Pressure Hessian and viscous contributions to velocity gradient statistics based on Gaussian random fields

Understanding the non-local pressure contributions and viscous effects on the small-scale statistics remains one of the central challenges in the study of homogeneous isotropic turbulence. Here we address this issue by studying the impact of the pressure Hessian as well as viscous diffusion on the statistics of the velocity gradient tensor in the framework of an exact statistical evolution equation. This evolution equation shares similarities with earlier phenomenological models for the Lagrangian velocity gradient tensor evolution, yet constitutes the starting point for a systematic study of the unclosed pressure Hessian and viscous diffusion terms. Based on the assumption of incompressible Gaussian velocity fields, closed expressions are obtained as the results of an evaluation of the characteristic functionals. The benefits and shortcomings of this Gaussian closure are discussed, and a generalization is proposed based on results from direct numerical simulations. This enhanced Gaussian closure yields, for example, insights on how the pressure Hessian prevents the finite-time singularity induced by the local self-amplification and how its interaction with viscous effects leads to the characteristic strain skewness phenomenon

On the small-scale structure of turbulence and its impact on the pressure field

Understanding the small-scale structure of incompressible turbulence and its implications for the non-local pressure field is one of the fundamental challenges in fluid mechanics. Intense velocity gradient structures tend to cluster on a range of scales which affects the pressure through a Poisson equation. Here we present a quantitative investigation of the spatial distribution of these structures conditional on their intensity for Taylor-based Reynolds numbers in the range [160, 380]. We find that the correlation length, the second invariant of the velocity gradient, is proportional to the Kolmogorov scale. It also is a good indicator for the spatial localization of intense enstrophy and strain-dominated regions, as well as the separation between them. We describe and quantify the differences in the two-point statistics of these regions and the impact they have on the non-locality of the pressure field as a function of the intensity of the regions. Specifically, across the examined range of Reynolds numbers, the pressure in strong rotation-dominated regions is governed by a dissipation-scale neighbourhood. In strong strain-dominated regions, on the other hand, it is determined primarily by a larger neighbourhood reaching inertial scales.Comment: Accepted for publication by the Journal of Fluid Mechanic

Optimal noise-canceling networks

Natural and artificial networks, from the cerebral cortex to large-scale power grids, face the challenge of converting noisy inputs into robust signals. The input fluctuations often exhibit complex yet statistically reproducible correlations that reflect underlying internal or environmental processes such as synaptic noise or atmospheric turbulence. This raises the practically and biophysically relevant of question whether and how noise-filtering can be hard-wired directly into a network's architecture. By considering generic phase oscillator arrays under cost constraints, we explore here analytically and numerically the design, efficiency and topology of noise-canceling networks. Specifically, we find that when the input fluctuations become more correlated in space or time, optimal network architectures become sparser and more hierarchically organized, resembling the vasculature in plants or animals. More broadly, our results provide concrete guiding principles for designing more robust and efficient power grids and sensor networks.Comment: 6 pages, 3 figures, supplementary materia

Relic gravitational waves and extended inflation

In extended inflation, a new version of inflation where the transition from the false-vacuum phase to a radiation-dominated Universe is accomplished by bubble nucleation and percolation, bubble collisions supply a potent-and potentially detectable-source of gravitational waves. The present energy density in relic gravity waves from bubble collisions is expected to be about 10(exp -5) of closure density-many orders of magnitude greater than that of the gravity waves produced by quantum fluctuations. Their characteristic wavelength depends upon the reheating temperature T(sub RH): lambda is approximately 10(exp 4) cm (10(exp 14) GeV/T(sub RH)). If large numbers of black holes are produced, a not implausible outcome, they will evaporate producing comparable amounts of shorter wavelength waves, lambda is approximately 10(exp -6) cm (T(sub RH)/10(exp 14) GeV)

Positron line radiation from halo WIMP annihilations as a dark matter signature

We suggest a new signature for dark matter annihilation in the halo: high energy positron line radiation. Because the cosmic ray positron spectrum falls rapidly with energy, e+'s from halo WIMP annihilations can be a significant, clean signal for very massive WIMP's (approx. greater than 30 GeV). In the case that the e+e- annihilation channel has an appreciable branch, the e+ signal should be above background in a future detector, such as have been proposed for ASTROMAG, and of potential importance as a dark matter signature. A significant e+e- branching ratio can occur for neutralinos or Dirac neutrinos. High-energy, continuum positron radiation may also be an important signature for massive neutralino annihilations, especially near or above the threshold of the W+W- and ZoZo annihilation channels

