Multiple Inhomogeneities Research Articles

Unconventional Polarization Response in Titanite-Type Oxides due to Hashed Antiferroelectric Domains.

Domains in a crystal, which have crystallographic uniformity and are geometrically segmented, typically arise from various phase transitions. The physical properties within individual domains are inherently the same as those in the homogeneous bulk. As a result, sufficiently large domains have little influence on the bulk properties. However, as the domains decrease in size to the nanoscale, for instance, due to multiple phase instabilities or spatial inhomogeneities, then the materials often acquire exceptional functionalities that are unattainable without these domains. This effect is exemplified by the ultrahigh dielectric and piezoelectric responses observed in ferroelectric oxides with nanoscale polar domains as well as in ferroelectric relaxors with polar nanoclusters. Here, we demonstrate that hashed nanoscale domains in an antiferroelectric material are also capable of boosting dielectric permittivity in an unconventional way. This discovery has been made in an antiferroelectric titanite-type oxide, CaTi(Si1-xGex)O5, in which the permittivity significantly increases when the antiferroelectric order becomes short-range. Our transmission electron microscopy observations have clarified that polar regions simultaneously appear around antiphase boundaries in the antiferroelectric phase of CaTi(Si1-xGex)O5. As the concentration of the antiphase boundary increases, the polar regions become denser and play a crucial role in boosting the permittivity. At the composition of x = 0.5, the value of the permittivity finally reaches double that in the bulk and shows excellent linearity, at least until an electric field of 500 kV/cm is applied. The present findings highlight the promise of domain engineering for boosting the permittivity in antiferroelectrics as a way to develop materials with excellent dielectric properties.

Propagations of multiple solitons in a deformed ferrite

In this work, we investigate the magnetic soliton profile and propagation properties of ultrashort waves in one-dimensional deformed ferrite. A generalized variable-coefficient (1+1)-dimensional ultrashort wave model is obtained by employing the multi-scale expansion method and short-wave approximation. Using numerical simulations, we examine the impact of multiple inhomogeneities on the transmission of magnetic solitons, which arise from local and periodic deformations. Our results indicate that the localized inhomogeneity alter the velocity of magnetic solitons, allowing for the manipulation of their acceleration or deceleration. Periodic type deformation inhomogeneities, on the other hand, provide the magnetic solitons with a period-like external potential that converts its transmission mode to a controlled oscillation.

High-fidelity control of spin ensemble dynamics via artificial intelligence: from quantum computing to NMR spectroscopy and imaging.

High-fidelity control of spin ensemble dynamics is essential for many research areas, spanning from quantum computing and radio-frequency (RF) engineering to NMR spectroscopy and imaging. However, attaining robust and high-fidelity spin operations remains an unmet challenge. Using an evolutionary algorithm and artificial intelligence (AI), we designed new RF pulses with customizable spatial or temporal field inhomogeneity compensation. Compared with the standard RF shapes, the new AI-generated pulses show superior performance for bandwidth, robustness, and tolerance to field imperfections. As a benchmark, we constructed a spin entanglement operator for the weakly coupled two-spin-1/2 system of 13CHCl3, achieving high-fidelity transformations under multiple inhomogeneity sources. We then generated band-selective and ultra-broadband RF pulses typical of biomolecular NMR spectroscopy. When implemented in multipulse NMR experiments, the AI-generated pulses significantly increased the sensitivity of medium-size and large protein spectra relative to standard pulse sequences. Finally, we applied the new pulses to typical imaging experiments, showing a remarkable tolerance to changes in the RF field. These AI-generated RF pulses can be directly implemented in quantum information, NMR spectroscopy of biomolecules, magnetic resonance imaging techniques for in vivo and materials sciences.

A Spherical Harmonics Decomposition Method (SHDM) for Irregular Matrix Coils Design.

