Different Degrees Of Anisotropy Research Articles

Anisotropic longitudinal water proton relaxation in white matter investigated ex vivo in porcine spinal cord with sample rotation

A variation of the longitudinal relaxation time T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} in brain regions that differ in their main fiber direction has been occasionally reported, however, with inconsistent results. Goal of the present study was to clarify such inconsistencies, and the origin of potential T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} orientation dependence, by applying direct sample rotation and comparing the results from different approaches to measure T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document}. A section of fixed porcine spinal cord white matter was investigated at 3 T with variation of the fiber-to-field angle θFB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta_{{{\ ext{FB}}}}$$\\end{document}. The experiments included one-dimensional inversion-recovery, MP2RAGE, and variable flip-angle T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} measurements at 22 °C and 36 °C as well as magnetization-transfer (MT) and diffusion-weighted acquisitions. Depending on the technique, different degrees of T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} anisotropy (between 2 and 10%) were observed as well as different dependencies on θFB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta_{{{\ ext{FB}}}}$$\\end{document} (monotonic variation or T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} maximum at 30–40°). More pronounced anisotropy was obtained with techniques that are more sensitive to MT effects. Furthermore, strong correlations of θFB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta_{{{\ ext{FB}}}}$$\\end{document}-dependent MT saturation and T1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T_{1}$$\\end{document} were found. A comprehensive analysis based on the binary spin-bath model for MT revealed an interplay of several orientation-dependent parameters, including the transverse relaxation times of the macromolecular and the water pool as well as the longitudinal relaxation time of the macromolecular pool.

A failure criterion for genuinely orthotropic materials and integration of a series of criteria for materials of different degrees of anisotropy

Existing failure criteria for orthotropic materials are subject to an underlying assumption which cause contradictions when applied to genuinely orthotropic materials that are significantly anisotropic in elasticity as well as in strengths. For such materials, there is lack of consistent failure criteria to support their applications in engineering structures. A general quadratic failure criterion tends to leave undetermined coefficients for interactive terms. A rational approach is adopted in this paper based on mathematical and logical considerations to determine these coefficients as the objective of this paper. Considerations are based on the intrinsic characteristics of the quadric surfaces introduced by the quadratic failure criterion. These coefficients must take the values as obtained, leaving no alternatives if logic prevails. The obtained criterion integrates for the first time a range of criteria separately formulated for materials of different degrees of anisotropy, from genuinely orthotropic, through transversely isotropic, cubically symmetric, to completely isotropic ones with different or identical tensile and compression strengths.

Study of the novel boron nitride polymorphs: First- principles calculations and machine learning

This study explores two new boron nitride polymorphs, namely C2221 BN and I-4 BN, characterized by sp2 hybridization. The investigation is conducted through first-principles calculations, including assessments of their structural properties, stability, elastic properties, anisotropy, and electronic properties. The newly discovered boron nitride polymorphs exhibit mechanical stability, dynamic stability, and thermodynamic stability, as ascertained by analyzing their elastic constants, phonon spectra, and associated enthalpies. The B/G values for both C2221 BN and I-4 BN far exceed the threshold of 1.75, thus confirming that they are ductile materials. The BN polymorphs investigated in this work exhibit different degrees of anisotropy in Young's modulus, shear modulus, and Poisson's ratio. Meanwhile, two different datasets were trained using four machine learning algorithms, and the random forest model with the m2ax dataset showed a high fitting degree, small error, and good stability. Then, the machine learning model, which has undergone training, is used to predict the elastic modulus of boron nitride polymorphs. Upon comparing the computed GGA values with the experimental values of c-BN, it is evident that the random forest model outperforms in accurately predicting the elastic modulus of boron nitride polymorphs.

