Field Approximation Research Articles

On the isogeometric analysis of vibration and buckling of bioinspired composite plates using inverse hyperbolic shear deformation theory

Inspired by the remarkable energy absorption and damage tolerance capabilities observed in mantis shrimp crustaceans, this study delves into the intricate realm of biological composites with helicoidal structures. However, the effect of the relative orientation of fibers within the helicoidal structure matrix on the buckling and vibration characteristics still warrants comprehensive investigation for the better design of the bioinspired structures. For the first time, a Non-Uniform Rational B-Splines (NURBS)-based isogeometric analysis (IGA) framework termed NURBio is proposed to investigate the vibration and buckling characteristics of bioinspired laminated composite structures. The framework employs NURBS basis functions for exact complex geometric representation and field approximation and offers superior computational accuracy and efficiency as compared to conventional finite element method (FEM). The present analysis is underpinned by an inverse hyperbolic shear deformation theory (IHSDT) capable of accurately capturing the interlaminar stress distribution. This research investigates the performance of various bioinspired layup configurations encompassing recursive, exponential, semicircular, and Fibonacci helicoidal designs and compares them with those of unidirectional, and cross-ply laminates. A series of numerical examples on the buckling and vibration response of bioinspired composite plates are presented to demonstrate the versatility and efficacy of the proposed isogeometric framework. The influence of different layups, loading and boundary conditions, and geometric properties on the response of different bioinspired plate structures are meticulously examined. The study offers valuable insights into the design and optimization of high-performance bioinspired structures.

Polarization-dependent intensity ratios in double resonance spectroscopy.

Double Resonance is a powerful spectroscopic method that unambiguously assigns the rigorous quantum numbers of one state of a transition. However, there is often ambiguity as to the branch (ΔJ) of that transition. Spectroscopists have resolved this ambiguity by using the dependence of the double resonance intensity on the relative polarization directions of pump and probe radiation. However, published theoretical predictions for this ratio are based upon a weak (i.e., non-saturating) field approximation. This paper presents theoretical predictions for these intensity ratios for cases where the pump field is strongly saturating in the two limits of transitions dominated by homogeneous or of inhomogeneous broadening. Saturation reduces but does not eliminate the magnitude of the polarization effect (driving the intensity ratio closer to unity) even with strong pump saturation. For the case of an inhomogeneously broadened line, such as when Doppler broadened linewidth dominates over the power-broadened homogeneous line width, a large fraction of the low pump power polarization anisotropy remains. This paper reports predicted polarization ratios for both linear and circular pump and probe field polarizations. The present predictions are compared with experimental measurements on CH4 ground state → ν3 → 3ν3 transitions recently reported by de Oliveira et al.63 and these are in better agreement than with the weak field predictions.

Magnetic properties and hysteresis loops of mixed spin - (3/2, 1) in core-shell hexagonal nanotube: comparative study of mean-field theory and Monte Carlo simulation

Based on the Ising model, Monte Carlo simulation (MCS) and the Mean- field approximation (MFA) were used to examine the magnetic properties and the phase diagram of a ferrimagnetic mixed-spin (2,3/2) hexagonal Ising nanotube with core-shell structure. The effects of exchange interactions ( ) and the single-ion anisotropies ( ) on the magnetization of the total system, the two sublattices and the hysteresis loops have been discussed in detail. The phase diagrams under the effect of different parameters have been provided. The results demonstrate the emergence of compensation phenomena as well as the second-order phase transitions. Multiple behaviors of hysteresis loop, including single and triple hysteresis loops, were identified as a result of competitions between various parameters.

General diffraction integral for converging freeform vectorial fields

Herein it is presented a new vector diffraction integral capable to compute the diffraction patterns for aspheric and freeform wavefronts, with different pupil shapes, and different polarization states. The aforementioned vector diffraction integral is based on the energy conservation theorem, the far field approximation, and the angular spectrum representation of optical fields. The integral is validated through illustrative examples whose results are as expected and coincides with the related works.