Persistent accelerations disentangle Lagrangian turbulence

Particles in turbulence frequently encounter extreme accelerations between extended periods of quiescence. The occurrence of extreme events is closely related to the intermittent spatial distribution of intense flow structures such as vorticity filaments. This mixed history of flow conditions leads to very complex particle statistics with a pronounced scale dependence, which presents one of the major challenges on the way to a non-equilibrium statistical mechanics of turbulence. Here, we introduce the notion of persistent Lagrangian acceleration, quantified by the squared particle acceleration coarse-grained over a viscous time scale. Conditioning Lagrangian particle data from simulations on this coarse-grained acceleration, we find remarkably simple, close-to-Gaussian statistics for a range of Reynolds numbers. This opens the possibility to decompose the complex particle statistics into much simpler sub-ensembles. Based on this observation, we develop a comprehensive theoretical framework for Lagrangian single-particle statistics that captures the acceleration, velocity increments as well as single-particle dispersion

Hands-on osteoporosis screening with digital x-ray radiogrammetry

According to epidemiological studies about one third of women and one fifth of men over 50 years will experience a fragility fracture. These fractures account for substantial mortality, morbidity and health care cost. Osteoporosis is a silent disease and thus often goes undiagnosed for a long time. Second to trauma it is considered to be the main cause of fractures among elderly. Several methods to reduce fracture risk have been developed. Identifying individuals with high fracture risk who would most benefit from such measures is of utmost importance for cost-efficient fracture prevention. Dual-energy X-ray absorptiometry (DXA) is widely considered to be the gold standard for assessing bone mass, diagnosing osteoporosis and estimating fracture risk. However, access to DXA is limited and not everyone in need of an examination is able to have one. Other fracture risk prediction models have therefore been developed, e.g. questionnaire-based tools. Different bone mass measuring devices have also been invented, e.g. qualitative ultrasound, peripheral DXA and digital X-ray radiogrammetry (DXR). None of these methods has been investigated nor validated as much as DXA. The aim of this study was to investigate the clinical use of DXR, which uses hand radiographs to determine bone mass. In paper I, we retrospectively analyzed already obtained radiographs from 8,257 patients with DXR and found that DXR was highly predictive for hip fractures in both women and men. Later we recruited study participants from the Swedish mammography screening program and sampled a prospective, population-based cohort, the so-called STOP cohort. In paper II, the cohort was described, and it was shown that self-reported information about established clinical risk factors for osteoporosis were significantly associated with DXR T-score. A subset of the STOP cohort based on those with the lowest bone mass for their age (Zscore) was studied in paper III. In this subset we found a high prevalence of DXA-verified osteoporosis. Underlying causes for secondary osteoporosis and risk factors for primary osteoporosis were also overrepresented. In paper IV the STOP cohort was matched with fracture data from the Swedish National Inpatient Register and fracture prediction with DXR-BMD with and without clinical risk factors was examined. DXR T-score was significantly associated with hip, major osteoporotic and any clinical fracture. In summary DXR derived bone mass was associated with fracture risk and known clinical risk factors for osteoporosis. Further research should focus on longer follow-up of the STOP cohort and health economical assessments concerning potential clinical implementation of the method

Nonuniversal power-law spectra in turbulent systems

Turbulence is generally associated with universal power-law spectra in scale ranges without significant drive or damping. Although many examples of turbulent systems do not exhibit such an inertial range, power-law spectra may still be observed. As a simple model for such situations, a modified version of the Kuramoto-Sivashinsky equation is studied. By means of semi-analytical and numerical studies, one finds power laws with nonuniversal exponents in the spectral range for which the ratio of nonlinear and linear time scales is (roughly) scale-independent.Comment: 5 pages, 5 figure

Turbulence and turbulent pattern formation in a minimal model for active fluids

Active matter systems display a fascinating range of dynamical states, including stationary patterns and turbulent phases. While the former can be tackled with methods from the field of pattern formation, the spatio-temporal disorder of the active turbulence phase calls for a statistical description. Borrowing techniques from turbulence theory, we here establish a quantitative description of correlation functions and spectra of a minimal continuum model for active turbulence. Further exploring the parameter space, we also report on a surprising type of turbulence-driven pattern formation far beyond linear onset: the emergence of a dynamic hexagonal vortex lattice state after an extended turbulent transient, which can only be explained taking into account turbulent energy transfer across scales.Comment: Supplemental videos available at https://youtu.be/gbf6cRho03w https://youtu.be/n0qUUhAUJFQ https://youtu.be/LGmamkM012