Kinetic Energy Contributions Research Articles

What is the Exchange Repulsion Energy? Insight by Partitioning into Physically Meaningful Contributions.

It is shown that the exchange repulsion energy, Exr, can be rationalized by partitioning the respective energy expression for two systems with Hartree-Fock orbitals into physically meaningful contributions. A division of Exr into a positive kinetic and a negative potential part is possible, but these contributions correlate only poorly with the actual exchange repulsion energy. A more meaningful partitioning is derived, where all kinetic energy contributions are collected in a term that vanishes for exact Hartree-Fock orbitals due to their stationarity conditions. The remaining terms can be distinguished into an exchange integral contribution as well as contributions to the repulsion energy with two, three and four orbital indices. The forms, relationships and absolute sizes of these terms suggest an intuitive partitioning of the exchange repulsion energy into Molecular Orbital Pair Contributions to the Exchange repulsion energy (MOPCE). Insight into the analytic form and quantitative size of these contributions is provided by considering the state of the H2 molecule, the water dimer, as well as an argon atom interacting with Cl2 and N2.

Asymptotic Behavior of Saxion–Axion System in Stringy Quintessence Model

AbstractThe late time behavior of the slow‐roll parameter in the stringy quintessence model is studied when axion as well as saxion are allowed to move. Even though the potential is independent of the axion at tree level, the axion can move through its coupling to the saxion and the background geometry. Then the contributions of the axion kinetic energy to the slow‐roll parameter and the vacuum energy density are not negligible when the slow‐roll approximation does not hold. As the dimension of the field space is doubled, the fixed point at which the time variation of the slow‐roll parameter vanishes is not always stable. It is found that the fixed point in the saxion–axion system is at most partially stable, in particular when the volume modulus and the axio‐dilaton, the essential ingredients of the string compactification, are taken into account. It seems that as more saxion–axion pairs are considered, achieving the stability of the fixed point becomes difficult.

Balancing the Contributions to the Gradient Expansion: Accurate Binding and Band Gaps with a Nonempirical Meta-GGA.

The gradient expansion has been a long-standing guide rail in density-functional theory. We here demonstrate that for exchange-correlation approximations that depend on the gradient of the density and the kinetic energy density, i.e., for meta-generalized gradient approximations (meta-GGAs), there is a so far unexploited degree of freedom in the gradient expansion that allows to shift the relative weight of gradient and kinetic energy contributions. As the dependence on the kinetic energy density determines the derivative discontinuity, this allows to construct meta-GGAs that adhere to the known exact constraints, yet have new properties. We demonstrate this with the construction of a meta-GGA that describes both electronic bonds and band gaps with remarkable accuracy.

Kinetically anisotropic Hamiltonians: plane waves, Madelung streamlines and superpositions

A Hamiltonian in two space dimensions whose kinetic-energy contributions have opposite signs is studied in detail. Solutions of the time-independent Schrödinger equation for fixed energy are superpositions of plane waves, with wavevectors on hyperbolas rather than circles. The local velocity (e.g. in the Madelung representation) is proportional to the kinetic momentum, i.e. local particle velocity, not the more familiar canonical momentum (phase gradient). The patterns of the associated streamlines are different, especially near phase singularities and phase saddles where the kinetic and canonical streamline patterns have opposite indices. Contrasting with the superficially analogous circular smooth solutions of kinetically isotropic Hamiltonians are wave modes that are anisotropic in position and also discontinuous. Pictures illustrating these phenomena are included. The occurrence of familiar concepts in unfamiliar guises could be useful for teaching quantum or wave physics at graduate level.

Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy functional

Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange–correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work, we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange–correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.

