Anisotropic Scaling Research Articles

A global analysis of the fractal properties of clouds revealing anisotropy of turbulence across scales

Abstract. The deterministic motions of clouds and turbulence, despite their chaotic nature, have nonetheless been shown to follow simple statistical power-law scalings: a fractal dimension D relates individual cloud perimeters p to a measurement resolution, and turbulent fluctuations scale with the air parcel separation distance through the Hurst exponent, ℋ. However, it remains uncertain whether atmospheric turbulence is best characterized by a split isotropy that is three-dimensional (3D) with H=1/3 at small scales and two-dimensional (2D) with ℋ=1 at large scales or by a wide-range anisotropic scaling with an intermediate value of ℋ. Here, we introduce an “ensemble fractal dimension” De – analogous to D – that relates the total cloud perimeter per domain area 𝒫 as seen from space to the measurement resolution, and we show theoretically how turbulent dimensionality and cloud edge geometry can be linked through H=De-1. Observationally and numerically, we find the scaling De∼5/3 or H∼2/3, spanning 5 orders of magnitude of scale. Remarkably, the same scaling relationship links two “limiting case” estimates of 𝒫 evaluated at resolutions corresponding to the planetary scale and the Kolmogorov microscale, which span 10 orders of magnitude. Our results are nearly consistent with a previously proposed “23/9D” anisotropic turbulent scaling and suggest that the geometric characteristics of clouds and turbulence in the atmosphere can be easily tied to well-known planetary physical parameters.

Explainable artificial intelligence on safe balance and its major determinants in stroke patients

This study develops explainable artificial intelligence for predicting safe balance using hospital data, including clinical, neurophysiological, and diffusion tensor imaging properties. Retrospective data from 92 first-time stroke patients from January 2016 to June 2023 was analysed. The dependent variables were independent mobility scores, i.e., Berg Balance Scales with 0 (45 or below) vs. 1 (above 45) measured after three and six months, respectively. Twenty-nine predictors were included. Random forest variable importance was employed for identifying significant predictors of the Berg Balance Scale and testing its associations with the predictors, including Berg Balance Scale after one month and corticospinal tract diffusion tensor imaging properties. Shapley Additive Explanation values were calculated to analyse the directions of these associations. The random forest registered a higher or similar area under the curve compared to logistic regression, i.e., 91% vs. 87% (Berg Balance Scale after three months), 92% vs. 92% (Berg Balance Scale after six months). Based on random forest variable importance values and rankings: (1) Berg Balance Scale after three months has strong associations with Berg Balance Scale after one month, Fugl-Meyer assessment scale, ipsilesional corticospinal tract fractional anisotropy, fractional anisotropy laterality index and age; (2) Berg Balance Scale after six months has strong relationships with Fugl-Meyer assessment scale, Berg Balance Scale after one month, ankle plantar flexion muscle strength, knee extension muscle strength and hip flexion muscle strength. These associations were positive in the SHAP summary plots. Including Berg Balance Scale after one month, Fugl-Meyer assessment scale or ipsilesional corticospinal tract fractional anisotropy in the random forest will increase the probability of Berg Balance Scale after three months being above 45 by 0.11, 0.08, or 0.08. In conclusion, safe balance after stroke strongly correlates with its initial motor function, Fugl-Meyer assessment scale, and ipsilesional corticospinal tract fractional anisotropy. Diffusion tensor imaging information aids in developing explainable artificial intelligence for predicting safe balance after stroke.

