Local Rotation Research Articles

Chiral-phonon-induced current in helical crystals

In this paper, we theoretically show that in a helical crystal, a current is induced by chiral phonons representing the microscopic local rotation of atoms. By treating the rotational motion as a perturbation, we calculate the time-dependent current by using the adiabatic Berry phase method. The time average of the current along the helical axis becomes finite in the metallic phase but it vanishes in the insulating phase. On the other hand, the current in the hexagonal plane changes with time, but its time average vanishes due to the threefold rotation space-time symmetry. We show that the time evolutions of the current follow the space-time symmetries of the helical systems. Moreover, we explain the reason for the vanishing of the time average of the current in the insulating phase from the aspect of the Chern number in the parameter space.

Multimethod palaeointensity results from a rapidly emitted upper Miocene lava flow sequence in São Vicente (Cape Verde): new data for the African record

SUMMARY We present new radiometric ages and full-vector palaeomagnetic data from São Vicente Island, Cape Verde. Samples were obtained from a sequence of 11 flows. A K-Ar age determination was performed on the lowermost flow of the sequence, yielding an upper Miocene age of 6.07 ± 0.16 (2σ) Ma. Considering the normal polarity observed in all flows, the age of the sequence could be narrowed down to an interval between 6.03 and 6.23 Ma. The mean palaeomagnetic direction of the studied sequence was compared with the expected direction, calculated from the African Apparent Polar Wander Path (5 Ma). While inclinations approximately agree, the palaeodeclination appears westwardly deviated by 26.5° ± 2.9°. Moreover, nearly no scatter of virtual geomagnetic poles around their mean value is observed and its comparison with the scatter observed in palaeomagnetic directions obtained from geomagnetic field model SHA.DIF.14k suggests that the sequence was very rapidly emplaced in only a few centuries. Thus, the obtained anomalous palaeomagnetic direction seems to reflect the effect of non-averaged secular variation, although a local vertical-axis counter-clockwise rotation of the sequence, cannot be entirely ruled out. Thellier–Coe palaeointensity experiments on 66 specimens yielded 22 successful determinations and multispecimen (MS) palaeointensity experiments on 11 samples yielded 8 successful determinations. In the upper part of the sequence, Thellier–Coe determinations fail due to the presence of multidomain (MD) grains, but the MS method yields successful results in several of these flows, demonstrating that this method can provide reliable palaeointensity determinations on samples with a higher MD grain fraction. A mean palaeointensity BSV = (18.5 ± 1.9) µT is obtained from the joint analysis of the results from both methods. This value lies clearly below the present-day value BP = 33.1 μT. The virtual axial dipole moment (VADM = 4.3 × 1022 Am2), however, cannot be considered anomalous if compared to available upper Miocene–Pliocene data and represents a new high-reliability contribution to the very limited African palaeointensity database.

Tailored nanophononic wavefield in a patterned bilayer system probed by ultrafast convergent beam electron diffraction

Optically excited nanostructures provide a versatile platform for the generation of confined nanophononic fields with potential (non-)linear interactions between different degrees of freedom. Control of resonance frequencies and the selective excitation of acoustic modes still remains challenging due to the interplay of nanoscale geometries and interfacial coupling mechanisms. Here, we demonstrate that a semiconductor membrane patterned with a platinum stripe acts as a tailored source for high-frequency strain waves generating a multi-modal distortion wave propagating through the membrane. To locally monitor the ultrafast structural dynamics at a specific distance from the deposited metal stripe, we employ ultrafast convergent beam electron diffraction in a laser-pump/electron-probe scheme. Experimentally observed acoustic deformations are reproduced by numerical simulations in a continuous medium model, revealing a spatiotemporal evolution of the lattice dynamics dominated by local rotations with minor strain and shear contributions.

