Similar Kinetic Energy Research Articles

The Influence of Mallet Mass and Velocity on the Fracture Patterns in Osteotomies.

Osteotomies are routinely incorporated in rhinoplasty, however, the influence of mass, velocity, kinetic energy (KE), and momentum (p) of the mallet on fracture patterns has not been studied. An experimental sledge guillotine setup was designed simulating a mallet strike with adjustable height and mass and 2 mm-thick Sawbone blocks. KE and p were calculated using KE = ½ mass × velocity2 and p = mass × velocity formulas. Fracture lengths and angles were measured. Ten groups with varying mallet masses and drop heights were tested with 10 bones per group. Fracture length positively correlated with KE (R = 0.542, p < 0.001) and p (R = 0.508, p < 0.001). Fracture angle also positively correlated with KE (R = 0.367, p < 0.001) and p (R = 0.329, p < 0.001). In groups with similar KE, osteotomies with higher p (heavier mallet with slower velocity) had greater fracture lengths (29.31 ± 0.68 vs. 27.68 ± 2.12 mm, p = 0.013) but similar fracture angles (p = 0.189). In groups with similar p, osteotomies with higher KE (lighter hammer with faster velocity) had significantly greater fracture lengths (28.28 ± 1.28 vs. 20.45 ± 12.20 mm, p = 0.041) and greater divergent fracture angles (3.13 ± 1.97° vs. 1.40 ± 1.36°, p = 0.031). Regression modeling of the relationship between KE and fracture lengths and angles demonstrated that cubic followed by logarithmic regression models had the best fits. Osteotomy fracture patterns positively correlated with the mallet's KE more so than its p, suggesting that the mallet's velocity has an increased impact effect than its mass. Clinically, a heavier mallet with a lower velocity will likely generate a smaller fracture length and fracture angle, indicating a more controlled and ideal fracture. NA Laryngoscope, 2024.

Ion imaging of spatially inhomogeneous nanoplasmas in NaCl particles.

Studying photoemission from free, unsupported aerosol particles is a powerful method for gaining insight into light-matter interactions at the nanoscale. We used single-shot velocity map imaging to experimentally measure kinetic energy and angular distributions of ions emitted following interaction of sub-micrometer NaCl particles with femtosecond pulses of near infrared (NIR, 800 nm) and ultraviolet (UV, 266 nm) light. We combined this with time-dependent simulations of light propagation through the particles and a rate equation approach to computationally address the origin of the observed ion emission. For both NIR and UV pulses, ion emission is caused by the formation of an under-dense nanoplasma with similar densities, although using an order of magnitude weaker UV intensities. Such conditions result in remarkably similar ion fragments with similar kinetic energies, and no obvious influence of the plasma formation mechanism (photoionization or collisional ionization). Our data suggests that Coulomb explosion does not play a significant role for ion emission, and we discuss alternative mechanisms that can lead to material ablation from under-dense nanoplasma. Finally, we show how finite size effects play an important role in photoemission through generation of spatially inhomogeneous nanoplasmas, which result in asymmetric ion emission that depends on particle size and laser wavelength. By utilizing the single-particle information available from our experiments, we show how finite size effects and inhomogeneous nanoplasma formation can be exploited to retrieve the size and orientation of individual submicrometer aerosol particles.

Assessment of Different Boundary Layer Parameterization Schemes in Numerical Simulations of Typhoon Nida (2016) Based on Aircraft Observations

This study aimed to find a boundary layer parameter scheme suitable for typhoons in the South China Sea based on a comparison with the aircraft detection data from Typhoon Nida (2016). We simulated the typhoon boundary layer wind field in different boundary layer schemes, such as YSU, MYNN, BouLac, and Shin-Hong, and with a no-boundary-layer parametrization scheme. The results were as follows: (1) In the eye and eyewall area, the YSU and MYNN schemes could better simulate the east–west wind characteristics and the YSU scheme could also simulate the jet current of the southerly wind component in the boundary layer in the eyewall. (2) Compared with the eye area, the easterly wind in the eyewall area was strong, and the overall vertical movement was weak. (3) The YSU and MYNN schemes had similar turbulent kinetic energies that were also similar to those from aircraft observations; the turbulent kinetic energy in the simulations of several schemes in the boundary layer was evidently lower than that in the aircraft observations. Thus, the MYNN and the YSU schemes yielded better simulations for the eye and eyewall areas, and the YSU scheme was more similar to the boundary layer observations.