With advantages of reduced coupling and compact structure, Matrix Coils (MCs) design extension to approximate multiple target inhomogeneities is necessary to improve its performance in shimming applications. A Spherical Harmonics Decomposition Method (SHDM) is proposed for the multi-target MCs optimization problem. The magnetic field generated by the MCs is represented in form of SHs' orthogonal basis, based on which the MCs pattern is optimized to adapt to multiple SH targets. With multi-target SHs of the 1st, 3rd, and mixed 1st&2nd degrees in Halbach magnet shimming, MCs structure optimizations were successfully performed. Comparisons with regular interleaved MCs show the optimized coil structure provides better performance, including reduction of power dissipation, maximum current amplitude, and total current requirement. This work proposed a simple and intuitive way of irregular MCs optimization, which is of high benefits in compact MR systems based on permanent magnets. This methodology may also be translated into local gradient & shimming matrix coils designs for conventional magnetic resonance device.

Multiple ellipsoidal/elliptical inhomogeneities embedded in infinite matrix by equivalent inhomogeneous inclusion method

Traditional equivalent inclusion method provides unreliable predictions of the stress concentrations of two spherical inhomogeneities with small separation distance. This paper determines the stress and strain fields of multiple ellipsoidal/elliptical inhomogeneities by equivalent inhomogeneous inclusion method. Equivalent inhomogeneous inclusion method is an inverse of equivalent inclusion method and substitutes the subdomains of matrix with known strains by equivalent inhomogeneous inclusions. The stress and strain fields of multiple inhomogeneities are decomposed into the superposition of matrix under applied load and each solitary inhomogeneous inclusion with polynomial eigenstrains by the iteration of equivalent inhomogeneous inclusion method. Multiple circular and spherical inhomogeneities are respectively used as examples and examined by the finite element method. The stress concentrations of multiple inhomogeneities with small separation distances are well predicted by equivalent inhomogeneous inclusion method and the accuracies improve with the increase of eigenstrain orders. Equivalent inhomogeneous inclusion method gives more accurate stress predictions than equivalent inclusion method in the problem of two spherical inhomogeneities.

Case-wise investigation of body-wave propagation in a cross-anisotropic soil with multiple inhomogeneity coefficients

The article investigates the propagation behavior of SV-wave, SH-wave, and P-wave in a continuously inhomogeneous cross-anisotropic material. The material properties such as Young’s moduli, shear modulus, and density have been assumed to vary as a function of depth. These functions have been considered as the possible combinations of a polynomial function, exponential function, and trigonometric function. A suitable mathematical formulation of the physical problem has been developed (an eigenvalue problem) with displacement components as fundamental variables. With the help of separation of variables, appropriate substitution, and applicable mathematical treatment, displacement components have been deduced. Furthermore, employing intrinsic boundary conditions, the closed-form expressions for quasi-wave velocities have been derived. Numerical examples have been investigated, and the dependency of phase velocity on phase angle and inhomogeneity coefficients have been shown graphically. It has been observed that the increment and decrement in the degree of material anisotropy disturb the magnitude of phase velocity to a great extent.

The interactions between multiple arbitrarily orientated inhomogeneities with thermo-porous eigenstrains and its applications in geothermal resources

The thermo-poroelastic model for the fluid migration and heat transport around reservoir may be employed to deal with many geophysical problems including underground resources and bounding rock system, etc. In this paper, interactions between multiple ellipsoidal inhomogeneities with arbitrary orientations and eigenstrains caused by the change of pore fluid pressure, localized heating and cooling are investigated. On the basis of equivalent inclusion method (EIM), an approximate analytical method is presented to evaluate the full displacement, strain and stress fields for arbitrarily distributed inhomogeneities. This method is an effective and straightforward way to study the elastic fields of multiple inhomogeneities, since it avoids increasing the computational complexity. The illustrative benchmark studies are served to demonstrate the accuracy of the present algorithm. Furthermore, applications in geostructures for the elastic distributions of arbitrarily orientated inhomogeneities subjected to the thermo-porous eigenstrains are provided, and the closed-form solutions for the degenerate case of spheroidal inclusions for both the prolate and oblate shapes, spherical and elliptical cylindrical inclusion are presented.

