Anisotropic Gradient Research Articles

Mathematical modeling of the elastic properties of cubic crystals at small scales based on the Toupin\u2013Mindlin anisotropic first strain gradient elasticity

In this work, a mathematical modeling of the elastic properties of cubic crystals with centrosymmetry at small scales by means of the Toupin–Mindlin anisotropic first strain gradient elasticity theory is presented. In this framework, two constitutive tensors are involved, a constitutive tensor of fourth-rank of the elastic constants and a constitutive tensor of sixth-rank of the gradient-elastic constants. First, 3+11 material parameters (3 elastic and 11 gradient-elastic constants), 3 characteristic lengths and 1+6 isotropy conditions are derived. The 11 gradient-elastic constants are given in terms of the 11 gradient-elastic constants in Voigt notation. Second, the numerical values of the obtained quantities are computed for four representative cubic materials, namely aluminum (Al), copper (Cu), iron (Fe) and tungsten (W) using an interatomic potential (MEAM). The positive definiteness of the strain energy density is examined leading to 3 necessary and sufficient conditions for the elastic constants and 7 ones for the gradient-elastic constants in Voigt notation. Moreover, 5 lattice relations as well as 8 generalized Cauchy relations for the gradient-elastic constants are derived. Furthermore, using the normalized Voigt notation, a tensor equivalent matrix representation of the two constitutive tensors is given. A generalization of the Voigt average toward the sixth-rank constitutive tensor of the gradient-elastic constants is given in order to determine isotropic gradient-elastic constants. In addition, Mindlin’s isotropic first strain gradient elasticity theory is also considered offering through comparisons a deeper understanding of the influence of the anisotropy in a crystal as well as the increased complexity of the mathematical modeling.

Antiferromagnetic skyrmion-based logic gates controlled by electric currents and fields

Antiferromagnets are promising materials for future spintronic applications due to their unique properties including zero stray fields, robustness vs external magnetic fields, and ultrafast dynamics, which have attracted extensive interest in recent years. In this work, we investigate the dynamics of isolated skyrmions in an antiferromagnetic nanotrack with a voltage-gated region. It is found that the skyrmion can be jointly controlled by the driving current and the voltage-controlled magnetic anisotropy gradient. We further propose a design of logic computing gates based on the manipulation of antiferromagnetic skyrmions, which is numerically realized combining several interactions and phenomena, including the spin Hall effect, voltage-controlled magnetic anisotropy effect, skyrmion–skyrmion interaction, and skyrmion–edge interaction. The proposed logic gates can perform the basic Boolean operations of the logic AND, OR, NOT, NAND, and NOR gates. Our results may have a great impact on fundamental physics and be useful for designing future nonvolatile logic computing devices with ultra-low energy consumption and ultra-high storage density.

Fluid identification and effective fracture prediction based on frequency-dependent AVOAz inversion for fractured reservoirs

Fluid and effective fracture identification in reservoirs is a crucial part of reservoir prediction. The frequency-dependent AVO inversion algorithms have proven to be effective for identifying fluid through its dispersion property. However, the conventional frequency-dependent AVO inversion algorithms based on Smith & Gidlow and Aki & Richards approximations do not consider the acquisition azimuth of seismic data and neglect the effect of seismic anisotropic dispersion in the actual medium. The aligned fractures in the subsurface medium induce anisotropy. The seismic anisotropy should be considered while accounting for the seismic dispersion properties through fluid-saturated fractured reservoirs. Anisotropy in such reservoirs is frequency-related due to wave-induced fluid-flow (WIFF) between interconnected fractures and pores. It can be used to identify fluid and effective fractures (fluid-saturated) by using azimuthal seismic data via anisotropic dispersion properties. In this paper, based on Rüger's equation, we derived an analytical expression in the frequency domain for the frequency-dependent AVOAz inversion in terms of fracture orientation, dispersion gradient of isotropic background rock, anisotropic dispersion gradient, and the dispersion at a normal incident angle. The frequency-dependent AVOAz equation utilizes azimuthal seismic data and considers the effect of both isotropic and anisotropic dispersion. Reassigned Gabor Transform (RGT) is used to achieve high-resolution frequency division data. We then propose the frequency-dependent AVOAz inversion method to identify fluid and characterize effective fractures in fractured porous reservoirs. Through application to high-qualified seismic data of dolomite and carbonate reservoirs, the results show that the method is useful for identifying fluid and effective fractures in fluid-saturated fractured rocks.

