Anisotropic Gaussian Research Articles

Direct comparison of Eulerian–Eulerian and Eulerian–Lagrangian simulations for particle‐laden vertical channel flow

AbstractParticle‐laden flows in a vertical channel were simulated using an Eulerian–Eulerian, Anisotropic Gaussian (EE‐AG) model. Two sets of cases varying the overall mass loading were done using particle sizes corresponding to either a large or small Stokes number. Primary and turbulent statistics were extracted from these results and compared with counterparts collected from Eulerian–Lagrangian (EL) simulations. The statistics collected from the small Stokes number particle cases correspond well between the two models, with the EE‐AG model replicating the transition observed using the EL model from shear‐induced turbulence to relaminarization to cluster‐induced turbulence as the mass loading increased. The EE‐AG model was able to capture the behavior of the EL simulations only at the largest particle concentrations using the large Stokes particles. This is due to the limitations involved with employing a particle‐phase Eulerian model (as opposed to a Lagrangian representation) for a spatially intermittent system that has a low particle number concentration.

Fast and Robust QEF Minimization using Probabilistic Quadrics

AbstractError quadrics are a fundamental and powerful building block in many geometry processing algorithms. However, finding the minimizer of a given quadric is in many cases not robust and requires a singular value decomposition or some ad‐hoc regularization. While classical error quadrics measure the squared deviation from a set of ground truth planes or polygons, we treat the input data as genuinely uncertain information and embed error quadrics in a probabilistic setting (“probabilistic quadrics”) where the optimal point minimizes theexpectedsquared error. We derive closed form solutions for the popular plane and triangle quadrics subject to (spatially varying, anisotropic) Gaussian noise. Probabilistic quadrics can be minimized robustly by solving a simple linear system— 50×faster than SVD. We show that probabilistic quadrics have superior properties in tasks like decimation and isosurface extraction since they favor more uniform triangulations and are more tolerant to noise while still maintaining feature sensitivity. A broad spectrum of applications can directly benefit from our new quadrics as a drop‐in replacement which we demonstrate with mesh smoothing via filtered quadrics and non‐linear subdivision surfaces.

Properties of off-axis hollow Gaussian-Schell model vortex beam propagating in turbulent atmosphere**Project supported by the Natural Science Foundation of Jilin Province, China (Grant No. 20180101031JC) and the Jilin Provincial Science Foundation for Basic Research, China (Grant No. 2019C040-7).

The analytical expression of off-axis hollow Gaussian–Schell model vortex beam (HGSMVB) generated by anisotropic Gaussian–Schell model source is first introduced. The evolution properties of off-axis HGSMVB propagating in turbulent atmosphere are analyzed. The results show that the off-axis HGSMVB with smaller coherence length or propagating in stronger turbulent atmosphere will evolve from dark hollow beam into Gaussian-like beam with a larger beam spot faster. The beams with different values of integer order N or the position for hollow and vortex factor R will have almost the same Gaussian-like spot distribution at the longer propagation distance.

Experimental validation and improvement of actuator line model in the large-eddy simulation of wind-turbine wakes

Wind-turbine wakes significantly affect the power output of downstream wind turbines. In order to improve the calculation accuracy of wind-turbine wakes in the atmospheric boundary layer, a new improved actuator line - large-eddy simulation (AL-LES) method is proposed and verified by experiments. The traditional AL-LES method is improved in three aspects. Firstly, the atmospheric turbulence is generated by a dynamic k-equation LES with a wall shear stress model and a buoyancy effect model. Secondly, the nacelle and tower are modelled based on the static actuator line method. Finally, the distribution of blade body force is improved by using an anisotropic 3D Gaussian function. Based on the results of three wind tunnel experiments conducted by Norwegian University of Science and Technology (NTNU), China Aerodynamics Research and Development Centre (CARDC) and Von Karman Institute for Fluid Dynamics (VKI), the improved AL-LES method is validated from the aspects of wind-turbine power performance, the generation of tip vortex, and the distribution of wake velocity under typical offshore and onshore conditions. In addition, a full-scale wind turbine installed in Gansu is used for the experimental and numerical research. The main conclusion is that compared with the traditional method, the new AL-LES method improves the numerical accuracy by nearly 22%, and can more accurately simulate the interaction between atmospheric turbulence and wind-turbine wakes. The results can help the research of wind-turbine wakes and the micro-location selection of wind farm.

