Anisotropic Scaling Research Articles

Constraining the surface curvature of an anisotropic neutron star

The anisotropy of pressure arises due to the various complex phenomena that happen inside the neutron star (NS). In this study, we calculate the degree of anisotropy inside the NS using the scalar pressure anisotropy model. Macroscopic properties such as mass, radius, compactness, redshift, tidal deformability, the moment of inertia, and surface curvature (SC) are computed for the anisotropic NS with the equation of states spanning from relativistic to nonrelativistic cases. The variation of SC as the functions of the above-mentioned quantities are computed by changing the degree of anisotropy. Pressure anisotropy has significant effects on the magnitude of SC. The relations between the canonical $\mathrm{SC}\ensuremath{-}\mathrm{\ensuremath{\Lambda}}$ and $\mathrm{SC}\ensuremath{-}\overline{I}$ are studied. From the GW170817 tidal deformability data, we constraints the magnitude of SC are found to be ${\mathrm{SC}}_{1.4}({10}^{14})={3.44}_{\ensuremath{-}1.0}^{+0.4},{2.85}_{\ensuremath{-}1.20}^{+0.62},{2.52}_{\ensuremath{-}1.02}^{+0.61}$ for ${\ensuremath{\lambda}}_{\mathrm{BL}}=0.0$, 1.0, and 2.0, respectively.

Scaling Anisotropy with Stationary Background Field in Near-Sun Solar Wind Turbulence

The scaling of magnetic fluctuations provides crucial information for the understanding of solar wind turbulence. However, the observed magnetic fluctuations contain not only turbulence but also magnetic structures, leading to the violation of time stationarity. This violation would conceal the true scaling and influence the determination of the sampling angle with respect to the local background magnetic field. Here, to investigate scaling anisotropy, we utilize a simple but effective criterion ϕ < 10° to ensure the time stationarity of the magnetic field, where ϕ is the angle between the two averaged magnetic fields after cutting the interval into two halves. We study the scaling anisotropy using higher-order statistics of structure functions under the condition of stationarity for near-Sun solar wind turbulence for the first time based on measurements obtained from the Parker Solar Probe at 0.17 au. We find that the scaling indices ξ of the magnetic field show a linear dependence on the order p close to ξ(p) = p/4. The multifractal scaling of the magnetic-trace structure functions becomes monoscaling close to ξ(p) = p/3 with the local magnetic field perpendicular to the sampling direction and close to ξ(p) = p/4 with the local magnetic field parallel to the sampling direction when measured with the stationary background magnetic field. The scaling of the velocity-trace structure functions has similar but less significant changes. The near-Sun solar wind turbulence displays different scaling anisotropies from the near-Earth solar wind turbulence, suggesting the evolution of the nonlinear interaction process during solar wind expansion.

More on entanglement properties of $$Lif_4^{(2)}\times {S}^1\times S^5$$ spacetime with string excitations

The $$Lif_{4}^{(2)} \times S^1 \times S^5$$ spacetime is an exact solution of $$F1-D2-D8$$ configuration in type IIA supergravity and can accommodate charged excitations of the fundamental string. By gauge/gravity duality, it is related to an excited state of a non-relativistic QFT with anisotropic Lifshitz scaling symmetry. We study mutual and tripartite information and entanglement wedge cross section in bulk gravity for boundary subsystems that are disjoint strips of very narrow width. Our work helps understand the nature of entanglement in the QFT excited state, which is in general a mixed one.