3D printing of porcelain: finite element simulation of anisotropic sintering

Sintering is a key step that determines the mechanical performances and shape quality of 3D printed ceramics. In this domain, there is an increasing interest in complex thin structures and low fill density shapes. However, these complex structures may suffer from distortions by gravity forces developed on the light structure, friction with supports, shrinkage anisotropy, or thermal gradients. Finite element simulation of the sintering process is then of high importance for predicting the specimens distortions. This paper focuses on the identification of the model parameters in the special case of anisotropic sintering of porcelain with final stage swelling. This study points out the printed specimen high resistance to high temperature shear deformation due to the alignment of the printed rods. A mesoscale simulation has been carried out to explain this mechanism. The resulting model was tested for the sintering of a thin wall cup shape.

Controlling Domain-Wall Nucleation in Ta / Co - Fe - B / MgO Nanomagnets via Local Ga+ Ion Irradiation

Comprehensive control of the domain-wall nucleation process is crucial for spin-based emerging technologies ranging from random-access and storage-class memories through domain-wall logic concepts to nanomagnetic logic. In this work, focused ${\mathrm{Ga}}^{+}$ ion irradiation is investigated as an effective means to control domain-wall nucleation in $\mathrm{Ta}$/$\mathrm{Co}$-$\mathrm{Fe}$-$\mathrm{B}$/$\mathrm{Mg}\mathrm{O}$ nanostructures. We show that, analogously to ${\mathrm{He}}^{+}$ irradiation, it is not only possible to reduce the perpendicular magnetic anisotropy but also to increase it significantly, enabling bidirectional manipulation schemes. First, the irradiation effects are assessed at the film level, sketching an overview of the dose-dependent changes in the magnetic energy landscape. Subsequent time-domain nucleation characteristics of irradiated nanostructures reveal substantial increases in the anisotropy fields but surprisingly small effects on the measured energy barriers, indicating shrinking nucleation volumes. Spatial control of the domain-wall nucleation point is achieved by employing focused irradiation of preirradiated magnets, with the diameter of the introduced circular defect controlling the coercivity. Special attention is given to the nucleation mechanisms, changing from the coherent radiation of a Stoner-Wohlfarth particle to depinning from an anisotropy gradient. Dynamic micromagnetic simulations and related measurements are used in addition to model and analyze this depinning-dominated magnetization reversal.

Effect of nonuniform perpendicular anisotropy in ferromagnetic resonance spectra in magnetic nanorings

The high frequency dynamic behaviors of magnetic nanorings with variable anisotropy along their radius have been studied using micromagnetic simulations. The dynamic susceptibility spectrum and spatial localization of the ferromagnetic resonance modes are investigated by varying anisotropy gradients in nanorings of 200 nm of external radius, with different internal radii. Both the resonant frequencies and the number of peaks depend on the lower energy magnetization configuration which in turn is a function of anisotropy gradients. Besides, it is shown that the effects of the anisotropy gradient are relevant even for the narrowest ring of 10 nm wide. The idea of controlling frequencies by modifying the anisotropy gradients of the system suggests the possibility of using these nanostructures in potential magnetic controllable frequency devices.

An L0-regularized global anisotropic gradient prior for single-image de-raining

We propose a method based on a global anisotropic gradient prior (GAGP) for addressing the problem of rain streak removal. We observe that both images and rain streaks have anisotropy at edges, and that the rain distribution in images is sparse. We therefore propose an L0-regularized sparse term with an L0-regularized GAGP term to efficiently detect the rain streaks. We applied the L0-regularized GAGP as the image regularization term to protect the image structure and details. We also developed an alternating half-quadratic algorithm to solve the proposed L0 optimization model by introducing the variable splitting method and analyzing the convergence of the algorithm. Experimental results show that the proposed method outperforms state-of-the-art methods in rain streak removal and preserving image structure on both synthesized and real-world images with different levels and types of rain.

