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Computational solution of chemistry problems

AB initio quantum chemical techniques have been used to investigate weakly bound complexes of H2O and SO2. An energy gradient program was used to locate stable structures for the H2O, SO2 complexes, and SCF calculations were carried out to determine the binding energies of complexes with multiple water molecules. A 4-31G basis set was used for most potential energy searches. More accurate basis sets including a generally contracted basis set with d orbitals on the sulfur were used for geometry and binding energy verification. For single water complexes, five different stable geometries were located with binding energies between 4 and 11 Kcal mol(-1), suggesting a binding shell for H2O around SO2 and a mechanism for the formation of an SO2-containing water droplet. Calculations on one of the complexes utilizing a larger double zeta basis and d functions on the sulfur atom lead to adjusted binding energies in the range 3 to 8 Kcal mol(-1). Very little charge transfer between SO2 and H2O was present. Addition of more than one H2O was found to be energetically favorable although the addition of the fourth water in certain geometries did not increase the stability of the complex. An alternative mechanism for the tropospheric gas phase production of acid rain is suggested.

Ake, Robert L.↗

The interaction of horizontal eddy transport and thermal drive in the stratosphere

The two processes that determine the average state of the circulation; i.e., horizontal eddy transport and thermal dissipation, are examined, and the effects of their interaction on circulation and on tracer distribution in the stratosphere are investigated using barotropic calculations on the sphere. It is shown that eddy advection tends to homogenize the meridional gradient Q at low latitudes, while thermal dissipation restores the gradient after episodes of mixing.

Salby, Murry L.↗

Empirical wind model for the middle and lower atmosphere. Part 1: Local time average

The HWM90 thermospheric wind model was revised in the lower thermosphere and extended into the mesosphere and lower atmosphere to provide a single analytic model for calculating zonal and meridional wind profiles representative of the climatological average for various geophysical conditions. Gradient winds from CIRA-86 plus rocket soundings, incoherent scatter radar, MF radar, and meteor radar provide the data base and are supplemented by previous data driven model summaries. Low-order spherical harmonics and Fourier series are used to describe the major variations throughout the atmosphere including latitude, annual, semiannual, and longitude (stationary wave 1). The model represents a smoothed compromise between the data sources. Although agreement between various data sources is generally good, some systematic differences are noted, particularly near the mesopause. Root mean square differences between data and model are on the order of 15 m/s in the mesosphere and 10 m/s in the stratosphere for zonal wind, and 10 m/s and 4 m/s, respectively, for meridional wind.

Hedin, A. E.↗

Advanced takeoff procedures for high-speed civil transport community noise reduction

Advanced takeoff procedures were developed for a Mach 2.62 high-speed civil transport configuration (HSCT) equipped with turbine bypass engines, with the goal of reducing the takeoff noise levels for certification to FAR 36, Stage 3 noise levels. The detailed takeoff and landing module for the Flight Optimizations System (FLOPS) computer program was used to generate takeoff profiles. All takeoff procedures were constrained to meet a FAR takeoff field length of 11,000 feet, as well as the minimum required engine-out climb gradients for each airbome segment. Aircraft noise levels at the FAR 36 certification points were calculated using the Aircraft Noise Prediction Program (ANOPP). The study showed that using advanced takeoff procedures in noise certification could result in a 2.25 dB reduction in the amount of noise suppression required to certify this configuration for Stage 3 noise limits. Advanced procedures also resulted in an 8 percent reduction in the 100 EPNdB noise footprint area compared to basic FAR 36 takeoff procedures. In addition, improvements in the lift-to-drag ratio using high-lift devices were shown to produce 1.81 dB more noise reduction when used in combination with advanced takeoff procedures.

Olson, E. D.↗

Magnetic Susceptibility Effects and Lorentz Damping in Diamagnetic Fluids

A great number of crystals (semi-conductor and protein) grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity and g-jitter. Both static and dynamic (rotating or travelling wave) magnetic fields can be used to reduce the effects of convection in materials processing. In semi-conductor melts, due to their relatively high electrical conductivity, the induced Lorentz force can be effectively used to curtail convective effects. In melts/solutions with reduced electrical conductivity, such as aqueous solutions used in solution crystal growth, protein crystal growth and/or model fluid experiments for simulating melt growth, however, the variation of the magnetic susceptibility with temperature and/or concentration can be utilized to better damp fluid convection than the Lorentz force method. This paper presents a comprehensive, comparative numerical study of the relative damping effects using static magnetic fields and gradients in a simple geometry subjected to a thermal gradient. The governing equations are formulated in general terms and then simplified for the numerical calculations. Operational regimes, based on the best damping technique for different melts/solutions are identified based on fluid properties. Comparisons are provided between the numerical results and available results from experiments in surveyed literature.

