Arbitrary Direction Research Articles

Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Natural frequency analysis of laminated piezoelectric beams with arbitrary polarization directions

Control of spin-wave polarity and velocity using a ferrimagnetic domain wall

We present a theoretical study of the scattering of spin waves by a domain wall (DW) in a ferrimagnetic (FiM) spin chain in which two sublattices carry spins of unequal magnitudes. We find that a narrow but atomically smooth FiM DW exhibits a different behavior in comparison with similarly smooth ferromagnetic and antiferromagnetic DWs due to the inequivalence of the two sublattices. Specifically, for sufficiently weak anisotropy, the smaller spin at the center of the DW is found to become precisely normal to the easy axis, selecting an arbitrary direction in the xy plane and thereby breaking the U(1) spin-rotational symmetry spontaneously. This particular form of a FiM DW does not occur in antiferromagnetic systems and is shown to lead to a strong dependence of spin-wave scattering pattern on the state of polarization of the spin wave, which can be either right-handed or left-handed, suggesting the utilization of such a narrow DW as a spin-wave filter. Moreover, we find that in the case of an atomically sharp DW, where all the spins point either up or down due to strong easy-axis anisotropy and therefore the polarization of the spin wave is conserved upon transmission, the wave vector of the spin-wave changes after passing through the DW leading to a change in the group velocity of the spin wave. This change of the wave vector indicates the acceleration or deceleration of the spin waves and thus a sharp FiM DW could serve as a spin-wave accelerator or decelerator in spintronics devices, offering a functionality absent in a ferromagnetic and an antiferromagnetic counterpart. Our results indicate that FiM spin textures can interact with spin waves distinctly from ferromagnetic and antiferromagnetic counterparts, suggesting that they may offer spin-wave functionalities that are absent in more conventional magnets. Published by the American Physical Society 2024

A semi-analytical transient undisturbed velocity correction scheme for wall-bounded two-way coupled Euler-Lagrange simulations

Force closure models employed in Euler-Lagrange (EL) point-particle simulations rely on the accurate estimation of the undisturbed fluid velocity at the particle center to evaluate the fluid forces on each particle. Due to the self-induced velocity disturbance of the particle in the fluid, two-way coupled EL simulations only have access to the disturbed velocity. The undisturbed velocity can be recovered if the particle-generated disturbance is estimated. In the present paper, we model the velocity disturbance generated by a regularized forcing near a planar wall, which, along with the temporal nature of the forcing, provides an estimate of the unsteady velocity disturbance of the particle near a planar wall. We use the analytical solution for a singular in-time transient Stokeslet near a planar wall (Felderhof [1]) and derive the corresponding time-persistent Stokeslets. The velocity disturbance due to a regularized forcing is then obtained numerically via a discrete convolution with the regularization kernel. The resulting Green's functions for parallel and perpendicular regularized forcing to the wall are stored as pre-computed temporal correction maps. By storing the time-dependent particle force on the fluid as fictitious particles, we estimate the unsteady velocity disturbance generated by the particle as a scalar product between the stored forces and the pre-computed Green's functions. Since the model depends on the analytical Green's function solution of the singular Stokeslet near a planar wall, the obtained velocity disturbance exactly satisfies the no-slip condition and does not require any fitted parameters to account for the rapid decay of the disturbance near the wall. The numerical evaluation of the convolution integral makes the present method suitable for arbitrary regularization kernels. Additionally, the generation of parallel and perpendicular correction maps enables to estimate the velocity disturbance due to particle motion in arbitrary directions relative to the local flow. The convergence of the method is studied on a fixed particle near a planar wall, and verification tests are performed in the Stokes regime on a settling particle parallel to a wall and a free-falling particle perpendicular to the wall.

Experimental validation of anomalous acoustic wave refraction using Double layered acoustic gratings

Acoustic metasurfaces (AMSs) have garnered increasing attention over the past decade due to their remarkable capability for wave manipulation. AMSs have been widely applied in diverse domains, including anomalous refraction and extraordinary sound absorption/isolation, among others. However, typical AMS designs, such as Helmholtz resonator-like or labyrinthine structures, are often geometrically complex, limiting their practical usability. In this paper, we introduce an ultracompact Double Layered Acoustic Grating (DLAG) to achieve anomalous acoustic wave refraction. The DLAG comprises double-layered rigid panels with multiple perforated subwavelength slits. By optimizing the positions of these slits on the rigid panels, the acoustic energy of an obliquely incident plane wave can be concentrated within a predetermined region in an arbitrary direction. The paper will first review the theoretical background to predict the wave propagation controlled by DLAGs based on the surface coupling approach. Subsequently, the underlying principle to achieve anomalous refraction using DLAGs will be discussed. A 3D-printed DLAG with the optimized slit positions is used for demonstration. In the experiment, the acoustic energy of a plane wave with an incident angle of 36 degrees was successfully collimated within a predetermined focusing region with a negative refracted angle of -36 degrees.