A volume of fluid method for three dimensional direct numerical simulations of immiscible droplet collisions

This paper presents an advanced Volume of Fluid (VOF) method that enables performant three dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g., binary droplet collisions. One of the challenges associated with the introduction of a third immiscible phase into the VOF method is the reconstruction of the phase boundaries near the triple line in arbitrary arrangements. For this purpose, an efficient method based on a Piecewise Linear Interface Calculation (PLIC) is shown. Moreover, the surface force modeling with the robust Continuous Surface Stress (CSS) model was enhanced to treat such three-phase situations with large topology changes and thin films. A consistent scaling of the fluid properties at the interfaces ensures energy conservation.The implementation of these methods in the multi-phase flow solver Free Surface 3D (FS3D) allowed a successful validation. A qualitative comparison of the morphology in binary collisions of immiscible droplets as well as a quantitative comparison regarding the threshold velocities that distinguish different collision regimes shows excellent agreement with experimental results.These simulations enable the evaluation of experimentally inaccessible data like the contributions of kinetic, surface and dissipative energy of both immiscible liquids during the collision process. Furthermore, the comparison against binary collisions of the same liquids highlights similarities and differences between immiscible and equal droplet collisions. Both can support the modeling of the immiscible liquid interaction in the future.

A NEW SEAWATER LOW-HEAD TURBINE FOR THE OBREC

The OBREC (Overtopping Breakwater for wave Energy Conversion) is based on the overtopping phenomenon [1] where incoming waves run over an overtopping ramp and fall into a reservoir located above the sea level inside a conventional rubble mound breakwater, or into a vertical caisson breakwater. The wave energy is transformed into potential energy, with some contribution of kinetic energy. Then, the flow is driven through a turbine addressing the final transformation into electrical energy. The OBREC prototype is located in the middle of the San Vincenzo breakwater, in Naples harbour (Italy). The key target of the whole pilot project was to demonstrate the high capacity factor of the system (expressed as the ratio of the electrical energy produced to the electrical energy that could have been produced at continuous full power operation), even in a low-energy wave climate. At the study site, in fact, the yearly average wave power was found to be 1.8 kW/m over the last 42 years [2]. However, during last 5 years, a maximum wave height of over 5 m has been registered, confirming the high reliability under severe wave conditions.
 Due to the short monitoring period and to the undersize of the previous power take-off (PTO) systems, no definitive power matrix is available for OBREC [3]. The energy conversion efficiency of OBREC has been deeply investigated over the last years through both physical and numerical model tests. Within the ongoing full-scale monitoring activities in real environments, a new set of power take-off was installed. A propeller-type pico-turbine equipment was in 2021, and its final setting was completed in 2022. Performance and reliability of the entire structure were closely monitored under different “stress tests”, i.e. start & stop cycle in marine environment with a high variable combination of flow rate/hydraulic head.
 This paper presents the design stage for the new equipment and preliminary results from these tests numerical and field tests.
 
 
 Contestabile, P., Crispino, G., Di Lauro, E., Ferrante, V., Gisonni, C., & Vicinanza, D. (2020). Overtopping breakwater for wave Energy Conversion: Review of state of art, recent advancements and what lies ahead. Renewable Energy, 147, 705-718.
 Contestabile, P., Russo, S., Azzellino, A., Cascetta, F., Vicinanza, D. (2022). "Combination of local sea winds/land breezes and nearshore wave energy resource: Case study at MaRELab (Naples, Italy)", Energy Conversion and Management, ISSN 0196-8904, 257, 115356, https://doi.org/10.1016/j.enconman.2022.115356 
 Mariani, A., Crispino, G., Contestabile, P., Cascetta, F., Gisonni, C., Vicinanza, D., & Unich, A. (2021). Optimization of Low Head Axial-Flow Turbines for an Overtopping BReakwater for Energy Conversion: A Case Study. Energies, 14(15), 4618.

An Analytic Formula for Entraining CAPE in Midlatitude Storm Environments

Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm-relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocity wmax in an updraft. Hence, these formulas are evaluated using wmax from past numerical modeling studies. Both of the new formulas improve predictions of wmax substantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance of by wmax, and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. Significance Statement Substantial mixing occurs between the upward-moving air currents in thunderstorms (updrafts) and the surrounding comparatively dry environmental air, through a process called entrainment. Entrainment controls thunderstorm intensity via its diluting effect on the buoyancy of air within updrafts. A challenge to representing entrainment in forecasting and predictions of the intensity of updrafts in future climates is to determine how much entrainment will occur in a given thunderstorm environment without a computationally expensive high-resolution simulation. To address this gap, this article derives a new formula that computes entrainment from the properties of a single environmental profile. This formula is shown to predict updraft vertical velocity more accurately than past diagnostics, and can be used in forecasting and climate prediction to improve predictions of thunderstorm behavior and impacts.