A new version of PyWolf for the propagation of partially coherent light in media other than free space

PyWolf is an open-source software capable of performing numerical simulations of partially coherent light propagation from two-dimensional light sources using parallel computation. In the original version of PyWolf, the graphical user interface (GUI) would only show free-space propagation as the only option for propagating partially coherent light, even though users could add their own source models and other objects such as lenses and apertures, which was recognized by PyWolf's GUI. We introduce here the new version of PyWolf, PyWolf 2.0, which among other improvements, enables users to easily add their own propagation medium, which can be used throughout the simulation in different propagation planes. New version program summaryProgram Title: PyWolfCPC Library link to program files:https://doi.org/10.17632/frjscxypkd.2Developer's repository link:https://github.com/tiagoecmagalhaes/PyWolfLicensing provisions: GPLv3Programming language: PythonSupplementary material: Detailed description of the main changes with an example.Journal reference of previous version: Comput. Phys. Commun. 276 (2022) 108336.Reasons for the new version: In the previous paper [1] describing the original version of PyWolf, the propagation kernel was limited to free space, even though optical elements such as lenses and apertures could be added. For propagation in other media (e.g., turbulent medium), users had to substitute the free space propagation by the desired propagation medium since PyWolf always uses the same propagator, which is present in a single Python script.Summary of revisions: Propagation model selection was added to PyWolf's graphical user interface (GUI), enabling users to select the propagation medium of interest. It also enables input parameters (e.g., refractive index) for each propagation model. PyWolf checks for the Python scripts present in the “propagation models” folder at startup and displays them in the GUI, similar to what is done, for instance, for the source models. Then, during the simulation, instead of using the same free space propagators, PyWolf will use the ones that are defined in the selected propagation model. Four examples of propagation models are present in the current version, namely, free space, constant refractive index (besides 1), Kolmogorov, and Tatarskii models [2,3]. Depending on the model used, some propagation quantities may not be valid. For instance, in the current implementation for free space propagation, both the spectral density and degree of coherence are valid, however, that is not the case for the current implementations of the Kolmogorov and Tatarskii models, where only the spectral density is valid. Besides this main feature added to PyWolf, other small issues have been improved and corrected, namely: (i) PyWolf now initiates without needing PyOpenCl platforms or devices; (ii) some errors associated with the importation of packages have been corrected; and (iii) phase correction in the FFT algorithm for odd arrays which can affect the propagation image.Nature of problem: Numerical simulations of the propagation of partially coherent light from planar sources in the Fresnel or far field approximations. Computation time can be improved by using optimized versions of the fast Fourier transform algorithm, but the computation time of other tasks can also be improved through parallel computation. PyWolf aims at using parallel computation to perform time-consuming calculations in the propagation of the cross-spectral density function [4,5].Solution method: The open-source toolkit PyOpenCL is used to perform parallel computation on time-consuming calculations. The user can easily modify and add more features to the software, such as source and propagation models. A graphical user interface is also built using PyQt5 which enables the user to set input parameters, including the user's custom models, view the simulation results, export data, and save and load sessions.

Transmission-Based Vertebrae Strength Probe Development: Far Field Probe Property Extraction and Integrated Machine Vision Distance Validation Experiments

We are developing a transmission-based probe for point-of-care assessment of vertebrae strength needed for fabricating the instrumentation used in supporting the spinal column during spinal fusion surgery. The device is based on a transmission probe whereby thin coaxial probes are inserted into the small canals through the pedicles and into the vertebrae, and a broad band signal is transmitted from one probe to the other across the bone tissue. Simultaneously, a machine vision scheme has been developed to measure the separation distance between the probe tips while they are inserted into the vertebrae. The latter technique includes a small camera mounted to the handle of one probe and associated fiducials printed on the other. Machine vision techniques make it possible to track the location of the fiducial-based probe tip and compare it to the fixed coordinate location of the camera-based probe tip. The combination of the two methods allows for straightforward calculation of tissue characteristics by exploiting the antenna far field approximation. Validation tests of the two concepts are presented as a precursor to clinical prototype development.

Vanishing of Black Hole Tidal Love Numbers from Scattering Amplitudes.

We extract the black hole (BH) static tidal deformability coefficients (Love numbers) and their spin-0 and spin-1 analogs by comparing on-shell amplitudes for fields to scatter off a spinning BH in the worldline effective field theory and in general relativity. We point out that the general relativity amplitudes due to tidal effects originate entirely from the BH potential region. Thus, they can be separated from gravitational nonlinearities in the wave region, whose proper treatment requires higher order effective field theory loop calculations. In particular, the elastic scattering in the near field approximation is produced exclusively by tidal effects. We find this contribution to vanish identically, which implies that the static Love numbers of Kerr BHs are zero for all types of perturbations. We also reproduce the known behavior of scalar Love numbers for higher-dimensional BHs. Our results are manifestly gauge invariant and coordinate independent, thereby providing a valuable consistency check for the commonly used off-shell methods.

