Kinetic Energy Density Research Articles

Nonlinear torsional wave propagation in a thin circular rod

Coupled nonlinear wave equations are obtained for the special case of wave motion in a thin rod with circular cross-section resulting from a large-amplitude torsional source. Lagrangian mechanics are employed to obtain the wave equations from expressions for the kinetic and potential energy densities in the rod due to an assumed displacement field. Longitudinal waves are generated at quadratic order in strain by the torsional wave through inertial (centrifugal) and elastic forces. Nonlinear effects on the torsional wave occur at cubic order in strain, due to both interaction with the longitudinal wave and strain-hardening shear nonlinearity. While the torsional wave propagates without dispersion, the longitudinal wave is subject to leading-order effects of geometrical dispersion when its wavelength is comparable to the rod radius. The case of weak nonlinearity is analyzed, for which the torsional wave propagates without nonlinear distortion while finite-amplitude effects generate a longitudinal wave. An analytical solution reveals that inertial and elastic forces resulting from a harmonic travelling torsional wave work against each other in the generation of the longitudinal second harmonic. Numerical solutions for transient source motion highlight interaction between the torsional and longitudinal modes near the source, and effects of geometrical dispersion on the longitudinal wave.

Nature of the bond, reduction potential, and solvation properties of ruthenium nitrosyl complexes of the type trans‐[Ru(NH3)4(L)(NO)]2+/3+ and [Ru(salen)(L)(NO)]2+/3+ in different charge and spin states

AbstractIn this work, we present a systematic study of the nature of the RuNO bond, reduction potential, and behavior in the solution of several ruthenium nitrosyl complexes of the type trans‐[Ru(NH3)4(L)(NO)]2+/3+ (L = Cl, H2O, NH3, OH, py = pyridine, POEt3 = triethylphosphite, TVP = trivinyl phosphite) and [Ru(salen)(L)(NO)]2+/3+ (L = Cl, H2O) in different charge and spin states. We employed density functional theory, complete active space self‐consistent field, the quantum theory of atoms in molecules, charge decomposition analysis, and Monte Carlo statistical simulation in aqueous solution to investigate how the different ligands on the coordination sphere of the ruthenium atom can affect the nature of the RuNO bond and, therefore, its reactivity, reduction potential, and solvation properties. The nature of the RuNO bond varies significantly between the singlet, doublet, and triplet electronic states of these complexes, in part due to the change in the coordination mode of the NO ligand and also due to the electron correlation effects along the RuNO bond that changes drastically. For all complexes studied, the RuNO bond shows some intriguing characteristics, such as large kinetic energy density and considerable amount of electron localization between the atoms, besides high multiconfigurational character, with a significant contribution from the RuIIINO0 configuration. In addition, for all the complexes investigated, the NO ligand does not interact with the solvent through hydrogen bonds, making this group accessible for chemical reactions in solution. Another important finding was that some of the RuIIINO compounds can be reduced by biological reducing agents in the singlet ground state, while all of them have high reduction potentials in the triplet excited state, making them suitable candidates for the photorelease of nitric oxide.

Data-driven kinetic energy density fitting for orbital-free DFT: Linear vs Gaussian process regression.

We study the dependence of kinetic energy densities (KEDs) on density-dependent variables that have been suggested in previous works on kinetic energy functionals for orbital-free density functional theory. We focus on the role of data distribution and on data and regressor selection. We compare unweighted and weighted linear and Gaussian process regressions of KEDs for light metals and a semiconductor. We find that good quality linear regression resulting in good energy-volume dependence is possible over density-dependent variables suggested in previous literature studies. This is achieved with weighted fitting based on the KED histogram. With Gaussian process regressions, excellent KED fit quality well exceeding that of linear regressions is obtained as well as a good energy-volume dependence, which was somewhat better than that of best linear regressions. We find that while the use of the effective potential as a descriptor improves linear KED fitting, it does not improve the quality of the energy-volume dependence with linear regressions but substantially improves it with Gaussian process regression. Gaussian process regression is also able to perform well without data weighting.

Machine Learning Approaches toward Orbital-free Density Functional Theory: Simultaneous Training on the Kinetic Energy Density Functional and Its Functional Derivative.

Orbital-free approaches might offer a way to boost the applicability of density functional theory by orders of magnitude in system size. An important ingredient for this endeavor is the kinetic energy density functional. Snyder et al. [Phys. Rev. Lett.2012, 108, 25300223004593] presented a machine learning approximation for this functional achieving chemical accuracy on a one-dimensional model system. However, a poor performance with respect to the functional derivative, a crucial element in iterative energy minimization procedures, enforced the application of a computationally expensive projection method. In this work we circumvent this issue by including the functional derivative into the training of various machine learning models. Besides kernel ridge regression, the original method of choice, we also test the performance of convolutional neural network techniques borrowed from the field of image recognition.

