Kinetic Energy Density Research Articles

Mean fields and fluctuations in compressible magnetohydrodynamic flows

We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a shearing box in size. The interstellar medium is highly compressible, as the turbulence is transonic or supersonic; it is thus an excellent context in which to explore the use of smoothing to represent physical variables in a compressible medium in terms of their mean and fluctuating parts. Unlike alternative averaging procedures, such as horizontal averaging, Gaussian smoothing retains the three-dimensional structure of the mean fields. Although Gaussian smoothing does not obey the Reynolds rules of averaging, physically meaningful and mathematically sound central statistical moments are defined as suggested by Germano [Turbulence – The filtering approach. J. Fluid Mech. 1992, 238, 325–336]. We discuss methods to identify an optimal smoothing scale ℓ and the effects of this choice on the results. From spectral analysis of the magnetic, density and velocity fields, we find a suitable smoothing length for all three fields, of . Such a smoothing scale is likely to be sensitive to the choice of simulation parameters; this may be considered in future work, but here we just explore the methodology. We discuss the properties of third-order statistical moments in fluctuations of kinetic energy density in compressible flows, and suggest their physical interpretation. The mean magnetic field, amplified by a mean-field dynamo, significantly alters the distribution of kinetic energy in space and between scales, reducing the magnitude of kinetic energy at intermediate scales. This intermediate-scale kinetic energy is a useful diagnostic of the importance of SN-driven outflows.

Experimental Investigation on the Effects of Injection Parameters on the Air-Assisted Diesel Spray Characteristics

The air-assisted fuel injection (AAFI) system may be installed in the spark ignition aviation piston engine for the atomization of heavy fuels. However, studies on the effects of injection parameters on the spray characteristics are insufficient, which affects the improvement of AAFI engine performance. In this study, air-assisted diesel spray characteristics are investigated experimentally using a high-speed backlit imaging technique. The effects of main air-assisted injection control parameters such as fuel injection pressure, fuel temperature, and fuel injection duration on the spray characteristics are examined. The results show that spray shape changes from “spindle” to “cone” with an increase in fuel injection pressure. As the fuel injection pressure increases to 1.0 MPa, both the spray penetration and spray width increase significantly. “Protrusions” appear on the spray edge at high fuel temperatures. When the fuel temperature drops to 268 K, the spray penetration and spray width increase slightly. The spray shrinks significantly in both the axial and radial directions with an increase in fuel injection duration. Key parameters that directly affect air-assisted spray characteristics include the difference between the fuel-air mixture injection pressure and the ambient pressure, the density of fuel-air mixture in the air-assisted injector premixed chamber, and the kinetic energy density of the fuel. The former two parameters affect the spray penetration while the latter affects the spray width. The study is beneficial for the design of AAFI engines.

Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

Quasi-periodic spicule-like cool jets driven by Alfvén pulses

ABSTRACT We perform a 2.5D magnetohydrodynamic simulation to gain a comprehensive understanding of the formation of spicule-like cool jets caused by initial transverse velocity pulses akin to Alfvén pulses in the solar chromosphere. We invoke multiple velocity (Vz) pulses between 1.5 and 2.0 Mm in the solar atmosphere, which create the initial transverse velocity perturbations. These pulses transfer energy non-linearly to the field-aligned perturbations via the ponderomotive force. This physical process further creates magnetoacoustic shocks followed by quasi-periodic plasma motions in the solar atmosphere. The field-aligned magnetoacoustic shocks move upwards, which subsequently causes the quasi-periodic rise and fall of chromospheric plasma into the overlying corona as thin and cool spicule-like jets. The magnitude of the initial applied transverse velocity pulses is taken in the range of 50–90 km s−1. These pulses are found to be strong enough to generate spicule-like jets. We analyse the evolution, kinematics and energetics of these spicule-like jets. We find that the transported mass flux and kinetic energy density are substantial in the local solar corona. These mass motions generate in situ quasi-periodic oscillations on the scale of ≃ 4.0 min above the transition region.

Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with high-dimensional model representation (HDMR), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.