The Effect of Thermal Pressure on Collisionless Magnetic Reconnection Rate

Abstract Modeling collisionless magnetic reconnection rate is an outstanding challenge in basic plasma physics research. While the seemingly universal rate of an order is often reported in the low-β regime, it is not clear how reconnection rate scales with a higher plasma β. Due to the complexity of the pressure tensor, the available reconnection rate model is limited to the low plasma-β regime, where the thermal pressure is arguably negligible. However, the thermal pressure effect becomes important when . Using first-principle kinetic simulations, we show that both the reconnection rate and outflow speed drop as β gets larger. A simple analytical framework is derived to take account of the self-generated pressure anisotropy and pressure gradient in the force balance around the diffusion region, explaining the varying trend of key quantities and reconnection rates in these simulations with different β. The predicted scaling of the normalized reconnection rate is in the high-β limit, where β i0 is the ion β of the inflow plasma.

A new method for estimating the correlation of seismic waveforms based on the NTFT

SUMMARY We propose a new correlation function called the similarity coefficient (SC) based on the normal time–frequency transform (NTFT) to evaluate the similarity between two non-stationary seismic signals as a function of the delay time. The SC is defined in the time–frequency spectrum of the NTFT, and the instantaneous phase and amplitude of each frequency component in a signal are used to calculate the SC. Our simulation experiments demonstrate that the SC method can effectively recognize similar signals compared to the conventional normalized cross-correlation coefficient (NCC) under high background noise conditions. The SC presents good robustness in identifying similar signals and performs well in the case of an extremely low signal-to-noise ratio (SNR), which makes it suitable for detecting weak seismic signals concealed by noise. As a real application case, we use the SC method to detect quasi-Love (QL) surface waves. QL waves are scattered Love waves and are important indicators for lateral anisotropic gradients in the upper mantle. We detect the QL waves at 21 stations deployed across Japan after the 23 December 2004 Mw 8.1 Macquarie earthquake by using the SC method. Obvious QL waves are observed at 19 stations, and we locate the Love-to-Rayleigh scatterers by applying the delay times between the QL and main Love waves. Our results show that the QL wave scatterers were mostly generated in two areas: Mariana subduction and Papua New Guinea. The observations of QL waves suggest the presence of lateral gradients in anisotropy beneath those two areas. The spatial distribution of the 13 scatterers in the Mariana subduction zone agrees well with the Mariana Island Arc, and we infer that the Mariana slab may have melted and coupled with the surrounding mantle at depth.

Anisotropy Gradients in the Middle of the Ross Sea Embayment, West Antarctica: Evidence From QL Scattered Surface Waves

AbstractLong‐period quasi‐Love (QL) waves in West Antarctica were detected using the band‐pass filtering. Rayleigh waves from March 11, 2011 Tohoku Mw 9.1 earthquake and March 9, 2011 Tohoku Mw 7.3 earthquake had evident QL waves in the frequency range of 7–13 mHz when crossing the Ross Sea Embayment (RSE), while exhibiting normal behavior when crossing the Southern Ocean adjacent to the RSE. We located an anisotropic boundary in the upper mantle beneath the RSE according to the QL waves. Surprisingly, the boundary was consistent with the sharp transition zone of magnetic anomalies discovered by the most recent airborne magnetic surveys. Thus, we speculate that the anisotropic boundary was most likely due to vertical mantle flow below the RSE, which may provide evidence of a vertically coherent boundary condition in the RSE. That anisotropic boundary may be an important tectonic imprint for maintaining the stability of the Ross Ice Shelf.

