Propagation Angle Research Articles

Elastic reverse time migration angle gathers using a stabilized Poynting vector without zero points within the wave propagation ranges

Generation of PP and PS angle gathers for elastic reverse time migration (ERTM) has important applications in velocity model updating and subsurface parameter inversion. The Poynting-vector-based method provides a cost-effective way to extract angle gathers from ERTM. However, the estimated propagation directions or angles based on Poynting vectors at or near zero points are unstable, and the reflection energy at these points is likely to be placed in an incorrect angle bin. This instability problem severely limits its use in the generation of high-quality angle gathers. To overcome this problem, we add the conventional Poynting vector with an ancillary one of the Hilbert transformed wavefield, a 90° phase-shifted version of the original wavefield. The Poynting vector of the Hilbert transformed wavefield points in the same propagation direction as the conventional Poynting vector, but they have different zero-point distributions. Adding them together allows us to obtain a stabilized Poynting vector which thoroughly eliminates the zero points within the wave propagation range, and thus we obtain a stable algorithm to extract high-quality angle gathers from ERTM. The Hilbert transformed wavefield already exists in the P/S and up/down wavefield decomposition procedure, which has become a necessary step for ERTM to separate overlapping wavefields at reflectors before the computation of Poynting vectors. Results from two synthetic numerical examples indicate the effectiveness of our method in generating high-quality angle gathers for ERTM.

Novel Measurement-Based Efficient Computational Approach to Modeling Optical Power Transmission in Step-Index Polymer Optical Fiber

Polymer optical fibers (POFs) are playing an important role in industrial applications nowadays due to their ease of handling and resilience to bending and environmental effects. A POF can tolerate a bending radius of less than 20 mm, it can work in environments with temperatures ranging from −55 °C to +105 °C, and its lifetime is around 20 years. In this paper, we propose a novel, rigorous, and efficient computational model to estimate the most important parameters that determine the characteristics of light propagation through a step-index polymer optical fiber (SI-POF). The model uses attenuation, diffusion, and mode group delay as functions of the propagation angle to characterize the optical power transmission in the SI-POF. Taking into consideration the mode group delay allows us to generalize the computational model to be applicable to POFs with different index profiles. In particular, we use experimental measurements of spatial distributions and frequency responses to derive accurate parameters for our SI-POF simulation model. The experimental data were measured at different fiber lengths according to the cut-back method. This method consists of taking several measurements such as frequency responses, angular intensity distributions, and optical power measurements over a long length of fiber (>100 m), then cutting back the fiber while maintaining the same launching conditions and repeating the measurements on the shorter lengths of fiber. The model derivation uses an objective function to minimize the differences between the experimental measurements and the simulated results. The use of the matrix exponential method (MEM) to implement the SI-POF model results in a computationally efficient model that is suitable for POF-based system-level studies. The efficiency gain is due to the independence of the calculation time with respect to the fiber length, in contrast to the classic analytical solutions of the time-dependent power flow equation. The robustness of the proposed model is validated by calculating the goodness-of-fit of the model predictions relative to experimental data.

Simulations of Structure and Morphology in Photoreactive Polymer Blends under Multibeam Irradiation

We present a theoretical study of the organization of photoreactive polymer blends under irradiation by multiple arrays of intersecting optical beams. In a simulated medium possessing an integrated intensity-dependent refractive index, optical beams undergo self-focusing and reduced divergence. A corresponding intensity-dependent increase in molecular weight induces polymer blend instability and consequent phase separation, whereby the medium can evolve into an intersecting waveguide lattice structure, comprising high refractive index cylindrical cores and a surrounding low refractive index medium (cladding). We conduct simulations for two propagation angles and a range of thermodynamic, kinetic, and polymer blend parameters to establish correlations to structure and morphology. We show that spatially correlated structures, namely, those that have a similar intersecting three-dimensional (3D) pattern as the arrays of intersecting optical beams, are achieved via a balance between the competitive processes of photopolymerization rate and phase separation dynamics. A greater intersection angle of the optical beams leads to higher correlations between structures and the optical beam pattern and a wider parameter space that achieves correlated structures. This work demonstrates the potential to employ complex propagating light patterns to create 3D organized structures in multicomponent photoreactive soft systems.