Tracking Movement of Long-lived Equatorial Coronal Holes from Analysis of Long-term McIntosh Archive Data

Features at the Sun’s surface and atmosphere are constantly changing due to its magnetic field. The McIntosh Archive provides a long-term (45 yr) record of these features, digitized from hand-drawn synoptic maps by Patrick McIntosh. Utilizing this data, we create stack plots for coronal holes, i.e., Hovmöller-type plots of latitude bands, for all longitudes, stacked in time, allowing tracking of coronal hole movement. Using a newly developed two-step method of centroid calculation, which includes a Fourier descriptor to represent a coronal hole’s boundary and calculate the centroid by the use of Green’s theorem, we calculate the centroids of 31 unique, long-lived equatorial coronal holes for successive Carrington rotations during the entire solar cycle 23, and estimate their slopes (time versus longitude) as the coronal holes evolve. We compute coronal hole centroid drift speeds from these slopes, and find an eastward (prograde) pattern that is actually retrograde with respect to the local differential rotation. By discussing the plausible physical mechanisms which could cause these long-lived equatorial coronal holes to drift retrograde, we identify either classical or magnetically modified westward-propagating solar Rossby waves, with a speed of a few tens to a few hundreds of meters per second, to be the best candidate for governing the drift of deep-rooted, long-lived equatorial coronal holes. To explore plausible physics of why long-lived equatorial coronal holes appear few in number during solar minimum/early rising phase more statistics are required, which will be studied in future.

Microscopic density-functional approach to nonlinear elasticity theory

Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the macroscopic phenomena of a solid crystal. As the relevant variables we specify the coarse-grained densities of the conserved quantities and a properly defined displacement field which describes the local translations, rotations, and deformations. In order to stay within the framework of the conventional density-functional theory we first and mainly consider the isothermal case and omit the effects of heat transport and warming by friction where later we extend our theory to the general case and include these effects. We proceed in two steps. First, we apply the concept of local thermodynamic equilibrium and minimize the free energy functional under the constraints that the macroscopic relevant variables are fixed. As results we obtain the local free energy density and we derive explicit formulas for the elastic constants which are exact within the framework of density-functional theory. Second, we apply the methods of nonequilibrium statistical mechanics with projection-operator techniques. We extend the projection operators in order to include the effects of coarse-graining and the displacement field. As a result we obtain the time-evolution equations for the relevant variables with three kinds of terms on the right-hand sides: reversible, dissipative, and fluctuating terms. We find explicit formulas for the transport coefficients which are exact in the limit of continuum mechanics if the projection operators are properly defined. By construction the theory allows the diffusion of particles in terms of point defects where, however, in a normal crystal this diffusion is suppressed.

Numerical solution of Arrhenius activation energy for rotational flow

We exhibit the theoretical studies of the rotational behavior on Carreau flow managed by an exponentially stretchable rotate surface with temperature-based viscosity. To begin a chemical reaction, Arrhenius energy is taken into account. Reynold's viscosity model, preserving the variable viscosity effects, has been utilized here. Moreover, nanoparticle effects are inspected using the Buongiorno model. The situation is controlled by employing the Cartesian coordinate system. The ordinary differential system is achieved by implementing an appropriate similarity approach. The solution of governing ordinary differential system has been calculated by the numerical scheme. The consequent solutions are sketched for various dimensionless numbers, including Weissenberg number, local rotation parameter, activation energy, Brownian diffusion parameter, Lewis number, and variable viscosity parameter. The friction factor coefficient, heat and mass diffusion rates are in graphs and tables. A comparative analysis has been made with previously published work.

Slip competition and rotation suppression in tantalum and copper during dynamic uniaxial compression

When compressed, a metallic specimen will generally experience changes to its crystallographic texture due to plasticity-induced rotation. Ultrafast x-ray diffraction techniques make it possible to measure rotation of this kind in targets dynamically compressed over nanosecond timescales to the kind of pressures ordinarily encountered in planetary interiors. The axis and the extent of the local rotation can provide hints as to the combination of plasticity mechanisms activated by the rapid uniaxial compression, thus providing valuable information about the underlying dislocation kinetics operative during extreme loading conditions. We present large-scale molecular dynamics simulations of shock-induced lattice rotation in three model crystals whose behavior has previously been characterized in dynamic-compression experiments: tantalum shocked along its [101] direction, and copper shocked along either [001] or [111]. We find that, in all three cases, the texture changes predicted by the simulations are consistent with those measured experimentally using in situ x-ray diffraction. We show that while tantalum loaded along [101] and copper loaded along [001] both show pronounced rotation due to asymmetric multiple slip, the orientation of copper shocked along [111] is predicted to be stabilized by opposing rotations arising from competing, symmetrically equivalent slip systems.

