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At least 1,675 records · Page 93

Notes on the restricted three body problem- approximate behavior of solutions near the collinear lagrangian points

Studies the solutions of the restricted three-body problem near those equilibrium points which are collinear with the two positive masses. This is done to gain insight toward the development of an analytic proof and classification of the periodic orbits that pass near these equilibrium points, which have been discovered numerically by M. Davidson, and also to hopefully gain insight into the nature of solutions of the restricted three-body problem in general. The qualitative observations that are made are all deduced from the linearized equations.

Approximation method↗

Comment on “Introduction of a Novel Figure of Merit for the Assessment of Transparent Conductive Electrodes in Photovoltaics: Exact and Approximate Form”

Anand et al. introduce an implicit equation for transparent conductive electrode (TCE) merit in photovoltaics (PV) by lumping series resistance in with the diode. However, an explicit equation has been previously derived by lumping series resistance external to the diode. For TCEs of practical interest for PV, the choice of where to lump series resistance does not affect merit, so external lumping is preferred. On the other hand, monolith deadspace, metal grid shadowing, and grid resistance shift TCE merit away from the figure of merit behavior published by Anand et al.

14 SOLAR ENERGY↗

Approximately 15% of Miscanthus yield is lost at current commercial cutting heights in Iowa

Various works have quantitatively characterized the effects of environmental and management factors on Miscanthus x giganteus Greef et Deu (mxg) yield and, therefore, anticipated land requirement per unit production. However, little work has addressed the effects of cutting height, which may significantly contribute to the difference between the standing aboveground biomass at harvest (i.e., biological yield) and harvested yield. This study quantitatively characterized the effect of cutting height using a replicated nitrogen trial of a 5-year-old mxg stand in southeast Iowa and related this information to observations of cutting height in nearby commercial fields. Nitrogen fertilizer did not significantly change the relationship of the stem segment mass to length, and overall, a 1-cm stem segment contributes 0.5% of the total stem biomass within the bottom 44 cm of the stem. This results in an average harvest loss of 15% of the aboveground standing biomass when cutting at 30 cm, typically seen in commercial mxg fields in eastern Iowa. Cutting height should be considered when accurately predicting commercial mxg harvest yields and changes in soil organic carbon in a commercial mxg agroecosystem.

60 APPLIED LIFE SCIENCES↗

On the Sensitivity to Density-Functional Approximations for CO Binding Energies of Single-Atom Catalysts in Nitrogen-Doped Graphene

Density functional theory (DFT) methods are the working horse in screening new catalytic materials. They are widely used to predict trends in binding energies, which are then used to compare the activity of different materials. Here, the binding strength of CO is an important descriptor to the CO 2 reduction catalytic activity of the single transition metal atoms embedded on nitrogen-doped graphene (TM/NG). In this work, however, we show that CO binding strengths in different TM/NG has very different sensitivity to DFT methods. Specifically, Fe/NG CO binding energy changes dramatically with the percentage of exact exchange in the functional; Co/NG does less so, while Ni/NG nearly has no change. Such varying behaviors is a direct result of different local spin configurations, similar to the performance of DFT methods for metal porphyrin complexes. Therefore, caution should be exercised when using DFT binding energies for quantitative predictions in TM/NG single atom catalysis.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

An International Laboratory Comparison Study on Approximating the Enthalpy of Adsorption via the Clausius‐Clapeyron Approach

Materials-based gas capture and storage is an increasingly important area of research. Robust and accurate determination of material properties is required for judicial selection of materials for specific applications and for engineering materials–based systems at scale. One key property is the strength of the adsorbate–adsorbent interaction often quantified via the isosteric enthalpy of adsorption. The heat of adsorption can be measured directly through calorimetry; however, a more widely used approach is to apply the Clausius-Clapeyron (CC) equation to adsorption isotherms collected at different temperatures. While this approach appears to be straightforward, there exist multiple variants in the application of the methodologies employed. This raises the question on how these variations may or may not affect the determined results. Presented here is a discussion of the most common methodologies and a comparison of indirect determinations (via CC) of the isosteric enthalpy of adsorption by different laboratories on identical material. Included in that comparison are discussions on the measurement and analysis reproducibility. Importantly, details of the methodologies are shown to be critical when comparing enthalpies among laboratories, and different methodologies contribute to significant discrepancies and artifacts in the results. Recommendations are provided to promote robust determination and the reporting thereof.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Influence of the complete basis set approximation, tight weighted-core, and diffuse functions on the DLPNO-CCSD(T1) atomization energies of neutral H,C,O-compounds

The impact of complete basis set extrapolation schemes (CBS), diffuse functions, and tight weighted core functions on enthalpies of formation predicted via the DLPNO-CCSD(T1) reduced Feller Peterson-Dixon approach has been examined for neutral H,C,O-compounds. All tested three-point (TZ/QZ/5Z) extrapolation schemes result in mean unsigned deviation (MUD) below 2 kJ mol -1 relative to the experiment. Here, the two-point QZ/5Z and TZ/QZ CBS 1/$l^3_{max}$ extrapolation schemes are inferior to their inverse power counterpart (1/($l_{max}$ + 1/2) 4 ) by 1.3 and 4.3 kJ mol -1 . The CBS extrapolated frozen core atomization energies are insensitive (within 1 kJ mol -1 ) to augmentation of the basis set with tight weighted core functions. The core-valence correlation effects converge already at triple-ζ, although double- ζ/triple- ζ CBS extrapolation performs better and is recommended. The effect of diffuse function augmentation converges slowly, and cannot be reproduced with double- ζ or triple- ζ calculations as these are plagued with basis set superposition and incompleteness errors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Approximation of periodic Green's operator in real space using numerical integration and its use in fast Fourier transform-based micromechanical models

In this work, we propose an expression for the periodic first derivative of Green's function in real space. The proposed expression allows an alternative way of computing the periodic Green's operator based on periodically summing the free-space Green's operator in terms of an appropriate quadrature rule. We provide computational examples, which show the accuracy of the proposed approach, together with reduced spurious oscillations in the solution fields.

42 ENGINEERING↗

Tetraquarks in the Born-Oppenheimer approximation

The conventional loosely bound molecule interpretation of the X(3872) is not compatible with the recent LHCb experimental measurement of the ratio of branching fractions $\mathcal{R}$ = Br(X → ψ′γ)/Br(X → ψγ). We systematically determine the entire tetraquark spectrum for J = 0, 1, 2 and refine the calculation of $\mathcal{R}$ in an improved Born-Oppenheimer description of the X(3872) compact tetraquark. This refinement yields a significantly better agreement with experimental data on $\mathcal{R}$ and on the spectroscopy of the states themselves. Extending the diquark-antidiquark paradigm to encompass tetraquarks that are linear super-positions of open charm singlets and color octets, we discover that these exotic resonances manifest as compact shallow bound states of quarks in color force potentials.

Effective Field Theories of QCD↗

Approximate symmetries in d = 4 CFTs with an Einstein gravity dual

By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor T ++ on a d = 2 plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the T -- component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of d = 4 scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/ $\mathcal{W}$-algebra vacuum block-like structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