Estimation of pollen dispersal distance in Job's tears (Coix lacryma-jobi L.) by using red leaf sheath as a morphological marker.

Job's tears (Coix lacryma-jobi L.) is grown widely in Asian countries and a crop that can fertilize with own pollen and pistils. The grains are used not only for food but also for medicinal purposes. The grain of many cultivars contains glutinous endosperm; only grains with this glutinous endosperm are suitable for use as medicine in Japan. Many wild types have non-glutinous endosperm and can easily cross with cultivar under natural environmental conditions. Because the non-glutinous endosperm trait is dominant to that of glutinous endosperm, F1 seeds produced by crosses between a cultivar and a wild type have non-glutinous endosperm. To reduce the rate of unwanted crosses, we investigated the pollen dispersal distance by using a red leaf sheath as a morphological marker. When plants were cultivated in rows 70 cm apart, the crossing rate was about 25%-35%. As the distance increased, the crossing rate decreased at a rate that could be fitted to a power approximation in fields without intervening plants and to an exponential equation in fields with intervening plants. Our data could be used as guidelines for preventing unwanted crossing with wild types when growing cultivars.

Weakly nonlinear two dimensional wave scattering in incompressible pre-stressed materials: Far field approximation

We develop a series expansion approach to the calculation of the scattering coefficients of in-plane transverse elastic waves. The waves are scattered by a cylindrical obstacle as they propagate through an incompressible nonlinear material which is inhomogeneously pre-stressed. We deal with the calculation using a distorted wave Born approximation in the far field. A neo-Hookean strain energy function is considered for the incompressible elastic material, and a rigid cylinder is considered as an obstacle. From the static equilibrium configuration, a small-on-large approach is constructed via a series expansion of the wave equation which allows us to compute both the scattered wave and the induced pressure field, and their dependence on the applied pre-stressed. In the far field limit, the pre-stress effect on the scattering coefficients is calculated via partial waves. The formalism can be expanded directly to three-dimensional media with different obstacle symmetries.

Efficient Local Refinement near Parametric Boundaries Using kd-Tree Data Structure and Algebraic Level Sets

In analysis of problems with parametric spline boundaries that are immersed or inserted into an underlying domain, the discretization on the underlying domain usually does not conform to the inserted boundaries. While the fixed underlying discretization is of great convenience as the immersed boundaries evolve, the field approximations near the inserted boundaries require refinement in the underlying domain, as do the quadrature cells. In this paper, a kd-tree data structure together with a sign-based and/or distance-based refinement strategy is proposed for local refinement near the inserted boundaries as well as for adaptive quadrature near the boundaries. The developed algorithms construct and utilize implicit forms of parametric Non-Uniform Rational B-Spline (NURBS) surfaces to algebraically (and non-iteratively) estimate distance as well as sign relative to the inserted boundary. The kd-tree local refinement is demonstrated to produce fewer sub-cells for the same accuracy of solution as compared to the classical quad/oct tree-based subdivision. Consistent with the kd-tree data structure, we describe a new a priori refinement algorithm based on the signed and unsigned distance from the inserted boundary. We first demonstrate the local refinement strategy coupled with the the kd-tree data structure by constructing Truncated Hierarchical B-spline (THB-spline) “meshes”. We next demonstrate the accuracy and efficiency of the developed local refinement strategy through adaptive quadrature near NURBS boundaries inserted within volumetric three-dimensional NURBS discretizations.

Hydrodynamic particle interactions in linear and radial viscosity gradients

We present a versatile perturbative calculation scheme to determine the leading-order correction to the mobility matrix for particles in a low-Reynolds-number fluid with spatially variant viscosity. To this end, we exploit the Lorentz reciprocal theorem and the reflection method in the far field approximation. To demonstrate how to apply the framework to a particular choice of a viscosity field, we first study particles in a finite-size, interface-like, linear viscosity gradient. The extent of the latter should be significantly larger than the particle separation. Both situations of symmetrically and asymmetrically placed particles within such an odd symmetric viscosity gradient are considered. As a result, long-range flow fields are identified that decay by one order slower than their constant-viscosity counterparts. Self-mobilities for particle rotations and translations are affected, while for asymmetric placement, additional correction appears for the latter. The mobility terms associated with hydrodynamic interactions between the particles also need to be corrected, in a placement-specific manner. While the results are derived for the system of two particles, they apply also to many-particle systems. Furthermore, we treat the viscosity gradients induced by two particles with temperatures different from that of the surrounding fluid. Assuming a linear relation between fluid temperature and viscosity, we find that both the self-mobilities of the particles as well as the mobility terms for hydrodynamic interactions increase for hot particles and decrease for cold particles.