Multi-Scale Anisotropic Gaussian Kernels for Image Edge Detection

In this paper, a new edge detection method is proposed where multi-scale anisotropic Gaussian kernels (AGKs) are used to obtain an edge map from an input image. The main advantage of the proposed method is that high edge detection accuracy and edge resolution are attained while maintaining good noise robustness. The proposed method consists of three aspects: First, anisotropic Gaussian directional derivatives (AGDDs) are derived from the AGKs which are used to acquire local intensity variation from an input image with multiple scales. Second, multi-scale AGDD based edge strength maps (ESMs) are fused into a new ESM with high edge resolution and little edge stretch effect which has the ability to solve the contradiction issue between noise robustness and accurate edge extraction. Third, the fused ESM is embedded into the framework of Canny detection for obtaining edge contours. Finally, the criteria on precision-recall curve, detection accuracy, and noise robustness are used to evaluate the proposed detector against four state-of-the-art methods. The experimental results show that our proposed detector outperforms all the other tested edge detection methods.

A Novel Configuration Tuning Method Based on Feature Selection for Hadoop MapReduce

Configuration parameter optimization is an important means of improving the performance of the MapReduce model. The existing parameter tuning methods usually optimize all configuration parameters in MapReduce. However, it is exceedingly challenging to tune all the parameters for the MapReduce model because there are massive configuration parameters in MapReduce. In this paper, a novel configuration parameter tuning method based on a feature selection algorithm is proposed, and it is composed of the feature selection objective function and feature selection process. The objective function is based on the kernel clustering algorithm, in which anisotropic Gaussian kernel is adopted instead of the traditional Gaussian kernel to accurately judge the importance of each parameter in MapReduce. Then, the relationship between the configuration parameters in MapReduce and the features in the feature selection algorithm is defined. Moreover, the importance of each parameter is reflected by the kernel width of anisotropic Gaussian kernels. At the same time, the method of gradient descent is introduced to update the kernel width and control the feature selection process of the iterative algorithm. Finally, experimental results show that the proposed algorithm performs suitably for the MapReduce model.

Hybrid image segmentation method based on anisotropic Gaussian kernels and adjacent graph region merging.

Image segmentation is a key technique in image analysis for object identification. In this paper, a hybrid segmentation method is proposed, which is based on the Anisotropic Gaussian Kernel (ANGK) edge detector and region adjacent graph (RAG) merging algorithm. An anisotropic directional derivative filter is constructed by angled ANGK to detect the edge contour of original images. Based on the gradient magnitude pattern of the edge contour from ANGK processing, watershed transform is adopted to produce initial partition (coarse segmentation result). Finally, combined with the RAG region merging algorithm, the proposed method performs fine segmentation by merging similar fragmented regions (initial partition) iteratively. Additionally, statistic similarity measure and shape cost function in merging cost are also introduced. They provide quantitative criteria for region merging, which have critical influences on the detection result. A series of experiments are conducted to evaluate the performance of this method, and a preferable localization accuracy as well as noise robustness is proved. Compared with conventional edge and region based methods, the proposed one has a superior segmentation effect. Another advantage is that the problem of oversegmentation can be solved effectively.

Automated Artemia length measurement using U-shaped fully convolutional networks and second-order anisotropic Gaussian kernels

The brine shrimp Artemia, a small crustacean zooplankton organism, is universally used as live prey for larval fish and shrimps in aquaculture. In Artemia studies, it would be highly desired to have access to automated techniques to obtain the length information from Artemia images. However, this problem has so far not been addressed in literature. Moreover, conventional image-based length measurement approaches cannot be readily transferred to measure the Artemia length, due to the distortion of non-rigid bodies, the variation over growth stages and the interference from the antennae and other appendages. To address this problem, we compile a dataset containing 250 images as well as the corresponding label maps of length measuring lines. We propose an automated Artemia length measurement method using U-shaped fully convolutional networks (UNet) and second-order anisotropic Gaussian kernels. For a given Artemia image, the designed UNet model is used to extract a length measuring line structure, and, subsequently, the second-order Gaussian kernels are employed to transform the length measuring line structure into a thin measuring line. For comparison, we also follow conventional fish length measurement approaches and develop a non-learning-based method using mathematical morphology and polynomial curve fitting. We evaluate the proposed method and the competing methods on 100 test images taken from the dataset compiled. Experimental results show that the proposed method can accurately measure the length of Artemia objects in images, obtaining a mean absolute percentage error of 1.16%.