A novel fatigue crack angle quantitative monitoring method based on rotating alternating current field measurement

Under complicated fatigue loading conditions, cracks initiate and grow in the arbitrary direction from corrosion pits in the aerospace equipment. The monitoring of crack propagation angle is very important for the safety assessment of the aerospace equipment, which is still a challenge by the conventional structural health monitoring (SHM) method. In this paper, a novel crack angle quantitative monitoring method is presented based on the rotating alternating current field measurement (RACFM). A theoretical model of the crack angle measuring method is established to analyze the perturbation principle of the induced electromagnetic field. The relationships between the angle, length and depth of the crack and the Bz signal are analyzed. The probe and testing system are established, and experiments are carried out. The results show that the phase of the Bz signal has a linear relationship with the crack angle for the same crack, and the amplitude of the Bz signal can correct the crack angle for the different cracks. The angle of fatigue cracks can be quantitatively measured by the Bz phase difference method based on the RACFM.

An overview of array invariant for source-range estimation in shallow water.

Traditional matched-field processing (MFP) refers to array processing algorithms, which fully exploit the physics of wave propagation to localize underwater acoustic sources. As a generalization of plane wave beamforming, the "steering vectors," or replicas, are solutions of the wave equation descriptive of the ocean environment. Thus, model-based MFP is inherently sensitive to environmental mismatch, motivating the development of robust methods. One such method is the array invariant (AI), which instead exploits the dispersion characteristics of broadband signals in acoustic waveguides, summarized by a single parameter known as the waveguide invariant β. AI employs conventional plane wave beamforming and utilizes coherent multipath arrivals (eigenrays) separated into beam angle and travel time for source-range estimation. Although originating from the ideal waveguide, it is applicable to many realistic shallow-water environments wherein the dispersion characteristics are similar to those in ideal waveguides. First introduced in 2006 and denoted by χ, the dispersion-based AI has been fully integrated with β. The remarkable performance and robustness of AI were demonstrated using various experimental data collected in shallow water, including sources of opportunity. Further, it was extended successfully to a range-dependent coastal environment with a sloping bottom, using an iterative approach and a small-aperture array. This paper provides an overview of AI, covering its basic physics and connection with β, comparison between MFP and AI, self-calibration of the array tilt, and recent developments such as adaptive AI, which can handle the dependence of β on the propagation angle, including steep-angle arrivals.

Towards developing a generalized semi-coherent three-dimensional energy flux model

The energy flux method can be interpreted as an integration over propagation angle of a semi-classical (WKB) modal continuum, which yields an averaged incoherent intensity field with depth-dependent intensity bands that decay in range. Range dependence is typically incorporated via the adiabatic modes approximation and use of the ray invariant to map propagation angles. Though the energy flux method averages out nearly all of the field structure, it has the primary advantages of avoiding finding eigenvalues and eigenrays and its computational effort does not directly scale with frequency or range. The method has also been extended in the past decade to include a convergence factor derived from the interference of neighboring modes, producing a semi-coherent solution that captures some convergence structure analogous to high-frequency caustics. Since the development of the semi-coherent energy flux method, it has so far only been applied to Nx2D environmental models, but should theoretically be applicable in a 3D environment without the assumption of azimuthal symmetry or the exclusion of horizontal refraction. This paper will discuss the theoretical derivation and numerical implementation of a generalized semi-coherent three-dimensional energy flux model. [This study is funded by the NDSEG Fellowship program.]

Extraction of dynamic effective material properties for 2D acoustic Willis media

Acoustic Willis media is characterized by coupling between the kinetic and potential energy through the pressure-strain and momentum density-velocityrelationships. The introduction of additional constitutive properties allows more appropriate characterization of complex unit cells, including effects related to physical asymmetry, finite phase and multiple scattering, and nonreciprocal biases. Similar to traditional composites or other metamaterials, homogenization is a valuable modeling tool that simplifies numerical study of Willis media. However, homogenization schemes must be altered to account for even and/or odd Willis coupling parameters. In this work, we extend a 2D homogenization approach to account for the Willis coupling using the modified dynamic equations. With this homogenization scheme, finite layers of N unit cells and N + 1 unit cells are utilized with different propagation angles and incident directions to isolate the response across a single unit cell. Numerical simulations with the finite element method will then be presented to validate the homogenization model and demonstrate the effective material properties obtained for an asymmetric unit cell. [This work was supported by the Office of Naval Research.]