Early and late observational tension: dark energy parametrizations in horava-lifshitz gravity via baryon acoustic oscillations

We investigate late-time cosmic expansion within the Horava Lifshitz gravity framework using Barboza Alcaniz (BA) and Jassal Bagla Padmanabhan Parametrizations (JBP) as alternatives to general relativity. Anisotropic scaling is introduced at ultraviolet scales. Our aim is to constrain each cosmological parameter using the crucial Baryon Acoustic Oscillation (BAO) scale, specifically the sound horizon (r d ), by treating (r d ) as a free parameter. We employ 30 Hubble parameter measurements (H(z)) from cosmic chronometers, along with Type Ia Supernovae, Gamma-Ray Bursts, Quasars, and 24 uncorrelated BAO measurements spanning z = 0.106 to z = 2.33. The analysis includes the 2022 Hubble constant measurement by Riess (R22) as an additional prior and aims to minimize errors by simulating random correlations in the covariance matrix. In both the BA and JBP frameworks, utilizing the full dataset yields sound horizon results of r d = 146.5399 ± 2.4519 Mpc and r d = 146.4533 ± 2.4519 Mpc, respectively. When incorporating R22 results, the sound horizon values become r d = 143.4721 ± 1.8324 Mpc and r d = 142.9826 ± 1.9084 Mpc. These findings reveal a discrepancy between early and late observations, echoing the H 0 tension. Notably, excluding R22 aligns r d with Planck and SDSS results. Model predictions are evaluated against Hubble Measurements and the ΛCDM Paradigm. A comparative study between BA and JBP Models using the Cosmography test shows both models fitting seamlessly within the phantom region. Statistical analysis suggests neither model can be ruled out based on the latest observational measurements.

Baryon Acoustic Oscillation Theory and Modelling Systematics for the DESI 2024 results

Abstract This paper provides a comprehensive overview of how fitting of Baryon Acoustic Oscillations (BAO) is carried out within the upcoming Dark Energy Spectroscopic Instrument’s (DESI) 2024 results using its DR1 dataset, and the associated systematic error budget from theory and modelling of the BAO. We derive new results showing how non-linearities in the clustering of galaxies can cause potential biases in measurements of the isotropic (αiso) and anisotropic (αap) BAO distance scales, and how these can be effectively removed with an appropriate choice of reconstruction algorithm. We then demonstrate how theory leads to a clear choice for how to model the BAO and develop, implement and validate a new model for the remaining smooth-broadband (i.e., without BAO) component of the galaxy clustering. Finally, we explore the impact of all remaining modelling choices on the BAO constraints from DESI using a suite of high-precision simulations, arriving at a set of best-practices for DESI BAO fits, and an associated theory and modelling systematic error. Overall, our results demonstrate the remarkable robustness of the BAO to all our modelling choices and motivate a combined theory and modelling systematic error contribution to the post-reconstruction DESI BAO measurements of no more than 0.1% (0.2%) for its isotropic (anisotropic) distance measurements. We expect the theory and best-practices laid out to here to be applicable to other BAO experiments in the era of DESI and beyond.

Improved Dementia Prediction in Cerebral Small Vessel Disease Using Deep Learning-Derived Diffusion Scalar Maps From T1.

Cerebral small vessel disease is the most common pathology underlying vascular dementia. In small vessel disease, diffusion tensor imaging is more sensitive to white matter damage and better predicts dementia risk than conventional magnetic resonance imaging sequences, such as T1 and fluid attenuation inversion recovery, but diffusion tensor imaging takes longer to acquire and is not routinely available in clinical practice. As diffusion tensor imaging-derived scalar maps-fractional anisotropy (FA) and mean diffusivity (MD)-are frequently used in clinical settings, one solution is to synthesize FA/MD from T1 images. We developed a deep learning model to synthesize FA/MD from T1. The training data set consisted of 4998 participants with the highest white matter hyperintensity volumes in the UK Biobank. Four external validations data sets with small vessel disease were included: SCANS (St George's Cognition and Neuroimaging in Stroke; n=120), RUN DMC (Radboud University Nijmegen Diffusion Tensor and Magnetic Resonance Imaging Cohort; n=502), PRESERVE (Blood Pressure in Established Cerebral Small Vessel Disease; n=105), and NETWORKS (n=26), along with 1000 normal controls from the UK Biobank. The synthetic maps resembled ground-truth maps (structural similarity index >0.89 for MD maps and >0.80 for FA maps across all external validation data sets except for SCANS). The prediction accuracy of dementia using whole-brain median MD from the synthetic maps is comparable to the ground truth (SCANS ground-truth c-index, 0.822 and synthetic, 0.821; RUN DMC ground truth, 0.816 and synthetic, 0.812) and better than white matter hyperintensity volume (SCANS, 0.534; RUN DMC, 0.710). We have developed a fast and generalizable method to synthesize FA/MD maps from T1 to improve the prediction accuracy of dementia in small vessel disease when diffusion tensor imaging data have not been acquired.