Simulation of solids with multiple rectangular inhomogeneities using non-uniform eigenstrain formulation of BIEs

In the present paper, a novel computational model of non-uniform eigenstrain formulation of boundary integral equations (BIEs) with corresponding iterative solution procedures is presented for simulating solids with multiple rectangular inhomogeneities in elastic range. The computational model is developed by introducing the concepts of the equivalent inclusion of Eshelby with eigenstrains into BIEs with the removal of the constant assumption of eigenstrain in previous works that are limited to solve the elliptical or ellipsoidal inhomogeneities. The non-uniform eigenstrains are expressed by Lagrange interpolation polynomials, which are determined in an iterative way for each inclusion embedded in the matrix. Moreover, to deal with the interactions among inclusions, all of the inclusions in the matrix are divided into two groups, namely the near-field group and the far-field group, according to the distance to the current inclusion in consideration. The local Eshelby matrix is constructed over the near-field group to guarantee the convergence of iterative procedure by getting rid of the strong interactions among the inclusions in the near-field group. Due to the unknowns appear only on the boundary of the solution domain in the present model, the solution scale is effectively reduced. The results of the elastic stress distributions across the interface of inclusions are compared with the subdomain BIE method, whereas the overall effective elastic properties of the media are verified by the reference results with doubly periodic square inclusions. In addition, the overall effective elastic properties of a square representative volume element (RVE) with various inclusion distributions are also investigated in considering a variety of factors, including the properties, the aspect ratios, the orientations and the total number of inclusions. Finally, the convergence behaviors and efficiencies of the solution procedure are studied numerically, showing the validity and efficiency of the proposed computational model.

Fingerprinting Redox Heterogeneity in Electrodes during Extreme Fast Charging

Conventionally, battery electrodes are rationalized as homogeneous reactors. It proves to be an erroneous interpretation for fast transients, where mass transport limitations amplify underlying heterogeneities. Given the lack of observability of associated fast spatiotemporal dynamics, redox activity in inhomogeneous electrodes is superficially explored. We resort to a physics-based description to examine the extreme fast charging of lithium-ion battery electrodes. Representative inhomogeneity information is extracted from electrode tomograms. We discover such electrodes to undergo preferential intercalation, localized lithium plating and nonuniform heat generation as a result of distributed long- and short-range interactions. The spatial correlations of these events with the underlying inhomogeneity are found to be nonidentical. Investigation of multiple inhomogeneity fields reveals an exponential scaling of plating severity and early onset in contrast to the homogeneous limit. Anode and cathode inhomogeneities couple nonlinearly to grow peculiar electrodeposition patterns. These mechanistic insights annotate the complex functioning of spatially nonuniform electrodes.

Single- and Multi-Frequency Direct Sampling Methods in a Limited-Aperture Inverse Scattering Problem

Although the direct sampling method (DSM) has demonstrated its feasibility and robustness for imaging of small inhomogeneities, mathematical analyses of DSM have been conducted only on the full-aperture inverse scattering problem. Numerous studies have shown that DSM can also be applied in the limited-aperture inverse scattering problem, but most of its applications are still heuristic. This study considers an application, mathematical analysis, and improvement of DSM with a single-incident field only in the limited-aperture inverse scattering problem. First, we introduce a traditional indicator function of DSM at a single frequency, establish its mathematical structure, and examine its inherent limitation. To demonstrate the theoretical result, various results of numerical simulations with synthetic and experimental data are presented. Next, we consider the multi-frequency indicator function of DSM with a single-incident direction to improve imaging performance. For this, we design a multi-frequency indicator function of MDSM, analyze its mathematical structure, and theoretically explain the improvement of the imaging of single inhomogeneity and the limitation on the identification of multiple inhomogeneities. Various numerical simulations with synthetic and experimental data are presented to validate our results.

Dirichlet-to-Neumann boundary conditions for multiple scattering in waveguides

In this paper, we study a multiple Dirichlet-to-Neumann (MDtN) boundary condition for solving a time-harmonic multiple scattering problem governed by the Helmholtz equation in waveguides that include multiple obstacles, cavities or inhomogeneities with straight waveguides placed between them. The MDtN condition is derived by analyzing analytic solutions represented by Fourier series in the straight waveguides between obstacles, cavities or inhomogeneities. The proposed method is then to remove the straight waveguides between scatterers and impose the MDtN condition on artificial boundaries resulting from domain truncation. This numerical technique can allow a great reduction of computational efforts. The well-posedness of the reduced problem with the full MDtN condition and the reduced problem with truncated MDtN conditions are established. Also the exponential convergence of approximate solutions satisfying truncated MDtN conditions will be proved.