Asymptotic steady state of a dissipative long-range interacting spin system at finite temperature

Many of the recently developed quantum systems that are considered promising candidates for the underlying technology of quantum computing enjoy long-range interaction, which is even tunable in some of them. Most of these systems can be described using the Heisenberg spin model to represent their interaction with the same system or a different one in hybrid structures. We consider here a finite two-dimensional spin system with a varying spin-spin long-range interaction under the effect of an external uniform magnetic field. We investigate the dynamics of the system and its asymptotic behavior at different degrees of anisotropy and interaction range under coupling to a thermal dissipative environment, starting from different initial states. We show that the system spin state and bipartite entanglement evolve in time to reach asymptotic values that are enhanced significantly by the degree of anisotropy and interaction range, whereas the thermal dissipative environment degrades the entanglement asymptotic equilibrium value as the temperature increases. Interestingly, while the robustness of the spin system against the environment’s thermal dissipative effects increases with the interaction range and degree of anisotropy, the entanglement between the far sites on the lattice shows its highest resilience in the partially anisotropic system, which might be attributed to a critical behavior taking place in the system. While the system’s early dynamics varies significantly depending on the initial state, the asymptotic equilibrium value is found to be completely independent.

An analytical model for variation of exit gradient downstream of a hydraulic structure with inclined downstream cutoff resting on infinite anisotropic soil

ABSTRACT An analytical solution is developed for the variation of the exit gradient along the downstream side of hydraulic structure with downstream-inclined cut-off resting on an anisotropic soil. The model is presented using dimensionless variables to demonstrate the relationship between the exit gradient rate and the ratio of the cut-off length to the seepage driving head (Ie*S/h), as well as the ratio of the distance from the structure toe to the cut-off length (X/S). Various ratios of the dam base length to the length of cut-off (b/S = 2, 3, 5, 10, and 15) are considered, along with different degrees of anisotropy of the underneath soil (Kr = 1, 0.5, 0.25, and 0.1). A MATLAB code is developed to implement the model. The results indicate that the maximum exit gradient is observed at an inclination angle of 75°, while the minimum exit gradient is observed at a 30° cutoff inclination angle for all cases. The variation of the exit gradient exhibits an increasing linear trend from X/S = 0 up to a certain distance (between 1 and 2). Beyond this distance, a non-linear decreasing trend is observed. The relationship between the exit gradient and the inclination angle cases after a distance of approximately 5X/S. The range of maximum exit gradient decreases with a decrease in the degree of anisotropy (Kr); with a significant reduction observed for Kr values of 0.25 and 0.1. Furthermore, for all degrees of anisotropy, the range of maximum exit gradient decreases as b/S increases.

Properties and special phenomena of strain sensors made of carbon particle-filled elastomers

Abstract Elastomers with a percolative network of carbon particles are a frequently studied class of materials for applications requiring high elongation and compliant sensors. For novel applications such as soft robots or smart textiles, these have some advantages over traditional strain gauges. However, their functionality is not fully understood. In this work, such materials are investigated as strain sensors in terms of their dynamic behavior, and their current limitations are demonstrated. It becomes clear that such sensors exhibit a non-monotonic behavior under dynamic loads that differs significantly from that observed in quasi-static tests. Two strategies for improving sensor characteristics are derived, modeled, and experimentally tested using the results and an electro-mechanical network model. First, a melt-spinning process that orients the carbon nanotube particles in the process direction creates different degrees of anisotropy. Second, to generate a local negative transverse contraction, an additional auxetic support structure is used. While the resulting anisotropy is insufficient to improve sensor properties, the auxetic structure can significantly improve strain sensitivity.

Stochastic (re)constructions of non-stationary material structures: Using ensemble averaged correlation functions and non-uniform phase distributions

Depending on the spatial distribution of mass or phases within the studied materials, they can be classified into two distinct property types: stationary and non-stationary. Stochastic reconstruction with simulated annealing and correlation functions is a powerful technique to produce material structural images from limited input data, but they usually deal with statistically homogeneous images only. In this work we show that the alteration of the initial phase distributions before starting annealing can produce non-stationary structures. The degree of such non-stationarity depends on numerous parameters of the annealing, including maximum correlation length, the choice of correlation function weights, annealing cooling schedule, in a convoluted manner—this makes it impossible to segregate the influence of each parameter. In general, we have shown that it is possible to choose such parameters in order to suppress the inhomogeneity of the resulting replicas. The degree of stationarity of the stochastic reconstructions had a significant influence on the physical properties of the reconstructed binary structures—computed full permeability tensors showed different degree of anisotropy and off-diagonal terms values depending on the reconstruction parameters. The proposed approach to produce non-stationary structures from ensemble averaged set of correlation functions opens numerous ways to attack theoretical and practical problems with natural and artificial materials with statistically inhomogeneous structure.