High-dimensional coding/decoding information with braiding period in free-space optical communication link

We present in principle a free-space optical coding/decoding method that based on the longitudinal braiding period of the structured laser beam. Different from the conventional techniques that mainly focuses on the field of time, frequency, amplitude, polarization and spatial structure, the longitudinal structure is added as a new freedom in our optical link. By combining the topological charge and propagation angle in the transmitter, the longitudinal intervals between the detectors are utilized as the key for decoding. The system using the braiding period as the information carrier has an advantage in security for it is difficult to be eavesdropped. The realization of the hexadecimal coding/decoding suggests that employing the braiding period as a new dimension may have a potential in increasing the capacity or security of the OAM-based free-space data transmission.

Effect of the Relativistic Electron Beam on Propagating Whistler-Mode Wave for Ring Distribution in the Saturn Magnetosphere

Cassini and many investigators reported whistler chorus near Saturn equatorial plane moving outwards. Whistler can propagate when going to high latitude and can alter its characteristics while interacting resonantly with available energetic electrons. Here investigating wave for a relativistic beam of the electron. It is observed and reported by Cassini Magnetospheric Imaging Instrument (MIMI) that inward radial injection of highly energetic particles is most dominant in Saturn intrinsic magnetosphere. Within this paradigm, an empirical energy dispersion relation for propagated whistler-mode oscillations in quasi Saturn magnetospheric plasma from such a non-monotonous ringed distribution function has been established. The kinetic approach and method of characteristics methodologies were used in the computations, which have been shown to be the best for building perturbed plasma states. The perturbed distribution function was estimated using the unperturbed particle routes. The ring distribution function was used to construct an unexpected growth rate expression for relativistic plasma in the inner magnetosphere. The results from the Saturn magnetosphere have been calculated and interpreted using a range of parameters. Temperature heterogeneity was shown to be a significant source of free energy that aided the propagation of a whistler-mode wave. By raising the peak value, the bulk injection of energetic hot electron injection impacts the growth rate. Growth was also demonstrated to be accelerated when the propagation angle increased. The research contributes to a better understanding of the relationship between wave and particle emissions and VLF emissions on a large scale.

Evaluation of T-stress in stationary and propagating adiabatic cracks in FGM subjected to thermo-mechanical loading

The aim of this paper is to study the T-stress and its effect on crack propagation in FGM materials with adiabatic cracks subjected to thermo-mechanical loading based on the J-integral formulation and the extended finite element method (XFEM). Path-independent J-integral responses of T-stress for adiabatic cracks and the effects of incompatible terms for FGMs are discussed. Having examined the T-stress parameter, the effect of fracture characteristic/process length on crack propagation angle in adiabatic cracks is studied. The results show that the initial crack propagation angle deviates from the standard propagation angle by increasing the size of the fracture process zone.

Fatigue Crack Growth Behavior of CP-Ti Cruciform Specimens with Mixed Mode I-II Crack under Biaxial Loading.

Investigations on the fatigue crack growth of commercial pure titanium are carried out with cruciform specimens under different biaxial load ratios (λ = 0, 0.5, and 1) and crack inclination angles (β = 90°, 60°, and 45°) in this paper. Based on the finite element results, the modified solution of stress intensity factors KI and KII for cruciform specimens containing mixed mode I-II crack is obtained by considering crack size, biaxial load ratio, and crack inclination angles. The experimental results show that the maximum tangential stress criterion is fit for the prediction of crack initiation angles for mixed model I-II crack under uniaxial or biaxial loading condition. When the biaxial load ratio increases, the crack propagation angle becomes smaller, and so does the fatigue crack growth rate of mode I crack or mixed mode I-II crack. Based on an equivalent stress intensity factor, a new valid stress intensity factor is proposed to better describe the biaxial fatigue crack growth behavior, which can demonstrate the contribution of mode I and mode II of stress intensity factor.