Coronal Mini-jets in an Activated Solar Tornado-like Prominence

Abstract High-resolution observations from the Interface Region Imaging Spectrometer reveal the existence of a particular type of small solar jet, which arose singly or in clusters from a tornado-like prominence suspended in the corona. In this study, we perform a detailed statistical analysis of 43 selected mini-jets in the tornado event. Our results show that the mini-jets typically have (1) a projected length of 1.0–6.0 Mm, (2) a width of 0.2–1.0 Mm, (3) a lifetime of 10–50 s, (4) a velocity of 100–350 km s−1, and (5) an acceleration of 3–20 km s−2. Based on spectral diagnostics and EM-Loci analysis, these jets seem to be multithermal small-scale plasma ejections with an estimated average electron density of ∼2.4 × 1010 cm−3 and an approximate mean temperature of ∼2.6 × 105 K. Their mean kinetic energy density, thermal energy density, and dissipated magnetic field strength are roughly estimated to be ∼9 erg cm−3, 3 erg cm−3, and 16 G, respectively. The accelerations of the mini-jets, the UV and EUV brightenings at the footpoints of some mini-jets, and the activation of the host prominence suggest that the tornado mini-jets are probably created by fine-scale external or internal magnetic reconnections (a) between the prominence field and the enveloping or background field or (b) between twisted or braided flux tubes within the prominence. The observations provide insight into the geometry of such reconnection events in the corona and have implications for the structure of the prominence magnetic field and the instability that is responsible for the eruption of prominences and coronal mass ejections.

DFTpy: An efficient and object‐oriented platform for orbital‐free DFT simulations

AbstractIn silico materials design is hampered by the computational complexity of Kohn–Sham DFT, which scales cubically with the system size. Owing to the development of new‐generation kinetic energy density functionals (KEDFs), orbital‐free DFT (OFDFT) can now be successfully applied to a large class of semiconductors and such finite systems as quantum dots and metal clusters. In this work, we present DFTpy, an open‐source software implementing OFDFT written entirely in Python 3 and outsourcing the computationally expensive operations to third‐party modules, such as NumPy and SciPy. When fast simulations are in order, DFTpy exploits the fast Fourier transforms from PyFFTW. New‐generation, nonlocal and density‐dependent‐kernel KEDFs are made computationally efficient by employing linear splines and other methods for fast kernel builds. We showcase DFTpy by solving for the electronic structure of a million‐atom system of aluminum metal which was computed on a single CPU. The Python 3 implementation is object‐oriented, opening the door to easy implementation of new features. As an example, we present a time‐dependent OFDFT implementation (hydrodynamic DFT) which we use to compute the spectra of small metal clusters recovering qualitatively the time‐dependent Kohn–Sham DFT result. The Python codebase allows for easy implementation of application programming interfaces. We showcase the combination of DFTpy and ASE for molecular dynamics simulations of liquid metals. DFTpy is released under the MIT license.This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory Data Science > Computer Algorithms and Programming

Deep Learning Emulation of Subgrid‐Scale Processes in Turbulent Shear Flows

AbstractDeep neural networks (DNNs) are developed from a data set obtained from the dynamic Smagorinsky model to emulate the subgrid‐scale (SGS) viscosity (νsgs) and diffusivity (κsgs) for turbulent stratified shear flows encountered in the oceans and the atmosphere. These DNNs predict νsgs and κsgs from velocities, strain rates, and density gradients such that the evolution of the kinetic energy budget and density variance budget terms is similar to the corresponding values obtained from the original dynamic Smagorinsky model. These DNNs also compute νsgs and κsgs ∼2–4 times quicker than the dynamic Smagorinsky model resulting in a ∼2–2.5 times acceleration of the entire simulation. This study demonstrates the feasibility of deep learning in emulating the subgrid‐scale (SGS) phenomenon in geophysical flows accurately in a cost‐effective manner. In a broader perspective, deep learning‐based surrogate models can present a promising alternative to the traditional parameterizations of the subgrid‐scale processes in climate models.

