Is nonhelical hydromagnetic turbulence peaked at small scales?

Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k^{-3/2}, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}. This is supported by the value of the second order structure function exponent that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure

Inertial range scaling in numerical turbulence with hyperviscosity

Numerical turbulence with hyperviscosity is studied and compared with direct simulations using ordinary viscosity and data from wind tunnel experiments. It is shown that the inertial range scaling is similar in all three cases. Furthermore, the bottleneck effect is approximately equally broad (about one order of magnitude) in these cases and only its height is increased in the hyperviscous case--presumably as a consequence of the steeper decent of the spectrum in the hyperviscous subrange. The mean normalized dissipation rate is found to be in agreement with both wind tunnel experiments and direct simulations. The structure function exponents agree with the She-Leveque model. Decaying turbulence with hyperviscosity still gives the usual t^{-1.25} decay law for the kinetic energy, and also the bottleneck effect is still present and about equally strong.Comment: Final version (7 pages

The "zeroth law" of turbulence: Isotropic turbulence simulations revisited

The dimensionless kinetic energy dissipation rate C_epsilon is estimated from numerical simulations of statistically stationary isotropic box turbulence that is slightly compressible. The Taylor microscale Reynolds number Re_lambda range is 20 < Re_lambda < 220 and the statistical stationarity is achieved with a random phase forcing method. The strong Re_lambda dependence of C_epsilon abates when Re_lambda approx. 100 after which C_epsilon slowly approaches approx 0.5 a value slightly different to previously reported simulations but in good agreement with experimental results. If C_epsilon is estimated at a specific time step from the time series of the quantities involved it is necessary to account for the time lag between energy injection and energy dissipation. Also, the resulting value can differ from the ensemble averaged value by up to +-30%. This may explain the spread in results from previously published estimates of C_epsilon.Comment: 7 pages, 7 figures. Submitted to Phys. Rev.

SPECIFICATION AND PROCUREMENT OF CP-5 FUEL TUBES.

Contains the specifications of CP-5 fuel tubes

Beta lives - some statistical perspectives on the capital asset pricing model

This note summarizes some technical issues relevant to the use of the idea of excess return in empirical modelling. We cover the case where the aim is to construct a measure of expected return on an asset and a model of the CAPM type is used. We review some of the problems and show examples where the basic CAPM may be used to develop other results which relate the expected returns on assets both to the expected return on the market and other factors

Spin Coupling Effect on Geometry-Dependent X-ray Absorption of Diradicals

We theoretically investigate the influence of diradical electron spin coupling on the time-resolved X-ray absorption spectra of the photochemical ring opening of furanone. We predict geometry dependent carbon K-edge signals involving transitions from core orbitals to both singly and unoccupied molecular orbitals. The most obvious features of the ring opening come from the carbon atom directly involved in the bond breaking, through its transition to both the newly formed SOMO and the available LUMO state. In addition to this primary feature, the singlet spin coupling of four unpaired electrons that arises in the core-to-LUMO states creates additional geometry dependence in some spectral features, with both oscillator strengths and relative excitation energies varying observably as a function of the ring opening. We attribute this behavior to a spin-occupancy-induced selection rule, which occurs when singlet spin coupling is enforced in the diradical state. Notably, one of these geometry-sensitive core-to-LUMO transitions excites core electrons from a backbone carbon not involved in the bond breaking, providing a novel non-local X-ray probe of chemical dynamics arising from electron spin coupling.Comment: 52 Pages, 13 Figure

The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence

The statistical properties of the dissipation process constrain the analysis of large scale numerical simulations of three dimensional incompressible magnetohydrodynamic (MHD) turbulence, such as those of Biskamp and Muller [Phys. Plasmas 7, 4889 (2000)]. The structure functions of the turbulent flow are expected to display statistical self-similarity, but the relatively low Reynolds numbers attainable by direct numerical simulation, combined with the finite size of the system, make this difficult to measure directly. However, it is known that extended self-similarity, which constrains the ratio of scaling exponents of structure functions of different orders, is well satisfied. This implies the extension of physical scaling arguments beyond the inertial range into the dissipation range. The present work focuses on the scaling properties of the dissipation process itself. This provides an important consistency check in that we find that the ratio of dissipation structure function exponents is that predicted by the She and Leveque [Phys. Rev. Lett 72, 336 (1994)] theory proposed by Biskamp and Muller. This supplies further evidence that the cascade mechanism in three dimensional MHD turbulence is non-linear random eddy scrambling, with the level of intermittency determined by dissipation through the formation of current sheets.Comment: 9 pages, 6 figures. Figures embedded in text. Typos corrected in text and references. Published in Physics of Plasmas. Abstract can be found at:http://link.aip.org/link/?php/12/02230

