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At least 973 records · Page 54

The value of continuity: Refined isogeometric analysis and fast direct solvers

Here, we propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method “refined Isogeometric Analysis (rIGA)”. To illustrate the impact of the continuity reduction, we analyze the number of Floating Point Operations (FLOPs), computational times, and memory required to solve the linear system obtained by discretizing the Laplace problem with structured meshes and uniform polynomial orders. Theoretical estimates demonstrate that an optimal continuity reduction may decrease the total computational time by a factor between p 2 and p 3 , with pp being the polynomial order of the discretization. Numerical results indicate that our proposed refined isogeometric analysis delivers a speed-up factor proportional to p 2 . In a 2D mesh with four million elements and p=5, the linear system resulting from rIGA is solved 22 times faster than the one from highly continuous IGA. In a 3D mesh with one million elements and p=3, the linear system is solved 15 times faster for the refined than the maximum continuity isogeometric analysis.

97 MATHEMATICS AND COMPUTING↗

Angular systematics-free cosmological analysis of galaxy clustering in configuration space

ABSTRACT Galaxy redshift surveys are subject to incompleteness and inhomogeneous sampling due to the various constraints inherent to spectroscopic observations. This can introduce systematic errors on the summary statistics of interest, which need to be mitigated in cosmological analysis to achieve high accuracy. Standard practices involve applying weighting schemes based on completeness estimates across the survey footprint, possibly supplemented with additional weighting schemes accounting for density-dependent effects. In this work, we concentrate on pure angular systematics and describe an alternative approach consisting in analysing the galaxy two-point correlation function where angular modes are nulled. By construction, this procedure removes all possible known and unknown sources of angular observational systematics, but also part of the cosmological signal. We use a modified Landy–Szalay estimator for the two-point correlation function that relies on an additional random catalogue where angular positions are randomly drawn from the galaxy catalogue, and provide an analytical model to describe this modified statistic. We test the model by performing an analysis of the full anisotropic clustering in mock catalogues of luminous red and emission-line galaxies at 0.43 < z < 1.1. We find that the model fully accounts for the modified correlation function in redshift space, without introducing new nuisance parameters. The derived cosmological parameters from the analysis of baryon acoustic oscillations and redshift-space distortions display slightly larger statistical uncertainties, mostly for the growth rate of structure parameter fσ8 that exhibits a $50{{\ \rm per\ cent}}$ statistical error increase, but free from angular systematic error.

79 ASTRONOMY AND ASTROPHYSICS↗

Correction to: Imaging Light–Induced Migration of Dislocations in Halide Perovskites with 3D Nanoscale Strain Mapping

Owing to an error in properly normalizing the reconstruction phase data into atomic displacements, the strain values that we used to calculate the root mean squared local strain, ε rms , and to calculate the fraction of the crystals more strain than 1%, f, quoted in the original paper, are roughly one order of magnitude too large. This error was only discovered recently whilst performing further analysis.

36 MATERIALS SCIENCE↗

Self‐Consistent Convolutional Density Functional Approximations: Application to Adsorption at Metal Surfaces

The exchange-correlation (XC) functional in density functional theory is used to approximate multi-electron interactions. A plethora of different functionals are available, but nearly all are based on the hierarchy of inputs commonly referred to as “Jacob's ladder.” This paper introduces an approach to construct XC functionals with inputs from convolutions of arbitrary kernels with the electron density, providing a route to move beyond Jacob's ladder. We derive the variational derivative of these functionals, showing consistency with the generalized gradient approximation (GGA), and provide equations for variational derivatives based on multipole features from convolutional kernels. A proof-of-concept functional, PBEq, which generalizes the PBEα framework with mathematical equation being a spatially-resolved function of the monopole of the electron density, is presented and implemented. It allows a single functional to use different GGAs at different spatial points in a system, while obeying PBE constraints. Analysis of the results underlines the importance of error cancellation and the XC potential in data-driven functional design. After testing on small molecules, bulk metals, and surface catalysts, the results indicate that this approach is a promising route to simultaneously optimize multiple properties of interest.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Field validation of dynamic mechanical torque measurements using fiber-optic strain sensors for geared wind turbines

