Anisotropic Constraints Research Articles

Seismic anisotropy indicates organized melt beneath the Mid-Atlantic Ridge aids seafloor spreading

Abstract Lithospheric plates diverge at mid-ocean ridges and asthenospheric mantle material rises in response. The rising material decompresses, which can result in partial melting, potentially impacting the driving forces of the system. Yet the geometry and spatial distribution of the melt as it migrates to the ridge axis are debated. Organized melt fabrics can cause strong seismic anisotropy, which can be diagnostic of melt, although this is typically not found at ridges. We present anisotropic constraints from an array of 39 ocean-bottom seismometers deployed on 0–80 Ma lithosphere from March 2016 to March 2017 near the equatorial Mid-Atlantic Ridge (MAR). Local and SKS measurements show anisotropic fast directions away from the ridge axis, which are consistent with strain and associated fabric caused by plate motions with short delay times, δt (<1.1 s). Near the ridge axis, we find several ridge-parallel fast splitting directions, φ, with SKS δt that are much longer (1.7–3.8 s). This is best explained by ridge-parallel sub-vertical orientations of sheet-like melt pockets. This observation is much different than anisotropic patterns observed at other ridges, which typically reflect fabric related to plate motions. One possibility is that thicker sub-ridge lithosphere with steep sub-ridge topography beneath slower spreading centers focuses melt into vertical, ridge-parallel melt bands, which effectively weakens the plate. Associated buoyancy forces elevate the sub-ridge plate, providing greater potential energy and enhancing the driving forces of the plates.

Beyond Chainmail: Computational Modeling of Discrete Interlocking Materials

We present a method for computational modeling, mechanical characterization, and macro-scale simulation of discrete interlocking materials (DIM)---3D-printed chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring force are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic deformation constraints. To model the mechanical behavior of these materials, we propose a computational approach that builds on three key components. ( a ): we explore the space of feasible deformations using native-scale simulations at the per-element level. ( b ): based on this simulation data, we introduce the concept of strain-space boundaries to represent deformation limits for in- and out-of-plane deformations, and ( c ): we use the strain-space boundaries to drive an efficient macro-scale simulation model based on homogenized deformation constraints. We evaluate our method on a set of representative discrete interlocking materials and validate our findings against measurements on physical prototypes.

Anisotropic rheology and friction of suspended graphene

Graphene is a powerful membrane prototype for both applications and fundamental research. Rheological phenomena including indentation, twisting, and wrinkling in deposited and suspended graphene are actively investigated to unravel the mechanical laws at the nanoscale. Most studies focused on isotropic setups, while realistic graphene membranes are often subject to strongly anisotropic constraints, with important consequences for the rheology, strain, indentation, and friction in engineering conditions. Graphene in particular is recognized as the thinnest solid lubricant material and a large amount of work has been dedicated to understanding the fundamentals mechanisms of this effect and to unravel parameters relevant to its technological development. Here, we experimentally show how graphene's frictional response to an external indenter is severely altered by conditions of anisotropic suspension, specifically when graphene is clamped across a long and narrow groove. Results show that the friction coefficient is significant when the tip is sliding parallel to the groove while becoming ultralow in the orthogonal direction. While the experimental data suggest that----rather unexpectedly----prestrain of the graphene sheet as a result of clamping is negligible, the key to understanding the underlying mechanism is provided by simulations. The paramount mechanism is provided by the extra anisotropic strain induced from indentation under anisotropic constraints, which in turn produces an anisotropic stiffening of the graphene. While the focus of this work is on graphene, we believe our experimental protocol and the physical mechanism uncovered by our model can be applicable to other 2D membranelike materials.

Stress-based topology optimization for fiber composites with improved stiffness and strength: Integrating anisotropic and isotropic materials

Fiber-reinforced materials offer high stiffness- and strength-to-mass ratios to lightweight composite structures. To design stiff, strong, and lightweight fiber-reinforced composite structures, we propose a multimaterial anisotropic stress-constrained topology optimization framework that simultaneously optimizes geometry, distribution of anisotropic (i.e., orthotropic) and isotropic material phases, and local orientations of fiber reinforcements in the anisotropic phase. To achieve high performance in both stiffness and strength, we discover that both isotropic and anisotropic materials are needed: anisotropic materials are preferred in uniaxial members to increase stiffness, while isotropic materials are crucial at multi-axially stressed joints to enhance strength. We introduce multimaterial interpolation schemes to characterize both the stiffness and strength of composites made up of anisotropic and isotropic materials. The characterization of strength is enabled by a novel load factor-based yield function interpolation that consistently integrates anisotropic Tsai–Wu and isotropic von Mises yield criteria. We optimize stress-sensitive domains considering materials with various levels of stiffness and strength anisotropy as well as multiple load cases. The anisotropic stress constraints in the proposed framework effectively inform geometries to reduce stress concentration in fiber composites. The proposed framework provides a rational design paradigm for composite structures, capitalizing on dissimilar stiffness and strength properties of anisotropic and isotropic materials, to potentially benefit various engineering applications.

