Combined effects of heterogeneity, anisotropy, and saturation on steady state flow and transport: A laboratory sand tank experiment

Field soils show rather different spreading behavior at different water saturations, frequently caused by layering of the soil material. We performed tracer experiments in a laboratory sand tank. Such experiments complement and help comprehension of field investigations. We estimated, by image analysis, the first two moments of small plumes traveling through a two-dimensional, heterogeneous medium with strongly anisotropic correlation structure. Three steady state regimes were analyzed. Two main conclusions were drawn. First, low saturation led to very large heterogeneity and to strong preferential flow. Thus the description of the flow paths and the prediction of the solute arrival times require, in this case, more accurate knowledge about the topological structure. Second, saturation-dependent macroscopic anisotropy is an essential element of transport in unsaturated media. For this reason, small structural soil features should be properly upscaled to give appropriate effective soil parameters to be input in transport models.

Upscaling of anisotropy in unsaturated Miller-similar porous media

Geological and pedological processes rarely form isotropic media as is usually assumed in transport studies. Anisotropy at the Darcy or field scale may be detected directly by measuring flow parameters or may become indirectly evident from movement and shape of solute plumes. Anisotropic behavior of a soil at one scale may, in many cases, be related to the presence of lower-scale directional structures. Miller similitude with different pore-scale geometries of the basic element is used to model macroscopic flow and transport behavior. Analytical expressions for the anisotropic conductivity tensor are derived based on the dynamic law that governs the flow problem at the pore scale. The effects of anisotropy on transport parameters are estimated by numerical modeling.

Nanometer-size anisotropy of injection-molded polymer micro-cantilever arrays

Understanding and controlling the structural anisotropies of injection-molded polymers is vital for designing products such as cantilever-based sensors. Such micro-cantilevers are considered as cost-effective alternatives to single-crystalline silicon-based sensors. In order to achieve similar sensing characteristics,structure and morphology have to be controlled by means of processing parameters including mold temperature and injection speed. Synchrotron radiation-based scanning small- (SAXS) and wide-angle x-ray scattering techniques were used to quantify crystallinity and anisotropy in polymer micro-cantilevers with micrometer resolution in real space. SAXS measurements confirmed the lamellar nature of the injection-molded semi-crystalline micro-cantilevers. The homogenous cantilever material exhibits a lamellar periodicity increasing with mold temperature but not with injection speed. We demonstrate that micro-cantilevers made of semi-crystalline polymers such as polyvinylidenefluoride, polyoxymethylene, and polypropylene show the expected strong degree of anisotropy along the injection direction.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions.

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.

Bone Volume Fraction and Fabric Anisotropy Are Better Determinants of Trabecular Bone Stiffness than Other Morphological Variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphologyelasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae and iliac crest were analysed. Their morphology was assessed via 25 variables and their stiffness tensor (inline image) was computed from six independent load cases using micro finite element analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multi-linear regression modelling the dependent variable inline image. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of inline image (inline image=0.889), especially in combination with fabric (inline image=0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (inline image=0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and post-elastic properties.

Nonequilibrium hysteresis and spin relaxation in the mixed-anisotropy dipolar-coupled spin-glass LiHo0.5Er0.5F4

We present a study of the model spin-glass LiHo0.5Er0.5F4 using simultaneous ac susceptibility, magnetization, and magnetocaloric effect measurements along with small angle neutron scattering (SANS) at sub-Kelvin temperatures. All measured bulk quantities reveal hysteretic behavior when the field is applied along the crystallographic c axis. Furthermore, avalanchelike relaxation is observed in a static field after ramping from the zero-field-cooled state up to 200–300 Oe. SANS measurements are employed to track the microscopic spin reconfiguration throughout both the hysteresis loop and the related relaxation. Comparing the SANS data to inhomogeneous mean-field calculations performed on a box of one million unit cells provides a real-space picture of the spin configuration. We discover that the avalanche is being driven by released Zeeman energy, which heats the sample and creates positive feedback, continuing the avalanche. The combination of SANS and mean-field simulations reveal that the conventional distribution of cluster sizes is replaced by one with a depletion of intermediate cluster sizes for much of the hysteresis loop.