Dynamic Response Simulation of the Slope Triggered by Fluctuating Pressure during High Dam Flood Discharge

The problem of slope vibration induced by flood discharge of high dams cannot be ignored. In this paper, this problem is simplified to be the relationship among the fluctuating pressures, the inherent properties of the slope system, and its dynamic responses. The characteristics of fluctuating pressures in the plunge pool during flood discharge are analyzed by the hydraulic model test. And a numerical slope model consisting of the finite element domain and the PML domain is established to study the inherent characteristics and vibration responses by numerical simulation. The results show that the flow fluctuation in plunge pool is a continuous and stable random vibration process. And the fluctuating pressures on the bottom area of the plunge pool are greater than that of the sidewall, but the fluctuation phenomenon at the sidewall is more intense. In addition, the slope displacement vibration intensity caused by fluctuating pressures is small, only at the micron level. The fluctuating pressures on the bottom area of the plunge pool are the dominant factor affecting the kinetic energy density distribution of the slope. This work provides a simple and efficient method for the study of slope vibration induced by high dam flood discharge.

Accurate parameterization of the kinetic energy functional.

The absence of a reliable formulation of the kinetic energy density functional has hindered the development of orbital free density functional theory. Using the data-aided learning paradigm, we propose a simple prescription to accurately model the kinetic energy density of any system. Our method relies on a dictionary of functional forms for local and nonlocal contributions, which have been proposed in the literature, and the appropriate coefficients are calculated via a linear regression framework. To model the nonlocal contributions, we explore two new nonlocal functionals-a functional that captures fluctuations in electronic density and a functional that incorporates gradient information. Since the analytical functional forms of the kernels present in these nonlocal terms are not known from theory, we propose a basis function expansion to model these seemingly difficult nonlocal quantities. This allows us to easily reconstruct kernels for any system using only a few structures. The proposed method is able to learn kinetic energy densities and total kinetic energies of molecular and periodic systems, such as H2, LiH, LiF, and a one-dimensional chain of eight hydrogens using data from Kohn-Sham density functional theory calculations for only a few structures.

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange.

Electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact-exchange or hybrid functionals are associated with a large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Although orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with a significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use a gradient expansion of the kinetic energy nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional (1D) systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C4H2, C4N2, and C3O2. We show that by using the data from model 1D KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems and electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it is possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

Adiabatic projection: Bridging ab initio, density functional, semiempirical, and embedding approximations.

Modern electronic structure approximations routinely employ reference systems described by approximate Hamiltonians. This work introduces the adiabatic projection formalism for building formally exact corrections to such reference systems. Starting from the real Hamiltonian of a many-electron system, one constructs a reference system Hamiltonian by projecting the kinetic and electron-electron interaction operators onto "interesting" states. The reference system is corrected by density functionals for the difference between the projected and unprojected kinetic and electron-electron energies. These density functionals are constructed from adiabatic connections between the reference and real systems. The Hohenberg-Kohn theorems imply the existence of exact functionals, which can ensure that the reference system's ground-state energy and density match the real system. Adiabatic projection further generalizes Kohn-Sham density functional theory (DFT) and the generalized adiabatic connection [W. Yang, J. Chem. Phys. 109, 10107 (1998)] and recovers these methods for certain choices of projection operators. Other choices of projection operators offer new opportunities, including formally exact and systematically improvable analogues to wavefunction-in-DFT embedding, DFT+U, and semiempirical theories. Numerical results are presented for two representative choices: a projected exchange-correlation correction to small-basis-set coupled cluster theory and a projected kinetic energy density functional correcting basis set errors in DFT. The latter offers performance for dimerization energies approaching the Boys-Bernardi counterpoise correction while also correcting intramolecular basis set superposition errors.

Energy density balance during shock wave implosion in water

Analytical modeling of the evolution of cylindrical and spherical shock waves (shocks) during an implosion in water is presented for an intermediate range of convergence radii. This range of radii was observed in experiments when the exploding wire expansion dynamics does not influence on shock propagation, but not yet described by well-known self-similar solutions. The model is based on an analysis of the change in pressure and kinetic energy density as well as on the corresponding fluxes of internal and kinetic energy densities behind the shock front. It shows that the spatial evolution of the shock velocity strongly depends on the initial compression, the adiabatic index of water, and the geometry of convergence. The model also explains the transition to a rapid like a self-similar increase in the shock velocity at only a certain radius of the shock that is observed in experiments. The dependence of the threshold radius, where the shock implosion follows the power law (quasi self-similarity), on the initial compression is determined. It is stated that in the entire range of the shock radii, the internal and kinetic energy density fluxes are equal, which agrees with known experimental data.