Assessing Mixed Quantum-Classical Molecular Dynamics Methods for Nonadiabatic Dynamics of Molecules on Metal Surfaces.

Mixed quantum-classical (MQC) methods for simulating the dynamics of molecules at metal surfaces have the potential to accurately and efficiently provide mechanistic insight into reactive processes. Here, we introduce simple two-dimensional models for the scattering of diatomic molecules at metal surfaces based on recently published electronic structure data. We apply several MQC methods to investigate their ability to capture how nonadiabatic effects influence molecule-metal energy transfer during the scattering process. Specifically, we compare molecular dynamics with electronic friction, Ehrenfest dynamics, independent electron surface hopping, and the broadened classical master equation approach. In the case of independent electron surface hopping, we implement a simple decoherence correction approach and assess its impact on vibrationally inelastic scattering. Our results show that simple, low-dimensional models can be used to qualitatively capture experimentally observed vibrational energy transfer and provide insight into the relative performance of different MQC schemes. We observe that all approaches predict similar kinetic energy dependence but return different vibrational energy distributions. Finally, by varying the molecule-metal coupling, we can assess the coupling regime in which some MQC methods become unsuitable.

A wave appropriate discontinuity sensor approach for compressible flows

In this work, we propose a novel selective discontinuity sensor approach for numerical simulations of the compressible Navier–Stokes equations. Since transformation to characteristic space is already a common approach to reduce high-frequency oscillations during interpolation to cell interfaces, we exploit the characteristic wave structure of the Euler equations to selectively treat the various waves that the equations comprise. The approach uses the Ducros shock sensing criterion to detect and limit oscillations due to shocks while applying a different criterion to detect and limit oscillations due to contact discontinuities. Furthermore, the method is general in the sense that it can be applied to any method that employs characteristic transformation and shock sensors. However, in the present work, we focus on the gradient-based reconstruction family of schemes. A series of inviscid and viscous test cases containing various types of discontinuities are carried out. The proposed method is shown to markedly reduce high-frequency oscillations that arise due to improper treatment of the various discontinuities; i.e., applying the Ducros shock sensor in a flow where a strong contact discontinuity is present. Moreover, the proposed method is shown to predict similar volume-averaged kinetic energy and enstrophy profiles for the Taylor–Green vortex simulation compared to the base Ducros sensor, indicating that it does not introduce unnecessary numerical dissipation when there are no contact discontinuities in the flow.

Comparing the kinetics of ionized and neutral atoms from single and multi-element laser-produced plasmas

Kinetics of ion and neutral atom emission features were compared for nanosecond laser-produced plasmas generated from several metal targets (i.e., Al, Ti, Zr, Nb, Ta) and an alloy containing all of these as principal alloying elements. Plasmas were produced by focusing 6 ns, 1064 nm pulses from an Nd:YAG laser on the targets of interest in a vacuum. A Faraday cup was used for collecting ion temporal features while spatially and temporally resolved emission spectroscopy was used for measuring the optical time of flight of various neutral atomic transitions. Our results highlight that most probable ion and atom velocities decay with increasing atomic mass. Trends for ions from the alloy target represent a weighted average where all ions contribute. For both ions and atoms, velocities decrease with increasing heat of vaporization and melting temperature, consistent with the thermal mechanisms that contribute to nanosecond laser ablation. Kinetic energies for neutral atoms from pure metal targets have some variability with atomic mass, whereas kinetic energies for atoms from the alloy target are more similar. These more similar kinetic energies observed for neutral atoms in the multi-element plasma may be attributed to collisions between species from all elements in the Knudsen layer.

