Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste,understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities.The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure.This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions.To investigate the mechanism of microscale mode-I ruptures,it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework.In this contribution,we derive the model from microstructures that contain periodically distributed microcracks within a porous material.The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical(HM)anisotropy at the microscale.The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation.Verification examples are presented to validate the developed model step by step.An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate,initial damage,and applied stress,on the gas migration process.Numerical examples of direct tension tests are used to demonstrate the model’s efficacy in describing localized failure characteristics.Finally,the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks.The model successfully captures the common behaviors observed in laboratory experiments,such as a sudden drop in gas injection pressure,rapid build-up of downstream gas pressure,and steady-state gas flow following gas breakthrough.

Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

P-and S-wave separation plays an important role in elastic reverse-time migration.It can reduce the artifacts caused by crosstalk between different modes and improve image quality.In addition,P-and Swave separation can also be used to better understand and distinguish wave types in complex media.At present,the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering,low-rank approximation,and vector Poisson equation.Most of these methods require multiple Fourier transforms or the calculation of large matrices,which require high computational costs for problems with large scale.In this paper,an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial domain.For 2D problems,the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation.Therefore,compared with existing methods based on pseudoHelmholtz decomposition operators,this method can significantly reduce the computational cost.Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

3D robust anisotropic diffusion filtering algorithm for sparse view neutron computed tomography 3D image reconstruction

The most critical part of a neutron computed tomography(NCT) system is the image processing algorithm,which directly affects the quality and speed of the reconstructed images.Various types of noise in the system can degrade the quality of the reconstructed images.Therefore,to improve the quality of the reconstructed images of NCT systems,efficient image processing algorithms must be used.The anisotropic diffusion filtering(ADF) algorithm can not only effectively suppress the noise in the projection data,but also preserve the image edge structure information by reducing the diffusion at the image edges.Therefore,we propose the application of the ADF algorithm for NCT image reconstruction.To compare the performance of different algorithms in NCT systems,we reconstructed images using the ordered subset simultaneous algebraic reconstruction technique(OS-SART) algorithm with different regular terms as image processing algorithms.In the iterative reconstruction,we selected two image processing algorithms,the Total Variation and split Bregman solved total variation algorithms,for comparison with the performance of the ADF algorithm.Additionally,the filtered back-projection algorithm was used for comparison with an iterative algorithm.By reconstructing the projection data of the numerical and clock models,we compared and analyzed the effects of each algorithm applied in the NCT system.Based on the reconstruction results,OS-SART-ADF outperformed the other algorithms in terms of denoising,preserving the edge structure,and suppressing artifacts.For example,when the 3D Shepp–Logan was reconstructed at 25 views,the root mean square error of OS-SART-ADF was the smallest among the four iterative algorithms,at only 0.0292.The universal quality index,mean structural similarity,and correlation coefficient of the reconstructed image were the largest among all algorithms,with values of 0.9877,0.9878,and 0.9887,respectively.

Experimental Investigation of the Anisotropic Thermal Conductivity of C/SiC Composite Thin Slab

Fiber-reinforced composites possess anisotropic mechanical and heat transfer properties due to their anisotropic fibers and structure distribution.In C/Si C composites,the out-of-plane thermal conductivity has mainly been studied,whereas the in-plane thermal conductivity has received less attention due to their limited thickness.

MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

Let X={X(t)∈R^(d),t∈R^(N)}be a centered space-time anisotropic Gaussian field with indices H=(H_(1),…,H_(N))∈(0,1)~N,where the components X_(i)(i=1,…,d)of X are independent,and the canonical metric√(E(X_(i)(t)-X_(i)(s))^(2))^(1/2)(i=1,…,d)is commensurate with■for s=(s_(1),…,s_(N)),t=(t_(1),…,t_(N))∈R~N,α_(i)∈(0,1],and with the continuous functionγ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly onγ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

Unveiling the in-plane anisotropic dielectric waveguide modes in α-MoO_(3) flakes

The unique in-plane and out-of-plane anisotropy of α-MoO_(3) has attracted considerable interest with regard to potential optoelectronic applications. However, most research has focused on the mid-infrared spectrum, leaving its properties and applications in the visible and near-infrared light spectrum less explored. This study advances the understanding of waveguiding properties of α-MoO_(3) by near-field imaging of the waveguide modes along the [100] and [001] directions of α-MoO_(3) flakes at 633 nm and 785 nm. We investigate the effects of flake thickness and documented the modes' dispersion relationships, which is crucial for tailoring the optical responses of α-MoO_(3) in device applications. Our findings enhance the field of research into α-MoO_(3), highlighting its utility in fabricating next-generation optoelectronic devices due to its unique optically anisotropic waveguide.