MMC-LES of spray combustion: Analysis of mixing timescales and flame structure

Large-eddy simulations (LES) of turbulent, pilot-stabilised, dilute acetone spray flames are performed using the sparse-Lagrangian multiple mapping conditioning approach (MMC-LES). The primary objective of this work is to assess the adaptability of the recently proposed dynamically evaluated molecular mixing timescale model for MMC-LES (Sharma et al., 2022, A fully dynamic mixing timescale model for the sparse Lagrangian multiple mapping conditioning approach, Combustion and Flame, 238, 111872), referred to as the dyn-aISO model, to the non-reacting and reacting two-phase flows. This work is the first application to perform a dynamic evaluation of the mixing timescale for turbulent spray combustion using the transported filtered density function (FDF) approach. A non-reacting case and four reacting flames with varying fuel mass loading are investigated, where the flame transitions from a diffusion flame to a premixed flame structure with a decrease in fuel loading. As is conventional for MMC-LES, a sparse resolution of one stochastic particle per six Eulerian finite-volume cells is used in this study, offering a much cheaper computing expense than the conventional transported FDF approach. The liquid evaporation is represented based on a non-equilibrium model at the droplet surface. The reaction chemistry is based on an augmented GRI 3.0 mechanism containing 39 species and 226 reactions to represent the oxidation of acetone. Predictions with the dyn-aISO model are compared with the constant coefficient anisotropic mixing time scale model and the isotropic C-K model. Thorough validation of liquid-phase statistics and gas-phase temperature is performed with available experimental data and popular studies from the literature. Analysis of the flame structure, with different timescale models, for both non-premixed and premixed type flames is also carried out. Quantification of the parameters affecting the timescale, such as model constants of the sub-Lagrangian-grid scale (slgs) mixture fraction variance (Cf) and its scalar dissipation rate (Scsgs−1Cν) is provided in comparison to their conventionally chosen static coefficient values. Predictions with the dyn-aISO model are quite good for the diffusion-type flames, while some discrepancies are noticed while predicting a premixed flame structure for lower liquid loading case having near stoichiometric jet-exit mixture composition.

Efficient anisotropic scaling and translation invariants of Tchebichef moments using image normalization

Anisotropic scaling and translation invariants of Tchebichef moments are commonly used in image analysis to address issues arising from patterns distorted by non-uniform scaling and translation. In this paper, we formulate a new fast computational algorithm and a new normalization scheme based on the properties of Tchebichef moments. The proposed model can correctly resolve the mirror reflection ambiguities caused by the scaling transformations and gives smaller size deviations for various patterns so that the canonical form can easily fit within the normalized space. An empirical study shows that the proposed method significantly improves numerical computation and classification accuracy under non-noisy and noisy conditions when compared with existing methods. The main contribution of this paper is a novel fast computational algorithm for anisotropic scaling and translation invariants of Tchebichef moments and a new normalization scheme that produces features with higher discriminative power. The proposed algorithm is useful for recognizing objects with non-uniform size and displacement deformations. It is also a key component in formulating a better affine invariant algorithm for the image analysis community.

Scale dependency and anisotropy of mechanical properties of jointed rock masses: insights from a numerical study

Scale dependency and anisotropy of mechanical properties of jointed rock masses: insights from a numerical study

Predicting the Future Appearances of Lost Children for Information Forensics with Adaptive Discriminator-Based FLM GAN

This article proposes an adaptive discriminator-based GAN (generative adversarial network) model architecture with different scaling and augmentation policies to investigate and identify the cases of lost children even after several years (as human facial morphology changes after specific years). Uniform probability distribution with combined random and auto augmentation techniques to generate the future appearance of lost children’s faces are analyzed. X-flip and rotation are applied periodically during the pixel blitting to improve pixel-level accuracy. With an anisotropic scaling, the images were generated by the generator. Bilinear interpolation was carried out during up-sampling by setting the padding reflection during geometric transformation. The four nearest data points used to estimate such interpolation at a new point during Bilinear interpolation. The color transformation applied with the Luma flip on the rotation matrices spread log-normally for saturation. The luma-flip components use brightness and color information of each pixel as chrominance. The various scaling and modifications, combined with the StyleGan ADA architecture, were implemented using NVIDIA V100 GPU. The FLM method yields a BRISQUE score of between 10 and 30. The article uses MSE, RMSE, PSNR, and SSMIM parameters to compare with the state-of-the-art models. Using the Universal Quality Index (UQI), FLM model-generated output maintains a high quality. The proposed model obtains ERGAS (12 k–23 k), SCC (0.001–0.005), RASE (1 k–4 k), SAM (0.2–0.5), and VIFP (0.02–0.09) overall scores.

