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At least 127 records · Page 7

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance of the spin-component-scaled methods for energy bands

The performance of various spin-component-scaled parameterisations is examined for the second-order many-body Green's-function [MBGF(2)] calculations of valence energy bands, taking three of the experimentally well-characterised polymers as examples: polyethylene, polytetrafluoroethylene, and polyacetylene. The parameterisations considered are Grimme's original SCS parameter set, Jung et al.'s original SOS set (retaining the opposite-spin component only), Śmiga et al.'s SCS(IP) set (calibrated specifically for ionization energies), and Śmiga et al.'s SOS(IP) set (calibrated for ionization energies with the opposite-spin component only; implicit in the os-D2 model of Opoku et al.). The SCS(IP) and SOS(IP) parameterisations are found to shift both outer and inner valence bands by up to a few electronvolts away from the experimental data. The original SCS and SOS parameter sets do not improve upon, but largely maintain the accuracy of the unscaled MBGF(2) methods. Given that the SOS-MBGF(2) method can be implemented in a quartic-scaling algorithm (for all roots), it is most promising for solid-state applications. Furthermore this observation is consistent with the success of the quartic-scaling GW methods without the vertex correction based on a density-functional theory reference.

Green’s-function theory↗

Slimmer Geminals For Accurate F12 Electronic Structure Models

The Slater-type F12 geminal length scales originally tuned for the second-order Mo̷ller-Plesset F12 method are too large for higher-order F12 methods formulated using the SP (diagonal fixed-coefficient spin-adapted) F12 ansatz. The new geminal parameters reported herein reduce the basis set incompleteness errors (BSIEs) of absolute coupled-cluster singles and doubles F12 correlation energies by a significant─and increase with the cardinal number of the basis─margin. The effect of geminal reoptimization is especially pronounced for the cc-pVXZ-F12 basis sets (specifically designed for use with F12 methods) relative to their conventional aug-cc-pVXZ counterparts. The BSIEs of relative energies are less affected, but substantial reductions can be obtained, especially for atomization energies and ionization potentials with the cc-pVXZ-F12 basis sets. The new geminal parameters are therefore recommended for all applications of high-order F12 methods, such as coupled-cluster F12 methods and transcorrelated F12 methods.

Powell, Samuel R. [Virginia Polytechnic Inst. and ↗

On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions

The statistics of velocity and density fields are crucial for cosmic structure formation and evolution. Here, this paper extends our previous work on the two-point second-order statistics for the velocity field [Phys. Fluids 35, 077105 (2023)] to one-point probability distributions for both density and velocity fields. The scale and redshift variation of density and velocity distributions are studied by a halo-based non-projection approach. First, all particles are divided into halo and out-of-halo particles so that the redshift variation can be studied via generalized kurtosis of distributions for halo and out-of-halo particles, respectively. Second, without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: (i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; (ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade on small scales with a constant rate $\varepsilon_u$; (iii) On small scales, the even order moments of pairwise velocity $\Delta u_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}$; (iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $\Delta u_L$=$u_L^{'}$-$u_L$ and velocity sum $\Sigma u_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; (v) On small scales, $u_L$ and $\Sigma u_L$ can be modeled by a $X$ distribution to maximize the entropy of the system. The distribution of $\Delta u_L$ can be different; (vi) On large scales, $\Delta u_L$ and $\Sigma u_L$ can be modeled by a logistic or a $X$ distribution, while $u_L$ has a different distribution; (vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $\alpha(z)$ decreasing with time.

79 ASTRONOMY AND ASTROPHYSICS↗

Cosmology with second- and third-order shear statistics for the Dark Energy Survey: Methods and simulated analysis

We present a new pipeline designed for the robust inference of cosmological parameters using both second- and third-order shear statistics. We build a theoretical model for rapid evaluation of three-point correlations using our fastnc code and integrate it into the cosmosis framework. We measure the two-point functions 𝜉 ± and the full configuration-dependent three-point shear correlation functions across all auto- and cross-redshift bins. We compress the three-point functions into the mass aperture statistic ⟨ℳ$^{3}_{ap}$⟩ for a set of 796 simulated shear maps designed to model the Dark Energy Survey Year 3 data. We estimate from it the full covariance matrix and model the effects of intrinsic alignments, shear calibration biases and photometric redshift uncertainties. We apply scale cuts to minimize the contamination from the baryonic signal as modeled through hydrodynamical simulations. We find a significant improvement of 83% on the figure of merit in the Ω m − 𝑆 8 plane when we add the ⟨ℳ$^{3}_{ap}$⟩ data to 𝜉 ± . Here, we present our findings for all relevant cosmological and systematic uncertainty parameters and discuss the complementarity of third-order and second-order statistics.