Optimal design of multi-cellular cores for sandwich panels under harmonic excitation

Sandwich panels with cellular cores are increasingly used in engineering due to their superb dynamic performance. In this type of structure, core design significantly affects its mechanical property. This article is to study optimal design of a multi-cellular core to minimize dynamic response of the sandwich panel under harmonic excitation by use of topology optimization. In this study, structural dynamic responses to harmonic excitation are discussed and formulations of the dynamic response in terms of strain and kinetic energy densities are derived. Topology optimization with multi-fractional volume constraint is conducted for multi-cellular core design to minimize the dynamic response of the sandwich panel under harmonic excitation. The optimization to minimize or maximize the dynamic responses are discussed in optimal core designs of sandwich panels. A multi-objective optimisation problem is also considered to optimally suppress harmonic vibrations with a range of several frequencies. Numerical examples are presented to validate the derived formulations and to optimally design multi-cellular cores for sandwich panels to achieve better dynamic performance.

Dual-processing by abrasive waterjet machining—A method for machining and surface modification of nickel-based superalloy

Abstract Abrasive waterjet (AWJ) is widely used for machining of advanced (e.g. nickel-based) superalloys as it offers high material removal rates and low cutting temperatures. However, the inadequate surface integrity, e.g. large number of scratches and embedded particles in the machined surface, which would induce severe deteriorations of the materials functional performance, has been one of the greatest issues of the AWJ machining technique. To solve this problem, this research proposed a dual-process abrasive waterjet machining method, whereby two different functions of abrasive waterjet were employed: materials removal (first process) and surface modification (secondary process), hence, to improve the workpiece surface integrity. Two types of entrained particles, i.e. with sharp cutting edges (e.g. garnet) and smooth surfaces (e.g. stainless steel ball), that depending on their kinetic energy density can either cut or modify the workpiece surface respectively, are employed for these the two constitutive processes of the proposed dual-waterjet machining method. A critical standoff distance and inclination angle of the waterjet nozzle has been defined for the surface modification process thus, to eliminate the embedded particles and scratches left by the first cutting process while also introducing a surface strengthening effect. To support this approach, a mathematical model has been proposed for determining the surface modification parameters (e.g. jet feed speed and abrasive flow rate). In-depth analysis of the microstructural and metallurgical alternations of the machined workpiece surface and superficial layer have also been conducted to reveal the mechanisms responsible for the surface damage elimination and surface strengthening. Moreover, a four point bending fatigue test has been conducted to validate the mechanical performance, whereby a significant improvement of the fatigue life on the machined workpiece was achieved when compared with the case that single AWJ cutting method (91 %) and conventional machining (34 %) are employed. This proves that the proposed dual-processing AWJ machining method is of high efficiency to improve the functional performance of components on a single machine tool platform.

The ballistic performance of bone when impacted by fragments

Physical models are required to generate the underlying algorithms that populate computer simulations of the effects of explosive fragmenting devices. These models and simulations are used for understanding weapon performance, designing buildings and optimising personal protective equipment. Previous experimental work has investigated the performance of skin and muscle when subjected to fragmentation threats, but limited evidence exists for the performance of bone when impacted by fragments. In the current work, ballistic testing was conducted using two types of internationally recognised steel fragment simulating projectiles (FSPs): (i) 5.5 mm diameter (0.68 g) ball bearing (BBs) and (ii) 1.10 g chisel nosed (CN). These projectiles were fired at isolated swine ribs at impact velocities between 99 and 1265 m/s. Impact events were recorded using a high-speed camera. Selected specimens were analysed post-impact with plain x-radiographs and micro-CT scanning to determine damage to the bone architecture. Bones were perforated with a kinetic energy density (KED) as low as 0.14 J/mm2. Energy transfer to the bone was greater for the CN FSPs, resulting in increased bone damage and the production of secondary bone fragments. The manner in which the bones failed with faster velocity impacts (> 551 m/s; KED > 6.44 J/mm2) was analogous to the behaviour of a brittle material. Slower velocity impacts (< 323 m/s; KED < 1.49 J/mm2) showed a transition in failure mode with the bone displaying the properties of an elastic, plastic and brittle material at various points during the impact. The study gives critical insight into how bone behaves under these circumstances.

On the local measurement of electric currents and magnetic fields using Thomson scattering in Weibel-unstable plasmas

We demonstrate the capability of the Thomson Scattering (TS) diagnostic to measure locally the microscopic electron and ion currents in counter-streaming plasmas unstable to the Weibel or current-filamentation instability. Synthetic TS spectra are calculated with particle distribution functions obtained from particle-in-cell simulations and used to accurately reproduce the simulated currents. We show that this technique allows accurate local measurements of the magnetic field, thus opening the way for the complete experimental characterization of the growth rate, saturation, and nonlinear dynamics of electromagnetic instabilities in plasmas. We illustrate the application of this diagnostic to experimental TS data, which yields local measurements of the magnetic field in Weibel-unstable plasmas and indicates that the magnetic energy density reaches ∼1% of the kinetic energy density of the flows, in agreement with previous numerical studies.

