Initial Anisotropy Research Articles

Particle morphology and principal stress direction dependent strength anisotropy through torsional shear testing

The major principal stress direction angle (ασ) experienced by granular soils varies widely in engineering, causing different strengths. However, how particle morphology affects the strength anisotropy behavior under different ασ remains unclear. To address this gap, this study performed drained hollow cylinder torsional shear tests under different ασ on six granular materials with distinct morphologies. Results highlight the significant dependence of peak strengths of granular materials on both particle morphology and ασ. Increasing particle shape irregularity and surface roughness leads to a considerable enhancement in peak strength, while this peak strength significantly degrades with increasing ασ. Materials with more irregular shapes were found to have a more pronounced strength anisotropy. Furthermore, the initial fabric of particle packings, derived from three-dimensional X-ray microtomography, was used to interpret microscopic mechanisms behind the morphology-dependent strength anisotropy. Irregular-shaped materials display broader preferred particle orientations and higher initial fabric anisotropy compared to relatively regular-shaped materials. This higher morphology-induced fabric anisotropy contributes to strength anisotropy, and a correlation was established for describing this trend. Additionally, an anisotropic failure criterion incorporating fabric anisotropy was developed to characterize the strength envelope for granular materials with diverse shapes.

A geometric-tension-dynamics model of epithelial convergent extension

Convergent extension of epithelial tissue is a key motif of animal morphogenesis. On a coarse scale, cell motion resembles laminar fluid flow; yet in contrast to a fluid, epithelial cells adhere to each other and maintain the tissue layer under actively generated internal tension. To resolve this apparent paradox, we formulate a model in which tissue flow in the tension-dominated regime occurs through adiabatic remodeling of force balance in the network of adherens junctions. We propose that the slow dynamics within the manifold of force-balanced configurations is driven by positive feedback on myosin-generated cytoskeletal tension. Shifting force balance within a tension network causes active cell rearrangements (T1 transitions) resulting in net tissue deformation oriented by initial tension anisotropy. Strikingly, we find that the total extent of tissue deformation depends on the initial cellular packing order. T1s degrade this order so that tissue flow is self-limiting. We explain these findings by showing that coordination of T1s depends on coherence in local tension configurations, quantified by a geometric order parameter in tension space. Our model reproduces the salient tissue- and cell-scale features of germ band elongation during Drosophila gastrulation, in particular the slowdown of tissue flow after approximately twofold elongation concomitant with a loss of order in tension configurations. This suggests local cell geometry contains morphogenetic information and yields experimentally testable predictions. Defining biologically controlled active tension dynamics on the manifold of force-balanced states may provide a general approach to the description of morphogenetic flow.

Exploring the Effects of Initial Fabric Anisotropy due to Preshearing Stress History in Different Directions on the Undrained Behavior of Loose Sands

Exploring the Effects of Initial Fabric Anisotropy due to Preshearing Stress History in Different Directions on the Undrained Behavior of Loose Sands

Dynamics of star clusters with tangentially anisotropic velocity distribution

Recent high-precision observations with HST and Gaia enabled new investigations of the internal kinematics of star clusters (SCs) and the dependence of kinematic properties on the stellar mass. These studies raised new questions about the dynamical evolution of self-gravitating stellar systems. We aim to develop a more complete theoretical understanding of how the various kinematical properties of stars affect the global dynamical development of their host SCs. We perform $N$-body simulations of globular clusters with isotropic, radially anisotropic, and tangentially anisotropic initial velocity distributions. We also study the effect of an external Galactic tidal field. We obtain three main results. First, compared to the conventional, isotropic case, the relaxation processes are accelerated in the tangentially anisotropic models and, in agreement with our previous investigations, are slower in the radially anisotropic ones. This leads to, for example, more rapid mass segregation in the central regions of the tangential models or their earlier core collapse. Second, although all SCs become isotropic in the inner regions after several relaxation times, we observe differences in the anisotropy profile evolution in the outer cluster regions --- all tidally filling models gain tangential anisotropy there, while the underfilling models become radially anisotropic. Third, we observe different rates of evolution towards energy equipartition (EEP). While all SCs evolve towards EEP in their inner regions (regardless of the filling factor), the outer regions of the tangentially anisotropic and isotropic models are evolving to an `inverted' EEP (i.e.\ with the high-mass stars having higher velocity dispersion than the low-mass ones). The extent (both spatial and temporal) of this inversion can be attributed to the initial velocity anisotropy --- it grows with increasing tangential anisotropy and decreases as the radial anisotropy rises.

