Small-scale Anisotropy Research Articles

Quantifying small-scale anisotropy in turbulent flows

Quantifying small-scale anisotropy in turbulent flows

LiteBIRD science goals and forecasts: a full-sky measurement of gravitational lensing of the CMB

We explore the capability of measuring lensing signals in LiteBIRD full-sky polarization maps. With a 30 arcmin beam width and an impressively low polarization noise of 2.16 μK-arcmin, LiteBIRD will be able to measure the full-sky polarization of the cosmic microwave background (CMB) very precisely. This unique sensitivity also enables the reconstruction of a nearly full-sky lensing map using only polarization data, even considering its limited capability to capture small-scale CMB anisotropies. In this paper, we investigate the ability to construct a full-sky lensing measurement in the presence of Galactic foregrounds, finding that several possible biases from Galactic foregrounds should be negligible after component separation by harmonic-space internal linear combination. We find that the signal-to-noise ratio of the lensing is approximately 40 using only polarization data measured over 80% of the sky. This achievement is comparable to Planck's recent lensing measurement with both temperature and polarization and represents a four-fold improvement over Planck's polarization-only lensing measurement. The LiteBIRD lensing map will complement the Planck lensing map and provide several opportunities for cross-correlation science, especially in the northern hemisphere.

Abstract PO3-07-01: Multiscale Computational Analysis of Patient-Matched Multi-Modal Imaging of Breast Tissue Microenvironment

Abstract Introduction: Mammographic breast density is a strong quantitative cancer risk factor, but its link to underlying tissue and cellular level changes are weakly understood. Understanding the complex restructuring changes in the breast tumor microenvironment and its impact on breast density is integral to improving risk assessment and treatment strategies. A novel approach was developed to stratify mammographic dense breast tissue into areas of active dense tissue and passive dense tissue. Active dense tissue is structurally reorganizing and links to cancer dynamics, whereas passive dense mammographic tissue remains organized.1,2 A complementary wavelet-based analysis technique to measure the multiscale anisotropy of collagen fibers from Second-Harmonic Generation (SHG) imaging demonstrated clinical cancer diagnostic potential in mouse carcinoma and human pancreatic cancer.3,4 This tool is now leveraged for a multi-modal study in which patient-matched H&E tissue biopsies are imaged using both bright-field microscopy and SHG imaging to compare with the patient’s corresponding mammograms. Stratifying the mammographic density into active and passive dense areas, a correlation between biopsy tissue anisotropy and mammographic density subtypes can be calculated to help understand how tumor microenvironment changes affect a patient’s mammographic breast tissue composition. Methods: SHG and brightfield-imaged biopsy slides from 10 patients (five malignant, five benign) collected from Maine Medical Center (Maine, US) were analyzed using the 2D Wavelet Transform Modulus Maxima (WTMM) Anisotropy Method generating a large-scale and a small-scale anisotropy factor as well as a scale-combined anisotropy calculated from their large- and small-scale anisotropy separation. A multi-modal anisotropy score was calculated by adding the imaged area’s H&E combined anisotropy score with its respective SHG combined anisotropy score. This analysis was done on eight randomly selected ductal areas for each imaging modality on a slide and correlated with the measured areas of density subtypes from the whole mammographic view. Linear regression was used for determining correlation between H&E and SHG anisotropy factors as well as with active and passive mammographic density subtype measurements. Results: The malignant patients’ small-scale H&E anisotropy factor positively correlated with their small scale SHG anisotropy factor (R2=0.571). No correlation was found for the benign patients (R2=0.011). The strongest correlations were found between benign patients’ mammographic passive (positive correlation) and active (negative correlation) dense tissues vs the H&E anisotropy scale-combined factor (R2=0.858 and R2=0.961, respectively). The largest malignant patient correlation was a negative relationship between SHG anisotropy scale-combined factor and overall mammographic density (inclusive of both active and passive dense tissue) (R2=0.891). The multi-modal anisotropy score correlated with overall mammographic density for both benign (positive correlation, R2=0.698) and malignant patients (negative correlation, R2=0.773). Combining the multi-modal anisotropy factor from SHG and H&E with the active dense tissue measurement using K-Means clustering, 5/5 malignant and 4/5 benign patients were correctly classified. Conclusion: Density in mammograms correlates with underlying quantitative changes in a patient’s tissue and collagen anisotropy. Combining both H&E and SHG analysis on tissue biopsy with active and passive density metrics from computational mammography leads to the best predictive potential than any one method on their own.