Variable-height stiffener design using topology optimization with anisotropic filter-based casting constraints

Variable-height stiffener design using topology optimization with anisotropic filter-based casting constraints

Waveform inversion of large data sets for radially anisotropic Earth structure

SUMMARY The amount of high-quality seismic data is expanding rapidly, and there is a need for algorithms that take advantage of classical methods to achieve high efficiency using widely available computing power. In this study, we develop a novel waveform inversion method to retrieve radially anisotropic Earth models that can be used to investigate deformation and flow in the mantle. Our method is comprised of two parts: (1) extraction and fitting of the fundamental mode and (2) fitting of the full synthetic waveform. The waveform inversion method results in path average model constraints with uniquely determined independent uncertainties. We demonstrate through synthetic testing that the method is able to retrieve radially anisotropic perturbations down to the mantle transition zone, and leakage effects due to ignoring P-wave anisotropy are minimal. We apply the method to ∼16 000 waveforms generated by earthquakes occurring in the East Sea (Sea of Japan) region, and we demonstrate that the subsequent linear inversion of radially anisotropic path constraints produces models that are similar to those resulting from full waveform adjoint tomography methods. We validate our model by predicting waveforms for earthquakes not included in our inversion, and we show that our method is able to extract structural information. Our results indicate low-velocity anomalies and weak radial anisotropy in NE Japan, which may be due to competing influences from ascending fluids and/or melts and horizontal flow in the lower crust and upper mantle. In the southern East Sea, we image low velocities and relatively high radial anisotropy, which may reflect high temperatures, shallow dehydration and olivine LPO in the upper mantle.

On Time-Dependent Rheology of Sutterby Nanofluid Transport across a Rotating Cone with Anisotropic Slip Constraints and Bioconvection.

The purpose and novelty of our study include the scrutinization of the unsteady flow and heat characteristics of the unsteady Sutterby nano-fluid flow across an elongated cone using slip boundary conditions. The bioconvection of gyrotactic micro-organisms, Cattaneo–Christov, and thermal radiative fluxes with magnetic fields are significant physical aspects of the study. Anisotropic constraints on the cone surface are taken into account. The leading formulation is transmuted into ordinary differential formate via similarity functions. Five coupled equations with nonlinear terms are resolved numerically through the utilization of a MATLAB code for the Runge–Kutta procedure. The parameters of buoyancy ratio, the porosity of medium, and bioconvection Rayleigh number decrease x-direction velocity. The slip parameter retard y-direction velocity. The temperature for Sutterby fluids is at a hotter level, but its velocity is vividly slower compared to those of nanofluids. The temperature profile improves directly with thermophoresis, v-velocity slip, and random motion of nanoentities.

Rate of estimation for the stationary distribution of jump-processes over anisotropic Holder classes

We study the problem of the non-parametric estimation for the density of the stationary distribution of the multivariate stochastic differential equation with jumps (Xt) , when the dimension d is bigger than 3. From the continuous observation of the sampling path on [0, T ] we show that, under anisotropic Holder smoothness constraints, kernel based estimators can achieve fast convergence rates. In particular , they are as fast as the ones found by Dalalyan and Reiss [9] for the estimation of the invariant density in the case without jumps under isotropic Holder smoothness constraints. Moreover, they are faster than the ones found by Strauch [29] for the invariant density estimation of continuous stochastic differential equations, under anisotropic Holder smoothness constraints. Furthermore, we obtain a minimax lower bound on the L2-risk for pointwise estimation, with the same rate up to a log(T) term. It implies that, on a class of diffusions whose invariant density belongs to the anisotropic Holder class we are considering, it is impossible to find an estimator with a rate of estimation faster than the one we propose.