A multi‐fidelity residual neural network based surrogate model for mechanical behaviour of structured sand

AbstractThe structured sand presents significant interparticle bonding and anisotropy, resulting in significant differences in the physical and mechanical properties from the pure sand. This study proposes a new surrogate model based on the concept of multi‐fidelity residual neural network (MR‐NN) as an alternative to DEM simulation for predicting the mechanical behaviours of structured sand with different initial anisotropy and saving largely computational costs. The model is initially trained using low‐fidelity (LF) data to focus on capturing the main underpinning correlations between macroscopic mechanical parameters with inter‐particle properties and anisotropic state variables (i.e., microscopic fabric and tilting angle of sand), where the LF data are generated from previously proposed anisotropic macro‐micro quantitative correlation. Subsequent training on sparser high‐fidelity (HF) data is used to calibrate and refine the model with HF data generated from DEM simulations for anisotropic structured sand. Feedforward neural network (FNN) is adopted as the baseline algorithm for training models. The macroscopic anisotropic parameters of structured sand predicted by the surrogate model are compared with DEM simulations to examine its feasibility and generalization ability. Furthermore, the robustness of the surrogate model is examined by discussing the effect of LF data on the performance of MR‐NN. The superiority of the MR‐NN is further verified by comparing the performance of the trained MR‐NN with the one‐shot trained FNN based on the same HF data. All results demonstrate that the proposed surrogate model can provide a fast and accurate simulation of the anisotropic parameters of structured sand.

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 (Δδ) in the isotropic process greater than the valley (δ1) 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.

The impact of initial fabric anisotropy on cyclic liquefaction behavior with polygonal particles using the discrete element method (DEM)

Liquefaction is one of the most significant phenomena that can occur in soil during an earthquake. The destructive effects of this phenomenon on earth structures have captured the attention of many geotechnical engineers. Additionally, the gradual increase in pore water pressure during the cyclic loading induced by the propagation of earthquake waves, known as cyclic liquefaction, is a crucial factor that might lead to the complete loss of shear strength in soils. A better understanding of cyclic liquefaction is essential for improving earthquake hazard analysis and mitigating structural damage. Factors influencing liquefaction behavior include particle size, particle grading, and soil fabric. By “soil fabric,” we refer to the arrangement and positioning of particles with each other, particle shape, and the shape of voids among particles. This research aims to focus on the effects of fabric anisotropy on cyclic liquefaction of granular soils with angular particles. To carry out this investigation, the discrete element method has been employed. In the discrete element method, the geometry of particles and, generally, the soil fabric can be considered. In this research, specimens with varying particle orientation angles were produced and subjected to cyclic loading tests under undrained conditions. By examining the stress paths of specimens during cyclic loading, it is observed that the initial fabric and inherent anisotropy significantly influence the behavior of the specimens. Inherent anisotropy leads to varying numbers of cycles required for the initial liquefaction of each specimen. Furthermore, it is observed that as the particle orientation angle increases, the localization of axial strains shifts from tensile to compressive directions. The effect of inherent anisotropy plays a substantial role in the initial liquefaction (ru = 1). If the liquefaction of specimens is of interest at lower values of ru, the effect of inherent anisotropy can be disregarded.

Deep learning insights into cosmological structure formation

The evolution of linear initial conditions present in the early Universe into extended halos of dark matter at late times can be computed using cosmological simulations. However, a theoretical understanding of this complex process remains elusive; in particular, the role of anisotropic information in the initial conditions in establishing the final mass of dark matter halos remains a long-standing puzzle. Here, we build a deep learning framework to investigate this question. We train a three-dimensional convolutional neural network to predict the mass of dark matter halos from the initial conditions, and quantify in full generality the amounts of information in the isotropic and anisotropic aspects of the initial density field about final halo masses. We find that anisotropies add a small, albeit statistically significant amount of information over that contained within spherical averages of the density field about final halo mass. However, the overall scatter in the final mass predictions does not change qualitatively with this additional information, only decreasing from 0.9 dex to 0.7 dex. Given such a small improvement, our results demonstrate that isotropic aspects of the initial density field essentially saturate the relevant information about final halo mass. Therefore, instead of searching for information directly encoded in initial conditions anisotropies, a more promising route to accurate, fast halo mass predictions is to add approximate dynamical information based e.g. on perturbation theory. More broadly, our results indicate that deep learning frameworks can provide a powerful tool for extracting physical insight into cosmological structure formation. Published by the American Physical Society 2024

