Using the Complex Jacobi Method to Simulate Kerr Non-linear Photonic Components

The iterative complex Jacobi technique has been extended to simulate the third order Kerr effect in wavelength scale dielectric structures. This method solves the Helmholtz equation in a discrete finite simulation space by an iterative process. An update equation refines the field values at each iteration step, until a desired accuracy is achieved. We have extended the iterative process with an extra calculation step which allows simulating materials with the non-linear third order Kerr effect. Our adjustment of the discrete field operators in the update equation also introduces PMLs as absorbing boundaries and the total field/scattered field formalism as field source for this method.     

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).     

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.     

Curves over every global field violating the local-global principle

There is an algorithm that takes as input a global field k and produces a curve over k violating the local-global principle. Also, given a global field k and a nonnegative integer n, one can effectively construct a curve X over k such that #X(k) = n. Bibliography: 26 titles.     

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.