Function Of Kinetic Energy Research Articles

Gaussian expansion of Yukawa non‐local kinetic energy functionals: Application to metal clusters

AbstractThe development of kinetic energy (KE) functionals is one of the current challenges in density functional theory (DFT). The Yukawa non‐local KE functionals [Phys. Rev. B 103, 155127 (2021)] have been shown to describe accurately the Lindhard response of the homogeneous electron gas (HEG) directly in the real space, without any step in the reciprocal space. However, the Yukawa kernel employs an exponential function which cannot be efficiently represented in conventional Gaussian‐based quantum chemistry codes. Here, we present an expansion of the Yukawa kernel in Gaussian functions. We show that for the HEG this expansion is independent of the electronic density, and that for general finite systems the accuracy can be easily tuned. Finally, we present results for atomistic sodium clusters of different sizes, showing that simple Yukawa functionals can give superior accuracy as compared to semilocal functionals.

Impact localization and force reconstruction for composite plates based on virtual time reversal processing with time-domain spectral finite element method

Composite structures are widely used in different industries as important load-carrying components due to their excellent performance. These structures are prone to be damaged under low-velocity impacts with invisible cracks. Hence, impact identification is a critical part of composite structural health monitoring. In this paper, an approach is developed, which is based on time-reversal (T-R) processing and time-domain spectral finite element method. The spatial and temporal focusing properties of T-R are utilized to locate the impact source and restore the impact force, respectively. Moreover, the impact energy is evaluated by establishing the function of impact force and kinetic energy at the impact moment. The proposed method is validated experimentally for different scenarios. The influences of the signal length and accuracy of the numerical model on the proposed method are discussed in detail. The results demonstrate that the proposed method can correctly locate the impact source in composite structures, and the identified impact force can reproduce the impact event efficiently. The impact localization is essentially independent of the effect of signal length while it is vulnerable to the mesh grid. Besides, the developed method has consistent results in the case of data perturbation of material properties in the numerical model, which shows its good robustness.

Three-Dimensional Vibrational Characteristics of Functionally Graded Rotating Microbeams Based on the Higher-Order Refined Shear Deformation Theory

This study establishes a novel three-dimensional dynamic model for functionally graded rotating microbeams simultaneously considering flapwise and chordwise shear effects based on a refined shear deformation theory and the modified couple stress theory. Five kinematic variables are introduced to describe the rotating microbeam’s axial, flapwise, and chordwise motions using a higher-order refined shear deformation theory. The related strain energy and kinetic energy functionals are discretized by the assumed mode method. Applying the Euler–Lagrange variational formulation, the governing equations for the rotating microbeam are obtained. Selective examples are provided to demonstrate the convergence and effectiveness of the proposed model. Finally, the impacts of slenderness ratio, rotation speed, material index, material length scale parameter (MLSP), and Poisson’s effect on the vibrational characteristics of the microbeam are examined. Numerical results indicate that the mode shape transition and frequency loci veering phenomena could easily occur under slight changes in the above factors when dense modes appear in the rotating microbeam; moreover, there is a positive/negative competitive relationship among the effects of rotation speed, MLSP, and shear deformation; Poisson’s effect seriously affects the coupling between axial and non-axial motions of the rotating microbeam. The results obtained are expected to provide data accumulation and methodological basis for the failure analysis and vibration shape determination of micro air vehicles.

Modeling the Effect of Multiscale Heterogeneities on Wave Attenuation and Velocity Dispersion

Wave attenuation and velocity dispersion are of great significance to fluid evaluation in fluid-saturated rocks. Inspired by the double-porosity and cracked porous elastic wave theory, we develop a multi-scale heterogeneities elastic wave theory to better describe the attenuation characteristics caused by wave-induced fluid flow at various scales in saturated rocks. First, we introduce penny-shaped and narrow-shaped coupled cracks into double-porosity model. The potential energy function is given by the stress-strain relationship. The kinetic energy function and dissipation function are derived based on the generalized Biot theory. Next, we derive the multi-scale wave equations through the Lagrange equation and obtain three compressional waves and one shear wave. According to the novel wave equations, we work out the phase velocity and inverse quality factor in double-porosity and cracked media based on plane-wave analysis. The numerical simulation results show that there are four attenuation peaks in the whole frequency band, corresponding to mesoscopic fluid flow, two kinds of squirt flow and Biot flow respectively. Then, we investigate the effect of poroelastic parameters on wave propagation. It is found that porosity, inclusion size, crack aspect ratio and other parameters significantly affect the dispersion and attenuation. Finally, we compare experimental data and theoretical prediction. Moreover, the new elastic wave theory can degenerate into classical Biot’s theory, double porosity theory and pore-crack theory under certain conditions, which demonstrates the consistency of this method. The proposed theory can better predict and simulate the wave propagation by incorporating the effects of microscopic, mesoscopic, and macroscopic heterogeneities.