MEQA: Manifold embedding quality assessment via anisotropic scaling and Kolmogorov-Smirnov test

Manifold learning methods unfold the manifold structures and embed them in a lower-dimensional space. The quality of such an embedding should be measured both qualitatively and quantitatively. The proposed manifold embedding quality assessment (MEQA) method does so by taking into account of local and global structure preservation as both are important traits of an embedding. To measure the local structure preservation MEQA uses two transformations. Initially anisotropic scaling, rotation and translation are incorporated to measure the closeness between the original and the embedded data points. In the next stage, rigid transformation is incorporated to quantify the previous transformation which involved anisotropic scaling. For quantifying the global structure preservation, the Kolmogorov-Smirnov test is applied in a distributed manner over each dimension and averaged over them. To establish the superiority of MEQA we conducted several studies over standard synthetic and real-life datasets across separate existing feature extraction techniques.

Study of residual stresses and distortions from the Ti6Al4V based thin-walled geometries built using LPBF process

The current paper focuses on the prediction of residual stresses and distortions in the Laser Powder Bed Fusion (LPBF) built Ti6Al4V thin-walled geometries using Ansys Additive Print (AAP) software which employs a layer-by-layer accumulation of inherent strain to calculate the deformations. Isotropic and anisotropic strain scaling factors were calibrated initially within the APP software for the Ti6Al4V based single cantilever beam geometry. Subsequently, the numerical simulations were performed in APP software and computed the residual stresses and distortions for the varied process parameters including laser power, scan speed and hatch distance while maintaining the layer thickness constant for all the design iterations. The numerical predictions were compared; they were found to match reasonably well with the XRD measurements within the calibrated regime.

An Improved Tropospheric Tomographic Model Based on Artificial Neural Network

Global navigation satellite systems (GNSS) tropospheric tomography can be used to build a three-dimensional water vapor field. In traditional tomography, the signals crossing from the four sides of the tomographic region are not utilized. To make the best use of these valuable side-crossing signals, an improved tomographic model based on back propagation artificial neural network (BP-ANN) is proposed. In the new tomographic model, the inside part of the slant wet delay (SWD) of the side-crossing signal is divided into two sections: the isotropic and anisotropic components. The former is estimated by the zenith wet delay multiplied by the mapping function multiplied by an isotropic scale factor using a BP-ANN model, and the latter is estimated by horizontal gradients of the SWD multiplied by an anisotropic scale factor using an empirical model. The new tomographic model is experimentally evaluated using the HK CORS network measurements for the period of 21 days from 1 to 21 August 2019. Statistical results show that the root mean square error (RMSE) of slant water vapor reconstructed from the improved model is reduced to 1.35 from 2.85 mm of the traditional model. Compared with the traditional/height factor models, the percentages of the reduction in the RMSE of the tomographic result derived from the new model are 16%/9% and 22%/16%, respectively, using radiosonde and ERA5 data as references. These results suggest a good performance of the new model for GNSS tropospheric tomography.

Fractal fuzzy logic using Kelly plots

Strictly defined, the concept of self-similarity or self-similarity applies only to mathematical fractals - which arise from the iteration of simple formulae but lead to very complex structures, Cantor Dust, Peano Curve, Koch Snowflake, whereas in natural or physical fractals - those found in nature, such as a fern leaf, an arborisation, capillaries - the concept of self-similarity applies, since their fractality is only statistical and they possess, consequently, an anisotropic scaling,(not having the same properties in all dimensions of analysis), which does not allow an amplified part of a figure to maintain exactly the characteristics of the figure as a whole, is where we find Kelly plots.