Time-dependent scalings and Fock quantization of a massless scalar field in Kantowski–Sachs

Abstract We address the issue of inequivalent Fock representations in quantum field theory in a curved homogenous and anisotropic cosmological background, namely Kantowski–Sachs spacetime, which can also be used to describe the interior of a nonrotating black hole. A family of unitarily equivalent Fock representations that are invariant under the spatial isometries and implement a unitary dynamics can be achieved by means of a field redefinition that consists of a specific anisotropic scaling of the field configuration and a linear transformation of its momentum. Remarkably, we show that this kind of field redefinition is in fact unique under our symmetry and unitary requirements. However, the physical properties of the Hamiltonian dynamics that one obtains in this way are not satisfactory, inasmuch as the action of the Hamiltonian on the corresponding particle states is ill defined. To construct a quantum theory without this problem, we need a further canonical transformation that is time- and mode-dependent and is not interpretable as an anisotropic scaling. The old and new Fock representations, nevertheless, are unitarily equivalent. The freedom that is introduced when allowing for this further canonical transformation can be fixed by demanding an asymptotic diagonalization of the Hamiltonian and a minimal absorption of dynamical phases. In this way, the choice of vacuum and the associated Fock representation are asymptotically determined.

Neural Gaussian Scale-Space Fields

Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in particular for continuous representations such as neural fields. We present an efficient and lightweight method to learn the fully continuous, anisotropic Gaussian scale space of an arbitrary signal. Based on Fourier feature modulation and Lipschitz bounding, our approach is trained self-supervised, i.e., training does not require any manual filtering. Our neural Gaussian scale-space fields faithfully capture multiscale representations across a broad range of modalities, and support a diverse set of applications. These include images, geometry, light-stage data, texture anti-aliasing, and multiscale optimization.

Cosmological test of dark energy parametrizations within the framework of Horava-Lifshitz gravity via baryon acoustic oscillation

We conduct an investigation to explore late-time cosmic acceleration through various dark energy parametrizations (Wettrich, Efstathiou, and Ma-Zhang) within the Horava-Lifshitz gravity framework. As an alternative to general relativity, this theory introduces anisotropic scaling at ultraviolet scales. Our primary objective is to constrain the key cosmic parameters and baryon acoustic oscillation (BAO) scale, specifically the sound horizon (rd ), by utilizing 24 uncorrelated measurements of BAOs derived from recent galaxy surveys spanning a redshift range from z = 0.106 to z = 2.33. Additionally, we integrate the most recent Hubble constant measurement by Riess in 2022 (denoted as R22) as an extra prior. For the parametrizations of Wettrich, Efstathiou, and Ma-Zhang, our analysis of BAO data yields sound horizon results of rd = 148.1560 ± 2.7688 Mpc, rd = 148.6168 ± 10.2469 Mpc, and rd = 147.9737 ± 10.6096 Mpc, respectively. Incorporating the R22 prior into the BAO dataset results in rd = 139.5806 ± 3.8522 Mpc, rd = 139.728025 ± 2.7858 Mpc, and rd = 139.6001 ± 2.7441 Mpc. These outcomes highlight a distinct inconsistency between early and late observational measurements, analogous to the H 0 tension. A notable observation is that, when we do not include the R22 prior, the outcomes for rd tend to be in agreement with Planck and SDSS results. Following this, we conducted a cosmography test and comparative study of each parametrization within the Lambda Cold Dark Matter paradigm. Our diagnostic analyses demonstrate that all models fit seamlessly within the phantom region. All dark energy parametrizations predict an equation of state parameter close to = –1, indicating a behavior similar to that of a cosmological constant. The statistical analysis indicates that neither of the two models can be ruled out based on the latest observational measurements.

