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At least 19 records

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 1{sup 1}A{sub 1} ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two {sup 1}A{sub 1} states. In the present work, valence correlated energies of the 1{sup 1}A{sub 1} state and the 2{sup 1}A{sub 1} state were calculated at the 1{sup 1}A{sub 1} open minimum, the 1{sup 1}A{sub 1} ring minimum, the transition state between these two minima, the minimum of the 2{sup 1}A{sub 1} state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 1{sup 1}A{sub 1} state, the present calculations yield the estimates of (ring minimum—open minimum) ∼45–50 mh and (transition state—open minimum) ∼85–90 mh. For the (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) excitation energy, the estimate of ∼130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (2{sup 1}A{sub 1}–{sup 1}A{sub 1}) is found to be between 1 and 10 mh. The geometry of the transition state on the 1{sup 1}A{sub 1} surface and that of the minimum on the 2{sup 1}A{sub 1} surface nearly coincide. More accurate predictions of the energy differences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to the energy differences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

The structure of water around the compressibility minimum

Here we present diffraction data that yield the oxygen-oxygen pair distribution function, g{sub OO}(r) over the range 254.2–365.9 K. The running O-O coordination number, which represents the integral of the pair distribution function as a function of radial distance, is found to exhibit an isosbestic point at 3.30(5) Å. The probability of finding an oxygen atom surrounding another oxygen at this distance is therefore shown to be independent of temperature and corresponds to an O-O coordination number of 4.3(2). Moreover, the experimental data also show a continuous transition associated with the second peak position in g{sub OO}(r) concomitant with the compressibility minimum at 319 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Could a future “Grand Solar Minimum” like the Maunder Minimum stop global warming?

A future Maunder Minimum type grand solar minimum, with total solar irradiance reduced by 0.25% over a 50 year period from 2020 to 2070, is imposed in a future climate change scenario experiment (RCP4.5) using, for the first time, a global coupled climate model that includes ozone chemistry and resolved stratospheric dynamics (Whole Atmosphere Community Climate Model). This model has been shown to simulate two amplifying mechanisms that produce regional signals of decadal climate variability comparable to observations, and thus is considered a credible tool to simulate the Sun's effects on Earth's climate. After the initial decrease of solar radiation in 2020, globally averaged surface air temperature cools relative to the reference simulation by up to several tenths of a degree Centigrade. By the end of the grand solar minimum in 2070, the warming nearly catches up to the reference simulation. Thus, a future grand solar minimum could slow down but not stop global warming.

54 ENVIRONMENTAL SCIENCES↗

Piecewise linear approximation with minimum number of linear segments and minimum error: A fast approach to tighten and warm start the hierarchical mixed integer formulation

In several areas of economics and engineering, it is often necessary to fit discrete data points or approximate nonlinear functions with continuous functions. Piecewise linear (PWL) functions are a convenient way to achieve this. PWL functions can be modeled in mathematical problems using only linear and integer variables. Moreover, there is a computational benefit in using PWL functions that have the least possible number of segments. This work proposes a novel hierarchical mixed integer linear programming (MILP) formulation that identifies a continuous PWL approximation with minimum number of linear segments for a given target maximum error. The proposed MILP formulation also identifies the solution with the least maximum error among the solutions with minimum number of segments. Then, this work proposes a fast iterative algorithm that identifies non necessarily continuous PWL approximations by solving O(S log N) linear programming (LP) problems, where N is the number of data points and S is the minimum number of segments in the non necessarily continuous case. This work demonstrates that tight bounds for the MILP problem can be derived from these approximations. Next, a fast algorithm is introduced to transform a non necessarily continuous PWL approximation into a continuous one. Finally, the tight bounds and the continuous PWL approximations are used to tighten and warm start the MILP problem. The tightened formulation is shown in experimental results to be more efficient, especially for large data sets, with a solution time that is up to two orders of magnitude less than the existing literature.

97 MATHEMATICS AND COMPUTING↗

IMPLICATIONS OF THE RECENT LOW SOLAR MINIMUM FOR THE SOLAR WIND DURING THE MAUNDER MINIMUM

The behavior of the Sun and near-Earth space during grand solar minima is not understood; however, the recent long and low minimum of the decadal-scale solar cycle gives some important clues, with implications for understanding the solar dynamo and predicting space weather conditions. The speed of the near-Earth solar wind and the strength of the interplanetary magnetic field (IMF) embedded within it can be reliably reconstructed for before the advent of spacecraft monitoring using observations of geomagnetic activity that extend back to the mid-19th century. We show that during the solar cycle minima around 1879 and 1901 the average solar wind speed was exceptionally low, implying the Earth remained within the streamer belt of slow solar wind flow for extended periods. This is consistent with a broader streamer belt, which was also a feature of the recent low minimum (2009), and yields a prediction that the low near-Earth IMF during the Maunder minimum (1640-1700), as derived from models and deduced from cosmogenic isotopes, was accompanied by a persistent and relatively constant solar wind of speed roughly half the average for the modern era.