Structure functions of turbulence through a degraded channel bed

This investigation deals with the turbulence characteristics for flow through degraded channel beds consisting of uniform and bimodal sediment particles. Three-dimensional velocity was measured throughout the depth at three different streamwise locations over a degraded bed. The velocity data were then processed to observe the spatial distributions of the longitudinal and vertical velocity components in vector form, turbulence indicator and length scales at different locations. The main intent of the present study was to observe the effect of bed degradation on the intermittency and anisotropy in higher order scaling exponents using the structure functions methodology. The extended self-similarity (ESS) technique was employed to estimate the scaling exponents from higher order structure functions of streamwise velocity component. The results show that below the bed-level (level of the bed surface measured before the degradation started), the scaling exponents deviate more from the theoretical values than that above the bed-level indicating higher intermittency of scaling exponents in the vicinity of the bed. Furthermore, data were analyzed to observe the scaling exponents from higher order mixed structure functions. To this end, the SO(3) symmetry decomposition was utilized to differentiate the isotropic and anisotropic parts of the scaling exponents. The anisotropic scaling exponents obtained from higher order mixed structure functions possess higher values than that of isotropic part. The experimental findings also specify that as one moves close to the degraded bed, the scaling exponents obtained from the higher order mixed structure functions deviate more significantly. However, according to the present experimental results, no significant differences were observed in the values of the scaling exponents and intermittency when they were compared between uniform and bimodal sedimentary beds. It is expected that the results of the present study will essentially lead to new contributions to the existing knowledge in the field of turbulence through degraded and scoured channel beds.

Gauss-Bonnet black holes in a special anisotropic scaling spacetime

Inspired by the Lifshitz gravity as a theory with anisotropic scaling behavior, we suggest a new (n + 1)-dimensional metric in which the time and spatial coordinates scale anisotropically as (t, r, θi) → (λzt, λ−1r, λxiθi). Due to the anisotropic scaling dimension of the spatial coordinates, this spacetime does not support the full Schrödinger symmetry group. We look for the analytical solution of Gauss-Bonnet gravity in the context of the mentioned geometry. We show that Gauss-Bonnet gravity admits an analytical solution provided that the constants of the theory are properly adjusted. We obtain an exact vacuum solution, independent of the value of the dynamical exponent z, which is a black hole solution for the pseudo-hyperbolic horizon structure and a naked singularity for the pseudo-spherical boundary. We also obtain another exact solution of Gauss-Bonnet gravity under certain conditions. After investigating some geometrical properties of the obtained solutions, we consider the thermodynamic properties of these topological black holes and study the stability of the obtained solutions for each geometrical structure.

I−Love−C relation for an anisotropic neutron star

One of the most common assumptions has been made that the pressure inside the star is isotropic in nature. However, the pressure is locally anisotropic in nature which is a more realistic case. In this study, we investigate certain properties of anisotropic neutron stars with the scalar pressure anisotropy model. Different perfect fluid conditions are tested within the star with the relativistic mean-field model equation of states (EOSs). The anisotropic neutron star properties such as mass ($M$), radius ($R$), compactness ($C$), Love number ($k_2$), dimensionless tidal deformability ($\Lambda$), and the moment of inertia ($I$) are calculated. The magnitude of the quantities as mentioned above increases (decreases) with the positive (negative) value of anisotropy except $k_2$ and $\Lambda$. The Universal relation $I-$Love$-C$ is calculated with almost 58 EOSs spans from relativistic to non-relativistic cases. We observed that the relations between them get weaker when we include anisotropicity. With the help of the GW170817 tidal deformability limit and radii constraints from different approaches, we find that the anisotropic parameter is less than 1.0 if one uses the BL model. Using the universal relation and the tidal deformability bound given by the GW170817, we put a theoretical limit for the canonical radius, $R_{1.4}=10.74_{-1.36}^{+1.84}$ km, and the moment of inertia, $I_{1.4} = 1.77_{-0.09}^{+0.17}\times10^{45}$ g cm$^2$ with 90\% confidence limit for isotropic stars. Similarly, for anisotropic stars with $\lambda_{\rm BL}=1.0$, the values are $R_{1.4}=11.74_{-1.54}^{+2.11}$ km, $I_{1.4} = 2.40_{-0.08}^{+0.17} \times10^{45}$ g cm$^2$ respectively.