Ramachandran, Narayanan↗

Small-Scale Gravity Waves in ER-2 MMS/MTP Wind and Temperature Measurements during CRYSTAL-FACE

Lower stratospheric wind and temperature measurements made from NASA's high-altitude ER-2 research aircraft during the CRYSTAL-FACE campaign in July 2002 were analyzed to retrieve information on small scale gravity waves (GWs) at the aircraft's flight level (typically approximately 20 km altitude). For a given flight segment, the S-transform (a Gaussian wavelet transform) was used to search for and identify small horizontal scale GW events, and to estimate their apparent horizontal wavelengths. The horizontal propagation directions of the events were determined using the Stokes parameter method combined with the cross S-transform analysis. The vertical temperature gradient was used to determine the vertical wavelengths of the events. GW momentum fluxes were calculated from the cross S-transform. Other wave parameters such as intrinsic frequencies were calculated using the GW dispersion relation. More than 100GW events were identified. They were generally high frequency waves with vertical wavelength of approximately 5 km and horizontal wavelength generally shorter than 20 km. Their intrinsic propagation directions were predominantly toward the east, whereas their ground-based propagation directions were primarily toward the west. Among the events, approximately 20% of them had very short horizontal wavelength, very high intrinsic frequency, and relatively small momentum fluxes, and thus they were likely trapped in the lower stratosphere. Using the estimated GW parameters and the background winds and stabilities from the NCAR/NCEP reanalysis data, we were able to trace the sources of the events using a simple reverse ray-tracing. More than 70% of the events were traced back to convective sources in the troposphere, and the sources were generally located upstream of the locations of the events observed at the aircraft level. Finally, a probability density function of the reversible cooling rate due to GWs was obtained in this study, which may be useful for cirrus cloud models.

Wang, L.↗

On a Technique of Studying the Interface Kinetics and Anisotropy of Specific Interfacial Energy Based on Experiments on Migration of Liquid Cylindrical Inclusions in a Crystal under Stationary Thermal Conditions

A method for processing experimental data on the migration of liquid cylindrical inclusions in a crystal under a temperature gradient has been considered on the assumption that the experimental thermal conditions are stationary. Formulas are derived to calculate the degree of interfacial energy anisotropy and relative hindrance of the crystallization and dissolution processes at atomically smooth interface areas based on the shapes of cross sections of cylindrical inclusions migrated perpendicular to the close-packed crystal planes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Influence of the Latitudinal Temperature Gradient on Soil Dust Concentration and Deposition in Greenland

To investigate the effects of changes in the latitudinal temperature gradient and the global mean temperature on dust concentration in the Northern Hemisphere, experiments with the GISS GCM (Goddard Institute for Space Studies General Circulation Model) are performed. The dust concentration over Greenland is calculated from sources in central and eastern Asia, which are integrated on-line in the model. The results show that an increase in the latitudinal temperature gradient increases both the Asian dust source strength and the concentration over Greenland. The source increase is the result of increased surface winds, and to a minor extent, the increase in Greenland dust is also associated with increased northward transport. Cooling the climate in addition to this increased gradient leads to a decrease in precipitation scavenging, which helps produce a further (slight) increase in Greenland dust in this experiment. Reducing the latitudinal gradient reduces the surface wind and hence the dust source, with a subsequent reduction in Greenland dust concentrations. Warming the climate in addition to this reduced gradient leads to a further reduction in Greenland dust due to enhanced precipitation scavenging. These results can be used to evaluate the relationship of Greenland ice core temperature changes to changes in the latitudinal and global temperatures.

Tegen, Ina↗

Influence of the Latitudinal Temperature Gradient on Soil Dust Concentration and Deposition in Greenland

To investigate the effects of changes in the latitudinal temperature gradient and the global mean temperature on dust concentration in the Northern Hemisphere, experiments with the Goddard Institute for Space Studies General Circulation Model (GISS GCM) are performed. The dust concentration over Greenland is calculated from sources in central and eastern Asia, which are integrated on-line in the model. The results show that an increase in the latitudinal temperature gradient increases both the Asian dust source strength and the concentration over Greenland. The source increase is the result of increased surface winds, and to a minor extent, the increase in Greenland dust is also associated with increased northward transport. Cooling the climate in addition to this increased gradient leads to a decrease in precipitation scavenging, which helps produce a further (slight) increase in Greenland dust in this experiment. Reducing the latitudinal gradient reduces the surface wind and hence the dust source, with a subsequent reduction in Greenland dust concentrations. Warming the climate in addition to this reduced gradient leads to a further reduction in Greenland dust due to enhanced precipitation scavenging. These results can be used to evaluate the relationship of Greenland ice core temperature changes to changes in the latitudinal and global temperatures.