Parametric, Semiparametric, and Semi-Nonparametric Estimates of the Kinetic Energy of Ordered Air Motion and Wind Outliers in the Atmospheric Boundary Layer from Minisodar Measurements

In the present work, we analyze the spatiotemporal dynamics of the kinetic wind energy with and without allowance for the kinetic energy of outliers. We first separated the contributions of the mean kinetic energy and the kinetic energy of the outliers and estimated the latter using robust parametric, semiparametric, and semi-nonparametric algorithms developed by the authors. The kinetic wind energy was estimated by the postprocessing of minisodar measurements of three wind velocity components and their variances in the lower 200 m layer of the atmosphere. By the outliers, we mean wind velocities, including wind gusts, the distribution of which deviates from the prior distribution of the majority of observations. A nonmonotonic increase in the kinetic energy of the outliers with sounding altitude was established. Physically, this can be explained by a nonmonotonic increase in the turbulent kinetic energy of local air vortices in the atmospheric boundary layer (ABL). The vertical extension of the outlier layers was of the order of 10–20 m.

Fission dynamics, dissipation, and clustering at finite temperature

The saddle-to-scission dynamics of the induced fission process is explored using a microscopic finite-temperature model based on time-dependent nuclear density functional theory (TDDFT), that allows to follow the evolution of local temperature along fission trajectories. Starting from a temperature that corresponds to the experimental excitation energy of the compound system, the model propagates the nucleons along isentropic paths toward scission. For the four illustrative cases of induced fission of $^{240}$Pu, $^{234}$U, $^{244}$Cm, and $^{250}$Cf, characteristic fission trajectories are considered, and the partition of the total energy into various kinetic and potential energy contributions at scission is analyzed, with special emphasis on the energy dissipated along the fission path and the prescission kinetic energy. The model is also applied to the dynamics of neck formation and rupture, characterized by the formation of few-nucleon clusters in the low-density region between the nascent fragments.

Effects of the kinetic energy in heat for overdamped systems

In the derivation of the thermodynamics of overdamped systems, one ignores the kinetic energy contribution since the velocity is a fast variable. In this paper, we show that the kinetic energy needs to be present in the calculation of the heat distribution to have a correct correspondence between the underdamped and overdamped cases, meaning that the velocity can not be fully ignored in the thermodynamics of these systems. We do this by investigating in detail the effect of the kinetic energy for three different systems: the harmonic potential, the logarithm potential, and an arbitrary non-isothermal process.

Вклад мезомасштабных вихрей Лофотенской котловины в ее энергетику

A comparative assessment of the contribution of eddies and other dynamic structures to the energy of the Lofoten Basin is carried out. The basis of the study is the data of global ocean reanalysis GLORYS12V1 for 1993–2019. We estimate the total kinetic and potential energy as well as the corresponding contribution of eddy energy for a region bounded by an isobath of 3000 m. We use the method of automatic identification of vortices for the analysis which allows us to calculate the eddy kinetic and potential energy in the automatically selected areas of the eddies. We establish that the potential energy of both cyclones and anticyclones is on average 2–3 times higher than the kinetic
 energy values, and the energy values of kinetic and potential for anticyclones dominate relative to the energy of cyclones. We also consider the interannual variability and seasonal course of eddy kinetic and potential energy. The seasonal course revealed an increase in both types of energy in the winter months. It is established that the contribution of eddies to the total energy of the basin is small. The contribution of eddy kinetic energy to the total energy of the basin is 7.3%, and the contribution of eddy potential energy is 8.4%. This means that the main contribution to the energy of the basin is made not by mesoscale eddies, but by other dynamic structures i.e. filaments and background flow.