Hausdorff Measure of the Range of Space–Time Anisotropic Gaussian Random Fields

Let $$X=\{X(t)\in {{\mathbb {R}}}^d, t\in {{\mathbb {R}}}^N\}$$ be a centered space–time anisotropic Gaussian random field with stationary increments, whose components are independent but may not be identically distributed. Under certain mild conditions, we determine the exact Hausdorff measure function for the range $$X([0,1]^N)$$ . Our result extends those in Talagrand (Ann Probab 23:767–775, 1995) for fractional Brownian motion and Luan and Xiao (J Fourier Anal Appl 18:118–145, 2012) for time-anisotropic and space-isotropic Gaussian random fields.

On critical points of Gaussian random fields under diffeomorphic transformations

Let {X(t),t∈M} and {Z(t′),t′∈M′} be smooth Gaussian random fields parameterized on Riemannian manifolds M and M′, respectively, such that X(t)=Z(f(t)), where f:M→M′ is a diffeomorphic transformation. We study the expected number and height distribution of the critical points of X in connection with those of Z. As an important case, when X is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field Z, while the height distribution remains the same as that of Z.

A Mixture Likelihood Model of the Anisotropic Gaussian and Uniform Distributions for Accurate Oblique Image Point Matching

In this letter, we propose a mixture likelihood model for accurate oblique image point matching. The basic prior assumption is that the noises are anisotropic with zero mean and different covariances in $x$ - and $y$ -directions for inliers, while the outliers have uniform distribution, which is more suitable for tilted scenes or viewpoint changes. Furthermore, the oblique image point matching problem is formulated as an improved maximum a posteriori (IMAP) estimation of a Bayesian model. In this model, based on the vector field interpolation framework, we combined the mixture likelihood model and our previous adaptive image mismatch removal method, where a two-order term of the regularization coefficient is introduced into the regularized risk function, and a parameter self-adaptive Gaussian kernel function is imposed to construct the regularization term. Subsequently, the expectation–maximization algorithm is utilized to solve the IMAP estimation, in which all the latent variances are able to obtain excellent estimation. Experimental results on real data sets verified that our method was superior to some similar methods in terms of precision and also had better self-adaptability characteristic than some hypothesis-and-verify methods. More experiments on viewpoint changes demonstrated our method’s effectiveness without loss of precision–recall tradeoffs, besides significant efficiency improvement.

A kinetic-based hyperbolic two-fluid model for binary hard-sphere mixtures

Starting from coupled Boltzmann–Enskog (BE) kinetic equations for a two-particle system consisting of hard spheres, a hyperbolic two-fluid model for binary, hard-sphere mixtures is derived with separate mean velocities and energies for each phase. In addition to spatial transport, the BE kinetic equations account for particle–particle collisions, using an elastic hard-sphere collision model, and the Archimedes (buoyancy) force due to spatial gradients of the pressure in each phase, as well as other forces involving spatial gradients (e.g. lift). In the derivation, the particles in a given phase have identical mass and volume, and have no internal degrees of freedom (i.e. the particles are adiabatic). The ‘hard-sphere-fluid’ phase is obtained in the limit where the particle diameter in one phase tends to zero with fixed phase density so that the number of fluid particles tends to infinity. The moment system resulting from the two BE kinetic equations is closed at second order by invoking the anisotropic Gaussian closure. The resulting two-fluid model for a binary, hard-sphere mixture therefore consists (for each phase $\unicode[STIX]{x1D6FC}=1,2$) of transport equations for the mass $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}$, mean momentum $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}$ (where $\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}$ is the velocity) and a symmetric, second-order, kinetic energy tensor $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\unicode[STIX]{x1D640}_{\unicode[STIX]{x1D6FC}}=\frac{1}{2}\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}(\boldsymbol{u}_{\unicode[STIX]{x1D6FC}}\otimes \boldsymbol{u}_{\unicode[STIX]{x1D6FC}}+\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}})$. The trace of the fluctuating energy tensor $\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}}$ is $\text{tr}(\unicode[STIX]{x1D748}_{\unicode[STIX]{x1D6FC}})=3\unicode[STIX]{x1D6E9}_{\unicode[STIX]{x1D6FC}}$ where $\unicode[STIX]{x1D6E9}_{\unicode[STIX]{x1D6FC}}$ is the phase temperature (or granular temperature). Thus, $\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}E_{\unicode[STIX]{x1D6FC}}=\unicode[STIX]{x1D71A}_{\unicode[STIX]{x1D6FC}}\text{tr}(\unicode[STIX]{x1D640}_{\unicode[STIX]{x1D6FC}})$ is the total kinetic energy, the sum over $\unicode[STIX]{x1D6FC}$ of which is the total kinetic energy of the system, a conserved quantity. From the analysis, it is found that the BE finite-size correction leads to exact phase pressure (or stress) tensors that depend on the mean-slip velocity $\boldsymbol{u}_{12}=\boldsymbol{u}_{1}-\boldsymbol{u}_{2}$, as well as the phase temperatures for both phases. These pressure tensors also appear in the momentum-exchange terms in the mean momentum equations that produce the Archimedes force, as well as drag contributions due to fluid compressibility and a lift force due to mean fluid-velocity gradients. The closed BE energy flux tensors show a similar dependence on the mean-slip velocity. The characteristic polynomial of the flux matrix from the one-dimensional model is computed symbolically and depends on five parameters: the particle volume fractions $\unicode[STIX]{x1D711}_{1}$, $\unicode[STIX]{x1D711}_{2}$, the phase density ratio ${\mathcal{Z}}=\unicode[STIX]{x1D70C}_{f}/\unicode[STIX]{x1D70C}_{p}$, the phase temperature ratio $\unicode[STIX]{x1D6E9}_{r}=\unicode[STIX]{x1D6E9}_{2}/\unicode[STIX]{x1D6E9}_{1}$ and the mean-slip Mach number $Ma_{s}=\boldsymbol{u}_{12}/\sqrt{5\unicode[STIX]{x1D6E9}_{1}/3}$. By applying Sturm’s Theorem to the characteristic polynomial, it is demonstrated that the model is hyperbolic over a wide range of these parameters, in particular, for the physically most relevant values.

