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The effect of model size on fluid flow through fractal rough fractures under shearing is investigated using a numerical simulation method. The shear behavior of rough fractures with self-affine properties was described using the analytical model, and the aperture fields with sizes varying from 25 to 200mm were extracted under shear displacements up to 20mm. Fluid flow through fractures in the directions both parallel and perpendicular to the shear directions was simulated by solving the Reynolds equation using a finite element code. The results show that fluid flow tends to converge into a few main flow channels as shear displacement increases, while the shapes of flow channels change significantly as the fracture size increases. As the model size increases, the permeability in the directions both parallel and perpendicular to the shear direction changes significantly first and then tends to move to a stable state. The size effects on the permeability in the direction parallel to the shear direction are more obvious than that in the direction perpendicular to the shear direction, due to the formation of contact ridges and connected channels perpendicular to the shear direction. The variances of the ratio between permeability in both directions become smaller as the model size increases and then this ratio tends to maintain constant after a certain size, with the value mainly ranging from 1.0 to 3.0.

The pores and fissures in loaded rock masses are the main channels for underground flow, and may cause serious accidents during the development of groundwater resources. This work presents an efficient method for analyzing the microstructure of the loaded rock mass using fractal theory and computed tomography (CT) scanning. A relation between the microstructure features of the sandstone porosity, fractal dimension, and loading stress is developed using an image identification technique. The results demonstrate that the distribution trends of sandstone samples’ slice porosities in the xz- and yz-directions are nearly identical, and the distribution in the xy-direction differs significantly from those in xz- and yz-directions. The total and connected porosities increase with the increase of stress, and the change can be fitted to straight lines. The fractal dimensions of the pores change significantly with stress or loading stress in the xy-direction.

We developed a model to describe polarized photon scattering in biological tissues. In this model, tissues are simplified to a mixture of scatterers and surrounding medium. There are two types of scatterers in the model: solid spheres and infinitely long solid cylinders. Variables related to the scatterers include: the densities and sizes of the spheres and cylinders, the orientation and angular distribution of cylinders. Variables related to the surrounding medium include: the refractive index, absorption coefficient and birefringence. In this paper, as a development we introduce an optical activity effect to the model. By comparing experiments and Monte Carlo simulations, we analyze the backscattering Mueller matrix patterns of several tissue-like media, and summarize the different effects coming from anisotropic scattering and optical properties. In addition, we propose a possible method to extract the optical activity values for tissues. Both the experimental and simulated results show that, by analyzing the Mueller matrix patterns, the microstructure and optical properties of the medium can be obtained. The characteristic features of Mueller matrix patterns are potentially powerful tools for studying the contrast mechanisms of polarization imaging for medical diagnosis.

Plate-like single-crystalline BaBi₄Ti₄${\text{O}}_{15}$ particles were synthesized by the molten salt synthesis (MSS) method. The effects of sintering temperature, holding time, and NaCl–KCl molten salt content on the phase structure and morphology of plate-like BaBi₄-Ti₄${\text{O}}_{15}$ particles were investigated. The results show that plate-like BaBi₄Ti₄${\text{O}}_{15}$ particles can be synthesized when the sintering temperature is above 800${}^{\circ }$C. The size of particles increases with increasing sintering temperature and molten salt content. Largely anisotropic plate-like BaBi₄Ti₄${\text{O}}_{15}$ particles with diameter $\ge$10$\mu$m and thickness of $\sim$0.3 $\mu$m can be obtained under the optimum process parameters. The crystal structure of BaBi₄Ti₄${\text{O}}_{15}$ was determined as A2₁am by TEM, which should be attributed to the Bi${}^{3+}$ and Ba${}^{2+}$ diffusing into [TiO₆] octahedrons.

A high performance of novel three-component composites with 2–1–2 connectivity is reported and discussed. Layers of the composites are parallel-connected, and each layer contains the ferroelectric (FE) component. The layer of the first type (LFT) represents domain-engineered single crystal poled along either [0 0 1] or [0 1 1]. The layer of the second type is described as a system of long FE ceramic rods that have the shape of an elliptic cylinder and are aligned in a polymer medium. Piezoelectric coefficients $d_{3j}^{\ast }$ and $g_{3j}^{\ast }$ and sets of figures of merit (FOM) (energy-harvesting $d_{3j}^{\ast }{g}_{3j}^{\ast }$, modified $F_{3j}^{\ast \sigma }$ for a stress-driven harvester and modified $F_{3j}^{\ast \xi }$ for a strain-driven harvester) are analyzed to show their large values and specifics of the anisotropy when varying volume fractions of components and a rotation angle of the ceramic rod bases. For the first time, the studied parameters are compared in two directions: (i) the composite based on [0 0 1]-poled single crystal versus the composite based on [0 1 1]-poled single crystal and (ii) the lead-free composite versus the lead-containing composite (both based on [0 0 1]-poled single crystals). The advantages of the high-performance lead-free composite are discussed. The 2–1–2 composites put forward in this paper are of interest as advanced materials suitable for piezoelectric sensors, actuators and energy-harvesting systems operating at constant stress or strain.

We study the dynamical stability of self-gravitating systems in presence of anisotropy. In particular, we introduce a stability criterion, in terms of the adiabatic local index, that generalizes the stability condition < ϒ >≥ 4/3 of the isotropic regime. Also, we discuss some applications of the criterion.

This paper explores the extended gravitational decoupling procedure for a static sphere in the context of f(ℝ, T) theory where ℝ denotes the scalar curvature and T represents the trace of the energy-momentum tensor. This method extends the domain of a seed solution by including a new gravitational source. Deformations in radial and temporal metric potentials split the set of field equations into two subsystems associated with isotropic and additional matter sources. We utilize the Korkina-Orlyanskii spacetime as a solution for the system describing the seed source and use some physical constraints to extend it to anisotropic domain. A linear gravity model, f(ℝ, T) = ℝ + 2χT (where χ couples geometry to matter) is employed to interpret the influence of the decoupling parameter on the developed solutions. It is found that physically acceptable solutions can be formulated in the background of f(ℝ, T) gravity through the decoupling approach.

In this paper we study nonrotating, spherical, gravitational equilibrium configurations of a semidegenerate collisionless Fermi gas, in a general relativistic framework. We consider a modified Fermi-Dirac distribution function, including an energy cutoff term to ensure solutions with finite mass and radius, as well as a second term taking into account the effect of the anisotropy with prevalence of transverse component of velocity. The problem of the dynamical stability is also considered in Newtonian regime by introducing a general criterion, for the anisotropic systems, in terms of adiabatic indexes.