A variational approach for the ground-state profile of a trapped spinor-BEC: a detailed study of phase transition in spin-1 condensate at zero magnetic field

In this article, we introduce a multi-modal variational method to analytically estimate the full number- and corresponding energy-density profile of a spin-1 Bose-Einstein condensate (BEC) for a number of particles as low as 500 under harmonic confinement. To apply this method, we consider a system of spin-1 BEC under three-dimensional isotropic and effective one-dimensional harmonic confinement in the absence (negligible presence) of the magnetic field which has ground-state candidates of comparable energy. It should be noted that in such circumstances kinetic energy contribution to the ground state cannot be neglected which puts the applicability of Thomas–Fermi (T-F) approximation to question. For anti-ferromagnetic condensates, the T-F approximated energy difference between the competing stationary states (ground state and the first excited state) is approximately 0.5%. As T-F approximation is only good for condensates with a large number of particles, T-F approximated predictions can completely go wrong especially for small condensates. This is where comes the role of a detailed analysis using our variational method, which incorporates the kinetic energy contribution and accurately estimates the number- and energy-density profile even for condensates having a small number of particles. Results of our analytical method are supported by numerical simulation. This variational method is general and can be extended to other similar/higher-dimensional problems to get results beyond the accuracy of the T-F approximation.

A numerical investigation of a wind turbine wake in non-neutral atmospheric conditions

Wind turbine wakes cause energy losses and increased blade fatigue loads in wind farms. The magnitude of these effects depend strongly on the atmospheric conditions. In nonneutral atmospheric conditions, there is a turbulence kinetic energy (TKE) contribution from buoyancy, either positive (convective boundary layer, CBL) or negative (stable boundary layer, SBL). In this work, both conditions are analyzed with new large-eddy simulation (LES) data of a single wind turbine wake in flat, homogeneous terrain to quantify the effects of buoyancy. It is found that the buoyancy contribution is negligible compared to the shear production in the wake region and the role of buoyancy is therefore mainly to alter the inflow profiles. This fact is used in a simple Reynolds-averaged Navier-Stokes (RANS) turbulence model, which shows reasonable results for wake velocity deficit compared to LES data.

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model * *Supported by in part by the National Natural Science Foundation of China (11775119, 12175109), the Natural Science Foundation of Tianjin

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.

Contribution of segmental kinetic energy to forward propulsion of the centre of mass: Analysis of sprint acceleration

ABSTRACT This study aimed to measure the contribution of each body segment to the production of total body kinetic energy (KE) during a 40-m sprint. Nine recreational sprinters performed two 40-m sprints wearing a MVN Biomech suit (Xsens). Data recorded were used to calculate total body KE, and the KE of each segment. The KE of each segment was then expressed as a percentage of the total body KE. We divided the sprint into three phases: 1 – start to maximal power (P max), 2 – P max to maximal velocity (V max), and 3 – V max to the end of the 40 m. Total body KE increased from the start to the end of the 40-m sprint (from 331.3 ± 68.4 J in phase 1 to 2378.8 ± 233.0 J in phase 3; p ≤ 0.001). The contribution of the head–trunk increased (from 39.5 ± 2.4% to 46.3 ± 1.1%; p ≤ 0.05). Contribution of the upper and lower limbs decreased over the three phases (respectively from 15.7 ± 2.5% to 10.6 ± 0.6% and from 44.8 ± 2.1% to 43.1 ± 1.5%; p ≤ 0.05). This study revealed the important contribution of the trunk to forward propulsion throughout the entire acceleration phase.

Mesoscale Horizontal Kinetic Energy Spectra of an Eastward-Moving Southwest Vortex

A high-resolution simulation with the Weather Research and Forecasting (WRF) model is performed to investigate the characteristics of the horizontal kinetic energy (HKE) spectra of an eastward-moving southwest vortex (SWV) generated in Sichuan Province, China, during 16–19 June 2011. The results indicate that the evolution of the SWV can be divided into the development, mature, and decay stages. In the troposphere, the HKE spectrum reproduces the typical atmospheric spectrum, with a slope of approximately −3 for wavelengths greater than 300 km and −5/3 for wavelengths between 300 and 30 km in each stage. The average scale of spectral transition is around 300 km. However, the HKE spectrum in the lower stratosphere shows a −5/3 slope at mesoscales and has no clear spectral transition. During the mature stage of the SWV, the HKE increases prominently for wavelengths between 300 and 30 km. Moreover, the relative contribution of the rotational kinetic energy (RKE) and the divergent kinetic energy (DKE) was investigated. It shows that the RKE spectrum dominates the DKE spectrum for wavelengths greater than 300 km in the lower troposphere, while in the upper troposphere the magnitudes of RKE and DKE are comparable over all scales. However, in the lower stratosphere, the DKE is an order of magnitude larger than the RKE, contributing more to the total HKE spectrum.