Temporally Varying Mesoscale Eddy Characteristics in the California Current System Identified from RAFOS Floats

The SOund Fixing And Ranging (RAFOS) floats were deployed by the Naval Postgraduate School (NPS) near California coast from 1992 to 2004 at depth between 150 and 600 m (http://www.oc.nps.edu/npsRAFOS/). Each drifter trajectory is adaptively decomposed using the empirical mode decomposition (EMD) into low-frequency (non-diffusive, i.e., current) and high-frequency (diffusive, i.e., eddies) components. The identified eddies are mostly anticyclonic with total 203 anticyclonic and 36 cyclonic spirals. Eddy characteristics are determined from the time series of individual RAFOS float trajectory. They are the current velocity scale, eddy radial scale, eddy velocity scale, eddy Rossby number, and eddy-current kinetic energy ratio. The California Current System is found an eddy-rich system with the overall eddy-current kinetic energy ratio of 1.78. It contains submesoscale and mesoscale eddies. The horizontal length scale of 10 km is a good threshold of the eddy radial scale (Leddy) to separate the two kinds of eddies. The mean eddy Rossby number is 0.72 for the submesoscale eddies and 0.06 for the mesoscale eddies. The current-eddy kinetic energy ratio is similar between submesoscale and mesoscale eddies. This may imply similar current-eddy kinetic energy transfer for submesoscale and mesoscale eddies. Statistical characteristics and interannual variability of current velocity scale and eddy characteristic parameters are also presented.

Dynamics and energy coupling of gas puff Z-pinches on a fast linear transformer driver

Gas puff Z-pinch experiments with annular Ar and Ne gas shells have been conducted on the Compact Experimental System for Z-pinch and Ablation Research (CESZAR) linear transformer driver (LTD) with 500 kA current and 160 ns rise time. Here, we present results from the first systematic gas puff Z-pinch experiments using a fast (≤200 ns) LTD as a driver, in which we show that 7% of the stored energy in the capacitors is coupled to plasma kinetic energy as estimated via self-emission and laser schlieren images. 0D and 1D simulations—which do not allow instability growth and thus reach greater maximum average velocities—using initial conditions inferred from experimental implosion trajectories predict coupling in excess of 10% of the stored energy. The Ar and Ne implosions were comparably massed and thus achieved similar maximum kinetic energies, though the Ne pinches were more stable and the x-ray pulses were longer and produced higher yield: 2–5 ns and 0.21–0.52 J (0.15–0.37 J/cm) of Ar K-shell and 12–25 ns and 2.2–3.9 J (1.6–2.6 J/cm) of Ne K-shell, respectively. The difference in stability is most likely attributed to variations in initial conditions such as density distribution and gas breakdown initiation.

Photoelectron circular dichroism of O 1s-photoelectrons of uniaxially oriented trifluoromethyloxirane: energy dependence and sensitivity to molecular configuration.

The photoelectron circular dichroism (PECD) of the O 1s-photoelectrons of trifluoromethyloxirane (TFMOx) is studied experimentally and theoretically for different photoelectron kinetic energies. The experiments were performed employing circularly polarized synchrotron radiation and coincident electron and fragment ion detection using cold target recoil ion momentum spectroscopy. The corresponding calculations were performed by means of the single center method within the relaxed-core Hartree-Fock approximation. We concentrate on the energy dependence of the differential PECD of uniaxially oriented TFMOx molecules, which is accessible through the employed coincident detection. We also compare the results for the differential PECD of TFMOx to those obtained for the equivalent fragmentation channel and similar photoelectron kinetic energy of methyloxirane (MOx), studied in our previous work. Thereby, we investigate the influence of the substitution of the methyl group by the trifluoromethyl group at the chiral center on the molecular chiral response. Finally, the presently obtained angular distribution parameters are compared to those available in the literature.