Abstract Accurate knowledge of the mechanical loads of wind turbine gearboxes has become essential in modern, highly loaded gearbox designs, as maintaining or even improving gearbox reliability with increasing torque density demands is proving to be challenging. Unfortunately, the traditional method of measuring dynamic mechanical torque using strain gauges placed on the outer surface of a rotating shaft and transmitting the resulting signal is unsuitable for serial deployment due to technical and economic constraints. An alternative method based on fiber-optic strain sensors placed on the stationary outer surface of the gearbox ring gear has been proposed. Like shaft torsion, the radial deformation of the ring gear is proportionate to the rotor torque. Placing the sensors on a stationary component is a cost-effective alternative for serial implementation because the need for complex and expensive data transfer via wireless transmission or a slip ring is eliminated. In this paper, we present the results of an extensive field experiment conducted to evaluate the torque measurement accuracy of this novel sensing solution installed on the gearbox of a Gamesa G97 2-MW wind turbine at the National Renewable Energy Laboratory’s Flatirons Campus. Torque measurements derived from fiber-optic strain sensors placed on the ring gear of the planetary stage are compared to conventional torque measurements from strain gauges placed on the main shaft. Two different torque estimation data processing methods were evaluated, with the method based on operational deflection shapes providing the most accurate results with an average normalized root mean square error below 0.7% for a load revolution distribution analysis. The effect of operating conditions on the torque estimate was also investigated, and the third planet-passing operational deflection shape was found to be the least sensitive to nontorque load-related effects. The fiber-optic strain sensors’ successful operation during the complete test campaign has demonstrated a robust and accurate solution for fleet-wide enhanced gearbox remaining useful life estimation.

17 WIND ENERGY↗

Enhancing the Range and Reliability of the Spacer Layer Imaging Method

The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.

EHL film geometry↗

On the Effect of Sphere-Overlap on Super Coarse-Grained Models of Protein Assemblies

Ion mobility mass spectrometry (IM/MS) can provide structural information on intact protein complexes. Such data, including connectivity and collision cross sections (CCS) of assemblies’ subunits, can in turn be used as a guide to produce representative super coarse-grained models. These models are constituted by ensembles of overlapping spheres, each representing a protein subunit. A model is considered plausible if the CCS and sphere-overlap levels of its subunits fall within predetermined confidence intervals. While the first is determined by experimental error, the latter is based on a statistical analysis on a range of protein dimers. Here, we first propose a new expression to describe the overlap between two spheres. Then we analyze the effect of specific overlap cutoff choices on the precision and accuracy of super coarse-grained models. Finally, we propose a method to determine overlap cutoff levels on a per-case scenario, based on collected CCS data, and show that it can be applied to the characterization of the assembly topology of symmetrical homo-multimers. .

74 ATOMIC AND MOLECULAR PHYSICS↗

Crank–Nicolson WSGI difference scheme with finite element method for multi-dimensional time-fractional wave problem

In this article, a second-order Crank–Nicolson weighted and shifted Grünwald integral (WSGI) time-discrete scheme combined with finite element method is studied for finding the numerical solution of the multi-dimensional time-fractional wave equation. The time-fractional wave equation with Caputo-fractional derivative is transformed into the time-fractional integral equation by integral technique, then the second-order Crank–Nicolson finite element scheme with a time second-order WSGI discrete approximation for fractional integral is formulated. The analysis of stability is made, then a priori error estimate is given by making use of the conversion technique between the WSGI formula and fractional integral. At the end of the article, some numerical examples covering two two-dimensional cases with rectangular element and triangular element and a three-dimensional case with tetrahedral element are shown to test and verify our theoretical results.