2D acoustic wavefield simulation by improved stiffness and mass matrices of bilinear square element

Abstract In the frequency domain, we optimize the entries of the element stiffness matrix computed on a square element with the purpose of approximating the 2D acoustic wave equation with the second spatial order. The optimized matrices are computed from the minimization of the normalized phase velocity as a function of propagation angle and the number of grid points per wavelength, leading to a remarkable reduction in the numerical error. The optimized number of 4.1 sample points in a wavelength, with a maximum error in velocities <0.3%, offering the simulation of large-scale realistic models. The superior performance of the optimized matrices to those from the lumped, consistent and eclectic matrices, is evident from the numerical examples presented, with consequent reduction not only in the numerical dispersion/anisotropy but also in an improved resolution. It is noteworthy that optimized matrices give modeling results with better accuracy than models from the high-order spectral element method. Our methodology is easily extendable to the accurate discretizing of the general 3D elastic wave equation that optimizes the bandwidth of the impedance matrix, availing computational resources for accurately modeling the compressional and shear wave velocities, density, as well as multi-parameter inversion.

An Equivalent Circuit/System by Design Approach to the Design of Reflection-Type Dual-Band Circular Polarizers

A dual-band reflection-mode wide-bandwidth and wide-angle scanning circular polarizer is designed. The proposed polarizer can convert linearly polarized waves into right- and left-hand circularly polarized (RHCP and LHCP) waves in the two separate nonadjacent receiving and transmitting K/Ka frequency bands. The polarizer is based on dual-layer dipole arrays printed on both sides of a dielectric substrate separated by a second substrate from the ground plane. An analytic model based on transmission line equivalent circuits is developed. Closed-form expressions are derived to demonstrate the operating principle providing a simple design procedure. The proposed model can be used to optimize the converter for a specific propagation angle of the incident wave. Finally, a system-by-design (SbD) strategy is proposed to improve the performance of analytically synthesized devices. Toward this goal, a computationally efficient “digital twin” of the accurate full-wave model is built to speed up the solution space exploration and efficiently reach the global optimum. A prototype is designed for the incident angle <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{0} = 30^{\circ }$ </tex-math></inline-formula> and it is shown that the axial ratio lower than 3 dB is maintained for a wide-angle field of view of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \theta = 60^{\circ }$ </tex-math></inline-formula> ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\theta }_{min}=0^{\circ },{\theta }_{max}=60^{\circ }$ </tex-math></inline-formula> ) in both frequency bands.

Coupling and Instability of Electrostatic Waves in Spin Magnetized Degenerate Plasmas

In this article, we study the coupling of low-frequency electrostatic waves in the electron-ion and the electron-ion-beam-spin quantum plasmas. The quantum effect of electrons are introduced via separate spin evolution-quantum hydrodynamic (SSE-QHD) model while the ion dynamics is governed by classical fluid equations. In the case of electron-ion plasma, it is found that the quantum effects shift both the coupling domain and the phase velocities of coupled waves. Furthermore, the coupling is observed to be strong at small propagation angles. In the beam interacting system, two coupling domains occur corresponding to small and large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> -values. In the first domain beam mode excites the ion cyclotron (IC) wave and moves with constant phase velocity while in the second domain it gains energy from the ion acoustic (IA) mode and travels with increasing phase velocity. In addition, the beam parameters affect both the coupling domain and the phase velocity. The presence of beam in electron-ion plasma drives the IC mode unstable. The beam parameters, the spin, and the obliqueness affect the instability. Our findings may be helpful in understanding the energy exchange of plasma waves via coupling phenomenon in degenerate plasma systems.