Determination of the Plasma Delay Time in PIPS detectors for fission fragments at the LOHENGRIN spectrometer

The VElocity foR Direct particle Identification spectrometer (VERDI) is a 2E-2v fission spectrometer that allows the measurement of the total mass distribution of secondary fission fragments with a resolving power of 1-2 u. It consists of two time-of-flight (ToF) arms, with one Micro Channel Plate (MCP) detector and up to 32 Silicon PIPS (Passive Implanted Planar Silicon) detectors per arm. The MCPs provide the start timing signals and the PIPS detectors provide both the energy and the stopping ToF signals. In real conditions, the PIPS signals are affected by the formation of plasma from the interaction between the heavy ions and the detector material. The plasma contributes to a reduction in signal amplitude, resulting in a Pulse Height Defect (PHD), and introduces a signal delay, known as Plasma Delay Time (PDT). An experiment to characterize the PDT and PHD was performed at the LOHENGRIN recoil separator of the Institut Laue Langevin (ILL). Characteristic fission fragments from the 239Pu(n,f) reaction were separated based on their A/Q and E/Q ratios, allowing the measurement of a wide range of energies from 21 to 110 MeV and masses between 80 and 149 u. Six PIPS detectors were characterized to study their individual responses to the PDT and PHD effects. The signals were recorded in a digital acquisition system to completely exploit the offline analysis capabilities. Achieved combined timing and energy resolutions for fission fragments varied between 72(2) ps and 100(4) ps and 1.4% - 2% (FWHM), respectively. Preliminary PHD and PDT data are presented from the masses A=85, 95, 130 and 143. The PHD trends are strongly correlated with both the ion energy and mass. The PDT, on the other hand, shows a strong variation as a function of the ion kinetic energy but a smaller dependence on the ion mass.

Angular momentum of doubly magic 132Sn fission product: Experimental and theoretical aspects

Despite the numerous theoretical and experimental works published very recently, the way in which fission fragments acquire their angular momentum is still an open question. This angular momentum generation mechanism is important not only for improving our understanding of the fission process, but also for nuclear energy applications, since the angular momentum of fission fragments strongly impact the prompt gamma spectra and consequently the decay heat in a reactor. In this context, within the framework of a collaboration between the ‘Laboratoire de Physique Subatomique et Corpusculaire’ (LPSC, France), the ‘Institut Laue Langevin’ (ILL, France) and the CEA-Cadarache (France), an experimental program was developed on the LO-HENGRIN mass-spectrometer with the aim of measuring isomeric ratio of some fission products for different thermal-neutron-induced fission reactions. This paper will be focused on the results obtained for the spherical nucleus 132Sn following thermal-neutron-induced fission of both 235U and 241Pu targets. To further challenge the angular momentum generation models, 132Sn isomeric ratio (IR) was measured as a function of 132Sn fission product kinetic energy (KE). The angular momentum was determined by combining our experimental data with the calculations performed with the FIFRELIN Monte Carlo code. A clear angular momentum decrease with KE was observed for both reactions. Lastly, we investigate the dependence of the 132Sn angular momentum with the incident neutron energy, from thermal region up to 5 MeV (below the second-chance fission). For that, the four free available parameters in FIFRELIN are selected in order to reproduce the average prompt neutron multiplicity. In this way, the angular momentum is deduced for each neutron energy. These results are discussed in terms of the impact of the available intrinsic excitation energy at scission on the spin generation mechanism.

Approximations for the Kinetic Energy Functionals

Approximations for the Kinetic Energy Functionals

Experimental Study on Water Distribution and Droplet Kinetic Energy Intensity from Non-Circular Nozzles with Different Aspect Ratios