Gravitational lens system as a long baseline detector of extremely low frequency primordial gravitational wave

ABSTRACT The effect of extremely low frequency primordial gravitational wave with arbitrary direction of propagation on a gravitational lens system in expanding universe is investigated. From the point of view of real astrophysical lens model, singular isothermal sphere lens model is adopted in the gravitational lens system. The results show that, under the perturbation from extremely low frequency primordial gravitational wave, time delay in the gravitational lens system is very sensitive to extremely low frequency primordial gravitational wave and could strongly deviate from that deduced from theoretical model. This means that the strongly deviated time delay could be the imprint of extremely low frequency primordial gravitational wave on gravitational lens system, indicating that gravitational lens system could be used as a long baseline detector to detect extremely low frequency primordial gravitational wave.

Measurement of transverse and longitudinal relaxation rates of double-beam atomic magnetometers in geomagnetic environment

Longitudinal relaxation rate (R1) and transverse relaxation rate (R2) are crucial for evaluating the performance of atomic magnetometers. Unfortunately, to the best of our knowledge, methods for measuring R1 and R2 under arbitrary direction of magnetic field have been rarely studied. We propose, for the first time, measurement methods for R1 and R2 in magnetic fields with arbitrary direction. R1 is measured using the linewidth under three axis modulated magnetic field, while R2 is measured based on demodulated dispersive and absorptive curves of the magnetic resonance signal. The experimental results show that the relative mean deviation of R1 and R2 are 2.5% and 3.6%, respectively. The R1 and R2 measurement methods proposed in this paper has advantage of simple to implement and is validity for measurement in magnetic fields with arbitrary direction, which has significant importance for the application of atomic magnetometers in geomagnetic environments.

Constitutive modelling and wave propagation through a class of anisotropic elastic metamaterials with local rotation

Elastic metamaterials are typically periodic materials possessing unit cells endowed with engineered architecture much smaller than the typical phenomenological length scale. The development of continuum models capable of accurately representing the effects of this aforementioned architecture is extremely challenging, and hence a sparsely developed area. This paper develops a novel 2-D continuum model capable of capturing the dynamic behaviour of a class of anisotropic elastic metamaterials with local rotational elements in the long wavelength limit. A constitutive relation incorporating these local rotational effects is proposed, and ratified using a representative discrete model using linear Hookean springs and identical rigid disks. The new continuum model is used to generate a dispersion relation for harmonic plane waves propagating in an arbitrary direction, which is subsequently compared to the dispersion behaviour of the original discrete model. The general behaviour of this continuum when subjected to 2-D planar harmonic wave propagation in the anisotropic medium is then analyzed, with specific attention given to the effect of material anisotropy and wave propagation direction. This work is the first of its kind to create a new continuum model of a class of anisotropic elastic metamaterials with local rotational effects.

Nano and micro-structural complexity of nematic liquid crystal configurations

Of our interest are frustration-driven pattern generating mechanisms in systems which in bulk equilibrium display spatially homogeneous long-range orientational order in absence of perturbations. As testbed material, we select thermotropic nematic liquid crystals. In bulk, they exhibit weakly discontinuous order–disorder phase transformation on varying temperature where the ordered nematic phase features spatially uniform axial order along an arbitrary symmetry breaking direction. However, due to continuous symmetry breaking (CSB) the established order is extremely susceptible to various perturbations which are in real systems in general always present. We theoretically illustrate how diverse complex patterns could be excited. Particularly intriguing configurations could appear if topological defects are present that could be generated via CSB. Our analysis is based on a relatively simple Lebwohl-Lasher-type model in which we could get analytical insight into phenomena of our interest. Using it we illustrate history dependent early stage isotropic-nematic phase evolution and final patterns in presence of “impurities” (e.g., nanoparticles). We show how characteristic effective interaction characteristics predict qualitatively different emerging patterns. Our analysis is based on CSB which is ubiquitous in nature. Consequently, demonstrated mechanisms are expected to manifest also in other condensed matter systems whose ordered phase is formed via CSB. We illustrate how kinetics and impurities could impact key structural properties of the systems of our interest.