Introducing emissivity directionality to the temperature-emissivity separation algorithm

Natural surfaces are mostly anisotropic emitters, contributing to the anisotropic behavior of Land Surface Temperature (LST). This characteristic of thermal infrared emissivity is well known and several studies have tried to simulate this behavior either with physical or empirical models. However, given the high heterogeneity of land surfaces, the translation of the angular dependence of emissivity as provided from measurements or models into satellite pixel scale anisotropy is generally very difficult. Here we propose a reformulation of the Mean Minimum-Maximum Difference (MMD) curve of the Temperature-Emissivity Separation (TES) algorithm to allow a correct adjustment of the TES retrievals by taking into account the emissivity angular distribution. For that purpose, the Multi-Sensor method is used to obtain directional emissivities at different sites in the Saharan and Namib desert. The data is then used to calibrate the view-angle dependence of the new MMD formulation. The TES retrievals obtained with the new formulation show a good agreement with the Multi-Sensor data. Results also suggest that the new coefficients of the MMD can be applied to other sensors with similar spectral channels. The new angle-dependent emissivities may lead to a reduction of LST bias as high as 2 K for view angles above 50o. The proposed formulation is currently only valid over barren surfaces.

What can be learnt from UHECR anisotropies observations

Context. Various signals of anisotropy of the ultra-high-energy cosmic rays (UHECRs) have recently been reported, whether at large angular scales, with a dipole modulation in right ascension observed in the data of the Pierre Auger observatory (Auger), as discussed in the first paper accompanying the present one, or at intermediate angular scales, with flux excesses identified in specific directions by Auger and the Telescope Array (TA) Collaborations. Aims. We investigated the implications of the current data regarding these intermediate scale anisotropies, and examined to what extent they can be used to shed light on the origin of UHECRs, and constrain the astrophysical and/or physical parameters of the viable source scenarios. We also investigated what could be learnt from the study of the evolution of the various UHECR anisotropy signals, and discussed the expected benefit of an increased exposure of the UHECR sky using future observatories. Methods. We simulated realistic UHECR sky maps for a wide range of astrophysical scenarios satisfying the current observational constraints, with the assumption that the UHECR source distribution follows that of the galaxies in the Universe, also implementing possible biases towards specific classes of sources. In each case, several scenarios were explored with different UHECR source compositions and spectra, a range of source densities and different models of the Galactic magnetic field. We also implemented the Auger sky coverage, and explored various levels of statistics. For each scenario, we produced 300 independent datasets on which we applied similar analyses as those recently used by the Auger Collaboration, searching for flux excesses through either blind or targeted searches and quantifying correlations with predefined source catalogues through a likelihood analysis. Results. We find the following. First, with reasonable choices of the parameters, the investigated astrophysical scenarios can easily account for the significance of the anisotropies reported by Auger, even with large source densities. Second, the direction in which the maximum flux excess is found in the Auger data differs from the region where it is found in most of our simulated datasets, although an angular distance as large as that between the Auger direction and the direction expected from the simulated models at infinite statistics, of the order of ∼20°, occurs in ∼25% of the cases. Third, for datasets simulated with the same underlying astrophysical scenario, and thus the same actual UHECR sources, the significance with which the isotropy hypothesis is rejected through the Auger likelihood analysis can be largest either when ‘all galaxies’ or when only ‘starburst’ galaxies are used to model the signal, depending on which model is used to model the Galactic magnetic field and the resulting deflections. Fourth, the study of the energy evolution of the anisotropy patterns can be very instructive and provide new astrophysical insight about the origin of the UHECRs. Fifth, the direction in which the most significant flux excess is found in the Auger dataset above 8 EeV appears to essentially disappear in the dataset above 32 EeV, and, conversely, the maximum excess at high energy has a much reduced significance in the lower energy dataset. Sixth, both of these appear to be very uncommon in the simulated datasets, which could point to a failure of some generic assumption in the investigated astrophysical scenarios, such as the dominance of one type of source with essentially the same composition and spectrum in the observed UHECR flux above the ankle. Seventh, given the currently observed level of anisotropy signals, a meaningful measurement of their energy evolution, say from 10 EeV to the highest energies, will require a significant increase in statistics and a new generation of UHECR observatories.

