Error estimation in the histogram Monte Carlo method

We examine the sources of error in the histogram reweighting method for Monte Carlo data analysis. We demonstrate that, in addition to the standard statistical error which has been studied elsewhere, there are two other sources of error, one arising through correlations in the reweighted samples, and one arising from the finite range of energies sampled by a simulation of finite length. We demonstrate that while the former correction is usually negligible by comparison with statistical fluctuations, the latter may not be, and give criteria for judging the range of validity of histogram extrapolations based on the size of this latter correction.Comment: 7 pages including 3 postscript figures, typeset in LaTeX using the RevTeX macro packag

Some implications of sampling choices on comparisons between satellite and model aerosol optical depth fields

The comparison of satellite and model aerosol optical depth (AOD) fields provides useful information on the strengths and weaknesses of both. However, the sampling of satellite and models is very different and some subjective decisions about data selection and aggregation must be made in order to perform such comparisons. This work examines some implications of these decisions, using GlobAerosol AOD retrievals at 550 nm from Advanced Along-Track Scanning Radiometer (AATSR) measurements, and aerosol fields from the GEOS-Chem chemistry transport model. It is recommended to sample the model only where the satellite flies over on a particular day; neglecting this can cause regional differences in model AOD of up to 0.1 on monthly and annual timescales. The comparison is observed to depend strongly upon thresholds for sparsity of satellite retrievals in the model grid cells. Requiring at least 25% coverage of the model grid cell by satellite data decreases the observed difference between the two by approximately half over land. The impact over ocean is smaller. In both model and satellite datasets, there is an anticorrelation between the proportion <i>p</i> of a model grid cell covered by satellite retrievals and the AOD. This is attributed to small <i>p</i> typically occuring due to high cloud cover and lower AODs being found in large clear-sky regions. Daily median AATSR AODs were found to be closer to GEOS-Chem AODs than daily means (with the root mean squared difference being approximately 0.05 smaller). This is due to the decreased sensitivity of medians to outliers such as cloud-contaminated retrievals, or aerosol point sources not included in the model

A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise

Zeros of the Jimbo, Miwa, Ueno tau function

We introduce a family of local deformations for meromorphic connections on the Riemann sphere in the neighborhood of a higher rank (simple) singularity. Following a scheme introduced by Malgrange we use these local models to prove that the zeros of the tau function introduced by Jimbo, Miwa and Ueno occur precisely at those points in the deformation space at which a certain Birkhoff-Riemann- Hilbert problem fails to have a solution.Comment: 59 page

Analytical Investigations of Coil-System Design Parameters for a Constant-Velocity Traveling Magnetic Wave Plasma Engine

Coil-system design parameters for constant velocity traveling-magnetic-wave plasma engin