Full Hermite Interpolation and Approximation in Topological Fields

By using generalized divided differences, we study the simultaneous interpolation of an m times continuously differentiable function and its derivatives up to a fixed order in a topological field K. If K is a valued field, then simultaneous Hermite interpolation and approximation are considered. Newton interpolating series are used in the case of an infinite number of conditions of interpolation. Applications to the numerical approximation of variational problems, the solution of a functional equation and, in the case of p-adic fields, the representation of solutions of a boundary value problem for an equation of the Fuchsian type illustrate the efficiency of the theoretical results.

History of the Method for Sourcewise Approximations of Geopotential Fields

History of the Method for Sourcewise Approximations of Geopotential Fields

PyWolf: A PyOpenCL implementation for simulating the propagation of partially coherent light

We present PyWolf, an open-source software capable of performing numerical simulations of partially coherent light propagation from two-dimensional light sources. PyWolf computes the evolution of a user-defined cross-spectral density function in the Fresnel and far field approximations, which enables the retrieval of second-order optical quantities of interest such as the spectral degree of coherence and spectral density for a given frequency. The open-source tool kit PyOpenCL is used to increase the computation speed. We present examples of propagation of different source models and optical systems to validate our implementation. Performance results for the computation speed when using parallel computation through PyOpenCL is shown. Source models and propagation systems can be easily added to PyWolf, which has a graphical user interface built with PyQt5. This software can be of great utility for partially coherent light simulation problems that are difficult to treat analytically. Program summaryProgram Title: PyWolfCPC Library link to program files:https://doi.org/10.17632/frjscxypkd.1Developer's repository link:https://github.com/tiagoecmagalhaes/PyWolfLicensing provisions: GPLv3Programming language: PythonExternal routines: NumPy, SciPy, Matplotlib, PyOpenCL, PyQt5Nature of problem: Numerical simulations of the propagation of partially coherent light from planar sources in the Fresnel or far field approximations. Computation time can be improved by using optimized versions of the Fast Fourier Transform (FFT) algorithm, but other calculations can only be increased through parallel computation.Solution method: We use the open-source toolkit PyOpenCL to perform parallel computation on time-consuming calculations. The user can easily modify and add more features to the software, such as source models and propagation methods. A graphical user interface is also built using PyQt5 which enables the user to set input parameters, including the user's custom models, view the simulation results, export data, and save and load sessions.

A duality‐based coupling of Cosserat crystal plasticity and phase field theories for modeling grain refinement

AbstractHigh‐rate deformation processes of metals entail intense grain refinement and special attention needs to be paid to capture the evolution of microstructure. In this article, a new formulation for coupling Cosserat crystal plasticity and phase field is developed. A common approach is to penalize kinematic incompatibility between lattice orientation and displacement‐based elastic rotation. However, this can lead to significant solution sensitivity to the penalty parameter, resulting in low accuracy and convergence rates. To address these issues, a duality‐based formulation is developed which directly imposes the rotational kinematic compatibility. A weak inf‐sup‐based skew‐symmetric stress projection is introduced to suppress instabilities present in the dual formulation. An additional least squares stabilization is introduced to suppress the spurious lattice rotation with a suitable parameter range derived analytically and validated numerically. The required high‐order continuity is attained by the reproducing kernel approximation. It is observed that equal order displacement‐rotation‐phase field approximations are stable, which allows efficient employment of the same set of shape functions for all independent variables. The proposed formulation is shown to yield superior accuracy and convergence with marginal parameter sensitivity compared to the penalty‐based approach and successfully captures the dominant rotational recrystallization mechanism including block dislocation structures and grain boundary migration.