Cylindrical microplane model for compressive kink band failures and combined friction/inelasticity in fiber composites II: Analyses

This two-part paper presents a novel 3D cylindrical microplane model for the longitudinal compressive failure of fiber reinforced composites by kink band formation. The model formulation was described in part I, and here in part II, its implementation and numerical analyses are described. Through both material point and structure level analyses, the model is shown to predict well the geometric features of the failure, including damage localization, in-plane and out of plane kink band formation, and local fiber rotation. Further, the model is able to capture the entire load displacement curve including the peak load, the prolonged post-peak load plateau, and most importantly, the quasi-brittle fracture mechanics-based strength size effect, in agreement with experiments. The model is also able to capture the effect of the misalignment angle on the peak and post-peak loads. The validated model is used to investigate and quantify the effect of friction on the failure behavior. Results suggest that friction is a major effect, contributing to a higher peak load and post-peak load plateau. Additionally, a simpler and efficient alternative for the combined friction/damage is proposed, which involves a simple modification of the microplane level damage law.

A novel approach to form Normal Distribution of Medical Image Segmentation based on multiple doctors' annotations.

Medical image segmentation annotated by experts provides the labeled data sets for many scientific researches. However, due to the unevenly experienced backgrounds of the experts and limited numbers of patients with certain diseases or illnesses, not only do such labeled data sets have smaller samples but their quality and normality also can range in wide variabilities and be ambiguous. In practice, these segmentations are usually assigned to be the ground truths for the scientific studies, so it may undermine the trustworthiness of the resulting findings. Therefore, it is meaningful to consider how to give a more unified opinion of the annotations among different experts. In this paper, a novel approach to form normal distributions of segmentation is proposed based on multiple doctors' annotations for the same patient. The proposed approach is developed through the following steps: (1) utilize a framework7 of averaging images to construct an averaged annotation based on different given annotations; (2) determine the image registration deformations from the averaged annotation to the given annotations; (3) build a joint multivariate Gaussian distribution over the logorithm of Jacobian determinants and curls of the registration deformations; lastly, (4) simulate a normal distribution of segmentation by the joint Gaussian distribution of registration deformation. This work translates the problem of forming a normal distribution of the image segmentation into a problem of forming joint Gaussian distribution of image registration deformations, which the latter can be reasoned by Jacobian determinant (models local size of pixel cells) and curl (models local rotation of pixel cells) information. In the following sections, a detailed walk-through of the proposed approach is provided along with its analytical mathematics and numerical examples for its effectiveness. A synthetic example of 3 manually defined label image is made to show how to construct a mean label image, and an example of a real cancer image annotated by 3 doctors demonstrates the formation of the normal distribution and the effectiveness of the propose method.

The impact of radial electric fields and plasma rotation on intermittence in TJ-II

This work explores the impact of an imposed radial electric field on the intermittence parameter in magnetically confined plasmas. The intermittence is sensitive to both the magnetic configuration (dominant helical modes or low order rational surfaces) and to poloidal flows or radial electric fields. This behaviour was verified both in numerical turbulence calculations using a resistive magnetohydrodynamic model, and using Langmuir probe data obtained in experiments at the TJ-II stellarator. It is shown that the intermittence parameter can be used to detect when the local plasma rotation velocity, with respect to the laboratory frame of reference, is minimum.

Local monoclinic polarization rotation promoting a different domain alignment in rhombohedral Pb(Zr,Ti)O3 ferroelectrics

Domain switching takes a substantial role in the macroscopic electrical properties of perovskite-type ferroelectric materials. However, the attainable domain alignment in polycrystalline states is often far away from the saturation due to the constraint of long-range crystallographic symmetry. Herein, we report a field-induced saturated polarization alignment, facilitated by local monoclinic polarization rotation in conventional rhombohedral $\mathrm{Pb}({\mathrm{Zr}}_{0.54}{\mathrm{Ti}}_{0.46}){\mathrm{O}}_{3}$ via advanced electrical basing in situ synchrotron x-ray diffraction and pair distribution function measurements. It is found that the polarization alignment can reach the upper limit of theoretically calculated value in rhombohedral ceramic during high electric-field poling, and such a state can be maintained upon removal of electric field. In situ pair distribution function analysis demonstrates the occurrence of monoclinic distortion at local length $(<10\phantom{\rule{0.16em}{0ex}}\AA{})$, where the electric-field driven polarization rotation emerges, and promoting the alignment of polarization variations. Concurrently, large local piezoelectric strain $(1000\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V})$ and intrinsic lattice piezoelectric response $(1400\phantom{\rule{0.16em}{0ex}}\mathrm{pm}/\mathrm{V})$ during poling are found to be generated, while large remanent strains are also observed. These results offer fresh insight into the role of local structure in domain switching behavior and have potential for the theoretical investigation of domain alignment in ferroelectrics.