97 MATHEMATICS AND COMPUTING↗

Snowmass2021 - Letter of interest cosmology intertwined II: The hubble constant tension

The current cosmological probes have provided a fantastic confirmation of the standard Λ Cold Dark Matter cosmological model, which has been constrained with unprecedented accuracy. However, with the increase of the experimental sensitivity, a few statistically significant tensions between different independent cosmological datasets emerged. While these tensions can be in part the result of systematic errors, the persistence after several years of accurate analysis strongly hints at cracks in the standard cosmological scenario and the need for new physics. In this Letter of Interest we will focus on the 4.4σ tension between the Planck estimate of the Hubble constant H0 and the SH0ES collaboration measurements. After showing the H0 evaluations made from different teams using different methods and geometric calibrations, we will list a few interesting models of new physics that could solve this tension and discuss how the next decade’s experiments will be crucial.

79 ASTRONOMY AND ASTROPHYSICS↗

Note: Derivation of two-photon circular dichroism—Addendum to “Two-photon circular dichroism” [J. Chem. Phys. 62, 1006 (1975)]

This addendum shows the detailed derivation of the fundamental equations for two-photon circular dichroism which are given in a very condensed form in the original publication [I. Tinoco, J. Chem. Phys. 62, 1006 (1975)]. In addition, some minor errors are corrected and some of the derivations in the original publication are commented.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A COMPREHENSIVE STATISTICAL ASSESSMENT OF STAR-PLANET INTERACTION

We investigate whether magnetic interaction between close-in giant planets and their host stars produce observable statistical enhancements in stellar coronal or chromospheric activity. New Chandra observations of 12 nearby (d < 60 pc) planet-hosting solar analogs are combined with archival Chandra, XMM-Newton, and ROSAT coverage of 11 similar stars to construct a sample inoculated against inherent stellar class and planet-detection biases. Survival analysis and Bayesian regression methods (incorporating both measurements errors and X-ray upper limits; 13/23 stars have secure detections) are used to test whether ''hot Jupiter'' hosts are systematically more X-ray luminous than comparable stars with more distant or smaller planets. No significant correlations are present between common proxies for interaction strength (M {sub P}/a {sup 2} or 1/a) versus coronal activity (L {sub X} or L {sub X}/L {sub bol}). In contrast, a sample of 198 FGK main-sequence stars does show a significant (∼99% confidence) increase in X-ray luminosity with M {sub P}/a {sup 2}. While selection biases are incontrovertibly present within the main-sequence sample, we demonstrate that the effect is primarily driven by a handful of extreme hot-Jupiter systems with M {sub P}/a {sup 2} > 450 M {sub Jup} AU{sup –2}, which here are all X-ray luminous but to a degree commensurate with their Ca II H and K activity, in contrast to presented magnetic star-planet interaction scenarios that predict enhancements relatively larger in L {sub X}. We discuss these results in the context of cumulative tidal spin-up of stars hosting close-in gas giants (potentially followed by planetary infall and destruction). We also test our main-sequence sample for correlations between planetary properties and UV luminosity or Ca II H and K emission, and find no significant dependence.

79 ASTRONOMY AND ASTROPHYSICS↗

Effective theory of dark energy at redshift survey scales

We explore the phenomenological consequences of general late-time modifications of gravity in the quasi-static approximation, in the case where cold dark matter is non-minimally coupled to the gravitational sector. Assuming spectroscopic and photometric surveys with configuration parameters similar to those of the Euclid mission, we derive constraints on our effective description from three observables: the galaxy power spectrum in redshift space, tomographic weak-lensing shear power spectrum and the correlation spectrum between the integrated Sachs-Wolfe effect and the galaxy distribution. In particular, with ΛCDM as fiducial model and a specific choice for the time dependence of our effective functions, we perform a Fisher matrix analysis and find that the unmarginalized 68% CL errors on the parameters describing the modifications of gravity are of order σ∼10{sup −2}–10{sup −3}. We also consider two other fiducial models. A nonminimal coupling of CDM enhances the effects of modified gravity and reduces the above statistical errors accordingly. In all cases, we find that the parameters are highly degenerate, which prevents the inversion of the Fisher matrices. Some of these degeneracies can be broken by combining all three observational probes.