Numerical analysis of water surface rising caused by underwater ultrasonic wave

When an underwater ultrasonic wave is emitted toward an air-water interface, the water surface rises and droplets are generated from the formed fountain. The rising process of water surface was numerically investigated for better understanding the mechanism of ultrasonic fountain prior to the atomization. To analyze the water surface rising that occurs in a very short time, it is necessary to simulate the rapid increase of acoustic radiation pressure and the rapid development of acoustic streaming. Therefore, the direct numerical simulation based on compressible fluid dynamics was carried out. The water surface rising as observed in the formation process of ultrasonic fountain was successfully reproduced. In the region between sound source and water surface, standing wave is established and acoustic kinetic energy density increases significantly while water surface rises with acceleration. The kinetic energy density is associated with the acoustic radiation pressure acted on free surface based on the theory of Yosioka-Kawasima (1955). After the rising speed becomes to be constant, the standing wave fades and the kinetic energy density decreases. These results suggest that the acoustic radiation pressure acted on water surface increases significantly due to temporary resonance and water surface rises rapidly. By drawing a fluid due to rapid rising of water surface, acoustic streaming is induced toward the risen region.

Development and systematization of indoor noise reduction methods under a new vibrationacoustic coupling using energy density distribution

When the interior shape is determined, the frequency range to be reduced, which is a particular problem, is determined. Until now, there has been no noise reduction countermeasure method using information on resonant frequency such as strain and kinetic energy density. For the first time in this report, it is shown that noise reduction of the resonant frequency, existing in the problematic frequency, can be effectively obtained after reducing the plate thickness from the energy density distribution. The greatest advantage of this method is that, unlike conventional optimization methods, it is possible to take countermeasures interactively and extremely reasonably, and systematization to draw out its effectiveness will also be discussed.

Limitation in velocity of converging shock wave

The commonly applied self-similar solution of the problem of the converging shock wave (shock) evolution with constant compression of the medium behind the shock front results in an unlimited increase in the medium velocity in the vicinity of the implosion. In this paper, the convergence of cylindrical shocks in water is analyzed using the mass conservation law, when the water compression behind the shock front is a variable. The model predicts a finite range of radii, which depends on the adiabatic index of water and where the increase in pressure exceeds the sum of the change in the kinetic and internal energy densities behind the shock front. In this range of radii, only the finite increase in the shock and water flow velocities is realized.

Design and synthesis of piezochromic materials exploring intermolecular charge transfer: chalconoids bound to the p-sulfonatocalix[6]arene macrocycle.

Solid-state systems composed of chalconoid encapsulated within p-sulfonatocalix[6]arene (SCX6) scaffolds that exhibit mechanochromism and thermochromism have been developed. An introduction of a supramolecular host promises a variety of applications in diverse areas, which makes them fascinating. Largely hydrogen bonding as well as π···π interactions are responsible for the host-guest complexation. The complex shows partial encapsulation of the guest with one of the phenyl rings of chalcone (guest) is held inside the SCX6 cavity, whilst other phenyl rings that exclude the cavity are hydrogen-bonded to sulfonate portals of the host. The hydrogen bonding conducing such complexation triggers proton transfer engendering a mechanochromic switch. The complexes are further characterized by a variety of experiments such as cyclic voltammetry (CV), steady-state fluorescence, vibrational spectroscopy, and 1H or 2D NMR (NOESY) spectroscopy experiments. Detailed structure furnished through the NMR shows deshielding of the Ha-e (guest) protons whereas, the hydroxyl protons from the host experience shielding as evidenced from the 1H NMR spectra. These inferences have further been corroborated through the density functional theory. Electrochemical investigations suggested an irreversible one-electron transfer in the host-guest binding. The characteristic 'frequency shift' for the intense carbonyl vibration in the infrared spectra, which can be correlated to the kinetic energy density parameter, G(r), in the quantum theory of atoms in molecules (QTAIM).

Energy considerations for nonlinear equatorial water waves

<p style='text-indent:20px;'>In this article we consider the excess kinetic and potential energies for exact nonlinear equatorial water waves. An investigation of linear waves establishes that the excess kinetic energy density is always negative, whereas the excess potential energy density is always positive, for periodic travelling irrotational water waves in the steady reference frame. For negative wavespeeds, we prove that similar inequalities must also hold for nonlinear wave solutions. Characterisations of the various excess energy densities as integrals along the wave surface profile are also derived.</p>

Similarity Clustering for Representative Sets of Inorganic Solids for Density Functional Testing.

