Isotropic Ones Research Articles

Cohesive fracture of plane orthotropic layers

Crack-like cohesive defect propagation within a plane orthotropic linear elastic layer is considered by assuming that the defect, and its growth under load, can be modeled as the evolving separation along a straight, predetermined nonlinear, nonuniform Needleman-type cohesive interface. The analysis exploits a general form of orthotropy rescaling originally developed for the displacement boundary value problem by Krenk (1979). It is shown that when the material is degenerate orthotropic (i.e., ρ=1, ρ is the orthotropic shear parameter) rescaling enables the determination of solutions from isotropic ones and, when the material is fully orthotropic, rescaling allows for solutions to be obtained from problems with the simpler cubic symmetry. (These are well known attributes of linear static sharp crack analysis, which depend on an alternative form of rescaling the traction boundary value problem (Suo, 1990; Suo et al, 1991).) The procedure is demonstrated by obtaining degenerate orthotropic response from isotropic solutions recently obtained by the authors in an investigation of both solitary as well as multiple cohesive defect interaction problems in layered systems under arbitrary loading (Nguyen and Levy, 2009, 2011). In order to obtain fully orthotropic solutions via rescaling, a novel integral equation formulation is developed based on exact infinitesimal strain elasticity solutions for rectangular domains composed of cubically symmetric media and subject to arbitrary loading. Explicit results are obtained for the simple edge notch bend configuration, chosen so as to shed light on the mechanisms of defect propagation in orthotropic layers. It is demonstrated that increasing the orthotropic stiffness ratio can precipitate a quasi-brittle defect growth response. Furthermore, it is well known that in a number of technically important problem geometries and loadings, static sharp crack solutions are only weakly dependent on shear parameter ρ enabling the estimation of fully orthotropic behavior from isotropic solutions (Suo et al, 1991). This result is shown to be true for nonlinear cohesive fracture analysis of the edge notch bend configuration analyzed in this study.

Guided wrinkling in swollen, pre-patterned photoresist thin films with a crosslinking gradient

A new thin film buckling system was developed from photosensitive SU-8 thin films doped with UV light absorbing dye, resulting in a depth-wise gradient modulus after photocrosslinking. When the film was swollen by an organic solvent, a wide range of wrinkling patterns was obtained, including lamella, peanut and semi-hexagonal patterns. Both the morphology and wavelength were found to be dependent on the original film thickness. By leveraging the thermoplasticity of SU-8, we imprinted one-dimensional (1-D) patterns on the dyed SU-8 with variable pitch and height from 1 μm to 20 μm and 15 nm to 2 μm, respectively. We then swelled the patterned films and investigated the interactions between the intrinsic buckling waves (both size and morphology) and the pre-patterns. As the pre-pattern pitch decreased, the swollen film in the patterned region evolved from isotropic wrinkles to out-of-phase, anisotropic waves, which further became in-phase when the pre-pattern pitch was smaller than the intrinsic wrinkle wavelength. For the latter, the aligned wrinkle morphology varied dramatically when the pre-pattern height decreased: from perpendicular to the pre-pattern wavevector to dual orientation with one set of wrinkles remained perpendicularly ordered and the other set of local buckling patterns aligned in parallel to the pre-pattern, and finally back to isotropic ones. Since the pre-patterns of different size and shape could be readily prepared, the combination of physical confinement together with controlled swelling in a graded thin film offers a new approach to access a wide range of controllable hierarchical patterns.

Auditory-Inspired Morphological Processing of Speech Spectrograms: Applications in Automatic Speech Recognition and Speech Enhancement

New auditory-inspired speech processing methods are presented in this paper, combining spectral subtraction and two-dimensional non-linear filtering techniques originally conceived for image processing purposes. In particular, mathematical morphology operations, like erosion and dilation, are applied to noisy speech spectrograms using specifically designed structuring elements inspired in the masking properties of the human auditory system. This is effectively complemented with a pre-processing stage including the conventional spectral subtraction procedure and auditory filterbanks. These methods were tested in both speech enhancement and automatic speech recognition tasks. For the first, time-frequency anisotropic structuring elements over grey-scale spectrograms were found to provide a better perceptual quality than isotropic ones, revealing themselves as more appropriate—under a number of perceptual quality estimation measures and several signal-to-noise ratios on the Aurora database—for retaining the structure of speech while removing background noise. For the second, the combination of Spectral Subtraction and auditory-inspired Morphological Filtering was found to improve recognition rates in a noise-contaminated version of the Isolet database.

Thermal effect on size dependent behavior of functionally graded microbeams based on modified couple stress theory

Thermal effect on buckling and free vibration behavior of functionally graded (FG) microbeams based on modified couple stress theory is presented. Classical and first order shear deformation beam theories are adopted to count for the effect of shear deformations. Hamilton’s principle is applied to give the governing equations, boundary and initial conditions of the FG microbeam. Using generalized differential quadrature (GDQ) method buckling load and natural frequency of FG microbeam with different boundary conditions are obtained. Some numerical results are presented to investigate effects of different parameters including temperature changes, material length scale parameter, beam thickness, Poisson’s ratio and power index of material distribution on the FG microbeam behavior. Numerical results show that modified couple stress theory predicts higher values of buckling load and natural frequency for FG microbeams. In addition, it is observed that higher temperature changes signify size dependency of FG microbeam. It is shown that Poisson’s effect on buckling load and natural frequency predicted by the current model differs significantly from classical one. Study of power index of material distribution proved that the behavior of FG microbeams differ considerably from homogeneous isotropic ones.