Properties of focused Laguerre–Gaussian beam propagating in anisotropic ocean turbulence

We analyze the properties of a focused Laguerre–Gaussian(LG)beam propagating through anisotropic ocean turbulence based on the Huygens–Fresnel principle.Under the Rytov approximation theory,we derive the analytical formula of the channel capacity of the focused LG beam in the anisotropic ocean turbulence,and analyze the relationship between the capacity and the light source parameters as well as the turbulent ocean parameters.It is found that the focusing mirror can greatly enhance the channel capacity of the system at the geometric focal plane in oceanic turbulence.The results also demonstrate that the communication link can obtain high channel capacity by adopting longer beam wavelength,greater initial beam waist radius,and larger number of transmission channels.Further,the capacity of the system increases with the decrease of the mean squared temperature dissipation rate,temperature-salinity contribution ratio and turbulence outer scale factor,and with the increase of the kinetic energy dissipation rate per unit mass of fluid,turbulence inner scale factor and anisotropy factor.Compared to a Hankel–Bessel beam with diffraction-free characteristics and unfocused LG beam,the focused LG beam shows superior anti-turbulence interference properties,which provide a theoretical reference for research and development of underwater optical communication links using focused LG beams.

THE INTERIOR TRANSMISSION EIGENVALUE PROBLEM FOR AN ANISOTROPIC MEDIUM BY A PARTIALLY COATED BOUNDARY

We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary?Ωis split into two disjoint parts and possesses different transmission conditions.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n≡1,where a fourth order differential operator is applied.In the case of n■1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.

Anisotropic swelling pressures of compacted GMZ bentonite infiltrated with salt solutions

In the high-level radioactive waste(HLW)deep geological repository,bentonite is compacted uniaxially,and then arranged vertically in engineered barriers.The assembly scheme induces the initial anisotropy,and with hydration,it develops more evidently under chemical conditions.To investigate the anisotropic swelling of compacted Gaomiaozi(GMZ)bentonite and the further response to saline effects,a series of constant-volume swelling pressure tests were performed.Results showed that dry density enhanced the bentonite swelling and raised the final anisotropy,whereas saline inhibited the bentonite swelling but still promoted the final anisotropy.The final anisotropy coefficient(ratio of radial to axial pressure)obeyed the Boltzmann sigmoid attenuation function,decreasing with concentration and dry density,converging to a minimum value of 0.76.The staged evolution of anisotropy coefficient was discovered,that saline inhibited the rise of the anisotropy coefficient(Dd)in the isotropic process greater than the valley(d1)in the anisotropic process,leading to the final anisotropy increasing.The isotropic stage amplified the impact of soil structure rearrangement on the macro-swelling pressure values.Thus,a new method for predicting swelling pressures of compacted bentonite was proposed,by expanding the equations of Gouy-Chapman theory with a dissipative wedge term.An evolutionary function was constructed,revealing the correlation between the occurrence time and the pressure value due to the structure rearrangement and the former crystalline swelling.Accordingly,a design reference for dry density was given,based on the chemical conditions around the pre-site in Beishan,China.The anisotropy promoted by saline would cause a greater drop of radial pressure,making the previous threshold on axial swelling fail.

Alleviating the anisotropic microstructural change and boosting the lithium ions diffusion by grain orientation regulation for Ni-rich cathode materials

Generally,layered Ni-rich cathode materials exhibit the morphology of polycrystalline secondary sphere composed of numerous primary particles.While the arrangement of primary particles plays a very important role in the properties of Ni-rich cathodes.The disordered particle arrangement is harmful to the cyclic performance and structural stability,yet the fundamental understanding of disordered structure on the structural degradation behavior is unclarified.Herein,we have designed three kinds of LiNi_(0.83)Co_(0.06)Mn_(0.11)O_(2) cathode materials with different primary particle orientations by regulating the precursor coprecipitation process.Combining finite element simulation and in-situ characterization,the Li^(+)transport and structure evolution behaviors of different materials are unraveled.Specifically,the smooth Li^(+)diffusion minimizes the reaction heterogeneity,homogenizes the phase transition within grains,and mitigates the anisotropic microstructural change,thereby modulating the crack evolution behavior.Meanwhile,the optimized structure evolution ensures radial tight junctions of the primary particles,enabling enhanced Li^(+)diffusion during dynamic processes.Closed-loop bidirectional enhancement mechanism becomes critical for grain orientation regulation to stabilize the cyclic performance.This precursor engineering with particle orientation regulation provides the useful guidance for the structural design and feature enhancement of Ni-rich layered cathodes.