Categorizing MHD Discontinuities in the Inner Heliosphere by Utilizing the PSP Mission

AbstractThe interplanetary discontinuities (IDs) have been widely observed in astrophysical and space plasmas, while their characteristics and evolutions within 0.3 AU are still unclear due to the limitation of spacecraft orbits in previous missions. Here, we report three ID events, including a rotational discontinuity (RD), a tangential discontinuity (TD), and a suspected contact discontinuity (CD), detected by the Parker Solar Probe in a previously unexplored region of the heliosphere as close to the Sun as 0.13 AU. By the combination of the minimum variance analysis technique, the Walén relation and the continuity condition of the electric field, the ID orientations, propagations, and thicknesses are determined, showing a smaller typical ID thickness on the order of 100 km therein. Automated event selection using a magnetic field change threshold criterion is conducted with the PSP field data on Orbits 4 and 5. In total, 3,948 IDs are collected, yielding a ratio of . The IDs within 0.4 AU account for 87% of the total IDs, resulting in sharp ID occurrence rate decrease with heliocentric distance, from ∼140 days−1 for RDs and ∼8 days−1 for TDs at 0.13 AU to about 1 day−1 for both RDs and TDs at r &gt; 0.6 AU. Within 0.3 AU, the RDs with tiny propagation angles, i.e., the angles between the magnetic fields and the RD normals, predominate in all kinds of IDs. We further analyze the jump conditions of these IDs statistically, and find that the changes in magnetic fields and particle parameters are theoretically consistent.

Impact Analysis of Initial Cracks’ Angle on Fatigue Failure of Flange Shafts

A fatigue test on the failure mode of flange shafts was conducted. The propagation characteristics of the initial crack at the junction between the shaft and the flange as well as its angle effect were studied. This study developed an analysis program of fatigue crack propagation, based on the APDL (ANSYS Parametric Design Language). It obtained the effective angle interval within which the initial crack is able to propagate. The fitting calculation formula was derived and the results showed that: (1) The initial crack at the junction between the shaft and the flange would propagate in the radial and axial directions; the unstable crack propagation would cause an abrupt fracture of the cross-section, failing connection; and the angle of initial crack was uncertain. (2) The crack followed the I-II-III mixed mode, which was dominated by mode I. An initial crack with a larger angle showed more noticeable II-III characteristics; KII and KIII affected the crack’s propagation angle in the radial and axial directions and they also affected the structure’s surface direction. (3) The deepest point A of the crack was located at the junction between the shaft and the flange. Its crack propagation can be divided into three stages: rapid growth (stage 1), steady decline (stage 2, buffer stage), and instability (stage 3). The initial crack angle not only affected the propagation rate at stage 1 but also influenced the fatigue life distribution of the structure during propagation. The larger the initial crack angle was, the smaller the proportion of buffer stage in the total fatigue life would be. Moreover, the propagation of crack with a larger initial angle reached instability faster after stage 1, which would cause an abrupt fracture of the cross-section. This was unfavorable for deciding the crack detection time or carrying out maintenance and reinforcement. (4) The crack propagation at the junction between the shaft and the flange was determined by the size relation between ΔKI and ΔKth, instead of the effective stress intensity factor. The effective stress intensity factor can partly reflect the law of crack propagation, but cannot serve as the only criterion for crack propagation; it must be combined with the effective angle interval, which was negatively correlated with the crack’s shape ratio, to determine whether the crack would propagate.

Waves in weakly ionized solar plasmas

ABSTRACT Here, we study the nature and characteristics of waves propagating in partially ionized plasmas in the weakly ionized limit, typical for the lower part of the solar atmosphere. The framework in which the properties of waves are discussed depends on the relative magnitude of collisions between particles, but also on the relative magnitude of the collisional frequencies compared to the gyro-frequency of charged particles. Our investigation shows that the weakly ionized solar atmospheric plasma can be divided into two regions, and this division occurs, roughly, at the base of the chromosphere. In the solar photosphere, the plasma is non-magnetized and the dynamics can described within the three-fluid framework, where acoustic waves associated to each species can propagate. Due to the very high concentration of neutrals, the neutral sound waves propagates with no damping, while for the other two modes the damping rate is determined by collisions with neutrals. The ion- and electron-related acoustic modes propagate with a cut-off determined by the collisional frequency of these species with neutrals. In the weakly ionized chromosphere, only electrons are magnetized, however, the strong coupling of charged particles reduces the working framework to a two-fluid model. The disassociation of charged particles creates electric currents that can influence the characteristic of waves. The propagation properties of waves with respect to the angle of propagation are studied with the help of polar diagrams.

