Study of low-order numerical effects in the two-dimensional cloud-top mixing layer

Large-eddy simulation (LES) has been extensively used as a tool to understand how various processes contribute to the dynamics of the stratocumulus layer. These studies are complicated by the fact that many processes are tied to the dynamics of the stably stratified interface that caps the stratocumulus layer, and which is inadequately resolved by LES. Recent direct numerical simulations (DNS) of isobaric mixing due to buoyancy reversal in a cloud-top mixing layer show that molecular effects are in some instances important in setting the cloud-top entrainment rate, which in turn influences the global development of the layer. This suggests that traditional LES are fundamentally incapable of representing cloud-top processes that depend on buoyancy reversal and that numerical artefacts can affect significantly the results. In this study, we investigate a central aspect of this issue by developing a test case that embodies important features of the buoyancy-reversing cloud-top layer. So doing facilitates a one-to-one comparison of the numerical algorithms typical of LES and DNS codes in a well-established case. We focus on the numerical effects only by switching off the subgrid-scale model in the LES code and using instead a molecular viscosity. We systematically refine the numerical grid and quantify numerical errors, validate convergence and assess computational efficiency of the low-order LES code compared to the high-order DNS. We show that the high-order scheme solves the cloud-top problem computationally more efficiently. On that basis, we suggest that the use of higher-order schemes might be more attractive than further increasing resolution to improve the representation of stratocumulus in LES.     

Multiscale approach to CO2 hydrate formation in aqueous solution: phase field theory and molecular dynamics. Nucleation and growth

A phase field theory with model parameters evaluated from atomistic simulations/experiments is applied to predict the nucleation and growth rates of solid CO(2) hydrate in aqueous solutions under conditions typical to underwater natural gas hydrate reservoirs. It is shown that under practical conditions a homogeneous nucleation of the hydrate phase can be ruled out. The growth rate of CO(2) hydrate dendrites has been determined from phase field simulations as a function of composition while using a physical interface thickness (0.85+/-0.07 nm) evaluated from molecular dynamics simulations. The growth rate extrapolated to realistic supersaturations is about three orders of magnitude larger than the respective experimental observation. A possible origin of the discrepancy is discussed. It is suggested that a kinetic barrier reflecting the difficulties in building the complex crystal structure is the most probable source of the deviations.     

Selective catalytic oxidation of organosulfur compounds with tert-butyl hydroperoxide

Rates and selectivities for the oxidation of various organosulfur compounds with tert-butyl hydroperoxide were measured on CoAPO-5 (APO = aluminophosphate; Co/P = 0.05), Co/H-Y (Co/Al = 0.15), and MoO(x)/Al2O3 (15 % wt MoO3). Rates increased with increasing electron density at the sulfur atom (methyl phenyl sulfide>diphenyl sulfide>4-methyldibenzothiophene>2,5-dimethyl thiophene). Rates (per metal atom) were significantly higher on CoAPO-5 than on Co/H-Y, MoO(x)/Al2O3, or homogeneous Co acetate catalysts. Small amounts of sulfoxides (1-oxide) were detected on all catalysts at low reactant conversions, together with their corresponding sulfones; at higher conversions, only sulfones (1,1-dioxide) were detected, indicating that the oxidation of sulfoxides is much faster than for organosulfur reactants in the sequential oxidation pathways prevalent on these catalysts. Framework Co cations were not leached from CoAPO-5 during the oxidation of 4-methyldibenzothiophene, but most exchanged Co cations in H-Y and >20 % of Mo cations in MoO(x)/Al2O3 were extracted during these reactions. The fraction of redox-active Co cations in CoAPO-5 and Co/H-Y was measured by reduction-oxidation cycles using H2 and O2 and by UV-visible spectroscopy. This fraction was much larger in CoAPO-5 (0.35) than in Co/H-Y (0.01), consistent with the higher oxidation rates measured on CoAPO-5 and with the involvement of redox-active species in kinetically-relevant steps in catalytic oxidation sequences. Redox-active Co cations at framework positions within accessible channels are required for catalytic activity and structural stability during oxidative desulfurization, whether hydroperoxides are used as reactants or as intermediates (when O2 is used as the oxidant).     