Improved constraints on anisotropic birefringent Lorentz invariance and CPT violation from broadband optical polarimetry of high redshift galaxies

In the framework of the Standard Model Extension (SME), we present improved constraints on anisotropic Lorentz invariance and Charge-Parity-Time (CPT) violation by searching for astrophysical signals of cosmic vacuum birefringence with broadband optical polarimetry of high redshift astronomical sources, including Active Galactic Nuclei and Gamma-Ray Burst afterglows. We generalize the work in Kislat 2018, which studied the SME mass dimension $d = 4$ case, to arbitrary mass dimension for both the CPT-even and CPT-odd cases. We then present constraints on all 10, 16, and 42 anisotropic birefringent SME coefficients for dimension $d = 4$, $d = 5$, and $d = 6$ models, respectively, using 7554 observations for odd d and 7376 observations for even d of 1278 unique sources on the sky, which, to our knowledge, comprises the most complete catalog of optical polarization from extragalactic sources in the literature to date. Compared to the smaller sample of 44 and 45 broadband optical polarimetry observations analyzed in Kislat 2018 and Kislat and Krawczynski 2017, our dimension $d = 4$ and $d = 5$ average constraints are more sensitive by factors of 35 and 10, corresponding to a reduction in allowed SME parameter space volume for these studies of 15 and 16 orders of magnitude, respectively. Constraints from individual lines of sight can be significantly stronger using spectropolarimetry. Nevertheless, due to the increased number of observations and lines of sight in our catalog, our average $d = 4$ and $d = 5$ broadband constraints are within factors of 2 and 12 of previous constraints using spectropolarimetry from Kislat 2018 and Kislat and Krawczynski 2017, respectively, using an independent data set and an improved analysis method. By contrast, our anisotropic constraints on all 42 birefringent SME coefficients for $d = 6$ are the first to be presented in the literature.

Adaptive invariant density estimation for ergodic diffusions over anisotropic classes

Consider some multivariate diffusion process $\mathbf{X}=(X_{t})_{t\geq0}$ with unique invariant probability measure and associated invariant density $\rho$, and assume that a continuous record of observations $X^{T}=(X_{t})_{0\leq t\leq T}$ of $\mathbf{X}$ is available. Recent results on functional inequalities for symmetric Markov semigroups are used in the statistical analysis of kernel estimators $\widehat{\rho}_{T}=\widehat{\rho}_{T}(X^{T})$ of $\rho$. For the basic problem of estimation with respect to $\mathrm{sup}$-norm risk under anisotropic Holder smoothness constraints, the proposed approach yields an adaptive estimator which converges at a substantially faster rate than in standard multivariate density estimation from i.i.d. observations.

Geostatistical regularization operators for geophysical inverse problems on irregular meshes

Summary Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

Cell dynamics underlying oriented growth of the Drosophila wing imaginal disc.

Quantitative analysis of the dynamic cellular mechanisms shaping the Drosophila wing during its larval growth phase has been limited, impeding our ability to understand how morphogen patterns regulate tissue shape. Such analysis requires explants to be imaged under conditions that maintain both growth and patterning, as well as methods to quantify how much cellular behaviors change tissue shape. Here, we demonstrate a key requirement for the steroid hormone 20-hydroxyecdysone (20E) in the maintenance of numerous patterning systems in vivo and in explant culture. We find that low concentrations of 20E support prolonged proliferation in explanted wing discs in the absence of insulin, incidentally providing novel insight into the hormonal regulation of imaginal growth. We use 20E-containing media to observe growth directly and to apply recently developed methods for quantitatively decomposing tissue shape changes into cellular contributions. We discover that whereas cell divisions drive tissue expansion along one axis, their contribution to expansion along the orthogonal axis is cancelled by cell rearrangements and cell shape changes. This finding raises the possibility that anisotropic mechanical constraints contribute to growth orientation in the wing disc.

Multitracing anisotropic non-Gaussianity with galaxy shapes

Correlations between intrinsic galaxy shapes on large-scales arise due to the effect of the tidal field of the large-scale structure. Anisotropic primordial non-Gaussianity induces a distinct scale-dependent imprint in these tidal alignments on large scales. Motivated by the observational finding that the alignment strength of luminous red galaxies depends on how galaxy shapes are measured, we study the use of two different shape estimators as a multi-tracer probe of intrinsic alignments. We show, by means of a Fisher analysis, that this technique promises a significant improvement on anisotropic non-Gaussianity constraints over a single-tracer method. For future weak lensing surveys, the uncertainty in the anisotropic non-Gaussianity parameter, $A_2$, is forecast to be $\sigma(A_2)\approx 50$, $\sim 40\%$ smaller than currently available constraints from the bispectrum of the Cosmic Microwave Background. This corresponds to an improvement of a factor of $4-5$ over the uncertainty from a single-tracer analysis.