Benchmarking DFT functionals is complicated since the results highly depend on which properties and materials were used in the process. Unwanted biases can be introduced if a data set contains too many examples of very similar materials. We show that a clustering based on the distribution of density gradient and kinetic energy density is able to identify groups of chemically distinct solids. We then propose a method to create smaller data sets or rebalance existing data sets in a way that no region of the meta-GGA descriptor space is overrepresented, yet the new data set reproduces average errors of the original set as closely as possible. We apply the method to an existing set of 44 inorganic solids and suggest a representative set of seven solids. The representative sets generated with this method can be used to make more general benchmarks or to train new functionals.

The Spatial and Temporal Variations of Turbulence in a Solar Flare

Abstract Magnetohydrodynamic plasma turbulence is believed to play a vital role in the production of energetic electrons during solar flares, and the nonthermal broadening of spectral lines is a key sign of this turbulence. Here, we determine how flare turbulence evolves in time and space using spectral profiles of Fe xxiv, Fe xxiii, and Fe xvi, observed by the Hinode/EUV Imaging Spectrometer. Maps of nonthermal velocity are created for times covering the X-ray rise, peak, and decay. For the first time, the creation of kinetic energy density maps reveal where energy is available for energization, suggesting that similar levels of energy may be available to heat and/or accelerate electrons in large regions of the flare. We find that turbulence is distributed throughout the entire flare, often greatest in the coronal loop tops, and decaying at different rates at different locations. For hotter ions (Fe xxiv and Fe xxiii), the nonthermal velocity decreases as the flare evolves and during/after the X-ray peak shows a clear spatial variation decreasing linearly from the loop apex toward the ribbon. For the cooler ion (Fe xvi), the nonthermal velocity remains relativity constant throughout the flare, but steeply increases in one region corresponding to the southern ribbon, peaking just prior to the peak in hard X-rays before declining. The results suggest turbulence has a more complex temporal and spatial structure than previously assumed, while newly introduced turbulent kinetic energy maps show the availability of the energy and identify important spatial inhomogeneities in the macroscopic plasma motions leading to turbulence.

Random Sampling High Dimensional Model Representation Gaussian Process Regression (RS-HDMR-GPR) for representing multidimensional functions with machine-learned lower-dimensional terms allowing insight with a general method

We present an implementation for the RS-HDMR-GPR (Random Sampling High Dimensional Model Representation Gaussian Process Regression) method. The method builds representations of multivariate functions with lower-dimensional terms, either as an expansion over orders of coupling or using terms of only a given dimensionality. This facilitates, in particular, recovering functional dependence from sparse data. The method also allows for imputation of missing values of the variables and for a significant pruning of the useful number of HDMR terms. It can also be used for estimating relative importance of different combinations of input variables, thereby adding an element of insight to a general machine learning method, in a way that can be viewed as extending the automatic relevance determination approach. The capabilities of the method and of the associated Python software tool are demonstrated on test cases involving synthetic analytic functions, the potential energy surface of the water molecule, kinetic energy densities of materials (crystalline magnesium, aluminum, and silicon), and financial market data.

Scaling analysis of a physics-guided kinetic energy density expansion

An approach guided by physical consistency in determining the general forms of D-dimensional kinetic energy density functionals (KEDF) has been demonstrated previously, producing an expansion which contains the majority of the known one-point KEDF forms. It is known that any noninteracting KEDF shall necessarily have a homogeneity degree of 2 in coordinate scaling. This paper demonstrates that this condition is already satisfied in the general expansion despite not being conceived with the scaling as a constraint.

Redistribution of Energy during Interaction of a Shock Wave with a Temperature Layered Plasma Region at Hypersonic Speeds

The paper is devoted to the problem of the interaction between a shock wave and a thermally stratified energy source for the purpose of supersonic/hypersonic flow control realization. The effect of the thermally stratified energy source on a shock wave with the Mach number in the range of 6–12 is researched numerically based on the Navier-Stokes system of equations. Redistribution of specific internal energy and volume density of kinetic energy behind the wave front is investigated. Multiple manifestations of the Richtmyer-Meshkov instability has been obtained which has caused the blurring and disappearance of shock wave and contact discontinuity fronts in density fields. A study of the efficiency of using a stratified energy source instead of a homogeneous one with the same value of the full energy is carried out. The agreement with the available experimental data for the shock wave Mach number 6 has been obtained.