In vitro experiments on ICOSA6 4D flow MRI measurement for the quantification of velocity and turbulence parameters

PurposeTo perform comprehensive in vitro experiments using six-directional icosahedral flow encoding (ICOSA6) 4D flow magnetic resonance imaging (MRI) under various scan conditions to analyze the robustness of velocity and turbulence quantification. Materials and methodsIn vitro flow phantoms with steady flow rates of 10 and 20 L/min were scanned using both conventional 4D flow MRI and ICOSA6. Experiments focused on comparisons between ICOSA6 and conventional four point (4P) methods, and the effects of contrast agents, velocity encoding range (Venc), and scan direction on velocity and turbulence quantification. ResultsThe results demonstrated that 1) ICOSA6 improves the velocity-to-noise ratio (VNR) of velocity estimation by 33% (on average) and results in similar turbulent kinetic energy (TKE) estimation as the 4P method. 2) Measurements with a contrast agent resulted in more than a 2.5 fold increase in average VNR. However, the improvement of total TKE quantification was not obvious. 3) TKE estimation was less affected by Venc and the scan direction, whereas turbulence production (TP) estimation was largely affected by these measurement conditions. The effects of Venc and scan direction accounted for less than 11.63% of TKE estimation, but up to 33.89% of TP estimation. ConclusionThe ICOSA6 scheme is compatible with conventional 4D flow MRI for velocity and TKE measurement. Contrast agents are effective at increasing VNR, but not signal-to-noise ratio for TKE quantification. The effects of Venc and scan direction influence total TP more than total TKE.

Understanding the Performance of an Unstructured-Mesh Global Shallow Water Model on Kinetic Energy Spectra and Nonlinear Vorticity Dynamics

A strategy for evaluating a global shallow water model based on aspects of kinetic energy spectra and nonlinear vorticity dynamics is proposed in this study. The kinetic energy spectra and nonlinear vorticity dynamics of a recently developed global shallow water model on an unstructured mesh are evaluated in comparison with the benchmark solutions from a global high-resolution spectral model. The results show that the kinetic energy spectra, the rotational and divergent components, the stationary and transient components, and the nonlinear spectral fluxes of the developed shallow water model agree well with those generated by the reference model. In addition, the influence of different flux operators for transporting the potential vorticity (PV) is assessed specifically. It is indicated that the second-order flux operator leads to a spurious increase in the kinetic energy at the tail of the spectrum, whereas the upwind third-order flux operator does not support this behavior owing to implicit numerical diffusion. Moreover, the nonlinear vorticity dynamics is studied by using colliding modons. It is found that the grid-point model maintains the symmetrical pattern of vortices, and generates similar kinetic energy spectra and nonlinear spectral fluxes to the reference model. The evaluation provides a reference for assessing the shallow water model in terms of nonlinear dynamics, and the developed global shallow water model presents a good example.

Improved accuracy in the determination of the thermal cross section of ${}^{14}{\rm N}({\rm n},{\rm p}){}^{14}{\rm C}$ for neutron lifetime measurement

Abstract In a neutron lifetime measurement at the Japan Proton Accelerator Complex, the neutron lifetime is calculated from the neutron decay rate and the incident neutron flux. The flux is obtained by counting the protons emitted from the neutron absorption reaction of ${}^{3}{\rm He}$ gas, which is diluted in a mixture of working gas in a detector. Hence, it is crucial to determine the amount of ${}^{3}{\rm He}$ in the mixture. In order to improve the accuracy of the number density of the ${}^{3}{\rm He}$ nuclei, we have suggested using the ${}^{14}{\rm N}({\rm n},{\rm p}){}^{14}{\rm C}$ reaction as a reference because this reaction involves similar kinetic energy to the $^3$He(n,p)$^3$H reaction and a smaller reaction cross section to introduce reasonable large partial pressure. The uncertainty of the recommended value of the cross section, however, is not satisfied with our requirement. In this paper we report the most accurate experimental value of the cross section of the $^{14}$N(n,p)$^{14}$C reaction at a neutron velocity of 2200 m s$^{-1}$, measured relative to the $^3$He(n,p)$^3$H reaction. The result was 1.868 $\pm$ 0.003 (stat.) $\pm$ 0.006 (sys.) b. Additionally, the cross section of the $^{17}$O(n,$\alpha$)$^{14}$C reaction at the neutron velocity is also redetermined as 249 $\pm$ 6 mb.