Microarchitecture-dependent nonlinear bending analysis for cellular plates with prismatic corrugated cores via an anisotropic strain gradient plate theory of first-order shear deformation

This study focuses on the microarchitecture-dependent nonlinear bending behavior of cellular plates with equitriangularly prismatic microarchitectures by adopting a dimensionally and constitutively reduced strain gradient plate model. The strain energy formulation is based on the dimension reduction of the first-order shear deformation plate theory along with von Kármán’s nonlinear strain relations and anisotropic strain gradient theory. The classical and higher-order constitutive parameters are obtained according to the recently published homogenization results for a corresponding linear plate model. The corresponding finite element simulations, numerically solving the anisotropic strain gradient plate problems, rely on a nonstandard, higher-order, six-node triangular element showing good convergence properties. Comparisons between the proposed (2D) strain gradient shear deformation plate model and the corresponding (3D) detailed full-field reference models demonstrate for a variety of cellular plate structures that the accuracy of the proposed approach is at a very good level with relatively low computational costs. A diverse set of numerical examples is provided in order to investigate the size-dependent nonlinear structural response of cellular plates having different numbers of microarchitectural layers, midsurface shapes and boundary conditions.

Microengineered 3D Collagen Gels with Independently Tunable Fiber Anisotropy and Directionality.

Cellular processes, including differentiation, proliferation, and migration, have been linked to the alignment (anisotropy) and orientation (directionality) of collagen fibers in the native extracellular matrix (ECM). Given the critical role that biophysical cell-matrix interactions play in regulating biological functions, several microfluidic-based methods have been used to establish 3D collagen gels with defined fiber properties; these gels have helped to establish quantitative relationships between structural ECM cues and observed cell responses. Although existing microfluidic fabrication methods provide excellent definition over collagen fiber anisotropy, they have not demonstrated the independent control over fiber anisotropy and directionality necessary to replicate in vivo collagen architecture. Therefore, to advance collagen microengineering capabilities, we present a user-friendly technology platform that uses controlled fluid flows within a non-uniform microfluidic channel network to create collagen landscapes that can be tuned as a function of extensional strain rate. Herein, we demonstrate capabilities to i) control the degree of fiber anisotropy, ii) create spatial gradients in fiber anisotropy, iii) independently define fiber directionality, and iv) generate multi-material interfaces within a 3D environment. We then address the practical issue of integrating cells into microfluidic systems by using a peel-off template technique to provide direct access to microengineered collagen gels, and demonstrate that cells respond to the defined properties of the landscape. Finally, the platform's modular capability is highlighted by integrating a sub-micrometer thick porous parylene membrane onto the microengineered collagen as a method to define cell-substrate interactions.

Domain wall mobility engineering by a perpendicular magnetic field in microwires with a gradient of perpendicular anisotropy

Fast domain wall propagation is a typical feature of amorphous glass-coated microwires with positive magnetostriction. The high domain wall velocity can be effectively tailored either by sample postprocessing or temperature. In this work, we show that the domain wall dynamics can be engineered by a perpendicular magnetic field. We perform the domain wall mobility measurements in microwires with a varying gradient of the perpendicular magnetic anisotropy. It is shown that domain wall mobility is mainly determined by counterplay between the amplitude of perpendicular anisotropy and externally applied perpendicular field. The presence of perpendicular magnetic anisotropy is observed by Scanning electron microscopy. The relation between the maximum applied perpendicular magnetic field, and the wire dimensions are provided based on the measured data.

Fabrication of gradient anisotropic cellulose hydrogels for applications in micro-strain sensing

A gradient anisotropic cellulose hydrogel was prepared by the diffusion of CaCl2 solution. The degree of orientation of the cellulose chains decreased along the ion diffusion direction, and the birefringence of the highly oriented area was up to 1.323×10−4. Importantly, we first propose and demonstrate the presence of sensitive region in the gradient anisotropy hydrogel. The sensitive region located in the order-disorder transition displayed large color variation with the optical path difference (R) range from 155 nm to 1200 nm, high sensitivity (1 % strain interval), low detection (minimum 1 % strain), good cycling ability of 50 times and frost resistance at −20℃. Based on this, the readable response colorimetric card was designed for micro-strain detection. The programmable Ca2+ diffusion design made it convenient to fabricate cylindrical and tubular hydrogels. This concept of sensitive region and this flexible strategy will broaden new horizons to materials that have excellent responsive properties for optical applications, sensors and multiscale bionics architectures.