79 ASTRONOMY AND ASTROPHYSICS↗

A second-order closure analysis of turbulent diffusion flames

A complete second-order closure computer program for the investigation of compressible, turbulent, reacting shear layers was developed. The equations for the means and the second order correlations were derived from the time-averaged Navier-Stokes equations and contain third order and higher order correlations, which have to be modeled in terms of the lower-order correlations to close the system of equations. In addition to fluid mechanical turbulence models and parameters used in previous studies of a variety of incompressible and compressible shear flows, a number of additional scalar correlations were modeled for chemically reacting flows, and a typical eddy model developed for the joint probability density function for all the scalars. The program which is capable of handling multi-species, multistep chemical reactions, was used to calculate nonreacting and reacting flows in a hydrogen-air diffusion flame.

Varma, A. K.↗

Effect of Liquid Droplets on Turbulence Structure in a Round Gaseous Jet

A second-order model which predicts the modulation of turbulence in jets laden with uniform size solid particles or liquid droplets is discussed. The approach followed is to start from the separate momentum and continuity equations of each phase and derive two new conservation equations. The first is for the carrier fluid's kinetic energy of turbulence and the second for the dissipation rate of that energy. Closure of the set of transport equations is achieved by modeling the turbulence correlations up to a third order. The coefficients (or constants) appearing in the modeled equations are then evaluated by comparing the predictions with LDA-measurements obtained recently in a turbulent jet laden with 200 microns solid particles. This set of constants is then used to predict the same jet flow but laden with 50 microns solid particles. The agreement with the measurement in this case is very good.

Elghobashi, S. E.↗

Turbulence energy and diffusion transport in a separating and reattaching flow

For accurate prediction of the turbulent flow in separated and reattaching regions, it is necessary to incorporate the second- and third-moments of turbulent fluctuations. The turbulence energy and the energy dissipation rate equations are modified by incorporating the second-order closure. Moreover, the third-order closure with near-wall correction is developed for the evaluation of the diffusive action of the second-moments. After comparison of the results with experimental data, it is shown that the models developed here improve the prediction of triple-velocity correlations in both recirculating and developing flow regions.

Amano, R. S.↗

Turbulence energy and diffusion transport of third-moments in a separating and reattaching flow

For accurate prediction of turbulent flow in separated and reattaching regions, it is necessary to incorporate second- and third-moments of turbulent fluctuations. The turbulence energy and the energy dissipation rate equations are modified by incorporating second-order closure. Moreover, a transport equation model for the third-order closure with a near-wall correction is developed for the evaluation of the diffusive action of the second-moments. After comparison of the results with experimental data, it is concluded that the models developed here improve the prediction of triple-velocity correlations in both recirculating and redeveloping flow regions.

Amano, R. S.↗

Structures and characteristics of commercially available 1.5 micron InGaAsP distributed feedback laser diodes

The characteristics of commercially available 1.5-micron distributed feedback (DFB) laser diodes obtained from seven manufacturers were investigated, and the results are correlated with the lasers' structural parameters. It was found that buried heterostructures with first-order gratings showed consistently good results (as opposed to buried heterostructures with second-order gratings). A ridge waveguide laser was near the bottom of most performance charts.

Cook, A. L.↗

Decentralized control experiments on the JPL flexible spacecraft

Decentralized control experiments were successfully demonstrated for the JPL/AFAL Flexible Structure. A simulation package using MATRIXx showed strong correlation between the simulations and experimental result, while providing a means for test and debug of the various control strategies. Implementation was simplified by a modular software design that was easily transported from the simulation environment to the experimental environment. Control designs worked well for suppression of the dominant modes of the structure. Static decentralized output feedback dampened the excited modes of the structure, but sometimes excited higher order modes upon startup of the controller. A second-order frequency shaping controller helped to eliminate excitation of the higher order modes by attenuating high frequencies in the control effort. However, it also resulted in slightly longer settling times.

Ozguner, U.↗

Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model

A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies.

Sommer, T. P.↗

Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence

Recently, several models have been proposed for closing the second-moment equations, in which the velocity-pressure gradient tensor and the dissipation rate tensor are two of the most important terms. In the literature, these correlation tensors are usually decomposed into a so-called rapid term and a return-to-isotropy term. Models of these terms have been used in global flow calculations together with other modeled terms. However, their individual behaviors in different flows have not been fully examined because they are unmeasurable in the laboratory. Recently, the development of direct numerical simulation (DNS) of turbulence has given us the possibility to do this kind of study. With direct numerical simulation, we may use the solution to calculate exactly the values of these correlation terms and then directly compare them with the values from their modeled formulations. In this paper, we make direct comparisons of five representative rapid models and eight return-to-isotropy models using the DNS data of 45 homogeneous flows, which were done by Rogers et al. (1986) and Lee and Reynolds (1985). The purpose of these direct comparisons is to explore the performance of these models in different flows and identify the ones that give the best performance. The paper also describes the modeling procedure, model constraints, and the various evaluated models. The detailed results of the direct comparisons are discussed, and a few concluding remarks on turbulence models are given.