Isotope dependence of the c 3Πu−b 3Σ and D 1Π−B′ 1Σ predissociation rates of molecular hydrogen

The state-specific predissociation rates of the (v,N,J) state by and the (v,J) state by the continuum of various isotopologues of molecular hydrogen have been calculated from accurate ab initio potential energy curves and electronic coupling matrix elements. Lifetimes and predissociation rates of the (v,N,J) and (v,J) levels and accurate energies of the (v,N) and (v,J) levels of the isotopologues have been obtained. Significant isotope dependence of state specific predissociation rate has been found even after adjustment for Franck-Condon factors and reduced mass. The use of average electronic matrix elements of H2 for other isotopologues underestimates the − predissociation rates of the HD, HT, D2, DT and T2 molecules by ∼12%, ∼16%, ∼30%, ∼40%, ∼52%, respectively, and the − rates of the HD, HT, D2, DT and T2 molecules by ∼10%, ∼15%, ∼26%, ∼35% and ∼45%, respectively. When compared at similar rotation, vibration and kinetic energies, the underestimation is nearly independent of the kinetic energy. The absolute value of the average electronic coupling matrix element increases with the reduced mass while that of the vibrational overlap integral decreases with the reduced mass. This accidental substantial cancellation in the − system is responsible for the experimental observation that the relative predissociation rate of two isotopologues approximately equals the squared inverse reduced mass ratio. The origin and implications of the isotope dependence of the averaged electronic coupling matrix elements are discussed.

Simulating effects of a wind‐turbine array using LES and RANS

AbstractGrowth in wind power production has motivated investigation of wind‐farm impacts on in situ flow fields and downstream interactions with agriculture and other wind farms. These impacts can be simulated with both large‐eddy simulations (LES) and mesoscale wind‐farm parameterizations (WFP). The Weather Research and Forecasting (WRF) model offers both approaches. We used the validated generalized actuator disk (GAD) parameterization in WRF‐LES to assess WFP performance. A 12‐turbine array was simulated using the GAD model and the WFP in WRF. We examined the performance of each scheme in both convective and stable conditions. The GAD model and WFP produced qualitatively similar wind speed deficits and turbulent kinetic energy (TKE) production across the array in both stability regimes, though the magnitudes of velocity deficits and TKE production levels were underestimated and overestimated, respectively. While wake growth slowed in the latter half of the WFP array as expected, wakes did not approach steady state by the end of the array as simulated by the GAD model. A sensitivity test involving the deactivation of explicit TKE production by the WFP resulted in turbulence levels within the array well that were below those produced by the GAD in both stable and unstable conditions. Finally, the WFP overestimated downwind power production deficits in stable conditions because of the lack of wake stabilization in the latter half of the array.

A D-Shaped Bileaflet Bioprosthesis which Replicates Physiological Left Ventricular Flow Patterns.

Prior studies have shown that in a healthy heart, there exist a large asymmetric vortex structure that aids in establishing a steady flow field in the left ventricle. However, the implantation of existing artificial heart valves at the mitral position is found to have a negative effect on this physiological flow pattern. In light of this, a novel D-shaped bileaflet porcine bioprosthesis (GD valve) has been designed based on the native geometry mitral valve, with the hypothesis that biomimicry in valve design can restore physiological left ventricle flow patterns after valve implantation. An in-vitro experiment using two dimensional particle velocimetry imaging was carried out to determine the hemodynamic performance of the new bileaflet design and then compared to that of the well-established St. Jude Epic valve which functioned as a control in the experiment. Although both valves were found to have similar Reynolds shear stress and Turbulent Kinetic Energy levels, the novel D-shape valve was found to have lower turbulence intensity and greater mean kinetic energy conservation.