Off-Normal Polarized Single-Photon Emission with Anisotropic Holography Metasurfaces.

Solid-state quantum emitters (QEs) with arbitrary direction emission and well-defined polarization are critical for scalable single-photon sources and quantum information processing. However, the design strategy for on-chip generation of off-normal photon emission with high-purity polarization characteristics has so far remained elusive. Here, we introduce the anisotropic holography metasurfaces for efficiently manipulating the emission direction and polarization of QE. The proposed method offers a flexible way to realize phase matching in surface plasmon scattering with spatially varying filling factors and provides an efficient route for designing advanced QE-coupled metasurfaces. By nonradiatively coupling nanodiamonds with metasurfaces, we experimentally demonstrate on-chip generation of well-collimated single-photon emission propagating along off-normal directions (i.e., 20° and 30°) featuring a divergence angle lower than 2.5°. The experimental average degree of linear polarization attains up to >0.98, thereby revealing markedly high polarization purity. This study facilitates applications of QEs in the deployment of integrated quantum networks.

A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves

We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or 1:-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1:-1$$\\end{document} semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.

Optimization Over Families of Quasi-Periodic Orbits

Quasi-periodic orbit families in astrodynamics are usually studied from a global standpoint without much attention to the specific orbits which are computed. Instead, we focus on the computation of particular quasi-periodic orbits and develop tools to do so. These tools leverage the parametric structure of families of quasi-periodic orbits to treat orbits only as a set of orbit frequencies instead of states in phase space. We develop a retraction on the family of quasi-periodic orbits to precisely navigate through frequency space, allowing us to compute orbits with specific frequencies. The retraction allows for movements in arbitrary directions. To combat the effects of resonances which slice through frequency space we develop resonance avoidance methods which detect resonances during continuation procedures and change the step size accordingly. We also develop an augmented Newton’s method for root-finding and an augmented gradient descent method for unconstrained optimization over a family of quasi-periodic orbits. Lastly, we implement an augmented Lagrangian method to solve constrained optimization problems. We note that many of the tools developed here are applicable to a wider range of solutions defined implicitly by a system of equations, but focus on quasi-periodic orbits.

Rayleigh–Taylor instability in an arbitrary direction electrostatic field

Based on the potential flow theory, we carry out the nonlinear analysis for the inviscid incompressible Rayleigh–Taylor instability (RTI) in an arbitrary direction electrostatic field. The analytical expressions for the bubble amplitude and growth rate are presented. The effects of tangential and vertical electrostatic fields upon the bubble dynamics are opposite and depend on permittivity ratio. Agreements with recent simulations are found in the bubble amplitude. The direction of electrostatic field determines which (tangential or vertical) component plays the main role. The stability of the interface depends on whether the tangential and vertical components of the electrostatic field exceed the cut-off electrostatic field which is dependent of the permittivity ratio and the Atwood number. The results of this work demonstrate the importance of the direction of electrostatic field when considering the impact of electrostatic field on RTI.

Establishment of DC Electric Field Measurements by Linear Dipole Type Sensor System

Nowadays, electric fields above the ground are measured mainly by so‐called ‘field mill type’ sensor systems. However, their measurements are limited to vertical field component only due to its technical constraint. Out of necessity of measurements of electric field components in arbitrary directions in any spaces, a linear dipole type DC electric field sensor system, which can be immersed within a fully uniform electric field, was developed. However, it had been remained unknown whether its sensor output is parameter‐dependent or not, and unknown whether it can provide reliable intensity value of measured electric fields or not. In order to clarify these points, test observations of natural electric fields have been conducted by means of plural sensor systems having different values of parameter. Obtained electric field intensity derived from the observed data has shown a parameter‐dependence despite that it should be constant for any parameter values. After a detailed analysis of the effect of the parameter along the equivalent electric circuit of the sensor system, a field‐calibrating formula, which can make the sensor system to be parameter‐independent, has been found. Finally, the linear dipole type DC electric field sensor system for obtaining reliable electric field intensities has been established. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