Shih, Tsan-Hsing↗

Comparison of remote sensing measurements with a two-scale polarimetric emission and scattering model for sea surfaces

Recently, it has been observed that the brightness temperatures of sea surfaces correlate with the azimuth angle of the ocean wind vector, indicating that ocean wind direction can not only be retrieved from the microwave backscatter, but also from the brightness temperature measurements. In this paper, comparison of the theoretical result calculated from a two-scale emission and scattering model with the Seasat and SSM/I model functions and aircraft measurements is presented and potential applications of microwave polarimetry are discussed. In our two-scale model, the modified reflectivities of large scale surfaces are calculated by extending the small perturbation method to the second order for small scale perturbation with anisotropic directional spectrum. It was found that the modified reflectivities derived from the second-order scattered field agree excellently well with the results obtained from a Monte Carlo simulation technique which numerically calculates the polarimetric reflectivities of one-dimensional random rough surfaces with a power-law spectrum. Without the second-order correction, the modified reflectivities of the rough surfaces are significantly over-estimated and sign errors are observed in the third and fourth Stokes parameters for thermal emissions. The surface spectrum parameters and two-scale cutoff are selected so that the calculated scattering and emission signatures agree with the reported model functions for Seasat and SSM/I. Subsequently, the polarimetric signatures of sea surfaces are illustrated to indicate the possibility of reducing the number of azimuthal looks required for spaceborne sensors in the remote sensing of ocean wind by using the polarimetric information. Furthermore, it is found that contrary to the dependence of backscattering coefficients on incidence angles, polarimetric brightness temperatures display a stronger wind direction dependence in the near nadir-looking direction than away from nadir. Finally, we discuss the potential of a single-look polarimetric radiometer for wind retrieval.

Yueh, S. H.↗

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗

A class of the van Leer-type transport schemes and its application to the moisture transport in a general circulation model

A generalized form of the second-order van Leer transport scheme is derived. Several constraints to the implied subgrid linear distribution are discussed. A very simple positive-definite scheme can be derived directly from the generalized form. A monotonic version of the scheme is applied to the Goddard Laboratory for Atmospheres (GLA) general circulation model (GCM) for the moisture transport calculations, replacing the original fourth-order center-differencing scheme. Comparisons with the original scheme are made in idealized tests as well as in a summer climate simulation using the full GLA GCM. A distinct advantage of the monotonic transport scheme is its ability to transport sharp gradients without producing spurious oscillations and unphysical negative mixing ratio. Within the context of low-resolution climate simulations, the aforementioned characteristics are demonstrated to be very beneficial in regions where cumulus convection is active. The model-produced precipitation pattern using the new transport scheme is more coherently organized both in time and in space, and correlates better with observations. The side effect of the filling algorithm used in conjunction with the original scheme is also discussed, in the context of idealized tests. The major weakness of the proposed transport scheme with a local monotonic constraint is its substantial implicit diffusion at low resolution. Alternative constraints are discussed to counter this problem.

Lin, Shian-Jiann↗

Identification of a second-order mechanical system model from a state space realization

Many system identification algorithms produce models in modern state variable form. When a mechanical system is identified one knows that there must be a model in second order form. In structural dynamics one is interested in either a modal model of the system, or in a model including a mass matrix, stiffness matrix and a damping matrix. In this paper, algorithms are developed that convert a modern state space realization into the above two representations of interest in mechanical systems. The algorithm can be used with any identification methods that produce a modern state variable representation such as the Eigensystem Realization Algorithm (ERA), its modified version by data correlation (ERA/DC), and combinations of these with Observer/Kalman Filter Identification (OKID). An algorithm is developed that allows one to identify the damping matrix in a model representation, so that one determines how near to modal the damping is in the system, and can therefore understand the degree to which the modes are coupled by the damping in the system. A second algorithm produced the mass, damping, and stiffness matrices, given the input and output matrices. It is assumed that the number of sensors (or the number of actuators) is greater than or equal to the number of modes in the system, and it is proved that this is a necessary condition to be able to uniquely identify these matrices. Experience with examples suggests that a singular value truncation involved in these algorithms can help one determine the true system order. This truncation has the benefit of knowledge of the correct form for a mechanical system model, which is not present in the modern control identification algorithm.

Tseng, Dong-Huei↗