(1) Background: In sprinkler irrigation systems, the water distribution and droplet kinetic energy are affected by the shape of the nozzle. In this paper, the effects of working pressure and aspect ratio (L/D) of circular and non-circular nozzles (diamond and ellipse) on water distribution and droplet kinetic energy intensity were investigated; (2) Methods: The hydraulic performance of a PY15 impact sprinkler with circular and non-circular nozzles was assessed under different working pressures, and the droplet diameter, velocity, and kinetic energy intensity were measured by a 2D video disdrometer. Moreover, the coefficient of variation (CV) and form factor (β) were introduced to represent the water distribution and droplet characteristics; (3) Results: The results revealed that, under the same working pressure, the CV of the diamond nozzle was the smallest compared with that of the circular and elliptical nozzles, reflecting a more uniform water distribution. The uniformity of water distribution was the best when the L/D of the elliptical nozzle was the smallest. In general, the larger the outlet diameter, the larger the wetted radius and water application rate. In addition, the smaller the L/D, the smaller the peak water distribution value and the radial increase of the kinetic energy intensity of a single nozzle. The maximum droplet kinetic energy per unit volume of the elliptical nozzle was the smallest compared with that of the circular and diamond nozzles. The circular nozzle at 200 kPa and the diamond and elliptical nozzles at 100 kPa obtained the highest uniformity coefficients of combined kinetic energy intensity distribution, which were 55.93% (circular), 67.59% (diamond), and 57.78% (elliptical) when the combination spacings were 1.0 R, 1.1 R and 1.2 R, and 1.0 R, respectively. Finally, the fitting function of unit volume droplet kinetic energy, distance from the nozzle, L/D, and working pressure of non-circular nozzles was established, and a fitting coefficient of 0.92 was obtained, indicating that the fitting equation was accurate; (4) Conclusions: At low working pressures, the elliptic and diamond nozzles showed better water distributions than the circular nozzle. The distal average droplet diameters of the sprinkler with non-circular nozzles were found to be smaller than those produced by the circular nozzle.

Multiplicative potentials for kinetic energy and exact exchange.

Harriman showed that within finite basis sets of one-electron functions that form linearly independent products (LIP), differential and integral operators can be represented exactly and unambiguously by multiplicative (local) potentials. Although almost no standard basis sets of quantum chemistry form LIPs in a numerical sense, occupied self-consistent field (SCF) orbitals routinely do so. Using minimal LIP basis sets of occupied SCF orbitals, we construct multiplicative potentials for electronic kinetic energy and exact exchange that reproduce the Hartree-Fock and Kohn-Sham Hamiltonian matrices and electron densities for atoms and molecules. The results highlight fundamental differences between local and nonlocal operators and suggest a practical possibility of developing exact kinetic energy functionals within finite basis sets by using effective local potentials.

Modeling a semi-optimal deceleration of a rigid body rotational motion in a resisting medium

This paper studies the shortest time of slowing rotation of a free dynamically asymmetric rigid body (RB), analogous to Euler’s case. This body is influenced by a rotatory moment of a tiny control torque with closer coefficients but not equal, a gyrostatic moment (GM) due to the presence of three rotors, and in the presence of a modest slowing viscous friction torque. Therefore, this problem can be regarded as a semi-optimal one. The controlling optimal decelerating law for the rotation of the body is constructed. The trajectories that are quasi-stationary are examined. The obtained new results are displayed to identify the positive impact of the GM. The dimensionless form of the regulating system of motion is obtained. The functions of kinetic energy and angular momentum besides the square module are drawn for various values of the GM’s projections on the body’s principal axes of inertia. The effect of control torques on the body's motion is investigated in a case of small perturbation, and the achieved results are compared with the unperturbed one. For the case of a lack of GM, the comparison between our results and those of the prior ones reveals a high degree of consistency, in which the deviations between them are examined. As a result, these outcomes generalized those that were acquired in previous studies. The significance of this research stems from its practical applications, particularly in the applications of gyroscopic theory to maintain the stability and determine the orientation of aircraft and undersea vehicles.

Application of a simple DNA damage model developed for electrons to proton irradiation

Proton beam therapy allows irradiating tumor volumes with reduced side effects on normal tissues with respect to conventional x-ray radiotherapy. Biological effects such as cell killing after proton beam irradiations depend on the proton kinetic energy, which is intrinsically related to early DNA damage induction. As such, DNA damage estimation based on Monte Carlo simulations is a research topic of worldwide interest. Such simulation is a mean of investigating the mechanisms of DNA strand break formations. However, past modellings considering chemical processes and DNA structures require long calculation times. Particle and heavy ion transport system (PHITS) is one of the general-purpose Monte Carlo codes that can simulate track structure of protons, meanwhile cannot handle radical dynamics simulation in liquid water. It also includes a simple model enabling the efficient estimation of DNA damage yields only from the spatial distribution of ionizations and excitations without DNA geometry, which was originally developed for electron track-structure simulations. In this study, we investigated the potential application of the model to protons without any modification. The yields of single-strand breaks, double-strand breaks (DSBs) and the complex DSBs were assessed as functions of the proton kinetic energy. The PHITS-based estimation showed that the DSB yields increased as the linear energy transfer (LET) increased, and reproduced the experimental and simulated yields of various DNA damage types induced by protons with LET up to about 30 keV μm−1. These results suggest that the current DNA damage model implemented in PHITS is sufficient for estimating DNA lesion yields induced after protons irradiation except at very low energies (below 1 MeV). This model contributes to evaluating early biological impacts in radiation therapy.