Tegen, Ina↗

Three dimensional numerical scattering from ocean-like surfaces

A new method of calculating the electric field scattered from two-dimensional conducting rough surfaces is presented. This method uses the operator conjugate gradients technique and the extended boundary condition equation. This avoids the build-up of round-off errors encountered in the inversion of large matrices. It also avoids the singularities of the integral kernels usually encountered in the method of moments. Techniques for improving the rate of convergence by applying physical constraints are discussed. This method is presently being used to calculate the polarization signatures from simulated ocean-like surfaces.

Rodriguez, Ernesto↗

Ab initio calculation of atomic solid hydrogen phases based on Gutzwiller many-body wave functions

We apply two ab initio many-body methods based on Gutzwiller wave functions, i.e., correlation matrix renormalization theory (CMRT) and Gutzwiller conjugate gradient minimization (GCGM), to the study of crystalline phases of atomic hydrogen. Both methods avoid empirical Hubbard U parameters and are free from double-counting issues. CMRT employs a Gutzwiller-type approximation that enables efficient calculations, while GCGM goes beyond this approximation to achieve higher accuracy at higher computational cost. By benchmarking against available quantum Monte Carlo (QMC) results, we demonstrate that while both methods are more accurate than the widely used density-functional theory, GCGM systematically captures additional correlation energy missing in CMRT, leading to significantly improved total energy predictions. We also show that by including the correlation energy Ec from local density approximation in the CMRT calculation, CMRT + E c produces energy in better agreement with the QMC results in these hydrogen lattice systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Assessment of electronic structure methods for the determination of the ground spin states of Fe( ii ), Fe( iii ) and Fe( iv ) complexes

Our ability to understand and simulate the reactions catalyzed by iron depends strongly on our ability to predict the relative energetics of spin states. In this work, we studied the electronic structures of Fe 2+ ion, gaseous FeO and 14 iron complexes using Kohn–Sham density functional theory with particular focus on determining the ground spin state of these species as well as the magnitudes of relevant spin-state energy splittings. The 14 iron complexes investigated in this work have hexacoordinate geometries of which seven are Fe(II), five are Fe(III) and two are Fe(IV) complexes. These are calculated using 20 exchange–correlation functionals. In particular, we use a local spin density approximation (LSDA) – GVWN5, four generalized gradient approximations (GGAs) – BLYP, PBE, OPBE and OLYP, two non-separable gradient approximations (NGAs) – GAM and N12, two meta-GGAs – M06-L and M11-L, a meta-NGA – MN15-L, five hybrid GGAs – B3LYP, B3LYP*, PBE0, B97-3 and SOGGA11-X, four hybrid meta-GGAs – M06, PW6B95, MPW1B95 and M08-SO and a hybrid meta-NGA – MN15. The density functional results are compared to reference data, which include experimental results as well as the results of diffusion Monte Carlo (DMC) calculations and ligand field theory estimates from the literature. For the Fe 2+ ion, all functionals except M11-L correctly predict the ground spin state to be quintet. However, quantitatively, most of the functionals are not close to the experimentally determined spin-state splitting energies. For FeO all functionals predict quintet to be the ground spin state. For the 14 iron complexes, the hybrid functionals B3LYP, MPW1B95 and MN15 correctly predict the ground spin state of 13 out of 14 complexes and PW6B95 gets all the 14 complexes right. Here, the local functionals, OPBE, OLYP and M06-L, predict the correct ground spin state for 12 out of 14 complexes. Two of the tested functionals are not recommended to be used for this type of study, in particular M08-SO and M11-L, because M08-SO systematically overstabilizes the high spin state, and M11-L systematically overstabilizes the low spin state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Self-interaction error overbinds water clusters but cancels in structural energy differences

Here, we gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi–Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew–Burke–Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction–corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/ H 2 O from about 42 meV/ H 2 O for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction–corrected SCAN. These findings suggest that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Detection of topological materials with machine learning

Databases compiled using ab initio and symmetry-based calculations now contain tens of thousands of topological insulators and topological semimetals. This makes the application of modern machine learning methods to topological materials possible. Using gradient boosted trees, we show how to construct a machine learning model which can predict the topology of a given existent material with an accuracy of 90%. Such predictions are orders of magnitude faster than actual ab initio calculations. In this work, we use machine learning models to probe how different material properties affect topological features. Notably, we observe that topology is mostly determined by the “coarse-grained” chemical composition and crystal symmetry and depends little on the particular positions of atoms in the crystal lattice. We identify the sources of our model's errors and we discuss approaches to overcome them.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A SPATIALLY RESOLVED VERTICAL TEMPERATURE GRADIENT IN THE HD 163296 DISK