Analysis of rapidly synthesized guest-filled porous complexes with synchrotron radiation: practical guidelines for the crystalline sponge method.

A detailed set of synthetic and crystallographic guidelines for the crystalline sponge method based upon the analysis of expediently synthesized crystal sponges using third-generation synchrotron radiation are reported. The procedure for the synthesis of the zinc-based metal-organic framework used in initial crystal sponge reports has been modified to yield competent crystals in 3 days instead of 2 weeks. These crystal sponges were tested on some small molecules, with two being unexpectedly difficult cases for analysis with in-house diffractometers in regard to data quality and proper space-group determination. These issues were easily resolved by the use of synchrotron radiation using data-collection times of less than an hour. One of these guests induced a single-crystal-to-single-crystal transformation to create a larger unit cell with over 500 non-H atoms in the asymmetric unit. This led to a non-trivial refinement scenario that afforded the best Flack x absolute stereochemical determination parameter to date for these systems. The structures did not require the use of PLATON/SQUEEZE or other solvent-masking programs, and are the highest-quality crystalline sponge systems reported to date where the results are strongly supported by the data. A set of guidelines for the entire crystallographic process were developed through these studies. In particular, the refinement guidelines include strategies to refine the host framework, locate guests and determine occupancies, discussion of the proper use of geometric and anisotropic displacement parameter restraints and constraints, and whether to perform solvent squeezing/masking. The single-crystal-to-single-crystal transformation process for the crystal sponges is also discussed. The presented general guidelines will be invaluable for researchers interested in using the crystalline sponge method at in-house diffraction or synchrotron facilities, will facilitate the collection and analysis of reliable high-quality data, and will allow construction of chemically and physically sensible models for guest structural determination.

Inflationary magnetogenesis without the strong coupling problem II:constraints from CMB anisotropies and B-modes

Recent observational claims of magnetic fields stronger than 10−16 G in the extragalactic medium motivate a new look for their origin in the inflationary magnetogenesis models. In this work we shall review the constraints on the simplest gauge invariant model f2(ϕ)FμνFμν of inflationary magnetogenesis, and show that in the optimal region of parameter space the anisotropic constraints coming from the induced bispectrum, due to the generated electromagnetic fields, yield the strongest constraints. In this model, only a very fine tuned scenario at an energy scale of inflation as low as 10−2 GeV can explain the observations of void magnetic fields. These findings are consistent with the recently derived upper bound on the inflationary energy scale. However, if the detection of primordial tensor modes by BICEP2 is confirmed, the possibility of low scale inflation is excluded. Assuming the validity of the BICEP2 claim of a tensor-to-scalar ratio r = 0.2+0.07−0.05, we provide the updated constraints on this model of inflationary magnetogenesis. On the Mpc scale, we find that the maximal allowed magnetic field strength from inflation is less than 10−30 G.

Mechanically Guided Cell Migration: Less of a Stretch than Ever

Mechanically Guided Cell Migration: Less of a Stretch than Ever

Antarctica, Greenland and Gulf of Alaska land-ice evolution from an iterated GRACE global mascon solution

AbstractWe have determined the ice mass evolution of the Antarctic and Greenland ice sheets (AIS and GIS) and Gulf of Alaska (GOA) glaciers from a new GRACE global solution of equal-area surface mass concentration parcels (mascons) in equivalent height of water. The mascons were estimated directly from the reduction of the inter-satellite K-band range-rate (KBRR) observations, taking into account the full noise covariance, and formally iterating the solution. The new solution increases signal recovery while reducing the GRACE KBRR observation residuals. The mascons were estimated with 10 day and 1 arcdeg equal-area sampling, applying anisotropic constraints. An ensemble empirical mode decomposition adaptive filter was applied to the mascon time series to compute annual mass balances. The details and causes of the spatial and temporal variability of the land-ice regions studied are discussed. The estimated mass trend over the total GIS, AIS and GOA glaciers for the time period 1 December 2003 to 1 December 2010 is −380 ± 31 Gt a−1, equivalent to −1.05 ± 0.09 mm a−1 sea-level rise. Over the same time period we estimate the mass acceleration to be −41 ± 27 Gt a−2 , equivalent to a −0.11 ± 0.08 mm a−2 sea-level acceleration. The trends and accelerations are dependent on significant seasonal and annual balance anomalies.