Sensitivity analysis of kinetic energy-intensity relationships and maximum rainfall intensities on rainfall erosivity using a long-term precipitation dataset

Summary This paper analyses and compares rainfall erosivity values that were computed with five different kinetic energy-intensity (KE-I) relationships using the 0.5-h and 1-h maximum rainfall intensities (I30 and I60, respectively). The KE-I relationships included three exponential equations (Brown and Foster, 1987 (BF); McGregor et al., 1995 (MG); van Dijk et al., 2002 (VD)), a logarithmic equation (Wischmeier and Smith, 1958 (WS)) and a linear equation (Hudson, 1961 (HU)). The KE-I relationships were used to compute rainfall erosivity from pluviographic records of 30 sites that are located in central Chile. A total of 415 years of data were used, and more than 18,000 storms were identified. The results showed that among the exponential equations, the MG relationship yielded erosivity results that were statistically identical to the VD and the BF relationships. However, when comparing the VD and the BF relationships, significant differences in erosivity were found, which showed that the exponential equation is highly sensitive to changes in its regression parameters and is therefore site-specific. Among all of the relationships, the WS logarithmic equation yielded the largest erosivity estimates; however, they were statistically equal to the estimates made with the MG and the VD relationships but were not statistically equal to estimates predicted by the BF relationship. In contrast, in comparison to the other equations, the HU linear relationship yielded significantly smaller erosivity values. Conversely, regardless of the KE-I relationship and the site, computing erosivity using I60 provided erosivity estimates that are 10% smaller than those obtained using I30. The relative size of the erosivity estimates is due to the relative values of I60 and I30; on average I60 was 10% smaller than I30 at the study sites. Finally, because the rainfall erosivity estimates at the study sites were highly affected by the type of KE-I relationship, these results demonstrate that selecting an appropriate KE-I relationship is crucial for accurately estimating erosivity. These differences were augmented because of the typically low rainfall intensities at the study sites. Under this condition, the differences between the KE-I relationships were greatest. However, with higher rainfall intensities, all of the KE-I relationships provide similar kinetic energy estimates, which makes the selection of the KE-I relationship less important than the use of a reliable I30 value for computing rainfall erosivity.

Analysis of late-time light curves of Type IIb, Ib and Ic supernovae

The shape of the light curve peak of radioactive--powered core--collapse "stripped--envelope" supernovae constrains the ejecta mass, nickel mass, and kinetic energy by the brightness and diffusion time for a given opacity and observed expansion velocity. Late--time light curves give constraints on the ejecta mass and energy, given the gamma--ray opacity. Previous work has shown that the principal light curve peaks for SN~IIb with small amounts of hydrogen and for hydrogen/helium--deficient SN~Ib/c are often rather similar near maximum light, suggesting similar ejecta masses and kinetic energies, but that late--time light curves show a wide dispersion, suggesting a dispersion in ejecta masses and kinetic energies. It was also shown that SN~IIb and SN~Ib/c can have very similar late--time light curves, but different ejecta velocities demanding significantly different ejecta masses and kinetic energies. We revisit these topics by collecting and analyzing well--sampled single--band and quasi--bolometric light curves from the literature. We find that the late--time light curves of stripped--envelope core--collapse supernovae are heterogeneous. We also show that the observed properties, the photospheric velocity at peak, the rise time, and the late decay time, can be used to determine the mean opacity appropriate to the peak. The opacity determined in this way is considerably smaller than common estimates. We discuss how the small effective opacity may result from recombination and asymmetries in the ejecta.