Small-scale Anisotropies of Cosmic Rays from Turbulent Flow

Within the classical convection–diffusion approximation, we show that the angular distribution of cosmic rays (CRs) in a highly turbulent flow may exhibit significant small-scale anisotropies. The CR intensity angular power spectrum C ℓ is then a direct reflection of interstellar turbulence, from which one expects C ℓ ∝ ℓ −γ−1 for ℓ ≫ 1, where γ is the power-law turbulence spectral index. Observations by IceCube and HAWC at TeV energies can be explained approximately with the Kolmogorov law γ = 5/3 with a convection velocity dispersion of 20 km s−1 on the scale of 10 pc.

Small-scale Cosmic-Ray Anisotropy Observed by the GRAPES-3 Experiment at TeV Energies

GRAPES-3 is a mid-altitude (2200 m) and near-equatorial (11.°4N) air shower array, overlapping in its field of view for cosmic-ray observations with experiments that are located in the Northern and Southern Hemispheres. We analyze a sample of 3.7 × 109 cosmic-ray events collected by the GRAPES-3 experiment between 2013 January 1 and 2016 December 31 with a median energy of ∼16 TeV for study of small-scale (<60°) angular-scale anisotropies. We observed two structures, labeled A and B, that deviate from the expected isotropic distribution of cosmic rays in a statistically significant manner. Structure A spans 50°–80° in R.A. and from −15° to 30° in decl. The relative excess observed in structure A is at the level of (6.5 ± 1.3) × 10−4 with a statistical significance of 6.8 standard deviations. Structure B is observed in the R.A. range 110°–140° and at decl. from −10° to 30°. The relative excess observed in this region is at the level of (4.9 ± 1.4) × 10−4 with a statistical significance of 4.7 standard deviations. These structures are consistent with those reported by Milagro, ARGO-YBJ, and HAWC. These observations could provide a better understanding of the sources of cosmic rays, their propagation, and the magnetic structures in our Galaxy.

Passive scalar small-scale anisotropy and mixing characteristics in magnetohydrodynamic turbulent channel flow

In wall-bounded turbulent flows, both velocity and scalar fluctuations exhibit inhomogeneity and anisotropy. This study investigates the statistical properties of the small-scale scalar fluctuations in a turbulent channel flow at Reτ≈585 using direct numerical simulations with and without a magnetic field. The influence of the Hartmann, Ha, and Prandtl, Pr, numbers on turbulent velocity and passive scalar fields is examined at Ha=0, 20, and 40 and Pr=0.7 and 1.4. Small-scale dynamics of the passive scalar and velocity fields are studied, analyzing their probability density functions and higher-order moments, as well as their gradients. We observed that the magnetic field substantially changes flow dynamics such as the typical cliff-and-ramp type structures. The presence of the magnetic field led to statistical anisotropy, even at small-scale gradient fields. The findings reveal that the skewness of the normal derivative of scalar fluctuations remains at the order of 2. We investigated mixing characteristics by analyzing scalar dissipation rates. Scalar dissipation rates near the wall remain close to unity and decrease sharply toward the channel center, reaching a minimum value. Moreover, an increase in scalar dissipation rates leads to a decrease in the corresponding mixing timescale of the flow. This could suggest a connection between an increase in the Lorentz force and potential adjustments in the mixing timescale, potentially contributing to enhance overall mixing. Additionally, we argue that combined effects of strong intermittency and persistency of anisotropy at small scales can influence the mixing characteristics of magnetohydrodynamic turbulent flow.