Effects of New Tunnelling on a Buried Pipeline with Joints and Its Detachment

The interactions between the buried pipeline and tunnelling-induced ground movement are studied in this paper, in which the jointed pipeline, Pasternak foundation, and the detachment are considered. A mathematical model using the pulse function is provided to simplify the jointed pipeline to a continuous pipeline with additional local rotations. The determination of detachment is used by the usual iteration method. The finite difference method is utilized to obtain the numerical results. The results calculated by our proposed method agree with the experimental data of centrifuge tests and are close to those obtained by the other methods. The deflection and bending moment of the jointed pipeline can be predicted reasonably, as well as its detachment location. Parametric analyses about the main influencing factors are carried out. The stiffness reduction factor is significant to the discontinuous behavior of the jointed pipeline. During the parametric analyses, the detachment beneath the jointed pipeline sometimes happens and sometimes does not. The responses of the jointed pipeline and its detachment require priority attention.

State of stress and stress rotations: Quantifying the role of surface topography and subsurface density contrasts in magmatic rift zones (Eastern Rift, Africa)

In rift settings, the crustal stress field is dominated by extension, which leads to rift-parallel topography and basin alignments. However in some continental rift systems, some observables of the orientation of principal stresses show substantial deviations from these patterns. Such stress field rotations are currently poorly understood and could reflect the critical role of rift magmatism in the creation of topography, the plate state-of-stress, and volcanic and tectonic processes. Yet the role of magma intrusions, crustal thinning, and rift basin and flank topography on rift zone stress field rotations remain poorly quantified. The seismically- and volcanically-active Magadi-Natron-Manyara region of the East African Rift shows a 60∘ local stress field rotation with respect to regional extension. Here, we test the hypothesis that such rotation is due to the cumulative effects of surface and subsurface loads (lateral subsurface density contrasts). We use analytical and calibrated numerical models of magmatic rift zones to simulate lithospheric deformation in the presence of magma bodies, crustal thinning, and topography to quantify their effect on intrusions and fault kinematics in a rift setting. Our 3D static models of a weakly extended rift suggest that surface topography influences shallow stress localization, whereas subsurface density contrasts play a larger role in lower crustal stress localization. Both patterns suggest a preferred region for melt storage beneath the rift valley. We show that the interaction between topography, crustal thinning, extension, and a pressurized magma reservoir could generate principal stress orientations consistent with the local stress rotation observed from earthquake focal mechanisms. Our results demonstrate how rift topography and the geometry of crustal thinning can guide magmatism and strain localization, highlighting the need for a three-dimensional treatment of rift kinematics.

Basics of surface reconstruction during selective area metalorganic chemical vapour-phase epitaxy of GaAs films in the stripe-type ultra-wide window

The evolution of the surface morphology and growth steps of the GaAs film during selective area epitaxy has been studied. It has been shown that during the selective area epitaxy three regions with different growth mode and the atomic-height step orientation can be formed. A correlation between the local misorientation and the specific features of these areas has been identified. The layer surface’ local misorientation angle causes the transition between growth modes. A simulation model of the change in the growth steps’ front in the window area is proposed. It is shown that the local rotation angle of the growth steps’ front is governed by the growth rate change across the window. It was experimentally and theoretically shown that a small change in the orientation of the growth steps in the central area of the window and a rotation of the front by nearly 90°for the outermost window areas are specific features due to the symmetric mask, whereas the size of the central area decreases sharply with increasing layer thickness.

Cylindrical microplane model for compressive kink band failures and combined friction/inelasticity in fiber composites I: Formulation

This two-part paper presents a novel 3D cylindrical microplane model for the longitudinal compressive failure of fiber reinforced composites by kink band formation. The formulation details are presented in part-I, while the implementation, calibration, and validation, in part-II. The primary novelty is the first adaptation of the semi-multiscale microplane modeling approach to compressive kink band failures in composites. The salient novel feature of this adaptation is a cylindrical system of microplanes, introduced to capture the transversely isotropic behavior of the unidirectional lamina. The model implicitly resolves the macro–micro compatibility to calculate the local fiber rotation in the kink band, thus defining the orientation of the cylindrical microplane system. This allows an intuitive formulation of the kink band triggering mechanism involving axial inter-fiber microcracks at the microplane level. As another new advance, the internal friction is formulated at the microplane level, via a thermodynamically consistent combined damage/friction scheme, which is integral to compressive failures. The model formulation is general enough to allow application to both brittle and ductile matrix materials, and to in-plane and out-of-plane kinking. The macro–micro elastic correlations are established via strain energy density equivalence, and the calculation of the stiffness tensor of one microplane system is demonstrated.