Fetal liver blood flow distribution: role in human developmental strategy to prioritize fat deposition versus brain development

Among primates, human neonates have the largest brains but also the highest proportion of body fat. If placental nutrient supply is limited, the fetus faces a dilemma: should resources be allocated to brain growth, or to fat deposition for use as a potential postnatal energy reserve? We hypothesised that resolving this dilemma operates at the level of umbilical blood distribution entering the fetal liver. In 381 uncomplicated pregnancies in third trimester, we measured blood flow perfusing the fetal liver, or bypassing it via the ductus venosus to supply the brain and heart using ultrasound techniques. Across the range of fetal growth and independent of the mother's adiposity and parity, greater liver blood flow was associated with greater offspring fat mass measured by dual-energy X-ray absorptiometry, both in the infant at birth (r = 0.43, P&lt;0.001) and at age 4 years (r = 0.16, P = 0.02). In contrast, smaller placentas less able to meet fetal demand for essential nutrients were associated with a brain-sparing flow pattern (r = 0.17, p = 0.02). This flow pattern was also associated with a higher degree of shunting through ductus venosus (P = 0.04). We propose that humans evolved a developmental strategy to prioritize nutrient allocation for prenatal fat deposition when the supply of conditionally essential nutrients requiring hepatic inter-conversion is limited, switching resource allocation to favour the brain if the supply of essential nutrients is limited. Facilitated placental transfer mechanisms for glucose and other nutrients evolved in environments less affluent than those now prevalent in developed populations, and we propose that in circumstances of maternal adiposity and nutrient excess these mechanisms now also lead to prenatal fat deposition. Prenatal developmental influences play important roles in the human propensity to deposit fa

Ultrafast X-ray Spectroscopy of Intersystem Crossing in Hexafluoroacetylacetone: Chromophore Photophysics and Spectral Changes in the Face of Electron Withdrawing Groups

Intersystem crossings between singlet and triplet states represent a crucial relaxation pathway in photochemical processes. Herein, we probe the intersystem crossing in hexafluoro-acetylacetone with ultrafast X-ray transient absorption spectroscopy at the carbon K-edge. We observe the excited state dynamics following excitation with 266 nm UV light to the $^1\pi\pi^{*}$ (S$_2$) state with element and site-specificity using a broadband soft X-ray pulse produced by high harmonic generation. These results are compared to X-ray spectra computed from orbital optimized density functional theory methods. It is found that the electron withdrawing fluorine atoms decongest the X-ray absorption spectrum by enhancing separation between features originating from different carbon atoms. This facilitates the elucidation of structural and electronic dynamics at the chromophore. The evolution of the core-to-valence resonances at the carbon K-edge reveals an ultrafast population transfer between the $^1n\pi^{*}$ (S$_1$) and $^3\pi\pi^{*}$ (T$_1$) states on a $1.6\pm0.4$ ps timescale, which is similar to the 1.5 ps timescale earlier observed for acetylacetone [J. Am. Chem. Soc. 139, 16576 (2017)]. It therefore appears that terminal fluorination has little influence on the intersystem crossing rate of the acetylacetone chromophore. In addition, the significant role of hydrogen-bond opened and twisted rotational isomers is elucidated in the excited state dynamics by comparison of the experimental transient X-ray spectra with theory

Accurate prediction of core-level spectra of radicals at density functional theory cost via square gradient minimization and recoupling of mixed configurations

State-specific orbital optimized approaches are more accurate at predicting core-level spectra than traditional linear-response protocols, but their utility had been restricted on account of the risk of `variational collapse' down to the ground state. We employ the recently developed square gradient minimization (SGM, J. Chem. Theory Comput. 16, 1699-1710, 2020) algorithm to reliably avoid variational collapse and study the effectiveness of orbital optimized density functional theory (DFT) at predicting second period element 1s core-level spectra of open-shell systems. Several density functionals (including SCAN, B3LYP and $\omega$B97X-D3) are found to predict excitation energies from the core to singly occupied levels to high accuracy ($\le 0.3$ eV RMS error), against available experimental data. Higher excited states are however more challenging by virtue of being intrinsically multiconfigurational. We thus present a CI inspired route to self-consistently recouple single determinant mixed configurations obtained from DFT, in order to obtain approximate doublet states. This recoupling scheme is used to predict the C K-edge spectra of the allyl radical, the O K-edge spectra of CO$^+$ and the N K-edge of NO$_2$ to high accuracy relative to experiment, indicating substantial promise in using this approach for computation of core-level spectra for doublet species (vs more traditional time dependent DFT, EOM-CCSD or using unrecoupled mixed configurations). We also present general guidelines for computing core-excited states from orbital optimized DFT.Comment: Added more dat