Measuring Sulfur Isotope Ratios from Solid Samples with the Sample Analysis at Mars Instrument and the Effects of Dead Time Corrections

The Sample Analysis at Mars (SAM) instrument suite comprises the largest science payload on the Mars Science Laboratory (MSL) "Curiosity" rover. SAM will perform chemical and isotopic analysis of volatile compounds from atmospheric and solid samples to address questions pertaining to habitability and geochemical processes on Mars. Sulfur is a key element of interest in this regard, as sulfur compounds have been detected on the Martian surface by both in situ and remote sensing techniques. Their chemical and isotopic composition can belp constrain environmental conditions and mechanisms at the time of formation. A previous study examined the capability of the SAM quadrupole mass spectrometer (QMS) to determine sulfur isotope ratios of SO2 gas from a statistical perspective. Here we discuss the development of a method for determining sulfur isotope ratios with the QMS by sampling SO2 generated from heating of solid sulfate samples in SAM's pyrolysis oven. This analysis, which was performed with the SAM breadboard system, also required development of a novel treatment of the QMS dead time to accommodate the characteristics of an aging detector

Exact diagonalization of the S=1/2 Heisenberg antiferromagnet on finite bcc lattices to estimate properties on the infinite lattice

Here we generate finite bipartite body-centred cubic lattices up to 32 vertices. We have studied the spin one half Heisenberg antiferromagnet by diagonalizing its Hamiltonian on each of the finite lattices and hence computing its ground state properties. By extrapolation of these data we obtain estimates of the T = 0 properties on the infinite bcc lattice. Our estimate of the T = 0 energy agrees to five parts in ten thousand with third order spin wave and series expansion method estimates, while our estimate of the staggered magnetization agrees with the spin wave estimate to within a quarter of one percent.Comment: 16 pages, LaTeX, 1 ps figure, to appear in J.Phys.

Spin-1/2 J1-J2 model on the body-centered cubic lattice

Using exact diagonalization (ED) and linear spin wave theory (LSWT) we study the influence of frustration and quantum fluctuations on the magnetic ordering in the ground state of the spin-1/2 J1-J2 Heisenberg antiferromagnet (J1-J2 model) on the body-centered cubic (bcc) lattice. Contrary to the J1-J2 model on the square lattice, we find for the bcc lattice that frustration and quantum fluctuations do not lead to a quantum disordered phase for strong frustration. The results of both approaches (ED, LSWT) suggest a first order transition at J2/J1 $\approx$ 0.7 from the two-sublattice Neel phase at low J2 to a collinear phase at large J2.Comment: 6.1 pages 7 figure

Accuracy and Stability of Computing High-Order Derivatives of Analytic Functions by Cauchy Integrals

High-order derivatives of analytic functions are expressible as Cauchy integrals over circular contours, which can very effectively be approximated, e.g., by trapezoidal sums. Whereas analytically each radius r up to the radius of convergence is equal, numerical stability strongly depends on r. We give a comprehensive study of this effect; in particular we show that there is a unique radius that minimizes the loss of accuracy caused by round-off errors. For large classes of functions, though not for all, this radius actually gives about full accuracy; a remarkable fact that we explain by the theory of Hardy spaces, by the Wiman-Valiron and Levin-Pfluger theory of entire functions, and by the saddle-point method of asymptotic analysis. Many examples and non-trivial applications are discussed in detail.Comment: Version 4 has some references and a discussion of other quadrature rules added; 57 pages, 7 figures, 6 tables; to appear in Found. Comput. Mat

Review of Inverse Laplace Transform Algorithms for Laplace-Space Numerical Approaches

A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used to solve the Laplace-transformed diffusion equation, producing a time-domain solution after a numerical Laplace transform inversion. Motivated by the needs of numerical methods posed in Laplace-transformed space, we compare five inverse Laplace transform algorithms and discuss implementation techniques to minimize the number of Laplace-space function evaluations. We investigate the ability to calculate a sequence of time domain values using the fewest Laplace-space model evaluations. We find Fourier-series based inversion algorithms work for common time behaviors, are the most robust with respect to free parameters, and allow for straightforward image function evaluation re-use across at least a log cycle of time