Automatic time series analysis for electric load forecasting via support vector regression

In this work, a strategy for automatic lag selection in time series analysis is proposed. The method extends the ideas of feature selection with support vector regression, a powerful machine learning tool that can identify nonlinear patterns effectively thanks to the introduction of a kernel function. The proposed approach follows a backward variable elimination procedure based on gradient descent optimisation, iteratively adjusting the widths of an anisotropic Gaussian kernel. Experiments on four electricity demand forecasting datasets demonstrate the virtues of the proposed approach in terms of predictive performance and correct identification of relevant lags and seasonal patterns, compared to well-known strategies for time series analysis designed for energy load forecasting and state-of-the-art strategies for automatic model selection.

Polarimetric Parameters of Scattered Radiation in the Magnetized Plasma

Second order statistical moments of scattered electromagnetic waves in the turbulent magnetized plasma slab with electron density fluctuations are calculated applying the modify stochastic smooth perturbation theory and the boundary conditions. The obtained results are valid for arbitrary correlation function of electron density fluctuations. Stokes parameters are analyzed both analytically and numerically. The theory predicts that depolarization effect caused by second Stokes parameter may be important in scintillation effects. Numerical calculations are carried out for new spectral function of electron density fluctuations containing both anisotropic Gaussian and power-law spectral functions using the experimental data. Polarimetric parameters are calculated for different anisotropy factor and inclination angle of elongated small-scale irregularities with respect to the magnetic lines of forces. The relationship between the scintillations and the polarimetric parameters is important.

Anisotropic functional deconvolution with long-memory noise: the case of a multi-parameter fractional Wiener sheet

We look into the minimax results for the anisotropic two-dimensional functional deconvolution model with the two-parameter fractional Gaussian noise. We derive the lower bounds for the -risk, , and taking advantage of the Riesz poly-potential, we apply a wavelet-vaguelette expansion to de-correlate the anisotropic fractional Gaussian noise. We construct an adaptive wavelet hard-thresholding estimator that attains asymptotically optimal or quasi-optimal convergence rates in a wide range of Besov balls. Such convergence rates depend on a delicate balance between the parameters of the Besov balls, the degree of ill-posedness of the convolution operator and the parameters of the fractional Gaussian noise under regular-smooth convolution, whereas the rates are not affected by long-memory under super-smooth convolution. A limited simulations study confirms the theoretical claims of the paper. The proposed approach is extended to the general r-dimensional case, with r>2, and the corresponding convergence rates do not suffer from the curse of dimensionality.