Investigation on swelling characteristics of GMZ bentonite with different initial water contents

Compacted bentonite has been identified as a suitable buffer material in the field of nuclear waste disposal due largely to its exceptional swelling potential. This study presents the swelling characteristics of compacted bentonite (1.50 Mg/m3) with different initial water content (5.0–29.0 %), accompanied with microstructural observation. Results showed that the swelling pressure was almost unchanged when the initial water content was less than 19.8 %, above which the swelling pressure continuously decreased by 25.9 %. The swelling deformation generally decreased with increasing initial water content, by up to 54.9 %. Microstructure features of specimens were largely affected by water contents and uniaxial compaction was expected to induce different degrees of anisotropy. This probably results in the variation in swelling potential of compacted bentonite, due to varying macro-microstructure coupling. The present study presents a new idea for the optimal design and manufacture of bentonite blocks.

Slope stability analysis considering the strength anisotropy of c-φ soil

In traditional slope stability analyses, soil is usually approximated as isotropic. However, naturally cohesive soil deposits are inherently anisotropic, primarily due to the directional arrangement of soil particles during their deposition process. In this paper, a generalized anisotropic constitutive model for c–φ soil is introduced to evaluate the influence of varying shear strength on slope stability. In this model, the initial strength anisotropy is defined by the variety of friction angles to the direction of the principle stress. This model is utilized by two approaches to estimate the slope stability. Firstly, the upper bound limit analysis solution for slope stability is developed, and the safety factor of the slopes is studied. Secondly, this model is coupled with the finite element method to get insight of the influence of anisotropy on slope stability. One typical slope case of slope is studied by numerical analyses. It is found that the slope stability is largely overestimated when the strength anisotropy is ignored, and the overestimation, in terms of safety factors, can reach up to 32.9%. The complex interrelations between the degree of anisotropy and evolution of the ensuing safety factor are revealed by a series of parametric studies in terms of different degrees of anisotropy.

Damage localization on CFRP composites by electrical impedance tomography

This work exploited the use of electrical impedance tomography (EIT) with one-step difference Gaussian-Newton (GN) algorithm to detect different types of damage on unidirectional carbon fibre/epoxy composite laminates. The major challenge concerning the implementation of EIT on composite materials has to do with their anisotropy. To assess this issue, this study was conducted on carbon fibre composites having different layup configurations with different degrees of anisotropy: a quasi-isotropic layup, to approximate as much as possible these layered materials to an isotropic material, and an unbalanced layup, with further degree of anisotropy. Damage detection in the highly anisotropic unbalanced laminates is a major challenge for EIT technique, which has not been assessed before in the literature. Severe damage, in the form of through-thickness holes, was created in the laminates with different diameters and at two locations of the specimen to evaluate the sensitivity of this technique to damage size and its capacity to detect multiple damages. EIT showed progressive decrease of electrical conductivity as the diameter of through-thickness holes increased. Impact damages of different severities were also created. The EIT technique was able to distinguish different damage shapes in the laminates with different anisotropy. EIT identified elongated shaped damages, produced by impact events of different impact energies, on unbalanced laminates. However, the EIT images overestimate the damaged area, as compared to non-destructive ultrasonic inspections. The EIT images of the quasi-isotropic laminates revealed damage in the central area of the specimens, but a well-defined damage shape could not be distinguished.