Cosmology in Minkowski space

Theoretical and observational challenges to standard cosmology such as the cosmological constant problem and tensions between cosmological model parameters inferred from different observations motivate the development and search of new physics. A less radical approach to venturing beyond the standard model is the simple mathematical reformulation of our theoretical frameworks underlying it. While leaving physical measurements unaffected, this can offer a reinterpretation and even solutions of these problems. In this spirit, metric transformations are performed here that cast our Universe into different geometries. Of particular interest thereby is the formulation of cosmology in Minkowski space. Rather than an expansion of space, spatial curvature, and small-scale inhomogeneities and anisotropies, this frame exhibits a variation of mass, length and time scales across spacetime. Alternatively, this may be interpreted as an evolution of fundamental constants. As applications of this reframed cosmological picture, the naturalness of the cosmological constant is reinspected and promising candidates of geometric origin are explored for dark matter, dark energy, inflation and baryogenesis. An immediate observation thereby is the apparent absence of the cosmological constant problem in the Minkowski frame. The formalism is also applied to identify new observable signatures of conformal inhomogeneities, which have been proposed as simultaneous solution of the observational tensions in the Hubble constant, the amplitude of matter fluctuations, and the gravitational lensing amplitude of cosmic microwave background anisotropies. These are found to enhance redshifts to distant galaxy clusters and introduce a mass bias with cluster masses inferred from gravitational lensing exceeding those inferred kinematically or dynamically.

Heterogeneous seismic anisotropy beneath Madeira and Canary archipelagos revealed by local and teleseismic shear wave splitting

SUMMARYMid-plate upward mantle flow is a key component of global mantle convection, but its patterns are poorly constrained. Seismic anisotropy is the most direct way to infer mantle flow as well as melt distribution, yet the convection patterns associated with plume-like mantle upwelling are understudied due to limited seismic data coverage. Here, we investigate seismic anisotropy beneath the Madeira and Canary hotspots using a dense set of shear wave splitting observations and combining teleseismic and local events recorded by three-component broad-band and short-period seismic stations. Using a total of 26 stations in the Madeira archipelago and 43 stations around the Canary Islands, we obtain 655 high-quality measurements that reveal heterogeneous flow patterns. Although local event results are sparse around most islands, we can observe a small average of S-wave splitting times of 0.16 ± 0.01 s, which significantly increase with source depth beneath El Hierro (&amp;gt;20 km) and Tenerife (&amp;gt;38 km) up to 0.58 ± 0.01 and 0.47 ± 0.05 s. This suggests an influence of melt pocket orientation in magma reservoirs developed at uppermost-mantle depths. Likewise, anisotropy increases significantly beneath the islands with shield stage volcanism (up to 9.81 ± 1.78 per cent at El Hierro, western Canaries, against values up to 1.76 ± 0.73 per cent at Lanzarote, eastern Canaries). On average, teleseismic SKS-wave splitting delay times are large (2.19 ± 0.05 s), indicating sublithospheric mantle flow as the primary source for anisotropy in the region. In the Canaries, the western islands show significantly smaller average SKS delay times (1.93 ± 0.07 s) than the eastern ones (2.25 ± 0.11 s), which could be explained by destructive interference above the mantle upwelling. Despite complex patterns of fast polarization directions throughout both regions, some azimuthal pattern across close stations can be observed and related to present-day mantle flow and anisotropy frozen in the lithosphere since before 60 Ma. Additionally, we infer that the current presence of a mantle plume beneath the archipelagos leads to the associated complex, small-scale heterogeneous anisotropy observations.

Redshift-space fluctuations in stochastic gravitational wave background

We study the redshift-space fluctuations induced by a stochastic gravitational wave background (SGWB) via the Sachs-Wolfe effect. The redshift-space fluctuations can be encapsulated in a line-of-sight integral that is useful for studying the imprint of short-wavelength gravitational waves on the cosmic microwave background (CMB) anisotropy. We thus derive constraints on the SGWB from small-scale CMB anisotropy measurements. Our results reproduce the constraint on the short-wavelength SGWB, previously derived from the Planck and BICEP/Keck array CMB data with a CMB Boltzmann numerical code. Furthermore, we improve the constraint and extend it to shorter wavelengths by using the CMB measurements made by the Atacama Cosmology Telescope and the South Pole Telescope. Also, the integral provides us with a precise redshift fluctuation correlation between a pair of pulsars in pulsar timing measurements, which conveniently incorporates the effect of the pulsar term into a small-angle correlation. We further discuss the observation of pulsar pairs in globular clusters to look for this small-angle correlation.