Modelling excess surface energy in dry and wetted calcite systems

We have combined the calcite force field of Hwang et al. (J. Phys. Chem. B 105:4,122–4,127, 2001) with the F3C water model and a hybrid Lennard-Jones/van der Waals 3-site potential for CO₂ to investigate the (10[`1]4){\left({10\overline14}\right)} and ( 10[`1]0){\left( {10\overline10}\right)} cleaving surfaces of calcite under dry and wetted conditions. The wetting fluid included both pure water and water–carbon dioxide mixture. Excess surface energies and structural features of the calcite–fluid interface were analyzed, with the simulation results for the relaxed surfaces confirming the experimentally observed morphology and supporting our conclusion that the relative stability order of calcite cleaving surfaces under investigation will remain unchanged in the presence of water–carbon dioxide mixture as well.     

Modeling the dissociation of carbon dioxide and methane hydrate using the phase field theory

Hydrate that is exposed to fluid phases which are undersaturated with respect to equilibrium with the hydrate will dissociate due to gradients in chemical potential. Kinetic rates of methane hydrate dissociation towards pure water and seawater is important relative to hydrate reservoirs that are partly exposed towards the ocean floor. Corresponding results for carbon dioxide hydrate is important relative to hydrate sealing effects related to storage of carbon dioxide in cold aquifers. In this work we apply a phase field theory to the prediction of carbon dioxide hydrate and methane hydrate dissociation towards pure water at various conditions, some of which are inside and some which are outside the stability regions of the hydrates with respect to temperature and pressure. As expected from the differences in water solubility the methane hydrate dissolves significantly slower towards pure water than carbon dioxide hydrate.     

Preconditioning by inverting the Laplacian: an analysis of the eigenvalues

Wolfgang Hackbusch ^{We study the eigenvalues of the operator generated by usingthe inverse of the Laplacian as a preconditioner for self-adjointsecond-order elliptic partial differential equations with smoothcoefficients. It is well-known that the spectral condition numberof the preconditioned operator can be bounded by , where k is the uniformly positive coefficientof the second-order elliptic equation. The purpose of this paperis to study the spectrum of the preconditioned operator. Wewill show that there is a strong relation between the spectrumof this operator and the range of the coefficient function.In the continuous case, we prove, both for mappings definedon Sobolev spaces and in terms of generalized functions, thatthe spectrum of the preconditioned operator contains the rangeof the coefficient function k. In the discrete case, we indicateby numerical examples that the entire discrete spectrum is approximatelygiven by values of k.}     

Quantum well earth science testbed

A thermal hyperspectral imager is underdevelopment which utilizes the compact Dyson optical configuration and the broadband (8–12 μm) quantum well infrared photodetector (QWIP) focal plane array technology. The Dyson configuration uses a single monolithic prism-like grating design which allows for a high throughput instrument (F/1.6) with minimal ghosting, stray light and large swath width. The configuration has the potential to be the optimal high resolution imaging spectroscopy solution for aerial and space remote sensing applications due to its small form factor and relatively low power requirements. The planned instrument specifications are discussed as well as thermal design trade-offs. The current design uses a single high power cryocooler which allows operation of the QWIP at 40 K with adequate temperature stability.Calibration testing results (noise equivalent temperature difference, spectral linearity and spectral bandwidth) and laboratory emissivity plots from samples are shown using an operational testbed unit which has similar specifications as the final airborne system. Field testing of the testbed unit was performed to acquire plots of emissivity for various known standard minerals (quartz, opal, alunite). A comparison is made using data from the ASTER spectral library. The current single band (8–9 μm) testbed utilizes the high uniformity and operability of the QWIP array and shows excellent laboratory and field spectroscopic results.     

The Cyclotomic Trace for S-Algebras

A functorial and categorical defined cyclotomic trace is given,extending the usual one for rings to ring spectra. There aretwo ingredients to this: first a cyclotomic trace is neededthat accepts a categorical input with few restrictive assumptions.This is important in its own right, since this allows one totransport rich structures through the cyclotomic trace. Secondly,a sufficiently nice model is needed for the category of finitelygenerated free modules which is functorial in the ring spectrum.     

Random polynomials having few or no real zeros

Consider a polynomial of large degree whose coefficients are independent, identically distributed, nondegenerate random variables having zero mean and finite moments of all orders. We show that such a polynomial has exactly real zeros with probability as through integers of the same parity as the fixed integer . In particular, the probability that a random polynomial of large even degree has no real zeros is . The finite, positive constant is characterized via the centered, stationary Gaussian process of correlation function . The value of depends neither on nor upon the specific law of the coefficients. Under an extra smoothness assumption about the law of the coefficients, with probability one may specify also the approximate locations of the zeros on the real line. The constant is replaced by in case the i.i.d. coefficients have a nonzero mean.