Towards improved description of plastic anisotropy in sheet metals under biaxial loading: A novel generalization of Hill48 yield criterion

Lightweight design and development of automobiles are strongly dependent on lightweight high-strength sheet metals. An accurate prediction of anisotropy and yield surface evolution of these materials under different sampling directions of biaxial tension (BT) is a necessary condition for the numerical analyses of stamping forming. In this work, the Hill48 model considering the principal stress direction is generalized to describe the anisotropic evolution and the yield loci on the normal and diagonal planes. The material parameters of the generalized M-Hill48 model (GM-Hill48) have analytical form and can be calibrated by the yield stresses and r-values expressed by the continuous equivalent plastic strain (EPS). A quadratic function interpolation method based on the near-plane strain (NPS) stress is established to control the yield locus under different plane stress states. In addition, a method for predicting the yield loci in arbitrary sampling directions under BT is proposed by tensor coordinate transformation. Different from the traditional model which can only determine material parameters by using equi-biaxial tension (EBT) or NPS stress along the rolling direction (RD) and transverse direction (TD), the yield stresses of BT in different sampling directions can be incorporated into the generalized model. The predictive capability of the GM-Hill48 model is verified by capturing the continuous evolution of yield stresses and strain for DP590 and AA6016-T4 materials. The convexity condition of the established modified model is given and discussed. Finally, the advantages of new model are further expounded in terms of the prediction accuracy and identified parameters compared with the advanced yield models.

Optical Longitudinal‐Lateral Force Directed in Arbitrary Directions by a Linearly Polarized Beam

AbstractOptical forces arise from the transfer of linear momentum between light and objects, while the tailoring schemes for longitudinal and lateral forces are always complicated and incompatible, which prevents them from achieving the same configuration. Here it is demonstrated that the exclusive longitudinal and lateral forces can be harnessed collaboratively, i.e., optical longitudinal‐lateral force (OLLF), which can scan the whole 2π space by solely rotating the half‐wave plate to switch the linear polarization of the incident beam. It is found that, through the interplay between s‐ and p‐polarized light induced by a particle on the interface, the longitudinal force can be altered from pushing to pulling, while the lateral force can be altered from left to right independently. Due to the merit of large amplitude and flexible tunability, the OLLF can act as the engine to drive a micro vehicle along the arbitrary direction in a 2D plane. This work paves a new way for versatile applications of optical manipulation in theory and applications.

Analysis of spin current in ferromagnetic graphene junctions

Magnetization transport in a ferromagnetic/normal/ferromagnetic graphene junction has been investigated. Inspired by a seminal paper [Phys. Rev. B 66, 014,407, 2002], the longitudinal and transverse components of spin current i.e. components parallel and perpendicular to the magnetization direction in the ferromagnetic layer have been studied. It has been shown that only when the reflected and transmitted waves from the interface between two normal/ferromagnetic layers have the same angle as that of the incident wave, there will be no torque associated with the transport of longitudinal spin current. In general, for an arbitrary direction of magnetization, all spin current components are coexisted and therefore the parallel and the perpendicular components of spin transfer torque are existed. Therefore it is not possible to draw a general conclusion that the torque associated with the transport of longitudinal spin current is always zero.

Characterization of Wormhole Growth and Propagation Dynamics during CHOPS Processes by Integrating Rate Transient Analysis and a Pressure-Gradient-Based Sand Failure Criterion in the Presence of Foamy Oil Behavior