We analyze sensitive, sub-arcsecond resolution ALMA science verification observations of CO emission lines in the protoplanetary disk hosted by the young, isolated Ae star HD 163296. The observed spatial morphology of the {sup 12}CO J = 3-2 emission line is asymmetric across the major axis of the disk; the {sup 12}CO J = 2-1 line features a much less pronounced, but similar, asymmetry. The J = 2-1 emission from {sup 12}CO and its main isotopologues have no resolved spatial asymmetry. We associate this behavior with the direct signature of a vertical temperature gradient and layered molecular structure in the disk. This is demonstrated using both toy models and more sophisticated calculations assuming non-local thermodynamic equilibrium conditions. A model disk structure is developed to reproduce both the distinctive spatial morphology of the {sup 12}CO J = 3-2 line as well as the J = 2-1 emission from the CO isotopologues assuming relative abundances consistent with the interstellar medium. This model disk structure has {tau} = 1 emitting surfaces for the {sup 12}CO emission lines that make an angle of {approx}15 Degree-Sign with respect to the disk midplane. Furthermore, we show that the spatial and spectral sensitivity of these data can distinguish between models that have sub-Keplerian gas velocities due to the vertical extent of the disk and its associated radial pressure gradient (a fractional difference in the bulk gas velocity field of {approx}> 5%)

79 ASTRONOMY AND ASTROPHYSICS↗

Fugacity and concentration gradients in a gravity field

Equations are reviewed which show that at equilibrium fugacity and concentration gradients can exist in gravitational fields. At equilibrium, the logarithm of the ratio of the fugacities of a species at two different locations in a gravitational field is proportional to the difference in the heights of the two locations and the molecular weight of the species. An analogous relation holds for the concentration ratios in a multicomponent system. The ratio is calculated for a variety of examples. The kinetics for the general process are derived, and the time required to approach equilibrium is calculated for several systems. The following special topics are discussed: ionic solutions, polymers, multiphase systems, hydrostatic pressure, osmotic pressure, and solubility gradients in a gravity field.

May, C. E.↗

Efficient derivative computation for unsteady fatigue-constrained nonlinear aero-structural wind turbine blade optimization

Gradient-based optimization offers significant efficiency advantages for wind turbine blade design, but its application has often been limited by the cost and accuracy of finite-difference derivative calculations, especially when fatigue constraints are considered. In this work, we systematically compare and evaluate four differentiation techniques, namely algorithmic differentiation, implicit differentiation, sparsity exploitation, and parallelization, to determine their effectiveness in computing accurate gradients through time-domain aero-structural simulations. By integrating these techniques with unsteady nonlinear aerodynamic and structural models, we develop software designed for accurate gradient computation. We show that combining these techniques addresses memory and runtime challenges associated with long simulations required by design load cases. Specifically, the most effective combination reduces derivative computation wall time by over an order of magnitude compared to finite differencing while maintaining superior accuracy. We demonstrate this approach in a proof-of-concept aero-structural optimization of a wind turbine blade that improves the cost of energy by 12.78 %. This comparative study establishes a viable approach for fatigue-aware blade design that balances computational efficiency with modeling accuracy.

17 WIND ENERGY↗

Kink Waves in Non-isothermal Stratified Solar Waveguides: Effect of the External Magnetic Field

We study the effect of an external magnetic field on the properties of kink waves, propagating along a thin non-isothermal stratified and diverging magnetic flux tube. A wave equation, governing the propagation of kink waves under the adopted model is derived. It is shown that the vertical gradient of temperature introduces a spatially local cut-off frequency ω {sub c}. The vertical distribution of the cut-off frequency is calculated for the reference VAL-C model of the solar atmosphere and for different values of a ratio of external to internal magnetic fields. The results show that the cut-off frequency is negative below the temperature minimum due to the negative temperature gradient. In the chromosphere the cut-off frequency at a given height is smaller for a stronger external magnetic field. For the appropriate range of a ratio B{sub e} / B{sub i} ≈ 0–0.8, the cutoff lies in the range ω{sub c} ≈ 0.003–0.010 s{sup −1} (periods 600 < P{sub c} < 2000 s). The estimate of the cut-off frequency in the transition region is provided as well. In the propagating wave regime, the effective wave energy flux in the non-isothermal diverging flux tubes is the same as in the straight and homogeneous cylindrical waveguides. The obtained wave equation in the limit β = 0 is used to study the kink oscillations of non-isothermal coronal loops. It is found that the gradient of temperature along the coronal loops reduces the frequency ratio of the first overtone to the fundamental mode, i.e., ω{sub 2}/ ω{sub 1} < 2. This reduction grows for a larger ratio of temperature at the loop top to the temperature at the footpoints. Moreover, the effect of reduction is most pronounced for the steeper temperature profiles.

79 ASTRONOMY AND ASTROPHYSICS↗