Diffusion of turbulence following both stable and unstable step stratification perturbations

The evolution of a two-phase, air and unsaturated water vapor, time-decaying, shearless, and turbulent layer has been studied in the presence of both stable and unstable perturbations of the normal temperature lapse rate. The top interface between a warm vapor cloud and clear air in the absence of water droplets was considered as the reference dynamics. Direct, three-dimensional, and numerical simulations were performed within a 6 × 6-m-wide and 12-m-high domain, which was hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor microscale Reynolds number was 250 inside the cloud portion. The squared Froude's number varied over intervals of [0.4; 981.6] and [−4.0; −19.6]. A sufficiently intense stratification was observed to change the mixing dynamics. The formation of a sublayer inside the shearless layer was observed. The sublayer, under a stable thermal stratification condition, behaved like a pit of kinetic energy. However, it was observed that kinetic energy transient growth took place under unstable conditions, which led to the formation of an energy peak just below the center of the shearless layer. The scaling law of the energy time-variation inside the interface region was quantified: this is an algebraic law with an exponent that depends on the perturbation stratification intensity. The presence of an unstable stratification increased the differences in statistical behavior among the longitudinal velocity derivatives, compared with the unstratified case. Since the mixing process is suppressed in stable cases, small-scale anisotropy is also suppressed.

The extragalactic γ-ray background: imprints from the physical properties and evolution of star-forming galaxy populations

ABSTRACT Star-forming galaxies (SFGs) harbour an abundant reservoir of cosmic rays (CRs). At GeV energies, these CRs undergo interactions with their environment to produce γ-rays, and the unresolved γ-ray emission from populations of SFGs form a component of the isotropic extragalactic γ-ray background (EGB). In this work, we investigate the contribution to the 0.01–50 GeV EGB from SFG populations located up to redshift z = 3. We find this is dominated by starbursts, while the contribution from main-sequence SFGs is marginal at all energies. We also demonstrate that most of the γ-ray contribution from SFGs emanates from low-mass galaxies, with over 80 per cent of the emission originating from galaxies with stellar masses below $10^8 \, {\rm M}_{\odot }$. Many of these galaxies are located at relatively high redshift, with their peak EGB contribution arising ∼700 Myr before the noon of cosmic star formation. We find that the precise redshift distributions of EGB sources at different energies imprint intensity signatures at different angular scales, which may allow their contribution to be distinguished using analyses of small-scale EGB intensity anisotropies, particularly if the diffuse EGB is dominated by hadronic CR-driven γ-ray emission from SFGs. We show that the EGB is sensitive to the evolution of low-mass populations of galaxies, particularly around z ∼ 2.5, and that it provides a new means to probe the engagement of CRs in these galaxies before the high noon of cosmic star formation.

No Longer Ballistic, Not Yet Diffusive—the Formation of Cosmic-Ray Small-scale Anisotropies

Abstract The arrival directions of TeV-PeV cosmic rays are remarkably uniform due to the isotropization of their directions by scattering on turbulent magnetic fields. Small anisotropies can exist in standard diffusion models, however, only on the largest angular scales. Yet, high-statistics observatories like IceCube and High-Altitude Water Cherenkov Observatory have found significant deviations from isotropy down to small angular scales. Here, we explain the formation of small-scale anisotropies by considering pairs of cosmic rays that get correlated by their transport through the same realization of the turbulent magnetic field. We argue that the formation of small-scale anisotropies is the reflection of the particular realization of the turbulent magnetic field experienced by cosmic rays on timescales intermediate between the early, ballistic regime and the late, diffusive regime. We approach this problem in two different ways: First, we run test particle simulations in synthetic turbulence, covering for the first time the TV rigidities of observations with realistic turbulence parameters. Second, we extend the recently introduced mixing matrix approach and determine the steady-state angular power spectrum. Throughout, we adopt magneto-static, slab-like turbulence. We find excellent agreement between the predicted angular power spectra in both approaches over a large range of rigidities. In the future, measurements of small-scale anisotropies will be valuable in constraining the nature of the turbulent magnetic field in our Galactic neighborhood.