79 ASTRONOMY AND ASTROPHYSICS↗

Generalized local-frame-transformation theory for excited species in external fields

A rigorous theoretical framework is developed for a generalized local-frame-transformation theory (GLFT). The GLFT is applicable to the following systems: Rydberg atoms or molecules in an electric field and negative ions in any combination of electric and/or magnetic fields. A first test application to the photoionization spectra of Rydberg atoms in an external electric field demonstrates dramatic improvement over the first version of the local- frame-transformation theory developed initially by U. Fano [Phys. Rev. A 24, 619 (1981)] and D. A. Harmin [Phys. Rev. A 26, 2656 (1982)]. This revised GLFT theory yields nontrivial corrections because it now includes the full on-shell Hilbert space without adopting the truncations in the original theory. Comparisons of the semianalytical GLFT Stark spectra with ab initio numerical simulations yield errors in the range of a few tens of MHz, an improvement over the original Fano-Harmin theory, whose errors are 10–100 times larger. Furthermore, our analysis provides a systematic pathway to precisely describe the corresponding photoabsorption spectra that should be accurate enough to meet most modern experimental standards.

74 ATOMIC AND MOLECULAR PHYSICS↗

Unveiling ν secrets with cosmological data: Neutrino masses and mass hierarchy

Using some of the latest cosmological datasets publicly available, we derive the strongest bounds in the literature on the sum of the three active neutrino masses, M ν , within the assumption of a background flat ΛCDM cosmology. In the most conservative scheme, combining Planck cosmic microwave background (CMB) temperature anisotropies and baryon acoustic oscillations (BAO) data, as well as the up-to-date constraint on the optical depth to reionization (τ), the tightest 95% confidence level (C.L.) upper bound we find is M ν <0.151~eV. The addition of Planck high-ℓ polarization data, which however might still be contaminated by systematics, further tightens the bound to M ν <0.118~eV. A proper model comparison treatment shows that the two aforementioned combinations disfavor the IH at ~64%~C.L. and ~71%~C.L. respectively. Furthermore, we compare the constraining power of measurements of the full-shape galaxy power spectrum versus the BAO signature, from the BOSS survey. Even though the latest BOSS full shape measurements cover a larger volume and benefit from smaller error bars compared to previous similar measurements, the analysis method commonly adopted results in their constraining power still being less powerful than that of the extracted BAO signal. Our research uses only cosmological data; imposing the constraint M ν >0.06eV from oscillations data would raise the quoted upper bounds by O(0.1σ) and would not affect our conclusions.

79 ASTRONOMY AND ASTROPHYSICS↗

Proton Isovector Helicity Distribution on the Lattice at Physical Pion Mass

We present a state-of-the-art calculation of the isovector quark helicity Bjorken-x distribution in the proton using lattice-QCD ensembles at the physical pion mass. We compute quasi-distributions at proton momenta P z ϵ {2.2; 2.6; 3.0} GeV on the lattice, and match them systematically to the physical parton distribution using large-momentum effective theory (LaMET).We reach an unprecedented precision through high statistics in simulations, large-momentum proton matrix elements, and control of excited-state contamination. The resulting distribution with combined statistical and systematic errors is in agreement with the latest phenomenological analysis of the spin-dependent experimental data; in particular, Δ$\bar{u}$(x) > Δ$\bar{d}$(x).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Assessment of Optimal Flexibility in Ensemble of Frequency Responsive Loads

Potential of electrical loads in providing grid ancillary services is often limited due to the uncertainties associated with the load behavior. A knowledge of the expected uncertainties with a load control program would invariably yield to better informed control policies, opening up the possibility of extracting the maximal load control potential without affecting grid operations. In the context of frequency responsive load control, a probabilistic uncertainty analysis framework is presented to quantify the expected error between the target and actual load response, under uncertainties in the load dynamics. A closed-form expression of an optimal demand flexibility, minimizing the expected error in actual and committed flexibility, is provided. Analytical results are validated through Monte Carlo simulations of ensembles of electric water heaters.

Kundu, Soumya↗