Effect of Aquifer Strength and Gas-cap Size on Oil Recovery Efficiency in Thin-Oil Rim

Recovering oil from thin oil rim reservoirs depends on some factors such as the gas-cap size, thickness of initial oil column, aquifer strength, permeability anisotropy (kV/kH), and rock and fluid properties. The arbitrary selection of these factors by researchers during investigation limits the systematic assessment of the influence of these factors on hydrocarbon recovery from thin oil rim reservoirs. This work investigated the effect of aquifer strength, gas cap size, and permeability anisotropy on hydrocarbon recovery, using design of experiment (DOE) as a tool in the systematic selection of some of the factors that influence hydrocarbon recovery. A static model of the base case oil rim was built in Petrel. Using Eclipse simulator, two other reservoir models having different gas cap sizes from the base case were built. Forty-eight simulation cases were generated using the result from the design of experiment (DOE). The aquifer model used is a Fetkovich analytical aquifer model, and the aquifer volume factors used for this investigation are 0.7, 1.0, 1.5 and 2.5, while the gas cap sizes (m-factor) used are 0.5, 1.0 and 2.0. The permeability anisotropy used are 0.01, 0.05, 0.10 and 0.40. Each simulation case was made to run for a period of twenty years (20years) and the results for the Field Oil Efficiency (FOE), Field Water Production Total (FWPT) and Field Gas Production Total (FGPT) were obtained and analyzed. It was found from this study that, the oil percentage recovery will increase as the gas cap size is decreased, while the percentage gas and water recoveries will increase as the size of the gas cap is increased for a thin oil rim reservoir. Again, for a thin oil rim reservoir with gas cap size of 0.50 ≤ m ≤ 2.00, percentage recovery of gas, oil and water will increase with aquifer volume. Also, based on the result obtained, a thin oil rim reservoir with small to moderate gas cap size (0.5≤ m≤1.0) will yield higher oil recoveries irrespective of the kV /kH ratio.

Effect of initial fabric anisotropy on cyclic liquefaction behavior of granular soils using discrete element method

Effect of initial fabric anisotropy on cyclic liquefaction behavior of granular soils using discrete element method

Undrained shear behavior of silty sand with a constant state parameter considering initial stress anisotropy effect

Field observations in sedimentation and erosion-prone areas indicate that most natural sand deposits may contain a certain amount of non-plastic fines and are often under anisotropic stress conditions. A series of triaxial compression tests were performed on clean and silty sand with fines content fc ranging from 0 to 20% at an initial mean effective stress of p0′ = 100 kPa and varying consolidation conditions to understand the impact of initial stress anisotropy on undrained shear behavior. The results indicate that the state parameter ψ is a superior predictor for characterizing the responses of sand-fines mixtures compared to the global void ratio and relative density. A comparison of the behavior of clean and silty sand with a constant ψ (= − 0.03) confirms that the sample with 10% fc exhibits the strongest dilation and greatest shear resistance, irrespective of the consolidation conditions. It is also demonstrated that the initial stress anisotropy with a comparably higher static stress ratio ηs typically diminishes the shear strength of mixtures. However, the influence of initial stress anisotropy on soil stiffness is not unilateral. The sample consolidated to a negative ηs is stiffer than that under isotropic consolidation, while the presence of a positive ηs leads to a decrease in the secant Young's modulus.

Gate tunable linear dichroism in monolayer 1T'-MoS2.