Derivation and numerical comparison of Shakhov and Ellipsoidal Statistical kinetic models for a monoatomic gas mixture

Gas mixtures are important for many practical applications. Extending kinetic model equations of the Bhatnagar–Gross–Krook (BGK) type from a single-species gas to a multi-species gas mixture presents a number of significant challenges. First, obtaining the correct species diffusions, viscous stresses as well as heat conduction in the continuum limit requires a careful design of the collision terms in the kinetic equations. Secondly, the derived model collision terms need to guarantee positivity of the macroscopic fields. In the present work, two new kinetic models are introduced and compared: an approach based on the Shakhov kinetic model and an approach involving an anisotropic Gaussian equilibrium function. The two new models are capable of modelling a binary mixture of monoatomic gases, with updated definitions for the relaxation parameters and target species velocities and temperature. Both methods account for separate species-mean velocity such that the species diffusion and velocity drift are accurately represented. The key contribution of the models is the exact recovery of the Fick, Newton and Fourier laws in the continuum limit, while preserving positive temperature fields and crucial properties of the Boltzmann equation. The profile of a normal shock wave is inspected under various flow conditions to numerically validate the two models. The results show improvement upon comparison with a model, which has two correct transport coefficients, and demonstrate the ability to reliably model inert gas mixtures.

Area Segmentation of Images Using Watershed and Anisotropic Gaussian Kernels

Image segmentation as one of the primary steps in image analysis for object identification has received much attention lately, the main aim being to recognize homogeneous regions of an image which belong to different objects. A noise-robust edge detector SCHEME based on anisotropic Gaussian Kernels (ANGKs) is proposed in this paper by combining the region-merging algorithm to obtain higher quality segmentation results, which consist of three basic blocks. The first two blocks give rise to an initial partition of an image, while the last block attains the final segmentation by iteratively merging similar fragmented regions. A series of experiments is used to evaluate the performance of the method. The experimental results show that the proposed method has good noise robustness and localization accuracy, and can solve the problem of over-segmentation effectively, the simulation result supports our proposed main ideas.

Recurrent approach to effective material properties with application to anisotropic binarized random fields

Building on the foundation work of Brown, Milton and Torquato, we present a tractable approach to analyse the effective permittivity of anisotropic two-phase structures. This methodology accounts for successive dipolar interactions, providing a recurrent series expansion of the effective permittivity to arbitrary order. Within this framework, we also demonstrate a progressive method to determine tight bounds that converge towards the exact solution. We illustrate the utility of these methods by using ensemble averaging to determine the micro-structural parameters of anisotropic level-cut Gaussian fields. We find that the depolarization factor of these structures is equivalent to that of an isolated ellipse with the same stretchingratio, and discuss the contribution of the fourth order term to the exact anisotropy.

Noise-robust line detection using normalized and adaptive second-order anisotropic Gaussian kernels

Abstract Line detection is an essential procedure for many tasks in computer vision. Although literature is rich in proposals for this topic, most of existing methods are vulnerable to noise, especially when lines are fairly narrow. In order to design a line detector that minimizes the impact of noise, regardless of the scale or direction of the lines, in this paper, we present a framework for multiscale line detection based on second-order anisotropic Gaussian kernels. Firstly, we model a line segment using a directional Gaussian function. Secondly, with the help of a newly proposed normalization method, we enable the second-order anisotropic Gaussian kernels to quantitatively measure the line prominence as well as the line scale. Subsequently, based on a noise-robustness analysis in terms of the signal-to-noise ratio, an adaptive anisotropy factor is proposed. By incorporating postprocessing techniques, an automated line detector using the normalized and adaptive second-order anisotropic Gaussian kernels is developed. The performance of the proposed method is quantitatively evaluated by comparing it with five competing methods on a publicly available dataset.

Continuity in law of some additive functionals of bifractional Brownian motion

ABSTRACTLet be a bifractional Brownain motion with indices and . We prove the continuity in law, in some anisotropic Besov spaces, with respect to H and K. Our result generalizes those obtained by Jolis and Viles [Continuity in law with respect to the Hurst parameter of the local time of the fractional Brownian motion, J. Theor. Probab. 20(2) (2007), pp. 133–152] of the fractional Brownian motion local time and gives a new result for the generalized fractional derivatives with kernel depending on slowly varying function of the local time of . Notice that their result was generalized by Wu and Xiao [Continuity in the Hurst index of the local times of anisotropic gaussian random fields, Stoch. Proc. Their Appl. 119 (2009), pp. 1823–1844] for wide class of anisotropic gaussian random fields satisfying some condition (A) which is not satisfied by . To prove our result, we use the decomposition in law of given by Lei and Nualart [A decomposition of the bifractional Brownian motion and some applications, Statist. Probab. Lett. 79 (2009), pp. 619–624]. Our result is also new in the space of continuous functions.