Robustness and stability of volume-based tractography in a multicenter setting.

Muscle diffusion tensor imaging (mDTI)-based tractography is a promising tool with which to detect subclinical changes in muscle injuries and to evaluate pathophysiology in neuromuscular diseases. Classic region of interest (ROI)-based tractography is very time-consuming and requires an examiner with extensive experience. (Semi)automatic approaches such as volume-based tractography (VBT) can diminish this problem but its robustness and stability are unknown. The aim of the current study was to assess the performance of VBT in a multicenter setting and to evaluate semiautomatic segmentation approaches in the analysis of VBT-derived data in terms of the comparability of the outcome measures. Five traveling volunteers underwent 3-T mDTI of seven calf muscles of both legs at six different MR sites. Tract properties and diffusion metrics were calculated using VBT. Within-subject coefficients of variance (wsCVs) and intraclass correlation coefficients (ICCs) were calculated to assess the multicenter reproducibility of tract properties such as tract density (TD), mean tract length, volume and tract propagation angle, and diffusion metrics such as fractional anisotropy, mean diffusivity, axial diffusivity (λ1 ) and radial diffusivity in traveling subjects. Furthermore, 50 individual datasets from five different centers (10 datasets per center) were pooled to assess the feasibility of VBT with manual and semiautomatic segmentation. To assess the differences of tract properties and diffusion metrics between segmentation approaches an ANOVA was performed, and ICC and Bland-Altman plots were analyzed. wsCVs and ICCs showed good reproducibility of the tract properties TD and volume, as well as diffusion metrics. ANOVA showed no significant differences between manual and semiautomatic approaches. ICCs were excellent (≥0.992) and Bland-Altman analysis did not reveal any systemic bias between the methods. Tract properties and diffusion metrics derived from VBT showed good comparability among centers. Semiautomatic approaches revealed excellent agreement with gold standard of manual segmentation. These findings suggest that pooling data from different centers to construct a reference database for tractography results is feasible using semiautomatic segmentation approaches.

The waveguide invariant for a Pekeris waveguide.

A closed-form waveguide invariant β for a Pekeris waveguide is derived. It is based on the modal Wentzel-Kramers-Brillouin (WKB) dispersion equation and implicit differentiation, in conjunction with the concept of the "effective boundary depth," ΔH(θ), where θ is the propagation angle. First, an explicit formula for β(m,n) between mode pairs is obtained assuming an ideal waveguide of the effective waveguide depth, H+ΔH(θ), and provides an excellent agreement with the reference value for the Pekeris waveguide of depth H obtained using the normal mode program kraken. Then, a closed-form expression for a group of adjacent modes is derived: β=(H+ΔH(θ))/(H/ cos2 θ-ΔH(θ)), which can be approximated by β=cos2 θ as ΔH(θ)/H≪1, the analytical expression for an ideal waveguide.

Statistical Analysis of Refractive and Diffractive Scintillation at High Latitudes

AbstractA comprehensive statistical analysis was performed on Global Positioning System scintillation data acquired at high latitudes from 2014 to 2017 after separating phase scintillation events originating from refraction and/or diffraction. Events exceeding a prescribed threshold were identified and analyzed statistically as a function of time, latitude, and propagation angle. The statistical analysis indicates that at high latitudes phase scintillation, which occurs more frequently than amplitude scintillation, is generated through refractive processes which can typically be treated as a stochastic Total Electron Content effect at high latitudes for Global Navigation Satellite System frequencies, and have the highest probability around magnetic noon in the Cusp. On average the phase scintillation index values decrease as a function of latitude, particularly during the first 6 hr of the evening. In addition, irregularities on the poleward side of the aurora are predominantly smaller than the Fresnel scale, when amplitude scintillation events are observed. By comparison, the mean of the phase scintillations on the equatorial side of the aurora, when amplitude scintillations are also present, indicates the existence of irregularities which are larger and smaller than the Fresnel scale. We also found that, during the day and at dusk, the spectral content of the irregularities apparently changes with decreasing off‐B Angle. No such increase is readily apparent at night or at dawn.