Postural control in gymnasts: anisotropic fractal scaling reveals proprioceptive reintegration in vestibular perturbation.

Dexterous postural control subtly complements movement variability with sensory correlations at many scales. The expressive poise of gymnasts exemplifies this lyrical punctuation of release with constraint, from coarse grain to fine scales. Dexterous postural control upon a 2D support surface might collapse the variation of center of pressure (CoP) to a relatively 1D orientation-a direction often oriented towards the focal point of a visual task. Sensory corrections in dexterous postural control might manifest in temporal correlations, specifically as fractional Brownian motions whose differences are more and less correlated with fractional Gaussian noises (fGns) with progressively larger and smaller Hurst exponent H. Traditional empirical work examines this arrangement of lower-dimensional compression of CoP along two orthogonal axes, anteroposterior (AP) and mediolateral (ML). Eyes-open and face-forward orientations cultivate greater variability along AP than ML axes, and the orthogonal distribution of spatial variability has so far gone hand in hand with an orthogonal distribution of H, for example, larger in AP and lower in ML. However, perturbing the orientation of task focus might destabilize the postural synergy away from its 1D distribution and homogenize the temporal correlations across the 2D support surface, resulting in narrower angles between the directions of the largest and smallest H. We used oriented fractal scaling component analysis (OFSCA) to investigate whether sensory corrections in postural control might thus become suborthogonal. OFSCA models raw 2D CoP trajectory by decomposing it in all directions along the 2D support surface and fits the directions with the largest and smallest H. We studied a sample of gymnasts in eyes-open and face-forward quiet posture, and results from OFSCA confirm that such posture exhibits the classic orthogonal distribution of temporal correlations. Head-turning resulted in a simultaneous decrease in this angle Δθ, which promptly reversed once gymnasts reoriented their heads forward. However, when vision was absent, there was only a discernible negative trend in Δθ, indicating a shift in the angle's direction but not a statistically significant one. Thus, the narrowing of Δθ may signify an adaptive strategy in postural control. The swift recovery of Δθ upon returning to a forward-facing posture suggests that the temporary reduction is specific to head-turning and does not impose a lasting burden on postural control. Turning the head reduced the angle between these two orientations, facilitating the release of postural degrees of freedom towards a more uniform spread of the CoP across both dimensions of the support surface. The innovative aspect of this work is that it shows how fractality might serve as a control parameter of adaptive mechanisms of dexterous postural control.

Enhancing undulation of soft robots in granular media: A numerical and experimental study on the effect of anisotropic scales

Generating efficient locomotion in granular media is important, although it is difficult for robots. Inspired by the fact that sand vipers usually have saw-like scales, in this study, we design a soft undulation robot with tangential anisotropic friction to enhance the undulation performance of soft robots in granular media. A mathematical model was derived and numerical simulations were conducted accordingly to investigate the effectiveness of tangential friction anisotropy for undulation gait generation in granular media. In particular, we introduce a pseudo-rigid-body dynamics model consisting of links and joints while simulating the pneumatic actuation method to more closely approximate the response of soft robots. Moreover, a soft snake-like robot was fabricated, and its forward and reverse undulations were compared in two sets of controlled experiments. The consistency between the experimental results and the numerical simulations confirms that tangential anisotropic friction induces a propulsive effect in undulation, thereby increasing the robot’s locomotion speed. This discovery provides new insights into the design of undulation robots in granular environments.

