9 research outputs found
Dynamical Heterogeneities Below the Glass Transition
We present molecular dynamics simulations of a binary Lennard-Jones mixture
at temperatures below the kinetic glass transition. The ``mobility'' of a
particle is characterized by the amplitude of its fluctuation around its
average position. The 5% particles with the largest/smallest mean amplitude are
thus defined as the relatively most mobile/immobile particles. We investigate
for these 5% particles their spatial distribution and find them to be
distributed very heterogeneously in that mobile as well as immobile particles
form clusters. The reason for this dynamic heterogeneity is traced back to the
fact that mobile/immobile particles are surrounded by fewer/more neighbors
which form an effectively wider/narrower cage. The dependence of our results on
the length of the simulation run indicates that individual particles have a
characteristic mobility time scale, which can be approximated via the
non-Gaussian parameter.Comment: revtex, 10 pages, 20 postscript figure
Interweaving PFASST and Parallel Multigrid
The parallel full approximation scheme in space and time (PFASST) introduced by Emmett and Minion in 2012 is an iterative strategy for the temporal parallelization of ODEs and discretized PDEs. As the name suggests, PFASST is similar in spirit to a space-time full approximation scheme multigrid method performed over multiple time steps in parallel. However, since the original focus of PFASST was on the performance of the method in terms of time parallelism, the solution of any spatial system arising from the use of implicit or semi-implicit temporal methods within PFASST have simply been assumed to be solved to some desired accuracy completely at each substep and each iteration by some unspecified procedure. It hence is natural to investigate how iterative solvers in the spatial dimensions can be interwoven with the PFASST iterations and whether this strategy leads to a more efficient overall approach. This paper presents an initial investigation on the relative performance of different strategies for coupling PFASST iterations with multigrid methods for the implicit treatment of diffusion terms in PDEs. In particular, we compare full accuracy multigrid solves at each substep with a small fixed number of multigrid V-cycles. This reduces the cost of each PFASST iteration at the possible expense of a corresponding increase in the number of PFASST iterations needed for convergence. Parallel efficiency of the resulting methods is explored through numerical examples
Comparison of quantification methods to measure fire-derived (black-elemental) carbon in soils and sediments using reference materials from soil, water, sediment and the atmosphere
Monofunctionalized pillar[5]arene as a host for alkanediamines
Alkanediamines serve as neutral guests for the recently discovered host pillar[5]arene. The proposed [2]pseudorotaxane nature of the superstructure of the 1:1 host-guest complexes is supported by the template-directed synthesis of a related [2]rotaxane. A synthetic route to monofunctional pillar[5]arenes has also been developed, allowing for the creation of a fluorescent sensor for alkylamine binding. The precursors to this host could act as starting points for a large library of monofunctional pillar[5]arene macrocycles