Nuclear cusps and singularities in the nonadditive kinetic potential bifunctional from analytical inversion

The non-additive kinetic potential $v^{\text{NAD}}$ is a key quantity in density-functional theory (DFT) embedding methods, such as frozen density embedding theory and partition DFT. $v^{\text{NAD}}$ is a bi-functional of electron densities $\rho_{\rm B}$ and $\rho_{\rm tot} = \rho_{\rm A} + \rho_{\rm B}$. It can be evaluated using approximate kinetic-energy functionals, but accurate approximations are challenging. The behavior of $v^{\text{NAD}}$ in the vicinity of the nuclei has long been questioned, and singularities were seen in some approximate calculations. In this article, the existence of singularities in $v^{\text{NAD}}$ is analyzed analytically for various choices of $\rho_{\rm B}$ and $\rho_{\rm tot}$, using the nuclear cusp conditions for the density and Kohn-Sham potential. It is shown that no singularities arise from smoothly partitioned ground-state Kohn-Sham densities. We confirm this result by numerical calculations on diatomic test systems HeHe, HeLi$^+$, and H$_2$, using analytical inversion to obtain a numerically exact $v^{\rm NAD}$ for the local density approximation. We examine features of $v^{\rm NAD}$ which can be used for development and testing of approximations to $v^{\rm NAD}[\rho_{\rm B},\rho_{\rm tot}]$ and kinetic-energy functionals.

Study on vibration behavior of functionally graded porous material plates immersed in liquid with general boundary conditions

This paper presents a novel energy method for vibration analysis of pre-loaded moving functionally graded material (FGM) plates in fluid. Porosity in plates, fluid–structure interactions and initial tensions are taken into consideration. The first-order shear deformation theory (FSDT) and linear potential flow theory are adopted to formulate the strain energy, kinetic energy and external work functions of the coupled system. The governing equations of the porous FGM plate immersed in liquid are deduced by the Hamilton’s principle and the unified solutions for general boundary conditions are obtained using the modified Ritz method. By comparing the obtained vibration results with those from the commercial software and literature, the accuracy of the proposed model is validated. The effects of axial speed, fluid density, material constituent, initial axial tension and porosity volume fraction on the vibration behaviors of the FGM plate are further discussed. Numerical cases show that the vibration behaviors of the FGM plate are significantly influenced by these key parameters.

Adaptive Subsystem Density Functional Theory.

Subsystem density functional theory (DFT) is emerging as a powerful electronic structure method for large-scale simulations of molecular condensed phases and interfaces. Key to its computational efficiency is the use of approximate nonadditive noninteracting kinetic energy functionals. Unfortunately, currently available nonadditive functionals lead to inaccurate results when the subsystems interact strongly such as when they engage in chemical reactions. This work disrupts the status quo by devising a workflow that extends subsystem DFT's applicability also to strongly interacting subsystems. This is achieved by implementing a fully automated adaptive definition of subsystems which is realized during geometry optimizations or ab initio molecular dynamics simulations. The new method prescribes subsystem merging and splitting events redistributing the resources (both for work and data) in an efficient way making use of modern parallelization strategies and object-oriented programming. We showcase the method with examples probing from moderate-to-strong inter-subsystem interactions, opening the door to using subsystem DFT for modeling chemical reactions in molecular condensed phases with a black box computational tool.

Three-Dimensional Dynamic Formation of Second-Order Multi-Agent System Based on Rigid Graphs

This paper studies the dynamic formation control of second-order multi-agent systems (MASs) in three-dimensional space based on the distance control approach. A rigid graph represents the communication topology between agents to improve the system’s robustness and stability and avoid collisions and deformations during formation operation. A distributed control strategy based on the relative states among neighbors is designed for each agent to achieve formation and formation maintenance under arbitrary initial conditions. The Lyapunov function, an error function of potential and kinetic energy, is constructed by rigid graph theory and a second-order integrator model. The decreasing of the Lyapunov function is proven by Barbalat’s theory, further indicating that the system is asymptotically stable. A second-order MAS composed of nine agents is constructed, and the dynamic scaling of rigid formations in 3D space is achieved through simulation to verify the effectiveness of the controller and the correctness of the theory.