Summary Characterization of wormhole growth and propagation dynamics has been made possible with the semi-analytical models developed in this work by integrating both rate transient analysis (RTA) and a pressure-gradient-based (PGB) sand failure criterion in the presence of foamy oil behavior. The nonlinearity caused by the foamy oil properties is linearized using pseudofunctions, while the source function and finite difference methods are applied to obtain the solutions for the linearized models in the matrix and wormhole subsystems, respectively. A sequential method is adopted to solve the coupling fluid-solid problem, where new wormhole segments can be generated once the PGB sand failure criterion has been achieved, while their updated petrophysical properties can be sent back to obtain the solutions for the fluid flow in the next time interval. Furthermore, the influence of sand failure/fluidizing and foamy oil properties on the dynamic wormhole network can be investigated with the generated type curves. Both wormhole growth and foamy oil flow dictate an upward fluid production at the early times, while the production-induced pressure depletion dominates the declining production at the late times. The fractal wormhole networks can be dynamically characterized by history matching the field fluid and sand production profiles. Both the sand failure degree and foamy oil properties dictate the effective wormhole coverage and intensity. Sand production is found to be influenced by both the breakdown pressure gradient and wormhole conductivities, while oil production rate can be dominated by the wormhole coverage and intensity. Foamy oil flow can increase the oil production rate and increase the wormhole coverage compared with the conventional oil. The newly developed method in this work has been validated and then applied at field scale to dynamically characterize the wormhole growth and propagation by considering both the sand failure phenomenon and foamy oil properties within a unified, consistent, and accurate framework. Compared to the conventional numerical simulations, the novelty of such a semi-analytical method can not only allow us to characterize the growth and propagation dynamics of the fractal-like wormholes without the need for grid refinement near the wormhole grids but also take the complex sand failure and foamy oil behavior into account. In addition, it can minimize the impact of grid orientation effects in numerical simulations, enabling the growth and propagation of the wormholes in arbitrary directions rather than orthogonal directions conditioned to the largest pressure gradient.

Precise and Omnidirectional Opto-Thermo-Elastic Actuation in Van Der Waals Contacting Systems.

Actuation of micro-objects along unconstrained trajectories in van der Waals contacting systems-in the same capacity as optical tweezers to manipulate particles in fluidic environments-remains a formidable challenge due to the lack of effective methods to overcome and exploit surface friction. Herein, a technique that aims to resolve this difficulty is proposed. This study shows that, by utilizing a moderate power beam of light, micro-objects adhered on planar solid substrates can be precisely guided to move in arbitrary directions, realizing sub-nanometer resolution across extended surfaces. The underlying mechanism is the interplay between surface friction and pulsed opto-thermo-elastic deformations, and to render a biased motion with off-centroid light illumination. This technique enables high-precision assembly, separation control of nanogaps, regulation of rotation angles in various material-substrate systems, whose capability is further tested in reconfigurable construction of optoelectronic devices. With simple set-up and theoretical generality, opto-thermo-elastic actuation opens up an avenue for versatile optical manipulation in the solid domain.

A porous elastomer with a cavity array for three-dimensional plantar force sensing

Human gait is an important indicator for diagnosis of various movement-related disorders. Three-dimensional (3D) plantar force monitoring enables real-time recording of contact forces in both the normal and tangential directions in each step, providing useful clues for identification of irregular gait patterns or gait-related health issues. Most flexible sensors for gait monitoring focus on contact forces in the normal direction, being limited to detect forces in the tangential direction. Herein we have developed a porous elastomer with a cavity array (PECA) to measure 3D contact forces for gait analysis. The sensor consists of two fabric electrodes and a dielectric layer of porous Ecoflex elastomer containing a 5 × 5 cavity array, forming four parallel-plate capacitor units in a soft construction. Therefore, a 3D force in any arbitrary direction generates four unique capacitive electrical signals. Importantly, the PECA includes a well-designed combination of micrometer-scale pores and millimeter-sized cavities, dramatically improving the detection sensitivity and linear elasticity range. We have demonstrated high sensitivities of 0.41 N−1 and 0.23 N−1 in the normal and tangential directions, respectively. The flexible PECA-based sensors have been tested to sensitively distinguish various standing postures and different stride lengths for gait analysis, promising reliable translation into areas such as healthcare monitoring, sports training, and rehabilitation engineering.

Arctic curves of the T-system with slanted initial data

We study the T-system of type A∞ , also known as the octahedron recurrence/equation, viewed as a 2+1 -dimensional discrete evolution equation. Generalizing earlier work on arctic curves for the Aztec Diamond obtained from solutions of the octahedron recurrence with ‘flat’ initial data, we consider initial data along parallel ‘slanted’ planes perpendicular to an arbitrary admissible direction (r,s,t)∈Z+3 . The corresponding solutions of the T-system are interpreted as partition functions of dimer models on some suitable ‘pinecone’ graphs introduced by Bousquet–Mélou, Propp, and West in 2009. The T-system formulation and some exact solutions in uniform or periodic cases allow us to explore the thermodynamic limit of the corresponding dimer models and to derive exact arctic curves separating the various phases of the system. This direct approach bypasses the standard general theory of dimers using the Kasteleyn matrix approach and uses instead the theory of Analytic Combinatorics in Several Variables, by focusing on a linear system obeyed by the dimer density generating function.