The linear dichroism demonstrates promising applications in the fields of polarization-resolved photodetectors and polarization optical imaging. Herein, we study the optical properties of monolayer 1T'-MoS2 based on a four-band effective k · p Hamiltonian within the framework of linear response theory. Owing to the anisotropic band structure, the k-resolved optical transition matrix elements associated with armchair(x) and zigzag(y) direction polarized light exhibit a staggered pattern. The anisotropy of the optical absorption spectrum is shown to sensitively depend on the photon energy, the light polarization and the gate voltage. A gate voltage can continuously modulate the anisotropy of the optical absorption spectra, rendering it isotropic or even reversing the initial anisotropy. This modulation leads to linear dichroism conversions across multiple wavelengths. Our findings are useful to design polarized photodetectors and sensors based on monolayer 1T'-MoS2. Our results are also applicable to other monolayer transition metal dichalcogenides with 1T' structure.

Experimental investigation and numerical optimization of sheet metal forming limits during deep drawing process of DD14 steel

This work aims to experimentally study the deep drawability of DD14 hot-rolled steel sheets and to optimize numerically the material formability. The material anisotropy was confirmed by metallographic analysis of the material and tensile tests on specimens taken in three orientations with respect to the sheet rolling direction. Where the stress-strain curves show a sensitivity of material to the Piobert-Lüders phenomenon. The die pressure and the blank holder were considered as controlling factors on plastic instability and the success of the deep drawing operation. The forming limit curves (FLC) were plotted to highlight the different deformation modes that the sheet metal underwent during the deep drawing process. The collected deep-drawn parts observation shows severe plastic instability, until fracture. The initial plastic anisotropy is determined by the Hill48 quadratic criterion and the work hardening by the Hollomon power law. It results, during the experimental tests, that the front bottom corners of the deep drawn part are the areas at high risk of damage. The various numerical simulation scenarios followed by comparisons with the experimental results, allowed us to confirm the optimum conditions that minimize the material's plastic instability risks, forming operation “Step” and BHP “Amplitude”.

Azimuthal anisotropies at high-pT from transverse momentum dependent (TMD) parton distribution and fragmentation functions

Unpolarized protons can generate transversely polarized quarks or linearly polarized gluons through a distribution known as the Boer-Mulders’ function. The fragmentation of similarly polarized partons to unpolarized hadrons is called the Collins’ function. Both of these functions include correlations between the spin or polarization and the relative transverse momentum of the incoming parton or outgoing hadron, with respect to the parent particle. We explore the effect of including these and other TMDs on the production of high-pT (unpolarized) hadron production from (unpolarized) proton-proton scattering. The resulting initial state anisotropies, modulated with similar final state effects, may account for the observed azimuthal anisotropy of the produced high transverse momentum hadrons, without modification to the angle integrated spectra (RAA). This may be an explanation for the existence of a v2 in high-pT hadron spectra in p-A collisions without any observable nuclear modification of the spectra.

Far-from-equilibrium attractors for massive kinetic theory in the relaxation time approximation

In this proceedings contribution, we summarize recent findings concerning the presence of early- and late-time attractors in non-conformal kinetic theory. We study the effects of varying both the initial momentum-space anisotropy and initialization times using an exact solution of the 0+1D boostinvariant Boltzmann equation with a mass- and temperature-dependent relaxation time. Our findings support the existence of a longitudinal pressure attractor, but they do not support the existence of distinct attractors for the bulk viscous and shear pressures. Considering a large set of integral moments, we show that for moments with greater than one power of longitudinal momentum squared, both early- and late-time attractors are present.

Excitation of proton firehose instability in magnetospheric cold and hot proton plasma: a quasilinear approach

Abstract Unstable states of different charged species in the solar wind and Earth’s magnetosphere are governed with the collective and collisional processes. For these dilute plasmas, the contribution of microinstabilities driven by the anisotropic particle distribution and heat flux becomes important in defining the stable/equilibrium states of electrons and ions/protons. The present paper highlights the key role of proton firehose instability to regulate an unchecked rise in the temperature anisotropy in these solar wind and magnetospheric environments. Right-handed circularly polarized proton firehose mode becomes unstable when the temperature condition of T ‖p > T ⊥p is satisfied, where the directional subscripts denote directions with respect to the ambient magnetic field. Based on the observations of magnetospheric multi-scale (MMS) space mission, we assume the bi-Maxwellian nature of the model distribution for the multi-component proton plasma. To study the time evolution of the unstable mode, we further allow the time variation in the cold and hot proton temperatures. For the choice of the initial conditions related with observations, we unveil the wave properties (growth and unstable wave number domain) corresponding to the cold/hot proton temperature anisotropy and the plasma betas of constituents proton components. In the back action of proton firehose instability, we highlight the time-scale modifications and saturation of initial bi-Maxwellian distributions and resulting wave-energy densities for various choices of initial cold-hot temperature anisotropy and plasma betas.