All sp2 hybridization BN polymorphs with wide bandgap

Four new boron nitride polymorphs hP24 BN, hP18-I BN, mP36 BN, and hP18-II BN with sp2 hybridization are investigated in this study by first-principles calculations, including the structural properties, stability, elastic properties, anisotropy, and electronic properties. Predicted by the electronic band structure, all the BN polymorphs in hP24, hP18-I, mP36, and hP18-II phase are wide bandgap semiconductor materials with a bandgap of 2.97–4.72 eV. Meanwhile, the bandgap of hP24 BN is larger than that of ZnO, and the bandgaps of hP18-I BN, mP36 BN, and hP18-II BN are larger than those of GaN and SiC. The new boron nitride polymorphs have mechanical stability, dynamic stability, and thermodynamic stability by analyzing the elastic constants, phonon spectra, and related enthalpies. The values of B/G of hP24 BN, hP18-I BN, mP36 BN, and hP18-II BN are all larger than 1.75, which confirms that they are ductile materials. Their densities are around 2.100 g/cm3, which are smaller than that of the c-BN (3.466 g/cm3). BN polymorphs in this study show different degrees of anisotropy in Young's modulus, and hP24 BN has the largest anisotropy in Young's modulus, while mP36 BN displays the smallest Young's modulus anisotropy.

Numerical study of the effect of rock anisotropy on stresses around an opening located in the fractured rock mass

The fractured rock mass is a discontinuous, heterogeneous, anisotropic medium in nature, including single, multiple or a network of joints with regular or irregular patterns located between the intact rocks. Anisotropy, as an inherent feature of rock mass, is a factor that causes the mechanical properties of rock to be various in different directions, so it is very important and necessary to be considered in the design of rock engineering structures. This study aims to investigate the effect of rock anisotropy on induced stresses around an opening like a borehole located in the fractured rock mass. For this purpose, the combination of discrete fracture network (DFN) method to construct a geometric model of rock mass, with distinct element method (DEM) to the numerical analysis of stress, was used. All coupled DEM-DFN models were developed based on the field data of the rock and joint system of the Sellafield site in the UK. The discrete fracture network models with different degrees of anisotropy, including a circular opening with two different cross-section areas placed at the center of model, were used for stress analysis. In each type of model, by applying different boundary conditions, the magnitude of induced stresses at selected points around opening is calculated, and then the obtained results are compared with the Kirsch method as a popular closed-form solution. The numerical results of this study showed that the presence of irregular joints with different orientations in the model caused anisotropy in the magnitude of induced stresses obtained around the opening. This is an important issue that the Kirsch method is not able to consider in the calculations. • Fractured rock mass is a discontinuous, heterogeneous and anisotropic medium including network of joints with the stochastic pattern located between intact rocks. • Anisotropy is a factor that causes the mechanical properties of rock to be various in different directions. • Coupled DEM-DFN models are developed to numerical analysis of stress around a borehole. • Presence of irregular joints with different orientations caused anisotropy in the amount of induced stresses around the borehole.

Modeling the Effect of Anisotropy in Ultrasonic-Guided Wave Tomography.

Most of the existing ultrasonic-guided wave tomography approaches to map structural changes in plate-like waveguides are based on the assumption of an isotropic material model. However, there are many other engineering applications that are made of anisotropic materials and structures. Applying these techniques on such structures becomes complicated due to the anisotropic wave propagation behavior. The main challenge is to develop a suitable forward model that describes the wave propagation in such material, thereby enabling accurate reconstruction of the material properties. The present study proposes an anisotropic formulation of the acoustic forward model to map velocity variations induced by defects in anisotropic plates. The anisotropic behavior of the waves along the plate is simulated by implementing approximate anisotropic parameters. The velocity reconstruction is based on a full-waveform inversion algorithm, and its performance is investigated in the case of different degrees of anisotropy of the plate material and the defect. The results suggest that the method is highly suitable for imaging velocity changes due to defects. This is found to be the case when the defect has a similar anisotropic structure to the surrounding plate material. The validation experiment is performed on a multilayered composite plate with a circular defect of stiffness reduction using A0 mode, showing a very good performance of the reconstruction algorithm.