Local scaling limits of Lévy driven fractional random fields

We obtain a complete description of local anisotropic scaling limits for a class of fractional random fields $X$ on ${\mathbb{R}}^2$ written as stochastic integral with respect to infinitely divisible random measure. The scaling procedure involves increments of $X$ over points the distance between which in the horizontal and vertical directions shrinks as $O(\lambda)$ and $O(\lambda^\gamma)$ respectively as $\lambda \downarrow 0$, for some $\gamma>0$. We consider two types of increments of $X$: usual increment and rectangular increment, leading to the respective concepts of $\gamma$-tangent and $\gamma$-rectangent random fields. We prove that for above $X$ both types of local scaling limits exist for any $\gamma>0$ and undergo a transition, being independent of $\gamma>\gamma_0$ and $\gamma<\gamma_0$, for some $\gamma_0>0$; moreover, the "unbalanced" scaling limits ($\gamma\ne\gamma_0$) are $(H_1,H_2)$-multi self-similar with one of $H_i$, $i=1,2$, equal to $0$ or $1$. The paper extends Pilipauskait\.e and Surgailis (2017) and Surgailis (2020) on large-scale anisotropic scaling of random fields on ${\mathbb{Z}}^2$ and Benassi et al. (2004) on $1$-tangent limits of isotropic fractional L\'evy random fields.

Tests of standard cosmology in Hořava gravity, Bayesian evidence for a closed universe, and the Hubble tension

We consider some background tests of standard cosmology in the context of Hořava gravity with different scaling dimensions for space and time, which has been proposed as a renormalizable, higher-derivative, Lorentz-violating quantum gravity model without ghost problems. We obtain the “very strong” and “strong” Bayesian evidences for our two cosmology models A and B, respectively, depending on the choice of parametrization based on Hořava gravity, against the standard, spatially-flat, LCDM cosmology model based on general relativity. An MCMC analysis with the observational data, including BAO, shows (a) preference of a closed universe with the curvature density parameter Omega _k=-0.005pm 0.001, -0.004^{+0.003}_{-0.001}, (b) reduction of the Hubble tension with the Hubble constant H_0=71.4^{+1.2}_{-0.9}, 69.5^{+1.6}_{-0.9}~ mathrm{km}, mathrm{s}^{-1}, mathrm{Mpc}^{-1} for the models A, B, respectively, and also (c) a positive result on the discordance problem. We comment on some possible further improvements for the “cosmic-tension problem” by considering the more complete early-universe physics, based on the Lorentz-violating standard model with anisotropic space-time scaling, consistently with Hořava gravity, as well as the observational data which are properly adopted for the closed universe.

SymmetryGrasp: Symmetry-Aware Antipodal Grasp Detection From Single-View RGB-D Images

Symmetry is ubiquitous in everyday objects. Humans tend to grasp objects by recognizing the symmetric regions. In this letter, we investigate how symmetry could boost robotic grasp detection. To this end, we present a learning-based method for detecting grasp from single-view RGB-D images. The key insight is to explicitly incorporate symmetry estimation into grasp detection, improving the quality of the detected grasps. Specifically, we first introduce a new grasp parameterization in grasp detection for parallel grippers based on symmetry. Based on this representation, a symmetry-aware grasp detection network method is present to simultaneously estimate object symmetry and detect grasp. We find that the learning of grasp detection greatly benefits from symmetry estimation, improving the training efficiency and the grasp quality. Besides, to facilitate the cross-instance generality of grasping unseen objects, we propose Principal-directional scale-Invariant Feature Transformer (PIFT), a plug-and-play module, that allows spatial deformation of points during the feature aggregation. The module essentially learns feature invariance to anisotropic scaling along the shape principal directions. Extensive experiments demonstrate the effectiveness of the proposed method. In particular, it outperforms previous methods, achieving state-of-the-art performance in terms of grasp quality on GraspNet-1-Billion and success rate on a real robot grasping experiment.