Small-scale CMB anisotropies induced by the primordial magnetic fields

The primordial magnetic fields (PMFs) produced in the early universe are expected to be the origin of the large-scale cosmic magnetic fields. The PMFs are considered to leave a footprint on the cosmic microwave background (CMB) anisotropies due to both the electromagnetic force and gravitational interaction. In this paper, we investigate how the PMFs affect the CMB anisotropies on smaller scales than the mean-free-path of the CMB photons. We solve the baryon Euler equation with Lorentz force due to the PMFs, and we show that the vector-type perturbations from the PMFs induce the CMB anisotropies below the Silk scale as ℓ > 3000. Based on our calculations, we put a constraint on the PMFs from the combined CMB temperature anisotropies obtained by Planck and South Pole Telescope (SPT). We have found that the highly-resolved temperature anisotropies of the SPT 2017 bandpowers at ℓ ≲ 8000 favor the PMF model with a small scale-dependence. As a result, the Planck and SPT's joint-analysis puts a constraint on the PMF strength normalized on the co-moving 1 Mpc scale as B1Mpc < 1.5 nG with Planck and SPT at 95% C.L., while B1Mpc < 3.2 nG only with the Planck data at 95% C.L. We also discuss the effects on the cosmological parameter estimate when including the SPT data and CMB anisotropies induced by the PMFs.

Optimal filters for the moving lens effect

We assess the prospects for detecting the moving lens effect using cosmological surveys. The bulk motion of cosmological structure induces a small-scale dipolar temperature anisotropy of the cosmic microwave radiation (CMB), centered around halos and oriented along the transverse velocity field. We introduce a set of optimal filters for this signal, and forecast that a high significance detection can be made with upcoming experiments. We discuss the prospects for reconstructing the bulk transverse velocity field on large scales using matched filters, finding good agreement with previous work using quadratic estimators.

Cosmic ray transport in mixed magnetic fields and their role on the observed anisotropies

ABSTRACT There is a growing set of observational data demonstrating that cosmic rays exhibit small-scale anisotropies (5°–30°) with amplitude deviations lying between 0.01–0.1 per cent that of the average cosmic ray flux. A broad range of models have been proposed to explain these anisotropies ranging from finite-scale magnetic field structures to dark matter annihilation. The standard diffusion transport methods used in cosmic ray propagation do not capture the transport physics in a medium with finite-scale or coherent magnetic field structures. Here, we present a Monte Carlo transport method, applying it to a series of finite-scale magnetic field structures to determine the requirements of such fields in explaining the observed cosmic ray, small-scale anisotropies.

H0 tension or T0 tension?

We study if the discrepancy between the local and cosmological measurements of the Hubble constant $H_0$ can be reformulated as a tension in the cosmic microwave background (CMB) monopole temperature $T_0$. The latter is customarily fixed to the FIRAS best-fit value in CMB data analyses. Although this value was confirmed by several independent experiments, it is interesting to see how much parameter constraints depend on this prior. We first provide a detailed pedagogical description of the $T_0$ effects on cosmological observables. We show that the recombination history and transfer functions do not depend on $T_0$, provided they are parametrized by the energy scale rather than redshift, and at fixed dark matter and baryon densities per CMB photon. Thus, $T_0$ is only a property of the observer, quantifying the amount of expansion between key cosmological events and today. As a consequence, the sole effect of $T_0$ on small-scale primary CMB anisotropies is through the angular diameter distance to the epoch of last scattering, resulting in a near-perfect degeneracy between $T_0$ and $H_0$. This geometric degeneracy is partially lifted by the late-time integrated Sachs-Wolfe effect and CMB lensing. Still, Planck data alone is consistent with a broad region in the $H_0-T_0$ plane, implying that removing the FIRAS prior on $T_0$ can make Planck and SH0ES less discrepant, without introducing new physics beyond $\Lambda$CDM. One may break the degeneracy by combining Planck with SH0ES, yielding an independent measurement of $T_0$, which happens to be in $3\sigma$ tension with FIRAS. Therefore, the Hubble tension indeed can be recast into the $T_0$ tension. The agreement with FIRAS is restored when combining Planck with the baryon acoustic oscillation data instead of SH0ES. Thus, the tension between SH0ES and cosmological measurements of $H_0$ persists even if we discard the FIRAS $T_0$ prior.