Anisotropy of magnetic susceptibility in natural olivine single crystals

Mantle flow dynamics can cause preferential alignment of olivine crystals that results in anisotropy of physical properties. To interpret anisotropy in mantle rocks, it is necessary to understand the anisotropy of olivine single crystals. We determined anisotropy of magnetic susceptibility (AMS) for natural olivine crystals. High-field AMS allows for the isolation of the anisotropy due to olivine alone. The orientations of the principal susceptibility axes are related to the olivine’s crystallographic structure as soon as it contains >3 wt % FeO. The maximum susceptibility is parallel to the c axis both at room temperature (RT) and at 77 K. The orientation of the minimum axis at RT depends on iron content; it is generally parallel to the a axis in crystals with 3–5 wt % FeO, and along b in samples with 6–10 wt % FeO. The AMS ellipsoid is prolate and the standard deviatoric susceptibility, k0, is on the order of 8*10210 m3/kg for the samples with <1wt % FeO, and ranges from 3.1*1029 m3/kg to 5.7*1029 m3/kg for samples with 3–10 wt % FeO. At 77 K, the minimum susceptibility is along b, independent of iron content. The shape of the AMS ellipsoid is prolate for samples with <5 wt % FeO, but can be prolate or oblate for higher iron content. The degree of anisotropy increases at 77 K with p0 7757.160.5. The results from this study will allow AMS fabrics to be used as a proxy for olivine texture in ultramafic rocks with high olivine content.

Magnetic anisotropy in clinopyroxene and orthopyroxene single crystals

Pyroxenes constitute an important component in mafic igneous and metamorphic rocks. They often possess a prismatic habit, and their long axis, the crystallographic c axis, helps define a lineation in a textured rock. Anisotropy of magnetic susceptibility (AMS) serves as a fabric indicator in igneous and metamorphic rocks. If a rock’s AMS is carried by pyroxenes, it can be related to their crystallographic preferred orientation and degree of alignment. This requires knowing the intrinsic AMS of pyroxene single crystals. This study provides a comprehensive low-field and high-field AMS investigation of chemically diverse orthopyroxene and clinopyroxene crystals in relation to crystal structure, chemical composition, oxidation state of Fe, and the possible presence of ferromagnetic inclusions. The paramagnetic anisotropy, extracted from high-field data, shows clear relationships to crystallographic directions and Fe concentration both in clinopyroxene and orthopyroxene. In the diopside-augite series, the intermediate susceptibility is parallel to b, and the maximum is at 45° to the c axis. In aegirine, the intermediate axis remains parallel to b, while the maximum susceptibility is parallel to c. The AMS of spodumene depends on Fe concentration. In enstatite, the maximum susceptibility aligns with c and the minimum with b, and in the case of hypersthene, the maximum susceptibility is normal to the exsolution lamellae. Magnetite inclusions within augite possess a ferromagnetic anisotropy with consistent orientation of the principal susceptibilities, which dominates the low-field anisotropy. These results provide better understanding of magnetic anisotropy in pyroxenes and form a solid basis for interpretation of magnetic fabrics in pyroxene-bearing rocks.

High-Spin Molecules: Synthesis, X-ray Characterization, and Magnetic Behavior of Two New Cyano-Bridged Ni II 9 Mo V 6 and Ni II 9 W V 6 Clusters with a S = 12 Ground State