Evaluation of the effective viscoelastic properties of a material containing multiple oblate inhomogeneities using fraction-exponential operators

The paper focuses on the calculation of the effective properties of a viscoelastic material containing multiple inhomogeneities of oblate shape (flakes). The orientation distribution of the inhomogeneities may vary from perfectly aligned to randomly oriented ones. Both matrix and flakes are assumed to be isotropic. Their viscoelastic behavior is described using fraction-exponential operators of Scott Blair-Rabotnov. Results are obtained in closed explicit form. A particular case of a viscous matrix containing randomly oriented viscoelastic inhomogeneities, relevant to modeling of the viscoelastic properties of blood, is discussed in detail.

Extending Esh3D Code to Solve Interacting Eshelby's Inhomogeneity Problems

I present a new development of an open source code Esh3D in solving interacting Eshelby's inhomogeneity problems in whole, half, and finite spaces. The code resolves the interaction between multiple inhomogeneity bodies by assembling and solving a global linear system. For half or finite space problems, the code imposes Neumann and Dirichlet boundary conditions and resolves the surface‐body interaction by hybridizing Eshelby's analytical solutions with a numerical part. I demonstrate the impact of multibody interaction and surface‐body interaction by comparing the results of different problems in whole and finite spaces. This analytical‐numerical hybrid approach, compared to conventional finite element method, is inexpensive and flexible in modeling multiple and evolving inhomogeneity bodies.

Effects of inhomogeneity on rolling contact fatigue life in elastohydrodynamically lubricated point contacts

PurposeThis paper aims to investigate the effects of inhomogeneities on the rolling contact fatigue (RCF) life in elastohydrodynamically lubricated (EHL) point contacts.Design/methodology/approachA numerical model for predicting the RCF life of inhomogeneous materials in EHL contacts was established by combining the EHL model and the inclusion model through the eigen-displacement and then connecting to the RCF life model through the subsurface stresses. Effects of the type, size, location and orientation of a single inhomogeneity and the distribution of multiple inhomogeneities on the RCF life were investigated.FindingsThe RCF life of a half-space containing manganese sulfide (MnS) inhomogeneity or the mixed inhomogeneity of aluminium oxide (Al2O3) and calcium oxide (CaO) was longer than that for the case of Al2O3inhomogeneity. For a single ellipsoidal MnS inhomogeneity, increases of its semi-axis length and decreases of its horizontal distance between the inhomogeneity and the contact center shortened the RCF life. Furthermore, the relationship between the depth of a single MnS inhomogeneity and the RCF life was found. For the half-space containing multiple inhomogeneitites, the RCF life decreased remarkably compared with the homogeneous half-space and showed discreteness.Originality/valueThis paper implements the prediction of the RCF life of inhomogeneous materials under EHL condition.

The Effect of the Frequency Inhomogeneity on the Synchronous States in Systems of Coupled Oscillators

Despite the ubiquity of systems with heterogeneous connectivity, the role of inhomogeneity on network synchronization has not been fully explored. We studied the effect of multiple inhomogeneities in coupling strengths and natural frequencies on the phase locking behaviors of coupled oscillators. In particular, we found that different Gaussian distributions in natural frequencies lead to diverse synchronization states of the coupled oscillator systems. With the stability analysis and numerical simulations, we analysed the transitions between synchronization states and its breakup in detail.

Replacement relations for a viscoelastic material containing multiple inhomogeneities

Classical replacement relations provide a connection between elastic properties of a porous material and the same material with fluid or solid infill of the porous space. We derive such relations for the case when both skeleton and infill materials are viscoelastic. For this goal, we use formalism of compliance/stiffness contribution tensors that lead to replacement relations for anisotropic elastic materials that, in the case of isotropy, coincide with classical Gassmann equation (Gassmann, 1951). We rewrite these relations using creep and relaxation contribution tensors that describe effect of individual inhomogeneities on the overall viscoelastic properties of a heterogeneous material. Explicit analytical expressions are obtained using elastic-viscoelastic correspondence principle and Laplace transform. It becomes possible when viscoelastic properties are expressed in terms of fraction-exponential operators of Scott Blair–Rabotnov. Results are obtained in closed explicit form.

