-3. Firstly, both deterministic and stochastic forcing schemes were employed to test the sensitivity of the simulation results on the large-scale driving mechanism. We found that, in general, the results are quantitatively similar, with the deterministic forcing giving a slightly larger RDF and collision kernel. This difference, however, is negligible for droplets of radius less than 30 μm. Secondly, we have shown that the dependence of pair statistics on the flow Reynolds number Rλ or larger scale fluid motion is of secondary importance, with a tendency for this effect to saturate at high enough Rλ leading to Rλ-independent results. Both DNS results and theoretical arguments show that the saturation happens at a smaller Rλ for smaller droplets. Finally, since most previous studies of turbulent collision of inertial particles concerned non-sedimenting particles, we have specifically addressed the role of gravity on collision statistics, by simultaneously simulating collision statistics with and without gravity. It is shown that the collision statistics is not affected by gravity when a \u3c ac, where the critical droplet radius ac is found to be around 30 μm for the RRV, and around 20 μm for the RDF. For larger droplets, gravity alters the particle-eddy interaction time and significantly reduces the RRV. The effect of gravity on the RDF is rather complex: gravity reduces the RDF for intermediate-sized droplets but enhances the RDF for larger droplets. In addition, we have studied the scaling exponents of both RDF and RRV, and found that gravity modifies the RDF scaling exponents for both intermediate and large particles, in a manner very similar to the effect of gravity on the RDF at contact. Gravity is shown to cause the scaling exponents for RDF and RRV to level off for large droplets, in contrast to diminishing exponents for non-sedimenting particles

How does the chain extension of poly (acrylic acid) scale in aqueous solution? A combined study with light scattering and computer simulation

This work adresses the question of the scaling behaviour of polyelectrolytes in solution for a realistic prototype: We show results of a combined experimental (light scattering) and theoretical (computer simulations) investigation of structural properties of poly (acrylic acid) (PAA). Experimentally, we determined the molecular weight (M_W) and the hydrodynamic radius (R_H) by static light scattering for six different PAA samples in aqueous NaCl-containing solution (0.1-1 mol/L) of polydispersity D_P between 1.5 and 1.8. On the computational side, three different variants of a newly developed mesoscopic force field for PAA were employed to determine R_H for monodisperse systems of the same M_W as in the experiments. The force field effectively incorporates atomistic information and one coarse-grained bead corresponds to one PAA monomer. We find that R_H matches with the experimental data for all investigated samples. The effective scaling exponent for R_H is found to be around 0.55, which is well below its asymptotic value for good solvents. Additionally, data for the radius of gyration (R_G) are presented.Comment: 17 pages, 3 figures, submitted to Macromolecule

Distributed Processing of Generalized Graph-Pattern Queries in SPARQL 1.1

We propose an efficient and scalable architecture for processing generalized graph-pattern queries as they are specified by the current W3C recommendation of the SPARQL 1.1 "Query Language" component. Specifically, the class of queries we consider consists of sets of SPARQL triple patterns with labeled property paths. From a relational perspective, this class resolves to conjunctive queries of relational joins with additional graph-reachability predicates. For the scalable, i.e., distributed, processing of this kind of queries over very large RDF collections, we develop a suitable partitioning and indexing scheme, which allows us to shard the RDF triples over an entire cluster of compute nodes and to process an incoming SPARQL query over all of the relevant graph partitions (and thus compute nodes) in parallel. Unlike most prior works in this field, we specifically aim at the unified optimization and distributed processing of queries consisting of both relational joins and graph-reachability predicates. All communication among the compute nodes is established via a proprietary, asynchronous communication protocol based on the Message Passing Interface