Quintessence anisotropic stellar models in quadratic and Born-Infeld modified teleparallel Rastall gravity

This study aims to discuss anisotropic solutions that are spherically symmetric in the quintessence field,which describe compact stellar objects in the modified Rastall teleparallel theory of gravity.To achieve this goal,the Krori and Barua arrangement for spherically symmetric components of the line element is incorporated.We explore the field equations by selecting appropriate off-diagonal tetrad fields.Born-Infeld function of torsion f(T)=β√λT+1-1 and power law form h(T)=δTn are used.The Born-Infeld gravity was the first modified teleparallel gravity to discuss inflation.We use the linear equation of state pr=ξρto separate the quintessence density.After obtaining the field equations,we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models.We use observational data,such as the mass and radius of the compact star candidates PSRJ 1416-2230,Cen X-3,&4U 1820-30,to ensure the physical plausibility of our findings.

Anisotropic strength,deformation and failure of gneiss granite under high stress and temperature coupled true triaxial compression

The anisotropic mechanical behavior of rocks under high-stress and high-temperature coupled conditions is crucial for analyzing the stability of surrounding rocks in deep underground engineering.This paper is devoted to studying the anisotropic strength,deformation and failure behavior of gneiss granite from the deep boreholes of a railway tunnel that suffers from high tectonic stress and ground temperature in the eastern tectonic knot in the Tibet Plateau.High-temperature true triaxial compression tests are performed on the samples using a self-developed testing device with five different loading directions and three temperature values that are representative of the geological conditions of the deep underground tunnels in the region.Effect of temperature and loading direction on the strength,elastic modulus,Poisson’s ratio,and failure mode are analyzed.The method for quantitative identification of anisotropic failure is also proposed.The anisotropic mechanical behaviors of the gneiss granite are very sensitive to the changes in loading direction and temperature under true triaxial compression,and the high temperature seems to weaken the inherent anisotropy and stress-induced deformation anisotropy.The strength and deformation show obvious thermal degradation at 200℃due to the weakening of friction between failure surfaces and the transition of the failure pattern in rock grains.In the range of 25℃ 200℃,the failure is mainly governed by the loading direction due to the inherent anisotropy.This study is helpful to the in-depth understanding of the thermal-mechanical behavior of anisotropic rocks in deep underground projects.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.

Active tuning of anisotropic phonon polaritons in natural van der Waals crystals with negative permittivity substrates and its application in energy transport

Phonon polaritons(PhPs)exhibit directional in-plane propagation and ultralow losses in van der Waals(vdW)crystals,offering new possibilities for controlling the flow of light at the nanoscale.However,these PhPs,including their directional propagation,are inherently determined by the anisotropic crystal structure of the host materials.Although in-plane anisotropic PhPs can be manipulated by twisting engineering,such as twisting individual vdW slabs,dynamically adjusting their propagation presents a significant challenge.The limited application of the twisted bilayer structure in bare films further restricts its usage.In this study,we present a technique in which anisotropic PhPs supported by bare biaxial vdW slabs can be actively tuned by modifying their local dielectric environment.Excitingly,we predict that the iso-frequency contour of PhPs can be reoriented to enable propagation along forbidden directions when the crystal is placed on a substrate with a moderate negative permittivity.Besides,we systematically investigate the impact of polaritonic coupling on near-field radiative heat transfer(NFRHT)between heterostructures integrated with different substrates that have negative permittivity.Our main findings reveal that through the analysis of dispersion contour and photon transmission coefficient,the excitation and reorientation of the fundamental mode facilitate increased photon tunneling,thereby enhancing heat transfer between heterostructures.Conversely,the annihilation of the fundamental mode hinders heat transfer.Furthermore,we find the enhancement or suppression of radiative energy transport depends on the relative magnitude of the slab thickness and the vacuum gap width.Finally,the effect of negative permittivity substrates on NFRHT along the[001]crystalline direction ofα-MoO3 is considered.The spectral band where the excited fundamental mode resulting from the negative permittivity substrates is shifted to the first Reststrahlen Band(RB 1)ofα-MoO_(3) and is widened,resulting in more significant enhancement of heat flux from RB 1.We anticipate our results will motivate new direction for dynamical tunability of the PhPs in photonic devices.

Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

ANISOTROPIC EFFECTS OF QUASI-ISOTROPIC COMPOSITES(I)──MODELLING

Experimental obseryations show that quasi-isotropic materials, such as N-axial fibre-reinforced composites and woven materials . exhibit various degrees of anisotrpy in elasticity and strength, and the anisotropy in strengty is normally stronger than that in elasticity.In view of some available experimental data and based on the general formulation of the constitutive equations and .failure criteria of quasi-isotropic materials established by using the theory of repesentations for tensor functions, we postulate several applicable models of the constitutive equations and strength for 3and 4-axial quasi-isotropic materials to reveal the anisotropic effects In a continued work (Part II) the anisotropic effect in strength of an infintely large plate with a single elliptical hole or crack is studied. and the proposed stiffness and strength modelsare verified in terms of micro-mechanical analyses.

Microscopic damage evolution of anisotropic rocks under indirect tensile conditions: Insights from acoustic emission and digital image correlation techniques

The anisotropy induced by rock bedding structures is usually manifested in the mechanical behaviors and failure modes of rocks.Brazilian tests are conducted for seven groups of shale specimens featuring different bedding angles. Acoustic emission (AE) and digital image correlation (DIC) technologies are used to monitor the in-situ failure of the specimens. Furthermore, the crack morphology of damaged samples is observed through scanning electron microscopy (SEM). Results reveal the structural dependence on the tensile mechanical behavior of shales. The shale disk exhibits compression in the early stage of the experiment with varying locations and durations. The location of the compression area moves downward and gradually disappears when the bedding angle increases. The macroscopic failure is well characterized by AE event location results, and the dominant frequency distribution is related to the bedding angle. The b-value is found to be stress-dependent.The crack turning angle between layers and the number of cracks crossing the bedding both increase with the bedding angle, indicating competition between crack propagations. SEM results revealed that the failure modes of the samples can be classified into three types:tensile failure along beddings with shear failure of the matrix, ladder shear failure along beddings with tensile failure of the matrix, and shear failure along multiple beddings with tensile failure of the matrix.

Anisotropic optical and electric properties of β-gallium oxide

The anisotropic properties and applications ofβ-gallium oxide(β-Ga_(2)O_(3))are comprehensively reviewed.All the anisotropic properties are essentially resulted from the anisotropic crystal structure.The process flow of how to exfoliate nanoflakes from bulk material is introduced.Anisotropic optical properties,including optical bandgap,Raman and photolumines-cence characters are comprehensively reviewed.Three measurement configurations of angle-resolved polarized Raman spec-tra(ARPRS)are reviewed,with Raman intensity formulas calculated with Raman tensor elements.The method to obtain the Raman tensor elements of phonon modes through experimental fitting is also introduced.In addition,the anisotropy in elec-tron mobility and affinity are discussed.The applications,especially polarization photodetectors,based onβ-Ga_(2)O_(3)were summa-rized comprehensively.Three kinds of polarization detection mechanisms based on material dichroism,1D morphology and metal-grids are discussed in-depth.This review paper provides a framework for anisotropic optical and electric properties ofβ-Ga_(2)O_(3),as well as the applications based on these characters,and is expected to lead to a wider discussion on this topic.

Medical Image Fusion Based on Anisotropic Diffusion and Non-Subsampled Contourlet Transform

The synthesis of visual information from multiple medical imaging inputs to a single fused image without any loss of detail and distortion is known as multimodal medical image fusion.It improves the quality of biomedical images by preserving detailed features to advance the clinical utility of medical imaging meant for the analysis and treatment of medical disor-ders.This study develops a novel approach to fuse multimodal medical images utilizing anisotropic diffusion(AD)and non-subsampled contourlet transform(NSCT).First,the method employs anisotropic diffusion for decomposing input images to their base and detail layers to coarsely split two features of input images such as structural and textural information.The detail and base layers are further combined utilizing a sum-based fusion rule which maximizes noise filtering contrast level by effectively preserving most of the structural and textural details.NSCT is utilized to further decompose these images into their low and high-frequency coefficients.These coefficients are then combined utilizing the principal component analysis/Karhunen-Loeve(PCA/KL)based fusion rule independently by substantiating eigenfeature reinforcement in the fusion results.An NSCT-based multiresolution analysis is performed on the combined salient feature information and the contrast-enhanced fusion coefficients.Finally,an inverse NSCT is applied to each coef-ficient to produce the final fusion result.Experimental results demonstrate an advantage of the proposed technique using a publicly accessible dataset and conducted comparative studies on three pairs of medical images from different modalities and health.Our approach offers better visual and robust performance with better objective measurements for research development since it excellently preserves significant salient features and precision without producing abnormal information in the case of qualitative and quantitative analysis.