Partitioning Waves and Eddies in Stably Stratified Turbulence

We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

A DFT study on the metal ion selectivity of deferiprone complexes

In this work, systematic density functional theory (DFT) calculations were performed to study the interactions of various metal ions (Al3+, Fe3+, Co2+, Ni2+, Cu2+, and Zn2+) and the clinically useful chelating agent called deferiprone (DFP) at the M05-2X/6-31G(d) level of theory. The thermodynamic parameters of metal-deferiprone complexes were determined in water. Based on the obtained data, the theoretical binding energy trend is as follows: Al3+ > Fe3+ > Cu2+ > Ni2+ > Co2+ > Zn2+, confirming that [Al(DFP)3] has the most interaction energy. Moreover, Natural bond orbital analysis was employed to determine and analyze the natural charges on different atoms and charge transfer between the metal ions and ligands (oxygen atoms) as well as the interaction energy (E(2)) values. The calculated value of ƩE(2) (donor-acceptor interaction energy) for [Al(DFP)3] complex is higher than other complexes, which is according to energy analysis. To confirm the type of effective interactions and bonding properties in the water, the quantum theory of atoms in molecules (QTAIM) analysis was applied. QTAIM analysis confirmed that the strongest M - O bond is found in the [Al(DFP)3] complex. The calculated topological properties at the bond critical points, such as the ratio of the kinetic energy density to the potential energy density, -G(r)/V(r), electronic energy density, H(r), confirm that M - O bonds in the Al-deferiprone complex are non-covalent, while in other complexes, they are electrostatic and partially covalent.

Constraints on the effective mass splitting by the isoscalar giant quadrupole resonance

Background: Previous theoretical work has found that the effective mass of the nucleon influences the excitation energy of the isoscalar giant quadrupole resonance (ISGQR).Purpose: The present paper presents an attempt to constrain the effective mass splitting by using the isospin dependence of the ISGQR energies.Methods: Using the macroscopic Langevin equation (LE), the ISGQR energies are calculated from the particle density and kinetic energy density of the nucleus in the ground state, obtained from either the Thomas-Fermi (TF) approach or the Skyrme Hartree-Fock-Bogolyubov (SHFB) model.Results: It is found that the calculations of the ISGQR energies by the SHFB+LE model agree with, or are even better than, the results by other approaches when applying the Skyrme functional Sly4. The values of the isoscalar and isovector effective masses are optimized by fitting the data for the ISGQR energies for a mass region from 28 to 238. The root-mean-squared deviation of the best fit to the data measured after the year 2000 is 0.22 MeV by the TF+LE model and 0.30 MeV by the SHFB+LE model. The extracted isoscalar effective mass is $0.70&lt;{m}_{s}^{*}/m&lt;0.73$. With respect to the isovector effective mass ${m}_{v}^{*}$, the constrained value is about half of the isoscalar effective mass ${m}_{s}^{*}$.Conclusions: The present work supports the statement that, in neutron-rich matter, the effective mass of the neutron is definitely larger than that of the proton.

Nature of Alkali Ion-Water Interactions: Insights from Many-Body Representations and Density Functional Theory. II.

Interaction energies of alkali ion-water dimers, M+(H2O), and trimers, M+(H2O)2, with M = Li, Na, K, Rb, and Cs, are investigated using various many-body potential energy functions and exchange-correlation functionals selected across the hierarchy of density functional theory approximations. Analysis of interaction energy decompositions indicates that close-range interactions such as Pauli repulsion, charge transfer, and charge penetration must be captured in order to reproduce accurate interaction energies. In particular, it is found that simple classical polarizable models must be supplemented with dedicated terms which account for these close-range interactions in order to achieve chemical accuracy. It is also found that the exchange-correlation functionals mostly differ from each other in their Pauli repulsion + dispersion energies and, hence, benefit from the inclusion of nonlocal terms such as Hartree-Fock exchange and dependence on the electronic kinetic energy density in order to reproduce the interactions that contribute to this term, namely, Pauli repulsion and intermediate-range dispersion. As a continuation of the analysis performed in J. Chem. Theory Comput. 2019, 15, 2983, 10.1021/acs.jctc.9b00064, we make comparisons between findings for alkali ion-water interactions with those for halide-water interactions.