The Pacific lithosphere‐asthenosphere boundary: Seismic imaging and anisotropic constraints from SS waveforms

The lithosphere‐asthenosphere boundary (LAB) separating the rigid lid from the underlying weaker, convecting asthenosphere is a fundamental interface in mantle dynamics and plate tectonics. However, the exact depth and defining mechanism of the LAB interface remain poorly understood. The ocean plates are ideal for testing hypotheses regarding the nature of a plate since they make up 70% of Earth's surface area and have a relatively simple geological history. Seismically imaging the oceanic LAB at high resolution has proved challenging. Yet, several studies have recently increased resolution with provocative results. We summarize recent imaging of discontinuity structure beneath much of the Pacific using receiver functions from ocean floor borehole seismometers and land stations located at ocean‐continent margins, SS precursors, and waveform modeling of multiple phases including multiple bounce S waves, ScS reverberations, and surface waves. Overall, there is much agreement among these different approaches about the reported depth of a negative discontinuity that occurs near the expected depth of the LAB. Some of the apparent discrepancies in depth are explained by the variation in sensitivity of seismic waves that sample structure at different wavelengths. Yet, when the results are considered together, no single age‐depth relationship is illuminated. There are also puzzling discrepancies in where the discontinuity is detected, which again suggests greater complexity. Here we test the possibility that discrepant detection of a strong sharp discontinuity is caused by anisotropic structure. We stack SS waveforms with bounce points in the central Pacific into azimuthal bins. We use two methods, one that inverts for discontinuity structure based on subtle variations in the character of the SS waveform, and another that considers SS at higher frequency. We find azimuthal variation in the amplitude of the waveform, including a polarity reversal. We suggest that anisotropy is an important factor in imaging and constraining discontinuity structure of the oceanic plate, and must be carefully considered to constrain the age‐depth dependence and defining mechanism of the oceanic lithosphere.

Constraints Imposed by the Membrane Selectively Guide the Alternating Access Dynamics of the Glutamate Transporter GltPh

Substrate transport in sodium-coupled amino acid symporters involves a large-scale conformational change that shifts the access to the substrate-binding site from one side of the membrane to the other. The structural change is particularly substantial and entails a unique piston-like quaternary rearrangement in glutamate transporters, as evidenced by the difference between the outward-facing and inward-facing structures resolved for the archaeal aspartate transporter GltPh. These structural changes occur over time and length scales that extend beyond the reach of current fully atomic models, but are regularly explored with the use of elastic network models (ENMs). Despite their success with other membrane proteins, ENM-based approaches for exploring the collective dynamics of GltPh have fallen short of providing a plausible mechanism. This deficiency is attributed here to the anisotropic constraints imposed by the membrane, which are not incorporated into conventional ENMs. Here we employ two novel (to our knowledge) ENMs to demonstrate that one can largely capture the experimentally observed structural change using only the few lowest-energy modes of motion that are intrinsically accessible to the transporter, provided that the surrounding lipid molecules are incorporated into the ENM. The presence of the membrane reduces the overall energy of the transition compared with conventional models, showing that the membrane not only guides the selected mechanism but also acts as a facilitator. Finally, we show that the dynamics of GltPh is biased toward transitions of individual subunits of the trimer rather than cooperative transitions of all three subunits simultaneously, suggesting a mechanism of transport that exploits the intrinsic dynamics of individual subunits. Our software is available online at http://www.membranm.csb.pitt.edu.

Anisotropic structures and wormholes with loop quantum gravity holonomy corrections

Anisotropic spherically symmetric systems are studied in the connection and densitized triad variables used in loop quantum gravity. The material source is an anisotropic fluid, which is arguably the most commonly used source term in anisotropic studies within general relativity. The gravitational+anisotropic fluid constraints are derived and analyzed and then quantum gravity inspired holonomy replacements are performed. The quantum properties of the fluid are dictated by the modified constraint equations. Particular attention is paid to wormhole throats, as they provide a simplistic model of the structures thought to be ubiquitous in the quantum gravity space-time foam at high energy scales. In comparison to the purely classical theory, the quantum corrections act to increase the energy density of the fluid, which indicates that they may lessen the energy condition violation present in the classical theory. Related to this, in principle it would be possible to have scenarios where the classical solution yields everywhere negative (with a zero at the throat) fluid energy density but the corresponding quantum corrected theory possesses only small regions of negative energy density or even everywhere non-negative energy density.