Посвящается памяти А.И. Морозова Фаза Имри-Ма в системах с дефектами типа "случайное локальное поле" и "случайная локальная анизотропия" (О б з о р)

The conditions for the appearance in systems with defects of the "random local field" and "random local anisotropy" type of the Imry-Ma phases, in which the direction of the order parameter follows large-scale fluctuations of a random field or random anisotropy, are considered. It is shown that the anisotropy of the distribution of random fields of defects in the space of the order parameter can lead to the appearance of the long-range order. An attention is paid to phase diagrams arising as a result of competition between random fields of defects and anisotropy induced by defects. By the example of a system with random anisotropy (nanocrystalline ferromagnet), the dependences of the coercive field on the crystallite size are considered.

SymPKF (v1.0): a symbolic and computational toolbox for the design of parametric Kalman filter dynamics

Recent research in data assimilation has led to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, whereby the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step rely on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial, while it can be tedious to do this by hand. This contribution introduces a Python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a nonlinear diffusive advection (the Burgers equation) over a 1D domain and the linear advection over a 2D domain. The computation of the PKF dynamics is performed at a symbolic level, but an automatic code generator is also introduced to perform numerical simulations. A final multivariate example illustrates the potential of SymPKF to go beyond the univariate case.

Computing the effective crack energy of heterogeneous and anisotropic microstructures via anisotropic minimal surfaces

A variety of materials, such as polycrystalline ceramics or carbon fiber reinforced polymers, show a pronounced anisotropy in their local crack resistance. We introduce an FFT-based method to compute the effective crack energy of heterogeneous, locally anisotropic materials. Recent theoretical works ensure the existence of representative volume elements for fracture mechanics described by the Francfort–Marigo model. Based on these formulae, FFT-based algorithms for computing the effective crack energy of random heterogeneous media were proposed, and subsequently improved in terms of discretization and solution methods. In this work, we propose a maximum-flow solver for computing the effective crack energy of heterogeneous materials with local anisotropy in the material parameters. We apply this method to polycrystalline ceramics with an intergranular weak plane and fiber structures with transversely isotropic crack resistance.

Nested anisotropic geostatistical gridding of airborne geophysical data

Airborne geophysical surveys routinely collect data along traverse lines at sample spacing distances that are two or more orders of magnitude less than between line separations. Grids and maps interpolated from such surveys can produce aliasing; features that cross flight lines can exhibit boudinage or string-of-beads artefacts. Boudinage effects can be addressed by novel gridding methods. Following developments in geostatistics, a non-stationary nested anisotropic gridding scheme is proposed that accommodates local anisotropy in survey data. Computation is reduced by including anchor points throughout the interpolation region that contain localised anisotropy information which is propagated throughout the survey area with a smoothing kernel. Additional anisotropy can be required at certain locations in the region to be gridded. A model selection scheme is proposed that employs Laplace approximations for determining whether increased model complexity is supported by the surrounding data. The efficacy of the method is shown using a synthetic data set obtained from satellite imagery. A pseudo geophysical survey is created from the image and reconstructed with the method above. Two case histories are selected for further elucidation from airborne geophysical surveys conducted in Western Australia. The first example illustrates improvement in gridding the depth of palaeochannels interpreted from along-line conductivity-depth models of a regional airborne electromagnetic survey in the Mid-West. The second example shows how improvements can be made in producing grids of aeromagnetic data and inverted electrical conductivity from an airborne electromagnetic survey conducted in the Pilbara. In both case histories, nested anisotropic kriging reduces the expression of boudinage patterns and sharpens cross-line features in the final gridded products permitting increased confidence in interpretations based on such products.

Local anisotropy in mineralized fibrocartilage and subchondral bone beneath the tendon-bone interface

The enthesis allows the insertion of tendon into bone thanks to several remarkable strategies. This complex and clinically relevant location often features a thin layer of fibrocartilage sandwiched between tendon and bone to cope with a highly heterogeneous mechanical environment. The main purpose of this study was to investigate whether mineralized fibrocartilage and bone close to the enthesis show distinctive three-dimensional microstructural features, possibly to enable load transfer from tendon to bone. As a model, the Achilles tendon-calcaneus bone system of adult rats was investigated with histology, backscattered electron imaging and micro-computed tomography. The microstructural porosity of bone and mineralized fibrocartilage in different locations including enthesis fibrocartilage, periosteal fibrocartilage and bone away from the enthesis was characterized. We showed that calcaneus bone presents a dedicated protrusion of low porosity where the tendon inserts. A spatially resolved analysis of the trabecular network suggests that such protrusion may promote force flow from the tendon to the plantar ligament, while partially relieving the trabecular bone from such a task. Focusing on the tuberosity, highly specific microstructural aspects were highlighted. Firstly, the interface between mineralized and unmineralized fibrocartilage showed the highest roughness at the tuberosity, possibly to increase failure resistance of a region carrying large stresses. Secondly, fibrochondrocyte lacunae inside mineralized fibrocartilage, in analogy with osteocyte lacunae in bone, had a predominant alignment at the enthesis and a rather random organization away from it. Finally, the network of subchondral channels inside the tuberosity was highly anisotropic when compared to contiguous regions. This dual anisotropy of subchondral channels and cell lacunae at the insertion may reflect the alignment of the underlying collagen network. Our findings suggest that the microstructure of fibrocartilage may be linked with the loading environment. Future studies should characterize those microstructural aspects in aged and or diseased conditions to elucidate the poorly understood role of bone and fibrocartilage in enthesis-related pathologies.

Wastewater Disposal Has Not Significantly Altered the Regional Stress State in Southern Kansas

Wastewater disposal is primarily responsible for the increased seismicity rate since ∼2013 in southern Kansas. Previous work that used shear-wave splitting (SWS) in southern Kansas interpreted an ∼90° temporal rotation in the fast polarization direction and attributed it to increased pore pressures resulting from fluid injection. However, this interpreted rotation coincided with a change in the stations used to make the SWS measurements. We investigate the temporal variability of fast azimuths in southern Kansas by making SWS measurements on earthquake families with similar source–receiver paths recorded on a stable local seismic network. We select high-quality SWS measurements by investigating the stability of results across 65 different frequency bands between 0.5 and 15 Hz. We find that the fast polarization direction in southern Kansas is relatively constant with an average east-northeast (∼N79°E) orientation between 2014 and 2017. Our fast polarization measurements are primarily a reflection of the maximum principal horizontal stress direction (SHmax). We observe a slight spatial change in SHmax to the northeast (∼N55°E) near the Nemaha ridge in Oklahoma. However, we do not observe any significant temporal rotation of SHmax or variation in delay time (i.e., crack density) in southern Kansas, contrary to the earlier study. The previously interpreted ∼90° rotation may either be a reflection of a very local stress change or a misinterpretation of SWS results potentially due to the use of inconsistent source–receiver paths. Our SWS measurements cover the period of peak wastewater disposal and seismicity rates and suggest an absence of significant temporal rotations in the local anisotropy and stress orientations associated with wastewater disposal.