Direct numerical simulation of turbulent flow through a ribbed square duct

Abstract

Widespread Small-Scale Anisotropic Structure in the Lowermost Mantle beneath the North American Continent and Northeastern Pacific

Abstract We constrain D″ anisotropy beneath the North American continent and northeastern Pacific using two approaches: (1) joint splitting analysis of SKS and SKKS phase pair for a common event, in which we obtain 158 pairs exhibiting discrepant splitting results and 791 pairs nondiscrepant splitting results; and (2) group splitting analysis of SKS (or SKKS) phase from neighboring events recorded at a common station, in which we observe 109 2°×2° grids with consistent splitting parameters, and 164 grids with abrupt changes from splitting to no splitting within 30–100 km. The seismic data from both analyses indicate that small-scale variations of D″ anisotropy are widespread beneath the studied regions, with a lateral scale up to tens of kilometers. For portion of the data recorded at the stations of simple upper-mantle anisotropy, we correct for the effects of upper-mantle anisotropy and obtain the splitting parameters of D″ anisotropy. The inferred D″ anisotropy exhibits a changing geographic pattern and lateral transition of anisotropy to a lateral scale of tens of kilometers. Such a length scale of changing anisotropy is also confirmed by synthetics modeling of the seismic data. We suggest that the inferred small-scale anisotropies could be best explained by the shape preferred orientation of widespread small-scale partial melt pockets derived by a composition change produced early in the Earth’s history, a similar compositional origin that was invoked to explain the African anomaly in the lower mantle.

Reducing the background anisotropy by using hexagonal Fourier transform in two-dimensional turbulent flows

The two-dimensional hexagonal Fourier transform is introduced to reduce the background anisotropy in the numerical calculations with periodic conditions. Comparing to traditional Fourier transform with cartesian mesh, the large-scale background anisotropy is significantly reduced under different energy spectra. In addition, the phenomenon of small-scale background anisotropy is found to be related to the type of low-pass filter. Considering the standard deviation of second-order velocity correlation function with fixed two-point distance, the scaling at small scales is a result of Taylor expansion, while the scaling at large scales can be explained by using a simplified single-wavenumber analytical model. The hexagonal Fourier transform can be easily implemented by using fast Fourier transform (FFT) libraries, and is expected to be applied in future pseudo-spectral methods of two-dimensional and quasi-three-dimensional turbulent flows to minimize the background anisotropy.

Multiscale Characterizations of Surface Anisotropies.

Anisotropy can influence surface function and can be an indication of processing. These influences and indications include friction, wetting, and microwear. This article studies two methods for multiscale quantification and visualization of anisotropy. One uses multiscale curvature tensor analysis and shows anisotropy in horizontal coordinates i.e., topocentric. The other uses multiple bandpass filters (also known as sliding bandpass filters) applied prior to calculating anisotropy parameters, texture aspect ratios (Str) and texture directions (Std), showing anisotropy in horizontal directions only. Topographies were studied on two milled steel surfaces, one convex with an evident large scale, cylindrical form anisotropy, the other nominally flat with smaller scale anisotropies; a µEDMed surface, an example of an isotropic surface; and an additively manufactured surface with pillar-like features. Curvature tensors contain the two principal curvatures, i.e., maximum and minimum curvatures, which are orthogonal, and their directions, at each location. Principal directions are plotted for each calculated location on each surface, at each scale considered. Histograms in horizontal coordinates show altitude and azimuth angles of principal curvatures, elucidating dominant texture directions at each scale. Str and Std do not show vertical components, i.e., altitudes, of anisotropy. Changes of anisotropy with scale categorically failed to be detected by traditional characterization methods used conventionally. These multiscale methods show clearly in several representations that anisotropy changes with scale on actual surface measurements with markedly different anisotropies.