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses

The elastic problem of anisotropic rotating disk with non-uniform thickness is studied. The material properties and thickness of the disk change in an arbitrary gradient along the radial direction, and the disk is constrained by displacement at the central axis of rotation and the outside is free. According to the equilibrium differential equation of the anisotropic rotating disk, the Fredholm integral equation of radial stress is obtained, and then numerically solved to calculate the displacement field and stress field. For any specific situation of gradient change, it is only need to substitute the corresponding gradient parameters. In the numerical part, firstly, assuming that the parameters such as thickness and elastic modulus are of special power functions, the numerical solution obtained by the Fredholm integral equation in this case is compared with the corresponding exact solution, and the FEM solutions by Ansys software for common Voigt model to validate the method. Then, we numerically analyzed the effect of the thickness change and gradient parameters, and different degree of anisotropy on the stress and displacement fields (with the common Voigt model). The proposed elastic analysis method for disk structure with arbitrary gradient changes along the radial direction, will be promising in the application of structural optimization. The analysis results can guide the engineers to design safer and more economical functionally graded structures.

Computational synthesis of large-scale three-dimensional heterogeneous lattice structures

This paper describes a methodology for designing the material distribution and orientation of three-dimensional non-uniform (heterogeneous) lattice structures. Recent advances in additive manufacturing enable fabrication across multiple length scales. Homogenization-based design optimization and the subsequent projection of the optimized design facilitate the synthesis of large-scale microstructures that form lightweight bionic designs. The main aspects of this research are (a) the construction, homogenization-based optimization, and projection of two types of lattices with different degrees of anisotropy and (b) the parallelization of the analysis, optimization, and projection framework in order to handle large-scale meshes and obtain high-resolution, heterogeneous lattice structures. Cubic and octet-truss lattices were selected to demonstrate the ability of the framework to design different types of lattices. A quadcopter arm and an internal wing structure were designed using the optimization and projection framework, verifying its capability to synthesize heterogeneous lattice structures for complex design domains. The ability to change the complexity of optimized microlattices using the characteristic parameters of the lattice is discussed. The relationship between the lattice anisotropy and the optimized, smoothed orientation is investigated, and the optimized design for each lattice is compared with those obtained using conventional design optimization procedures.

Bayesian inference of rock strength anisotropy: Uncertainty analysis of the Hoek–Brown failure criterion

Strength properties of most sedimentary and metamorphic rocks are known to vary with direction. Knowledge of this so-called rock anisotropy is of utmost importance for reliability analysis and engineering design. The purpose of this paper is twofold. First, we propose a formulation of the Hoek–Brown (HB) failure criterion, which calculates strength anisotropy using a non-uniform scaling of the stress tensor. We use two scaling factors, CN and CS, to link the orientation of the anisotropy planes with the loading direction. As we assume isotropic parameters for intact rock, our HB model formulation is relatively easy to use and has the additional advantage that it does not demand any modifications to the HB failure criterion. Second, we embed our HB model formulation in a Bayesian framework and illustrate its power and usefulness using experimental data of anisotropic rock samples published in the literature. Results demonstrate that our HB model formulation predicts accurately measured peak strengths of rocks with different degrees of anisotropy, confining stresses and anisotropy orientations. The uncertainty in peak strength of anisotropic rocks can be quite large, reiterating the need for an explicit treatment of strength anisotropy uncertainty in rock mechanics studies. The Bayesian methodology is general-purpose, and, as such, can help better inform geotechnical engineers, contractors and other professionals about rock conditions and design reliability and assist decision makers in determining the overall risks of engineering structures.

Development of a New Empirical Relation to Assess P-wave Velocity Anisotropy of Rocks

Several physical parameters and anisotropy related to rock textural arrangements, schistosity and weakness planes such as cracks and joints affect the P-wave velocity (VP). First, VP anisotropy of quartz-mica schist as a common type of widespread metamorphic rock was compared with VP anisotropy of jointed homogeneous limestone specimens to clarify effect of these two different types of anisotropies. The results showed that the VP anisotropy of quartz-mica schist texture is stronger than the VP anisotropy of jointed limestone, because all body of quartz-mica schist specimens have VP anisotropy behavior. Many rocks are anisotropic and degree of anisotropy varies from one to another. Various investigations have been carried out on VP anisotropy but there is not a unique comprehensive relation to represent the influence of different degrees of anisotropy on the VP for different rocks. The relation between VP and angle (θ) between the axis of symmetry (perpendicular to weakness planes) with the wave propagation direction was analyzed for a wide range of anisotropy degrees using the results of nine different types of rocks including: Angouran quartz-mica schist, Golgohar mica schist, amphibole schist, mica-quart schist, Marcellus shale, Withby shale WUK47B, WUK70 and WUK2, and Veroia-Polymylos gneiss. A new simple empirical relation fitted to all groups of results was obtained to assess VP for different degrees of anisotropies with a good correlation of determination (R2 = 0.937), low RMSE (RMSE = 320 m/s) and low CV (CV = 7.0%). P wave velocity anisotropy can simply be predicted by the developed relation using only two parameters of VP0 and VP90 or ε that is the percentage change of VP0 with respect to VP90. A VP anisotropy classification diagram was also developed based on the different values of ε.