Early Evolution of Spin Direction in Dark Matter Halos and the Effect of the Surrounding Large-scale Tidal Field* *Thesis work conducted at Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Córdoba, Argentina. † † PhD Thesis directed by Manuel Merchán; PhD Degree awarded 2023 July 31.

It is usually assumed that the angular momentum (AM) of dark matter halos arises during the linear stages of structure formation, as a consequence of the coupling between the proto-haloes’ shape and the tidal field produced by their surrounding density perturbations. This approach, known as linear tidal torque theory (TTT), has been shown to make fairly good predictions about the mean evolution of both the AM amplitude and orientation up to approximately the time when the proto-haloes collapse. After this point, proto-haloes are increasingly affected by nonlinear processes that are not taken into account by the model. However, it has been seen in numerical simulations that, even at very early stages, the AM of proto-haloes is systematically reoriented toward perpendicularity with respect to the forming cosmic filaments, in contradiction with the fixed direction expected from the TTT. In this work we present a novel analytical approach that introduces an anisotropic scaling factor to the standard TTT equations, which allows the AM orientation to change in time, even during the linear regime. The amplitude and direction of this shift depend on the large scale tidal field around the forming proto-haloes. Our results significantly improve the predictions for the AM direction up to the time of protohalo collapse and, in some cases, even further in time.

Finite-size versus finite-temperature effects in the critical long-range O(N) model

In this paper we consider classical and quantum versions of the critical long-range O(N) model, for which we study finite-size and finite-temperature effects, respectively, at large N. First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub fractional Lifshitz field theory. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators.In both the classical and quantum model, we find that, as previously noted for the short-range O(N) model in [1], the large-N two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in 1/N, namely powers of the Hubbard-Stratonovich intermediate field.

Casimir effect of a rough membrane in 2 + 1 Hořava–Lifshitz theory

We investigate the Casimir effect of a rough membrane within the framework of the Hořava–Lifshitz theory in 2+1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2+1$$\\end{document} dimensions. Quantum fluctuations are induced by an anisotropic scalar field subject to Dirichlet boundary conditions. We implement a coordinate transformation to render the membrane completely flat, treating the remaining terms associated with roughness as a potential. The spectrum is obtained through perturbation theory and regularized using the ζ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\zeta $$\\end{document}-function method. We present an explicit example of a membrane with periodic border. Additionally, we consider the effect of temperature. Our findings reveal that the Casimir energy and force depend on roughness, the anisotropic scaling factor and temperature.

Anisotropic Scale-Invariant Ellipse Detection.

Detecting ellipses poses a challenging low-level task indispensable to many image analysis applications. Existing ellipse detection methods commonly encounter two fundamental issues. First, inferior detection accuracy could be incurred on a small ellipse than that on a large one; this introduces the scale issue. Second, inferior detection accuracy could be yielded along the minor axis than along the major one of the same ellipse; this leads to the anisotropy issue. To address these issues simultaneously, a novel anisotropic scale-invariant (ASI) ellipse detection methodology is proposed. Our basic idea is to perform ellipse detection in a transformed image space referred to as the ellipse normalization (EN) space, in which the desired ellipse from the original image is 'normalized' to the unit circle. With the establishment of the EN-space, an analytical ellipse fitting scheme and a set of distance measures are developed. Theoretical justifications are then derived to prove that both our ellipse fitting scheme and distance measures are invariant to anisotropic scaling, and thus each ellipse can be detected with the same accuracy regardless of its size and ellipticity. By incorporating these components into two recent state-of-the-art algorithms, two ASI ellipse detectors are finally developed and exploited to verify the effectiveness of our proposed methodology.