Large eddy simulations and modal decomposition analysis of flow past a cylinder subject to flow-induced vibration

Large eddy simulations (LES) are carried out to investigate the flow around a vibrating cylinder in the subcritical Reynolds number regime at Re = 3900. Three reduced velocities, Ur = 3, 5, and 7, are chosen to investigate the wake structures in different branches of a vortex-induced vibration (VIV) lock-in. The instantaneous vortical structures are identified to show different coherent flow structures in the wake behind the vibrating cylinder for various branches of VIV lock-in. The combined effects of the frequency and amplitude of the oscillation on the flow pattern in the wake region, the hydrodynamic quantities of the cylinder, and the spanwise length scale of the energetic wake flow structures are discussed in detail. It is found that the typical spanwise lengths of the flow structures are 0.22D at Ur = 5 and 0.3D at Ur=[3,7] in the near-wake region and level out at 0.5D further downstream. Furthermore, multiscale proper orthogonal decomposition (mPOD) is used to analyze the dominant flow features in the wake region. With the increasing Ur, the total kinetic energy contribution of superharmonic modes increases and the contribution of subharmonic modes decreases. The dominant flow characteristics associated with the vortex shedding and their super harmonics, and the low-frequency modulation of the wake flow can be captured by the mPOD modes.

Reynolds and dispersive shear stress in free-surface turbulent channel flow over square bars.

Reynolds and dispersive shear stresses in turbulent flow over spanwise-aligned square bars in an open channel flow are examined. Results of large-eddy simulation of flow over two different bar spacings corresponding to transitional and k-type (reattaching flow) roughness are analyzed. The Reynolds shear stress contribution to the momentum loss (or the friction factor, respectively) is greater than the dispersive shear stress contribution. By increasing the bars spacing, however, the contribution of the dispersive shear stress increases while the Reynolds shear stress contribution decreases, which is due to a standing wave at the water surface in the flow over k-type roughness which results in significant spatial variations in the time-averaged velocities. Strong sweep events take place and contribute to the friction coefficient. Investigating the dynamics of the flow reveals that there is momentum source below the crest of the bars and momentum sink above them, leading to acceleration or deceleration of flow, respectively. The contribution of dispersive shear stress is significant only in the deceleration of the flow near the crest of the bars and in the acceleration of the flow under the water surface. Quantification of the three components of total kinetic energy, i.e. mean, turbulent, and wake kinetic energy, reveals that the largest contribution is that of the mean flow in both geometries. By increasing the bar spacing, the contributions of turbulent and wake kinetic energy, which are localized at the bar height, increase, while the kinetic energy of the mean flow decreases.

A molecular dynamics study on the mechanical properties of defective CNT/epoxy nanocomposites using static and dynamic deformation approaches

Abstract In this paper, the mechanical behavior of epoxy polymer nanocomposite with continuous single-walled carbon nanotubes (SWCNT) with and without vacancy defects has been investigated based on two approaches of deformation, molecular mechanics (static) and molecular dynamics. In this regard, molecular simulation has been performed on the basis of the compass force field. In order to validate the research steps, the results obtained for pure epoxy polymer were compared with similar molecular dynamic simulations, which confirmed the simulation process. The research process proposed a method for controlling the symmetry of the system during equilibration with an asymmetric barostat. The Souza-Martins barostat was also used to apply loading and deformation control over a constant strain rate range. The results showed that in both deformation approaches (with and without calculating the contribution of kinetic energy), the presence of defects improved the transverse tensile and shear moduli, while the longitudinal tensile modulus decreased. Also, the improvement and decrease of the longitudinal tensile modulus and longitudinal shear modulus of the nanocomposite in comparison with the net polymer have been observed in both approaches, respectively. As a general result, it was observed that the contribution of kinetic energy has a major effect on the mechanical properties of pristine and defective nanocomposites.