Lessons learned from matching 3D DEM and experiments at macro, meso and fabric scales for triaxial compression tests on lentils

A series of discrete element method (DEM) triaxial compression simulations on specimens of an anisometric granular material starting from distinct initial fabric anisotropy states are conducted and compared with physical experiments on lentils at different scales, assisted by operando X-ray tomography measurements. A quantitative reproduction of the group of experimental results is achieved by appropriate idealization and determination of particle shape, boundary conditions, contact parameters, and initial state. The reliability of DEM in quantitative representation of macro scale stress–strain response, meso scale strain localization, and micro scale fabric anisotropy evolution is thus comprehensively validated against measurements from physical experiments, which is a step forward from comparisons only at the macro or particle kinematics level. Several key factors that govern realistic DEM simulations are also identified. The friction coefficient between particles during specimen generation, particle shape, and specimen preparation method can significantly affect the initial state of DEM specimens. Differences in initial state at macro and micro scales and boundary conditions can strongly influence the stress–strain response. However, the evolution of fabric anisotropy appears to be insensitive to changes in initial state and boundary conditions.

Non-coaxiality behaviours and unified flow rule of soil–structure interfaces

Non-coaxiality is one of the key characteristics of soil–structure interfaces that broadly occur in geotechnical engineering. A series of interface tests between gravel and a structure was performed to address and model the non-coaxiality behaviours of interfaces subjected to various three-dimensional (3D) loadings. Non-coaxiality of the interface was identified during the yielding phase when subjected to 3D cycling of shear stress and could be captured by the non-coaxiality angle. The non-coaxiality angle does not evolve as a result of 3D cyclic shearing but depends primarily on the magnitude and direction of the current shear stress and the direction of the shear stress increment. The shear stress amplitude ratio, shear stress amplitude, shear stress rotation and initial shear stress significantly affect the magnitude and change pattern of the non-coaxiality angle, attributed to varied shear stress and shear stress increment vectors. A unified flow rule for interfaces was established based on 3D interface test analysis. The flow rule perfectly determines the flow direction of different kinds of interfaces prior to and at the mobilisation of shear strength under diverse two-dimensional and 3D loading conditions, such as arbitrary shear paths and differing shear stress amplitudes, shear stress amplitude ratios, initial shear stresses, normal stresses, shear strengths and anisotropy characteristics.

On the analytical description of the nonlinear stage of the Weibel instability in collisionless anisotropic plasma

On the basis of the energy invariants for the Weibel instability in a collisionless non-relativistic plasma, an analytical relation is obtained between the instantaneous values of the space-averaged energy density of the magnetic field, its dominant wavenumber and the average plasma anisotropy parameter. The relation is valid for arbitrary particle velocity distribution functions, including ones that vary with time at the nonlinear stage of instability. It is obtained under the assumption that the plasma is homogeneous along a certain axis, determined, for example, by an external magnetic field, and taking into account only the modes with wavevectors orthogonal to this axis. We give an estimate of the maximum magnetic field energy achievable during the Weibel instability and show that its ratio to the initial longitudinal energy of particles, even for a large initial plasma anisotropy parameter, cannot exceed the value approximately equal to 0.2. The obtained analytical relation is verified using two-dimensional particle-in-cell simulations.

Anisotropic Universes Sourced by Modified Chaplygin Gas

In this work, we perform a comparative study of the Kantowski–Sachs (KS) and Bianchi-I anisotropic universes with Modified Chaplygin gas (MCG) as matter source. We obtain the volume and scale factors as solutions to the Einstein Field Equations (EFEs) for the anisotropic universes, and check whether the initial anisotropy is washed out or not for different values of the MCG parameters present in the solution by obtaining the anisotropy parameters for each solution. The deceleration parameter is also obtained for each solution, the significance of which is discussed in the concluding section. Interestingly there are a number of notable results that appear from our study which help us to compare and contrast the two different anisotropic models along with proper understanding of the role of MCG as matter source in these models.