Slip-induced mechanism of the orientation-dependent deformation banding in cold rolled Al-Mg alloy

The mechanism of deformation banding in cold rolling AlMg alloy is investigated in detail with regards to local lattice rotation and related dislocation slip. The formation of deformation bands (DBs) has a strong orientation dependency where they populate in grains with 〈111〉 and 〈001〉 directions close to the normal direction and 〈101〉 directions close to the rolling direction. On the contrary, DBs are hardly observed in grains close to the {101}〈111〉 orientations. Experimental and numerical analysis indicates that activated secondary slips and their related lattice rotation account for this orientation dependency. The activation of secondary single slip or secondary coplanar slip plays a vital role in the formation of DBs. DBs are formed when the primary and secondary slips lead to sustainable opposite lattice rotations, which gradually split the grain and develop into DBs. Meanwhile, the tendency of the development of Goss texture during the early rolling stage is observed to arise from the generation of DBs.

Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D

In this paper, we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space. Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions. We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes. The method is an extension of the inverse Lax-Wendroff (ILW) procedure in our works (Cheng et al., Appl Math Mech (Engl Ed) 42: 841–854, 2021; Liu et al.) for 2D problems. Different from the 2D case, the local coordinate rotation in 3D required in the ILW procedure is not unique. We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation, ensuring the method is feasible and valid. Both translation and rotation of the body are taken into account in this paper. In particular, we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition, which plays a key role in the proposed algorithm. Numerical simulations on the cylinder and sphere are given, demonstrating the good performance of our numerical boundary treatments.

Dynamic Friedel oscillations on the surface of a topological insulator

We study theoretically the dynamic Friedel oscillations of electrons at the surface of a topological insulator (TI) that are generated by the rotation of a localized impurity spin. We show that the spin-orbit interaction (SOI) in Rashba form, which is an integral part of the TI Hamiltonian, yields a highly anisotropic response to the localized spin rotation. As a result, the response to a flip of a localized spin $z$ projection involves the reaction of all $x$, $y$, and $z$ components of the local magnetization. Additionally, the dynamic spin moment (and thus also Friedel oscillations) emitted by the localized dynamical spin depends on the orientation in the TI plane. The resulting unusual dynamics is due to the interplay of SOI and Ruderman-Kittel-Kasuya-Yoshida interactions. This provides the basis for manipulation of the spin transport in topological insulators decorated with localized impurity spins, which may be important for technological applications.

Sodium mechanics: effects of temperature, strain rate, and grain rotation and implications for sodium metal batteries

Sodium-metal batteries are an attractive energy storage technology, owing to the low cost and relative earth abundance of sodium. However, despite the importance of electro-chemo-mechanical phenomena in alkali-metal batteries, experiments on the mechanical properties of metallic Na are relatively scarce, especially in terms of its viscoplastic response. In this work, we measured the temperature- and rate-dependent deformation of sodium by performing tensile tests in inert gas environments. Digital image correlation measurements were performed to track the local strain and rotation fields. Temperature-dependent experiments were used to experimentally calibrate the activation energy for creep. Furthermore, local deformation measurements of sodium suggest that grain-size and crystallographic orientation effects may be important considerations for sodium-based batteries. Finally, the implications of creep on the performance of Na-metal batteries discussed, providing guidance for future modeling efforts.

Cyclic deformation and dislocation structure evolution of a copper bicrystal with components rotating gradually along the grain boundary

Abstract The push –pull cyclic deformation of a copper bicrystal with components rotating gradually along the grain boundary (GB) was carried out under constant plastic strain amplitude at room temperature in air. The evolution of slip morphology and dislocation structure was observed by scanning electron microscopy electron channelling contrast technique. It was shown that slip morphology and dislocation structure in one of the grains changed gradually along the GB. This phenomenon can be understood based on the local irreversible rotation of crystals, which exists during the symmetrical push– pull loading. When the secondary slip was localized to form the secondary persistent slip bands, which interacted with the regular walls in the second type of deformation band, then the cell structure was formed. The second type of deformation band is one kind of sites for cell formation.