Applying Dispersive Changes to Lagrangian Particles in Groundwater Transport Models

Method-of-characteristics groundwater transport models require that changes in concentrations computed within an Eulerian framework to account for dispersion be transferred to moving particles used to simulate advective transport. A new algorithm was developed to accomplish this transfer between nodal values and advecting particles more precisely and realistically compared to currently used methods. The new method scales the changes and adjustments of particle concentrations relative to limiting bounds of concentration values determined from the population of adjacent nodal values. The method precludes unrealistic undershoot or overshoot for concentrations of individual particles. In the new method, if dispersion causes cell concentrations to decrease during a time step, those particles in the cell having the highest concentration will decrease the most, and those with the lowest concentration will decrease the least. The converse is true if dispersion is causing concentrations to increase. Furthermore, if the initial concentration on a particle is outside the range of the adjacent nodal values, it will automatically be adjusted in the direction of the acceptable range of values. The new method is inherently mass conservative.     

Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem

The analysis of incomplete data is a long-standing challenge in practical statistics. When, as is typical, data objects are represented by points in ℝ ^d , incomplete data objects correspond to affine subspaces (lines or Δ-flats). With this motivation we study the problem of finding the minimum intersection radius r(ℒ) of a set of lines or Δ-flats ℒ: the least r such that there is a ball of radius r intersecting every flat in ℒ. Known algorithms for finding the minimum enclosing ball for a point set (or clustering by several balls) do not easily extend to higher-dimensional flats, primarily because “distances” between flats do not satisfy the triangle inequality. In this paper we show how to restore geometry (i.e., a substitute for the triangle inequality) to the problem, through a new analog of Helly’s theorem. This “intrinsic-dimension” Helly theorem states: for any family ℒ of Δ-dimensional convex sets in a Hilbert space, there exist Δ+2 sets ℒ′⊆ℒ such that r(ℒ)≤2r(ℒ′). Based upon this we present an algorithm that computes a (1+ε)-core set ℒ′⊆ℒ, |ℒ′|=O(Δ ⁴/ε), such that the ball centered at a point c with radius (1+ε)r(ℒ′) intersects every element of ℒ. The running time of the algorithm is O(n ^Δ+1 dpoly (Δ/ε)). For the case of lines or line segments (Δ=1), the (expected) running time of the algorithm can be improved to O(ndpoly (1/ε)). We note that the size of the core set depends only on the dimension of the input objects and is independent of the input size n and the dimension d of the ambient space. An extended abstract appeared in ACM–SIAM Symposium on Discrete Algorithms, 2006. Work was done when J. Gao was with Center for the Mathematics of Information, California Institute of Technology. Work was done when M. Langberg was a postdoctoral scholar at the California Institute of Technology. Research supported in part by NSF grant CCF-0346991. Research of L.J. Schulman supported in part by an NSF ITR and the Okawa Foundation.     

Zum Nachweis von Formaldehyd

Ohne Zusammenfassung     

A test of comparative equilibration for determining non‐exchangeable stable hydrogen isotope values in complex organic materials

Comparative equilibration has been proposed as a methodological approach for determining the hydrogen isotopic composition (δD) of non‐exchangeable hydrogen in complex organic materials, from feathers to blood and soils. This method depends on using homogenized standards that have been previously calibrated for their δD values of non‐exchangeable H, that are compositionally similar to unknown samples, and that span an appropriate isotopic range. Currently no certified organic reference materials with exchangeable H exist, and so isotope laboratories have been required to develop provisional internal calibration standards, such as the keratin standards currently used in animal migration studies. Unfortunately, the isotope ratios of some samples fall outside the range of keratin standards currently used for comparative equilibration. Here we tested a set of five homogenized keratin powders as well as feathers from Painted Buntings and Dark‐eyed Juncos to determine the effects of extrapolating comparative equilibration normalization equations outside the isotopic range of keratin standards. We found that (1) comparative equilibration gave precise results within the range of the calibration standards; (2) linear extrapolation of normalization equations produced accurate δD results to ～40‰ outside the range of the keratins standards used (?187 to ?108); and (3) for both homogenized keratin powders and heterogeneous unknown samples there was no difference in variance between samples within and outside the range of keratin standards. This suggested that comparative equilibration is a robust and practical method for determining the δD of complex organic matrices, although caution is required for samples that fall far outside the calibration range. Copyright © 2009 John Wiley & Sons, Ltd.