Maximal polynomial modulations of singular Radon transforms

We prove L2→Lp estimates on the torus for maximal polynomial modulations of Calderón-Zygmund operators with anisotropic scaling. We obtain improved constants in these estimates. As a corollary, maximal polynomial modulations of a mollified version of the Hilbert transform along the parabola are bounded with only logarithmic dependence of the estimate on the Lipschitz constant of the mollifier.

Influence of Intermittency on the Energy Transfer Rate of Solar Wind Turbulence

The intermittency in the solar wind turbulence manifests itself in the anisotropic scaling due to the anisotropic spectral index and the intermittent level based on the extended P model. However, the influence of intermittency on the energy transfer rate remains unclear. Here we apply the partial variance of increments method to identify the intermittency for the magnetic field measurements in the fast solar wind from the Ulysses spacecraft. We distinguish the sampling direction using the angle θ RB between the local magnetic field and radial direction to study the anisotropy. We perform the multiorder structure function analyses and adopt the log-Poisson cascade model to describe the role of intermittency in the cascade process. We find that the anisotropy of the scaling becomes isotropic with a complete removal of intermittency. We compare explicitly the anisotropy of the energy transfer rate before and after removing the intermittency for the same interval for the first time. We find a distinct anisotropy with a cascade enhancement in the direction perpendicular to the local magnetic field. The removal of the intermittency greatly weakens the anisotropy by mainly reducing the perpendicular energy transfer rate. Our findings suggest that the intermittency effectively enhances the energy transfer rate, in particular in the perpendicular direction in the solar wind turbulence.

Numerical analysis method of equivalent deformation parameters for grouted arch dam abutment fractured rock masses considering scale effects and anisotropy

Research on the equivalent deformation parameters of grouted arch dam abutment rock masses has recently emerged as a key in the design, construction and stability assessment of arch dams. With the aim of synthetically considering scale effects and anisotropy of the rock mass equivalent deformation parameters after grouting, in this paper, a practical numerical calculation method is developed. First, the Latin hypercube sampling method is introduced to generate a network of fractures of the arch dam abutment rock mass. Subsequently, the finite element models of the rock masses with different sizes in various directions are constructed. On this basis, equivalent continuum theory and cohesive element model are applied for numerical calculation of grouting fractured rock masses. Then, the scale effect and anisotropy of the deformation modulus of rock mass under different grouting conditions are investigated. Finally, the Jinping super-high arch dam is taken as an example to validate the theoretical significance and application effect of the proposed method. The analysis results indicate that the process of fracture and fragmentation of grouted rock masses is characterized precisely, and the deformation of material units can be described as fully as possible to calculate more realistic equivalent deformation parameters of the fractured rock masses.

Well-posed evolution of field theories with anisotropic scaling: the Lifshitz scalar field in a black hole space-time

Partial differential equations exhibiting an anisotropic scaling between space and time — such as those of Hořava-Lifshitz gravity — have a dispersive nature. They contain higher-order spatial derivatives, but remain second order in time. This is inconvenient for performing long-time numerical evolutions, as standard explicit schemes fail to maintain convergence unless the time step is chosen to be very small. In this work, we develop an implicit evolution scheme that does not suffer from this drawback, and which is stable and second-order accurate. As a proof of concept, we study the numerical evolution of a Lifshitz scalar field on top of a spherically symmetric black hole space-time. We explore the evolution of a static pulse and an (approximately) ingoing wave-packet for different strengths of the Lorentz-breaking terms, accounting also for the effect of the angular momentum eigenvalue and the resulting effective centrifugal barrier. Our results indicate that the dispersive terms produce a cascade of modes that accumulate in the region in between the Killing and universal horizons, indicating a possible instability of the latter.