Two-Center Interference in the Photoionization Delays of Kr_{2}.

We present the experimental observation of two-center interference in the ionization time delays of Kr_{2}. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schrödinger equation of a 1D double-well potential, as well as coupled-channel multiconfigurational quantum-scattering calculations of Kr_{2}. This work opens the door to the study of a broad class of quantum-interference effects in photoionization delays and demonstrates the potential of attosecond coincidence spectroscopy for studying weakly bound systems.

Effects of amplitude modulated capacitively coupled discharge Ar plasma on kinetic energy and angular distribution function of ions impinging on electrodes: particle-in-cell/Monte Carlo collision model simulation

We investigated the effects of amplitude modulated (AM) capacitively coupled Ar discharge plasma on the ion energy distribution function (IEDF) and the ion angular distribution function (IADF) incident on electrodes using the particle-in-cell/Monte Carlo collision model. For AM discharge, the electron density and electron temperature and the kinetic energy and angle of ions incident on the ground electrode change periodically with AM frequency, whereas ones for continuous wave discharge are almost constant. For AM discharge, the plasma had hysteresis characteristics. The peak energy of IEDF varies from 53 to 135 eV and the FWHM of IADF varies from 1.82 to 3.34 degrees for gas pressure 10mTorr, the peak-to-peak input voltage 400 V and AM level of 50%. The variation width of the peak energy of IEDF and FWHM of IADF increases with the AM level. These effects of AM method discharge are more noticeable at lower pressures. Thus, the AM discharge offers a way to control simultaneously IEDF and IADF, which opens a new avenue for plasma processes such as an ALD-like PECVD.

Attosecond dynamics of multi-channel single photon ionization

Photoionization of atoms and molecules is one of the fastest processes in nature. The understanding of the ultrafast temporal dynamics of this process often requires the characterization of the different angular momentum channels over a broad energy range. Using a two-photon interferometry technique based on extreme ultraviolet and infrared ultrashort pulses, we measure the phase and amplitude of the individual angular momentum channels as a function of kinetic energy in the outer-shell photoionization of neon. This allows us to unravel the influence of channel interference as well as the effect of the short-range, Coulomb and centrifugal potentials, on the dynamics of the photoionization process.

Density Embedding Method for Nanoscale Molecule-Metal Interfaces.

In this work, we extend the applicability of standard Kohn-Sham DFT (KS-DFT) to model realistically sized molecule-metal interfaces where the metal slabs venture into the tens of nanometers in size. Employing state-of-the-art noninteracting kinetic energy functionals, we describe metallic subsystems with orbital-free DFT and combine their electronic structure with molecular subsystems computed at the KS-DFT level resulting in a multiscale subsystem DFT method. The method reproduces within a few millielectronvolts the binding energy difference of water and carbon dioxide molecules adsorbed on the top and hollow sites of an Al(111) surface compared to KS-DFT of the combined supersystem. It is also robust for Born-Oppenheimer molecular dynamics simulations. Very large system sizes are approached with standard computing resources thanks to a parallelization scheme that avoids accumulation of memory at the gather-scatter stage. The results as presented are encouraging and open the door to ab initio simulations of realistically sized, mesoscopic molecule-metal interfaces.

An atomistic approach to study the dynamic and structural response in 2D nanofiller reinforced polyethylene nanocomposites under ultra-short shock pulse loading

An atomistic model was developed to systematically investigate the shock propagation and its attenuation behavior in two-dimensional (2D) nanofiller reinforced polyethylene (PE) nanocomposites. Under the framework of non-equilibrium molecular dynamics, an explicit ultra-short shock pulse with an impact velocity of 1.0 km/s was applied on the mono- and bi-crystalline 2D nanofiller reinforced PE nanocomposites. Their dynamic and structural responses were captured in terms of particle velocity, mean pressure, kinetic energy, and radial distribution function (RDF). The trends depicted that the energy dissipated from graphene (GNS) and boron nitride nanosheet (BNNS) reinforced PE nanocomposites were 30.69% and 24.92%, respectively, whereas the energy dissipation improves up to 45.33% and 41.77% for bi-crystalline GNS and bi-crystalline BNNS, respectively. Higher energy dissipation in GNS reinforced PE nanocomposites can be attributed to extreme impedance mismatch and superior interfacial interaction energy between GNS and PE chains.