79 ASTRONOMY AND ASTROPHYSICS↗

Minimum Energy of Multicomponent Distillation Systems Using Minimum Additional Heat and Mass Integration Sections

Heat and mass integration to consolidate distillation columns in a multicomponent distillation configuration can lead to a number of new energy efficient and cost effective configurations. In this paper, we identify a powerful and simple-to-use fact about heat and mass integration. The newly developed heat and mass integrated configurations, which we call as HMP configurations, involve first introducing thermal couplings to all intermediate transfer streams, followed by consolidating columns associated with a lighter pure product reboiler and a heavier pure product condenser. A systematic method of enumerating all HMP configurations is introduced. We compare the energy savings of HMP configurations with the well-known fully thermally coupled (FTC) configurations. We demonstrate that HMP configurations can have very similar and sometimes even the same minimum total vapor duty requirement as the FTC configuration, while using far less number of column sections, intermediate transfer streams, and thermal couplings than the FTC configurations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonlinear control of the minimum safety factor in tokamaks by optimal allocation of spatially moving electron cyclotron current drive

The minimum value of the safety factor profile is related to the magnetohydrodynamic (MHD) stability of the plasma confined in a tokamak. Therefore, active control of the minimum safety factor may mitigate MHD instabilities that can degrade or even terminate plasma confinement. Typically, in most tokamak scenarios, the minimum safety factor evolves spatially with time, i.e., the location at which the safety factor achieves the minimum value changes with time. In addition to the inherent nonlinearities in the minimum safety factor evolution, its spatial variation makes the control design challenging. In particular, complexity in control design may arise from the need for time-dependent nonlinear models that account for spatial variation of the minimum safety factor. Furthermore, the minimum safety factor may drift to locations where the actuator authority is low. The problem of minimum safety factor control with target location tracking and moving electron cyclotron current drive (ECCD) is addressed in this work. A nonlinear time-dependent model that incorporates the spatial variation of the minimum safety factor is presented. A nonlinear controller based on optimal feedback linearization is developed to track a target minimum safety factor. The proposed controller treats the ECCD position as a controllable variable. In other words, the controller prescribes the ECCD position (in addition to the non-inductive powers) in real time based on an optimal criterion that is defined a priori. This work also presents the steps necessary to integrate the minimum safety factor controller with a total energy controller to achieve multiple control objectives simultaneously. In conclusion, the proposed integrated control algorithm is tested using nonlinear simulations in the Control Oriented Transport SIMulator (COTSIM) for a DIII-D tokamak scenario.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Minimum critical masses and their uncertainties for several fissile nuclides and reflectors - 14296

A systematic effort was undertaken to reevaluate the minimum critical mass for several fissile nuclides and reflectors. This was done using MCNP6 in combination with several modern nuclear data libraries, viz. ENDF/B-VII.1, JENDL-4.0 and JEFF-3.1.1. This combination was benchmarked extensively against criticality safety benchmarks. The procedure to extract the minimum critical mass from the MCNP6 calculations was carefully implemented, so that it would have a negligible impact on the accuracy of the end results. All parts of the calculation, i.e. nuclear data processing, MCNP6 models, and post-processing, were applied consistently for all cases, involving varying fissile nuclides and reflectors. Results for the minimum critical mass were generated for {sup 233,235}U, {sup 236,239,241}Pu, {sup 242m}Am, {sup 243,245,247}Cm, and {sup 249,251}Cf, for the case of water moderation and water reflection. For {sup 235}U, the minimum critical mass was also calculated for cases with other reflectors, such as beryllium, heavy water, graphite, lead, and concrete. The results for the water reflection cases are in good agreement with most of the literature values, but for the cases with reflectors such as graphite, lead, or concrete, there are sizable differences. The accuracy of the results was assessed in two ways. First, a comparison was made with criticality safety benchmark results, by selecting benchmarks that resemble the minimum mass systems the most. It was clear that for {sup 233,235}U and {sup 239}Pu with water reflection, the differences in minimum critical masses between the libraries are consistent with the differences obtained for benchmark cases. The difference between the benchmark calculations and the benchmark values is then an indication of the accuracy with which one can simulate comparable systems. Secondly, sensitivity runs were performed with the new MCNP6 sensitivity option, based on ENDF/B-VII.1 nuclear data. For each fissile nuclide, the sensitivity of k{sub eff} to cross sections such as capture, fission, elastic, inelastic was calculated for the minimum critical mass case. The same was done for the {sup 1}H and {sup 16}O cross sections in the moderator and reflector. The uncertainty in k{sub eff} was calculated by combining the sensitivity profiles with the appropriate ENDF/B-VII.1 covariance matrix, using the SUSD code. As a final step, the uncertainty in k{sub eff} can be translated to an uncertainty in the minimum critical mass. (author)

42 ENGINEERING↗