Abstract 16393: Right Ventricular Energetics and Power in Pulmonary Regurgitation vs. Stenosis Using Four-Dimensional Phase-Contrast Magnetic Resonance

Background: We investigated kinetic energy (KE) and power efficiency in porcine models of pressure and volume loaded right ventricle (RV) using four-dimensional phase-contrast magnetic resonance imaging (4DPC-MRI). Methods: 4DPC-MRI was performed in pig models of pulmonary stenosis (PS) and pulmonary regurgitation (PR) at baseline and at 10-12 weeks of creation of the model, in conjunction with cardiac catheterization. Phase-contrast velocities were computed over 1 cardiac cycle (25 time-steps, MevisFlow and CAIPI, Fraunhofer MEVIS, Germany), with segmentation of a moving left ventricle mask based on cine images. The segmented mask was applied to the respective calculated 3D velocity vector field per time-step. Mean KE and KE curve profiles were measured, normalized for RV volumes and compared between PS and PR groups. Catheterization pressures and pressure-volume loops (Transonic Scisense Inc.) were used to calculate RV stroke work (RVSW) and stroke power. RV power efficiency was calculated as the ratio between RV power output and stroke power. Results: Eight pigs (4 PS and 4 PR) were studied. Table shows demographics, volumetry, KE and power data compared between groups. Both groups had similar KE pre-procedure but significant changes in KE post-procedure. In addition, the PR group had higher RV power efficiency and KE (87.1%±14.3%; 23.5±5.3, respectively) than PS group (21.4%±15.7%; 10.9±3.9) post-procedure. Conclusions: Volume loaded RV from PR had higher KE and power efficiency compared to pressure load from PS. These parameters represent the KE of blood in the RV and the net energy transferred into the pulmonary artery over one cardiac cycle. PS and PR groups have different RV work load, and they operate at different energy levels.

Kinematic analysis of a sample of X-ray luminous distant galaxy clusters

Observations and cosmological simulations show galaxy clusters as a family of nearly self-similar objects with properties that can be described by scaling relations as a function of e.g. mass and time. Here we study the scaling relations between the galaxy velocity dispersion and X-ray quantities like X-ray bolometric luminosity and temperature in galaxy clusters at high redshifts (0.64 $\leq$ z $\leq$ 1.46). We also compare our results with the similar study of the local HIFLUGCS sample. For the analysis, we use a set of 15 distant galaxy clusters extracted from the literature plus a sample of 10 newly discovered clusters selected in X-rays by the \XMM Distant Cluster Project (XDCP) with more than 10 confirmed spectroscopic members per cluster. We also study the evolution of this scaling relation by comparing the high redshift results with the data from the local HIFLUGCS sample. We also investigated the $L_X - T_X$ and the $\sigma_v - T_X$ relations for the 15 clusters in the literature sample. We report the results of the X-ray and kinematic analysis of 10 newly detected high redshift clusters and provide their spectroscopic and kinematic details. For the entire, distant sample we find a slope fully consistent with the one typical of local clusters, albeit with a large associated uncertainty. The study on the evolution of the amplitude reveals a positive offset if the self-similar evolution is neglected, hence possibly indicating the need for including evolutionary effects. However, the $L_X - T_X$ relation is found to be in good agreement with the local relation without any significant redshift evolution. Finally, the $\sigma_v - T_X$ relation appears to slightly deviate from the theoretical expectation that galaxies and gas particles have a similar specific kinetic energy. However, the associated uncertainty is currently too large for making any conclusive statement in this regard.

The Pauli energy grows exponentially with the electronic localisation

We investigate the Pauli energy in atoms and molecules as a measure of electron localisation. Our results indicate that the Pauli energy has an exponential dependence on the number of localised electrons. This relationship yields to a kinetic energy density expression that depends on the electron density ρ(r) and the pair density ρ2(r, r′). The proposed equation shows certain advantages over a similar orbital-free kinetic energy functional recently proposed by Delle Site and co-workers. The methodology introduced here is a novel approach for exploring electronic quantities with a partition scheme that might be useful for research in density functional theory.