Application of Differential Geometry to the Array Manifolds of Linear Arrays in Antenna Array Processing

This article deals with the application of differential geometry to the array manifolds of non-uniform linear antenna array (NULA) when estimating the direction of arrival (DOA) of multiple sources present in an environment using far field approximation. In order to resolve this issue, we utilized a doublet linear antenna array (DLA) comprising two individual NULAs, along with a proposed algorithm that chooses correct directions of the impinging sources with the help of the prior knowledge of the ambiguous directions calculated with the application of differential geometry to the manifold curves of each NULA. The algorithm checks the correlation of the estimated direction of arrival (DOAs) by both the individual NULA with its corresponding ambiguous set of directions and chooses the output of the NULA, which has a minimum correlation between their estimated DOAs and corresponding ambiguous DOAs. DLA is designed such that the intersection of all the ambiguous set of DOAs among the individual NULAs are null sets. DOA of sources, which imping signals from different directions on the DLA, are estimated using three direction finding (DF) techniques, such as, genetic algorithm (GA), pattern search (PS), and a hybrid technique that utilizes both GA and PS at the same time. As compared to the existing techniques of ambiguity resolution, the proposed algorithm improves the estimation accuracy. Simulation results for all the three DF techniques utilizing the DLA along with the proposed algorithm are presented using MATLAB. As compared to the genetic algorithm and pattern search, the intelligent hybrid technique, such that, GA–PS, had better estimation accuracy in choosing corrected DOAs, despite the fact that the impinging DOAs were from ambiguous directions.

Meshless Numerical Simulation of Singular Fields at Crack Tips of Branched Crack

One of the most important tasks in the numerical analysis of the fracture problem is to achieve a high-precision approximation of the singular stress fields at crack tips. Partially or fully enriched basis functions are often used as enhancements on the whole problem domain or just near the crack tips when constructing the meshless shape functions to simulate the singularity fields at crack tips, namely: global enhancement with fully enriched basis, global enhancement with partially enriched basis, local enhancement with fully enriched basis and local enhancement with partially enriched basis. The scheme of the enriched basis has been extensively and successfully employed in handling problems with a single crack, but its applicability in the branched crack problem remains to be studied. In this paper, the stress intensity factors, the displacement field and the stress field near crack tip are calculated by these four schemes, respectively, and the singular field at the crack tip of a branching crack is also considered. The numerical results show that: for the problems with a single crack, the accuracy of the stress intensity factor obtained by the meshless method with different kinds of enriched basis is basically the same, but the accuracy of the crack tip field variables is obviously different; for the problems with branched crack, the accuracy of the stress intensity factors differs depending on the problems.

NURBS-enhanced line integration BEM for thermo-elastic problems considering the gravity load

This paper is aimed at solving the thermo-elastic problems with the gravity load by the line integration boundary element method (LIBEM). The boundary-only discretization, as one of the significant advantages of BEM, will disappear due to considering the thermal and gravity loads, specifically, domain integrals turn up in the original boundary integral equations (BIEs). Hence, the LIBEM, owning the dimension reduction ability, is introduced to reduce domain integrals dimensionally to ensure that no domain discretization appears during the numerical simulation. Furthermore, as a well-known isogeometry characterization method, the non-uniform rational B-spline (NURBS), is exerted during geometrical construction. Thus, the boundary shape of the numerical models will not change during the refinement and the error of model discretization will be prevented. It is worth mentioning that, to ensure boundary conditions are imposed without difficulty, the field approximation is conducted by the Lagrangian basis functions (LBFs) owning the characteristic of the Kronecker delta function.

An asymptotic model based on matching far and near field expansions for thin gratings problems

In this paper, we devise an asymptotic model for calculating electromagnetic diffraction and absorption in planar multilayered structures with a shallow surface-relief grating. Far from the grating, we assume that the solution can be written as a power series in terms of the grating thickness δ, the coefficients of this expansion being smooth up to the grating. However, the expansion approximates the solution only sufficiently far from the grating (far field approximation). Near the grating, we assume that there exists another expansion in powers of δ (near field approximation). Moreover, there is an overlapping zone where both expansion are valid. The proposed model is based on matching the two expansions on this overlapping domain. Then, by truncating terms of order δ2 or higher, we obtain explicitly the equations satisfied by the lowest order terms in the power series. Under appropriate assumptions, we prove second order convergence of the error with respect to δ. Finally, an alternative form, more convenient for implementation, is derived and discretized with finite elements to perform some numerical tests.

On the optimal approximation of geophysical fields

On the optimal approximation of geophysical fields