Interferences and localization in disordered media with anisotropic structural correlations

Anisotropic photonic structures play a vital role in tailoring micro- and nanoscale light-matter interactions. In this work, we investigate the interference and localization effects in two-dimensional disordered media containing dipolar scatterers with anisotropic positional correlations. We study the anisotropy-induced frequency shifts in the transmission spectra, which cannot be accounted for by the independent scattering approximation or effective medium theory. We reveal that the distribution of eigenmodes strongly depends on the anisotropic structural correlations, and in all cases, Anderson localized modes are observed although their spatial extent exhibits different degrees of anisotropy. By calculating the level statistics, we demonstrate that the introduction of anisotropy to structural correlations has nontrivial effects on the level spacing statistics, which can be somewhat captured by a critical distribution function that works in the metal–insulator transition regime. This work can provide physical insights into the wave aspects of light transport in disordered media due to anisotropic structural correlations and guide the design of novel nanophotonic devices based on resonant scatterers.

Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field.

Recently new novel magnetic phases were shown to exist in the asymptotic steady states of spin systems coupled to dissipative environments at zero temperature. Tuning the different system parameters led to quantum phase transitions among those states. We study, here, a finite two-dimensional Heisenberg triangular spin lattice coupled to a dissipative Markovian Lindblad environment at finite temperature. We show how applying an inhomogeneous magnetic field to the system at different degrees of anisotropy may significantly affect the spin states, and the entanglement properties and distribution among the spins in the asymptotic steady state of the system. In particular, applying an inhomogeneous field with an inward (growing) gradient toward the central spin is found to considerably enhance the nearest neighbor entanglement and its robustness against the thermal dissipative decay effect in the completely anisotropic (Ising) system, whereas the beyond nearest neighbor ones vanish entirely. The spins of the system in this case reach different steady states depending on their positions in the lattice. However, the inhomogeneity of the field shows no effect on the entanglement in the completely isotropic (XXX) system, which vanishes asymptotically under any system configuration and the spins relax to a separable (disentangled) steady state with all the spins reaching a common spin state. Interestingly, applying the same field to a partially anisotropic (XYZ) system does not just enhance the nearest neighbor entanglements and their thermal robustness but all the long-range ones as well, while the spins relax asymptotically to very distinguished spin states, which is a sign of a critical behavior taking place at this combination of system anisotropy and field inhomogeneity.

Optimal Design of Barrage Profile on Anisotropic Soil Using Multi‐Objective Optimization Approach

Weirs and barrages are costly hydraulic diversion structures; therefore, any attempt to improve their design is a worthy contribution. Diversion structures, such as weir or barrage, may be designed on permeable formations considering homogenous soil properties. But in reality, soil properties are hardly homogeneous. In this paper, an approach is described to determine an economically efficient barrage profile by considering soil’s anisotropic behaviour. Hydraulic conductivity is considered to be an anisotropic soil property. An optimization-based methodology is developed to obtain the optimal barrage profile. The minimization of the material cost and minimization of the exit gradient is considered for multi-objective formulation. The multi-objective formulation is solved using NSGA-II, and a Pareto optimal front is obtained for different degrees of anisotropy. The flow interaction under a diversion structure in anisotropic soil is incorporated using the Modified Lane theory and is embedded in optimization formulation. The developed methodology is illustrated with a barrage profile as a hydraulic structure. A parametric study is carried out to study the effects of varying barrage design elements on the barrage’s optimum material cost.