Solutions of the elastic fields in a half-plane region containing multiple inhomogeneities with the equivalent inclusion method and the applications to properties of composites

This paper presents a solution of the elastic fields of a half-plane composite structure containing distributed multiple circular inhomogeneities under boundary loading. The solution is obtained with a semi-analytical approach by combining the Green’s function and the equivalent inclusion method. This approach can achieve high accuracy and can be easily implemented with less computational effort compared with other numerical methods. Then, this solution is further used to explore the boundary effects on the elastic fields and effective elastic properties of the half-plane composite structure containing square periodically distributed circular inhomogeneities. Influences of the boundary and the inhomogeneity volume fraction on the elastic fields are examined in detail. Local effective elastic constants of the composite structure are predicted using the unit cells. The results show that the boundary has a significant effect on the elastic fields and elastic properties of the half-plane composite structure. The average displacement predicted with the conventional effective elastic constants of unit cells may deviate from the real value. Thus, we propose a design of a composite structure with a uniform elastic constant and develop an analytical model to calculate the average displacement.

Overall elastic properties of a material containing inhomogeneities of concave shape

In this paper, we consider materials containing superspherical inhomogeneities and compare effects produced by pores and rigid particles of this shape. The overall properties are expressed in terms of compliance contribution tensors calculated for inhomogeneities using Finite Element Method (FEM) and Gaussian Approximation (GA) method. Consistency of the results obtained by two numerical techniques is observed for most of the shapes (except of strongly concave inhomogeneities). Based on the numerical solution for octahedron and analytical results for sphere, contributions of a single inhomogeneity to the effective properties are approximated analytically with high accuracy. Effective properties of materials containing multiple superspherical pores or multiple superspherical rigid inhomogeneities are calculated using Non-Interaction Approximation (NIA) and Mori–Tanaka–Benveniste scheme (MTB) using results for compliance contribution tensors. Results of micromechanical predictions are compared against direct FEM simulations performed on artificial periodic representative volume elements containing parallel oriented pores and rigid particles with volume fraction up to 25%. It is shown that MTB scheme provides reasonably accurate approximations.

Randomly oriented cracks in a transversely isotropic material

Our work focuses on the calculation of the overall elastic properties of a transversely isotropic material containing multiple randomly oriented circular cracks. We first propose a new methodology to estimate (approximately) the contribution of a single arbitrarily oriented crack in an infinite transversely isotropic media into the overall elastic moduli. This effect is described by a forth rank compliance contribution tensor which serves as the basic building block for various homogenization schemes aimed at calculation of the overall elastic properties of the materials containing multiple inhomogeneities. In this paper we use the Mori–Tanaka–Benveniste scheme which coincides with non-interaction approximation for the case of crack-like inhomogeneities. The approach is illustrated by examples of Berea sandstone and wet bovine dentin.

Local fields and overall transverse properties of unidirectional composite materials with multiple nanofibers and Steigmann–Ogden interfaces

This paper presents the semi-analytical solution for the transverse local fields and overall transverse properties of composite materials with aligned multiple cylindrical nanofibers. The interface between each fiber and the matrix is treated as a material surface described by the Steigmann–Ogden model, which accounts for the effects of surface tension as well as for membrane and bending stiffness of the surface. Assuming a plane strain setting, the problem is formulated in the transverse plane as an infinite elastic matrix with multiple circular inhomogeneities subjected to a uniform far-field load. The expressions for all elastic fields in the composite system are obtained analytically in the form of infinite series expressions. The Maxwell methodology is used to obtain the overall transverse elastic properties. The goal of this work is twofold: (a) to study the influence of the interactions between the inhomogeneities on the local fields and overall transverse properties of the composite system, and (b) to reveal the connection of the Steigmann–Ogden model (with zero surface tension) to a specific uniform interphase layer model. The results presented in this paper demonstrate that for fiber composite materials with medium to high volume fractions, the influence of the interactions can be significant.