Dimensional transmutation and nonconventional scaling behavior in a model of self-organized criticality

This paper addresses two unusual scaling regimes (types of critical behavior) predicted by the field-theoretic renormalization group analysis for a self-organized critical system with turbulent motion of the environment. The system is modeled by the anisotropic stochastic equation for a “running sandpile” introduced by Hwa and Kardar in [Phys. Rev. Lett. 62, 1813 (1989)]. The turbulent motion is described by the isotropic Kazantsev–Kraichnan “rapid-change” velocity ensemble for an incompressible fluid. The original Hwa–Kardar equation allows for independent scaling of the spatial coordinates [Formula: see text] (the coordinate along the preferred dimension) and [Formula: see text] (the coordinates in the orthogonal subspace to the preferred direction) that becomes impossible once the isotropic velocity ensemble is coupled to the equation. However, it is found that one of the regimes of the system’s critical behavior (the one where the isotropic turbulent motion is irrelevant) recovers the anisotropic scaling through “dimensional transmutation.” The latter manifests as a dimensionless ratio acquiring nontrivial canonical dimension. The critical regime where both the velocity ensemble and the nonlinearity of the Hwa–Kardar equation are relevant simultaneously is also characterized by “atypical” scaling. While the ordinary scaling with fixed IR irrelevant parameters is impossible in this regime, the “restricted” scaling where the times, the coordinates, and the dimensionless ratio are scaled becomes possible. This result brings to mind scaling hypotheses modifications (Stell’s weak scaling or Fisher’s generalized scaling) for systems with significantly different characteristic scales.

A scale-elastic discrete grid structure for voxel-based modeling and management of 3D data

• A scale-elastic grid structure (SEGS) for 3D discrete grid systems is proposed. • The SEGS satisfies the anisotropic scale requirements of voxels in three dimensions. • Voxel-based modeling and management are fundamental for processing 3D voxel data. • SEGS method can effectively compress the voxel model while retaining accuracy. • SEGS method can greatly improve the efficiencies of indexing and querying voxel data. Three-dimensional (3D) discrete grid systems have been widely applied to voxel-based modeling and the management of 3D data. In the existing rigid grid structure (RGS), the scales of the RGS-based voxel grid in X/Y/Z dimensions are interrelated. Therefore, the RGS cannot satisfy the anisotropic scale requirements of voxels in different dimensions, rendering RGS-based methods unable to compress the voxel model effectively and manage voxels efficiently. A scale-elastic grid structure (SEGS) was proposed to solve these problems and applied to voxel-based modeling and management. Comparisons with the RGS showed that when the voxel model accuracy remained unchanged, the storage space of the voxel model generated by the SEGS-based method decreased to 12.9% on average, whereas the efficiency of decoding the voxel model increased by 3.34 times on average. The efficiencies of importing, indexing, and querying voxel data by the SEGS-based method increased by 5.27, 6.84, and 3.19 times on average.

DC conductance and memory in 3D gravity

Transport properties are investigated in the two-dimensional dual dynamics of AdS3 gravity. By providing boundary conditions that deform the ADM lapse and shift functions, we construct a lower dimensional model comprising two copies of chiral boson excitations with anisotropic scaling symmetry. Using bosonization, an electric current is identified. By means of the Kubo formula, we find a DC conductance depending on the level of the theory and the dynamical exponents. The bulk realization of the linear response is related to a type of gravitational memory emerging in the context of near-horizon boundary conditions. The process is adiabatic and represents a permanent spacetime deformation parametrized by anisotropic chiral bosons through a large gauge transformation.