Metastability in graded and step like variation of field and anisotropy of the Blume–Capel ferromagnet

The metastable behaviour of two dimensional anisotropic Blume–Capel ferromagnet, under the influence of graded and stepped like variations of magnetic field, has been investigated by extensive Monte Carlo simulation using Metropolis single spin flip algorithm. Starting from the initial perfectly ordered state, reversal of magnetisation has been studied in presence of the field. Metastable lifetime or the reversal time of magnetisation for the system having uniform anisotropy and in the presence of both graded and stepped field has been studied. Also the same has been explored for a graded and stepped anisotropic system in presence of a uniform field. Finite size effect is analysed for the variation of reversal time with gradient of field (Gh) and a scaling relation 〈τ〉∼L−βf(GhLα) is proposed. Spatial variation of density profile for the projection states (i.e., +1, 0 and -1) has also been studied at the moment of reversal of magnetisation. The spatial variation of the number of spin flips per site is studied. Motion of the interface (or domain wall) with the gradient of field and gradient of anisotropy are investigated and are found to follow the hyperbolic tangent like behaviours in both cases. Since, both the anisotropy and the applied field have significant impact on the metastable lifetime, an interesting competitive scenario is observed for a graded anisotropic system in graded field and a stepped anisotropic system in stepped field. A line of marginal competition has been found out for both the cases separating the regions of field dominated reversal and anisotropy dominated reversal. The decay of the metastable volume fraction was found to follow the Avrami’s law. The mean reversal time was observed to decrease monotonically across the phase boundary of the ferro–para transition.

Chiral Symmetry Breaking for Deterministic Switching of Perpendicular Magnetization by Spin-Orbit Torque.

Symmetry breaking is a characteristic to determine which branch of a bifurcation system follows upon crossing a critical point. Specifically, in spin-orbit torque (SOT) devices, a fundamental question arises: how can the symmetry of the perpendicular magnetic moment be broken by the in-plane spin polarization? Here, we show that the chiral symmetry breaking by the antisymmetric Dzyaloshinskii-Moriya interaction (DMI) can induce the deterministic SOT switching of the perpendicular magnetization. By introducing a gradient of saturation magnetization or magnetic anisotropy, the dynamic noncollinear spin textures are formed under the current-driven SOT, and thus, the chiral symmetry of these dynamic spin textures is broken by the DMI, resulting in the deterministic magnetization switching. We introduce a strategy to induce an out-of-plane (z) gradient of magnetic properties as a practical solution for the wafer-scale manufacture of SOT devices.

Magnetic skyrmionium diode with a magnetic anisotropy voltage gating

The magnetic skyrmionium can be seen as a coalition of two magnetic skyrmions with opposite topological charges and has potential applications in next-generation spintronic devices. Here, we report the current-driven dynamics of a skyrmionium in a ferromagnetic nanotrack with the voltage-controlled magnetic anisotropy. The pinning and depinning of a skyrmionium controlled by the voltage gate are investigated. The current-driven skyrmionium can be used to mimic the skyrmionium diode effect in the nanotrack with a voltage gate. We have further studied the skyrmionium dynamics in the nanotrack driven by a magnetic anisotropy gradient in the absence of spin current. The performance of a single wedge-shaped voltage gate at different temperatures is studied. Our results may provide useful guidelines for the design of voltage-controlled and skyrmionium-based spintronic devices.

Tumor Habitat-derived Radiomic Features at Pretreatment MRI That Are Prognostic for Progression-free Survival in Glioblastoma Are Associated with Key Morphologic Attributes at Histopathologic Examination: A Feasibility Study.