Correlation between structural and optical properties of π-conjugated acrylonitrile derivatives: Insights from X-ray, energy frameworks, TD-DFT and charge density analysis

The 2/3/4-pyridyl substituents incorporated into a π-conjugated acrylonitrile system have been synthesized and X-ray structure analysis of two of the isomers (Z)-3-(4-pyridin-2yl)phenyl-2-(pyridine-3yl)acrylonitrile (II) and (Z)-3-(4-pyridin-2yl)phenyl-2-(pyridine-4yl)acrylonitrile (III) are reported. The molecular structure and UV–Vis absorption properties of (Z)-3-(4-pyridin-2yl)phenyl-2-(pyridine-2yl)acrylonitrile (I) has been explored by density functional theory (DFT) with the M06–2X/cc-pVTZ level of theory. The molecular structure analysis reveals that the isomer in para position shows a conformation more planar than the isomer in meta position. The electrostatic potential surface maps of these isomers highlight the similarities and differences in the most positive and the most negative electrostatic potentials and also reveal the effect of crystal packing. Intermolecular interactions present in the crystal structures of isomers II and III have been qualitatively characterized using Hirshfeld surface analysis and 2D-fingerprint plots. Differences in the contribution of intermolecular H⋯C and C⋯C interactions were found between isomers. The theoretical charge density analysis has been performed for selected molecular pairs identified from the crystal structures. The results revealed that the C–H⋯N and C–H⋯C(π) interactions showed H-bond character. The Laplacian of the electron density, the ratio between potential and kinetic energy densities and the total energy density for intermolecular H⋯H interactions suggest that these interactions were closed-shell in nature. Further, experimental and theoretical UV–Vis absorption properties for isomers I-III are compared and agreed well.

Orbital-free density functional theory calculation applying semi-local machine-learned kinetic energy density functional and kinetic potential

This letter proposes a scheme of orbital-free density functional theory (OF-DFT) calculation for optimizing electron density based on a semi-local machine-learned (ML) kinetic energy density functional (KEDF). The electron density, which is represented by the square of the linear combination of Gaussian functions, is optimized using derivatives of electronic energy including ML kinetic potential (KP). The numerical assessments confirmed the accuracy of optimized density and total energy for atoms and small molecules obtained by the present scheme based on ML-KEDF and ML-KP.

Damping design of harmonically excited flexible structures with graded materials to minimize sound pressure and radiation

Topology optimization is an effective method in the design of acoustic media. This article presents optimization for graded damping materials to minimize sound pressure at a reference point or sound power radiation under harmonic excitation. The Helmholtz integral equation is used to calculate an acoustic field to satisfy the Sommerfeld conditions. The equation of motion is solved using a unit dynamic load method. Formulations for the sound pressure or sound power radiation in an integral form are derived in terms of mutual kinetic and strain energy densities. These integrals lead to novel physical response functions for solving the proposed optimization problem to design graded damping materials. The response function derived for individual frequency is utilized to solve the multi-objective optimization problem of minimizing sound pressure at the reference point for excitations with a range of frequencies. Numerical examples are presented to verify the efficiency of the present formulations.

A Curious Case of Circular Polarization in the 25 GHz Methanol Maser Line toward OMC-1

Abstract We report the detection of a circular polarization signature in the Stokes V profile of a 25 GHz Class I CH3OH maser toward the high-mass star-forming region OMC-1. Such a feature usually constitutes a detection of the Zeeman effect. If due to a magnetic field in OMC-1, this would represent the first detection and discovery of the Zeeman effect in the 25 GHz Class I CH3OH maser. The feature in Stokes V is detected in two observations with different angular resolutions taken eight years apart with the Very Large Array; for our 2009 D-configuration observations, the fitted value for z is 152 ± 12 Hz, where z is the Zeeman splitting factor and is the line-of-sight magnetic field. For our 2017 C-configuration observations, the fitted value for z = 149 ± 19 Hz, likely for the same maser spot. These correspond to in the range 171–214 mG, depending on which hyperfine transition is responsible for the maser line. While these values are high, they are not implausible. If the magnetic field increases in proportion to the molecular hydrogen density in shocked regions, then our detected fields predict values for the pre-shock magnetic field that are in agreement with observations. With = 171–214 mG, the magnetic energy in the post-shocked regions where these 25 GHz Class I CH3OH masers occur would dominate over the kinetic energy density and be at least of the order of the pressure in the shock, implying that the magnetic field would exert significant influence over the dynamics of these regions.

Front Cover: Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions (ChemPhysChem 3/2020)

Front Cover: Laplacian of the Hamiltonian Kinetic Energy Density as an Indicator of Binding and Weak Interactions (ChemPhysChem 3/2020)