The preparations, X-ray structures, and magnetic characterizations are presented for two new pentadecanuclear cluster compounds:  [NiII{NiII(MeOH)3}8(μ-CN)30{MV(CN)3}6]·xMeOH·yH2O (MV = MoV (1) with x = 17, y = 1; MV = WV (2) with x = 15, y = 0). Both compounds crystallize in the monoclinic space group C2/c, with cell dimensions of a = 28.4957(18) Å, b = 19.2583(10) Å, c = 32.4279(17) Å, β = 113.155(6)°, and Z = 4 for 1 and a = 28.5278(16) Å, b = 19.2008(18) Å, c = 32.4072(17) Å, β = 113.727(6)°, and Z = 4 for 2. The structures of 1 and 2 consist of neutral cluster complexes comprising 15 metal ions, 9 NiII and 6 MV, all linked by μ-cyano ligands. Magnetic susceptibilities and magnetization measurements of compounds 1 and 2 in the crystalline and dissolved state indicate that these clusters have a S = 12 ground state, originating from intracluster ferromagnetic exchange interactions between the μ-cyano-bridged metal ions of the type NiII−NC−MV. Indeed, these data show clearly that the cluster molecules stay intact in solution. Ac magnetic susceptibility measurements reveal that the cluster compounds exhibit magnetic susceptibility relaxation phenomena at low temperatures since, with nonzero dc fields, χ‘ ‘M has a nonzero value that is frequency dependent. However, there appears no out-of-phase (χ‘ ‘M) signal in zero dc field down to 1.8 K, which excludes the expected signature for a single molecule magnet. This finding is confirmed with the small uniaxial magnetic anisotropy value for D of 0.015 cm-1, deduced from the high-field, high-frequency EPR measurement, which distinctly reveals a positive sign in D. Obviously, the overall magnetic anisotropy of the compounds is too low, and this may be a consequence of a small single ion magnetic anisotropy combined with the highly symmetric arrangement of the metal ions in the cluster molecule.

Magnetic anisotropy in natural amphibole crystals

Anisotropy of magnetic susceptibility (AMS) is often used as a proxy for mineral fabric in deformed rocks. To do so quantitatively, it is necessary to quantify the intrinsic magnetic anisotropy of single crystals of rock-forming minerals. Amphiboles are common in mafic igneous and metamorphic rocks and often define rock texture due to their general prismatic crystal habits. Amphiboles may dominate the magnetic anisotropy in intermediate to felsic igneous rocks and in some metamorphic rock types, because they have a high Fe concentration and they can develop a strong crystallographic preferred orientation. In this study, the AMS is characterized in 28 single crystals and I crystal aggregate of compositionally diverse clino- and ortho-amphiboles. High-field methods were used to isolate the paramagnetic component of the anisotropy, which is unaffected by ferromagnetic inclusions that often occur in amphibole crystals. Laue imaging, laser ablation-inductively coupled plasma-mass spectrometry, and Mossbauer spectroscopy were performed to relate the magnetic anisotropy to crystal structure and Fe concentration. The minimum susceptibility is parallel to the crystallographic a*-axis and the maximum susceptibility is generally parallel to the crystallographic b-axis in tremolite, actinolite, and hornblende. Gedrite has its minimum susceptibility along the a-axis, and maximum susceptibility aligned with c. In richterite, however, the intermediate susceptibility is parallel to the b-axis and the minimum and maximum susceptibility directions are distributed in the a-c plane. The degree of anisotropy, k', increases generally with Fe concentration, following a linear trend: k' = 1.61 x 10(-9) Fe - 1.17 x 10(-9) m(3)/kg. Additionally, it may depend on the Fe2+/Fe3+ ratio. For most samples, the degree of anisotropy increases by a factor of approximately 8 upon cooling from room temperature to 77 K. Fen-oactinolite, one pargasite crystal and riebeckite show a larger increase, which is related to the onset of local ferromagnetic (s.l.) interactions below about 100 K. This comprehensive data set increases our understanding of the magnetic structure of amphiboles, and it is central to interpreting magnetic fabrics of rocks whose AMS is controlled by amphibole minerals.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Prediction of Trabecular Bone Anisotropy from Quantitative Computed Tomography using Supervised Learning and a Novel Morphometric Feature Descriptor

Patient-specific biomechanical models including local bone mineral density and anisotropy have gained importance for assessing musculoskeletal disorders. However the trabecular bone anisotropy captured by high-resolution imaging is only available at the peripheral skeleton in clinical practice. In this work, we propose a supervised learning approach to predict trabecular bone anisotropy that builds on a novel set of pose invariant feature descriptors. The statistical relationship between trabecular bone anisotropy and feature descriptors were learned from a database of pairs of high resolution QCT and clinical QCT reconstructions. On a set of leave-one-out experiments, we compared the accuracy of the proposed approach to previous ones, and report a mean prediction error of 6% for the tensor norm, 6% for the degree of anisotropy and 19◦ for the principal tensor direction. These findings show the potential of the proposed approach to predict trabecular bone anisotropy from clinically available QCT images.