To identify radiomic features extracted from the tumor habitat on routine MR images that are prognostic for progression-free survival (PFS) and to assess their morphologic basis with corresponding histopathologic attributes in glioblastoma (GBM). In this retrospective study, 156 pretreatment GBM MR images (gadolinium-enhanced T1-weighted, T2-weighted, and fluid-attenuated inversion recovery [FLAIR] images) were curated. Of these 156 images, 122 were used for training (90 from The Cancer Imaging Archive and 32 from the Cleveland Clinic, acquired between December 1, 2011, and May 1, 2018) and 34 were used for validation. The validation set was obtained from the Ivy Glioblastoma Atlas Project database, for which the percentage extent of 11 histologic attributes was available on corresponding histopathologic specimens of the resected tumor. Following expert annotations of the tumor habitat (necrotic core, enhancing tumor, and FLAIR-hyperintense subcompartments), 1008 radiomic descriptors (eg, Haralick texture features, Laws energy features, co-occurrence of local anisotropic gradient orientations [CoLIAGe]) were extracted from the three MRI sequences. The top radiomic features were obtained from each subcompartment in the training set on the basis of their ability to risk-stratify patients according to PFS. These features were then concatenated to create a radiomics risk score (RRS). The RRS was independently validated on a holdout set. In addition, correlations (P < .05) of RRS features were computed, with the percentage extent of the 11 histopathologic attributes, using Spearman correlation analysis. RRS yielded a concordance index of 0.80 on the validation set and constituted radiomic features, including Laws (capture edges, waves, ripple patterns) and CoLIAGe (capture disease heterogeneity) from enhancing tumor and FLAIR hyperintensity. These radiomic features were correlated with histopathologic attributes associated with disease aggressiveness in GBM, particularly tumor infiltration (P = .0044) and hyperplastic blood vessels (P = .0005). Preliminary findings demonstrated significant associations of prognostic radiomic features with disease-specific histologic attributes, with implications for risk-stratifying patients with GBM for personalized treatment decisions. Supplemental material is available for this article. © RSNA, 2020.

Improving strain in single crystal by composition-gradients design

Domain switching is one of the essential contributions for strain in ferroelectric materials. In this work, we utilize anisotropic composition gradients (CGs) to induce anisotropic orientation of both defects and spontaneous dipoles, aiming to enhance the contribution of domain switching on strain in KTa1–xNbxO3 single crystal. In this way, a remarkable improvement (over 60%) of strain is obtained in KTa0.58Nb0.42O3 single crystal along the smallest CG direction, achieving a large unipolar strain, i.e. 0.29%, at low driving electric field 10 kV cm–1. It is attributed to the preferred orientation of both defects and spontaneous dipoles along the largest CG directions, then improving the contribution of domain switching on strain along the smallest CG direction. Particularly, owing to the existence of Ein as recoverable forces caused by both flexoelectric fields and defects pinning effect, KTN show nearly zero remnant strain (srem) along with the small CG directions, corresponding to the double P-E loops. Moreover, the V–PFM images confirm that CGs can influence the microdomain structures. Thus, designing special anisotropic CGs materials is expected to be a novel method to improve the strain properties and a potential way to flexibly design next-generation anisotropic piezoelectric materials.

Kinematic modelling of clusters with Gaia: the death throes of the Hyades

ABSTRACT The precision of the Gaia data offers a unique opportunity to study the internal velocity field of star clusters. We develop and validate a forward-modelling method for the internal motions of stars in a cluster. The model allows an anisotropic velocity dispersion matrix and linear velocity gradient describing rotation and shear, combines radial velocities available for a subset of stars, and accounts for contamination from background sources via a mixture model. We apply the method to Gaia DR2 data of the Hyades cluster and its tidal tails, dividing and comparing the kinematics of stars within and beyond 10 pc, which is roughly the tidal radius of the cluster. While the velocity dispersion for the cluster is nearly isotropic, the velocity ellipsoid for the tails is clearly elongated with the major axis pointing towards the Galactic centre. We find positive and negative expansions at ≈2σ significance in Galactic azimuthal and vertical directions for the cluster but no rotation. The tidal tails are stretching in a direction tilted from the Galactic centre while equally contracting as the cluster in Galactic vertical direction. The tails have a shear (A) of 16.90 ± 0.92 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$ and a vorticity (B) of −6.48 ± 1.15 $\mathrm{m}\, \mathrm{s}^{-1}\, \mathrm{pc}^{-1}$, values distinct from the local Oort constants. By solving the Jeans equations for flattened models of the Hyades, we show that the observed velocity dispersions are a factor of ≈2 greater than required for virial equilibrium due to tidal heating and disruption. From simple models of the mass loss, we estimate that the Hyades is close to final dissolution with only a further ≲30 Myr left.