Magnetic properties of the spin‐1/2 Ising–Heisenberg diamond chain with the four‐spin interaction

AbstractA symmetric spin‐1/2 Ising–Heisenberg diamond chain with the Ising four‐spin interaction is exactly solved by means of the generalized decoration‐iteration mapping transformation. The ground state, the magnetization process and thermodynamics are particularly examined for the case of antiferromagnetic pair interactions (Ising and isotropic Heisenberg ones). It is shown that an interplay between pair interactions, the four‐spin interaction and the external magnetic field gives rise to several quantum ground states with entangled spin states in addition to some semi‐classically ordered ones. Besides, the temperature dependence of the magnetic susceptibility multiplied by the temperature is studied and the interesting triple‐peak specific heat curve is also detected when considering the zero‐field region rather close to the triple point, where three different ground states coexist.

Differential cross sections on fragment (2 ≤ Z ≤ 9) production for carbon, aluminum and silicon induced by tens-of-MeV protons

The double-differential cross sections (DDXs) for the inclusive reactions producing heavy nuclei with Z = 2–9 (fragments) from carbon, aluminum, and silicon targets induced by 50 and 70 MeV protons are systematically measured at several angles (30°, 60°, 90°, and 135°) using a specially developed Bragg curve counter and the energy-time-of-flight method. The DDXs of a silicon target for the proton-induced reaction producing fragments heavier than lithium were measured for the first time. The present results are compared with past experimental data, the LA150 evaluated data by the Los Alamos group and several intranuclear cascade models (Bertini and ISOBAR), and the JAEA-version quantum molecular dynamics model (JQMD) coupled with the Generalized Evaporation Model (GEM), which are implemented in the Particle and Heavy Ion Transport code System (PHITS). The present results agree well with the past experimental data and LA150 data for α -particle production. For the fragments heavier than lithium, the present results show forward-peak angular distributions rather than isotropic ones stored in LA150. Calculations with the ISOBAR and GEM models well reproduced our experimental results except for light fragments especially in the high-energy region.

Understanding of dynamic earthquake slip behavior using damage as a tensor variable: Microcrack distribution, orientation, and mode and secondary faulting

The importance of the damage effect on dynamic earthquake slip behavior is clarified using the damage tensor variable. Dynamic mode II faults that are embedded in damage‐inducing media are assumed to relate to damage effects. This study confirms that the rupture velocity for spontaneous fault tip growth in the damage medium is reduced, being slightly smaller than rupture velocities observed for classical elastic material. Inelastic energy loss resulting in damage is relatively small but nonnegligible to the accumulated fracture energy. Two framework parameters employed in this study determine microcrack orientations and modes of microcracks and provide information on deviations in microcrack distribution between isotropic and nonisotropic ones. Spatial microcrack distribution patterns in isotropic and homogeneous systems are strongly dependent on a parameter related to the damage creation criterion. When considering secondary faulting, two apparently different behaviors, pulverization and branch development, are understood in a single framework, which gives a new insight into fault zone formation. The present results show that damage effect must be treated as a tensor variable rather than a scalar one as employed in many previous studies.

Role of Anisotropy in Electrodynamically Induced Colloidal Aggregates

We investigate the assembly of spherical and anisotropic colloidal particles with the shape of peanuts when subjected to an external alternating electric field. By varying the strength and frequency of the applied field, we observe that both types of particles form clusters at low frequencies due to attractive electrohydrodynamic interactions or disperse into a liquidlike phase at high frequencies due to repulsive dipolar interactions. We characterize the observed structures via pair correlation functions and radius of gyration, and observe a clear difference in the ordering process between the isotropic and anisotropic colloids. Further on, we interpret the cluster formation kinetics in terms of dynamic scaling theory, and observe a faster aggregation of the anisotropic colloids with respect to the isotropic ones.

A NONSINGULAR BOUNDARY ELEMENT METHOD FOR THE TORSION PROBLEM OF THE ANISOTROPIC UNIFORM BAR

The presentation is mainly devoted to the research on the regularized boundary integral equations (BIEs) with indirect unknowns for torsion problem of the anisotropic uniform bar. Based on a new view and idea, a novel regularization technique is pursued, in which the nonsingular indirect BIE (IBIE) excluding the CPV and HFP integrals is established. Such torsion problems can be solved directly by using the presented technique without transforming them into isotropic ones, for this reason, no inverse transform is required. Moreover, a unique feature of the shear stress BIEs expressed by density functions is that they are independent of the warp BIEs and, as such, can be collocated at the same locations as the warp BIEs. This provides additional and concurrently useable equations for various purposes. Besides, in the numerical implementation, the boundary geometric is depicted by exact elements, while the distribution of the boundary quantity on each element is approximated by a discontinuous quadratic element. Some numerical examples will be applied to validate the current scheme. It is shown that a better precision and high-computational efficiency can be achieved by the presentation.

Low-temperature magnetization curves of anisotropic ferrimagnets

Anisotropic ferrimagnets—unlike isotropic ones—exhibit a rich variety of shapes of magnetization curves. The possibilities are analyzed in an exhaustive fashion within a model with second-order anisotropy on both sublattices, limited to low temperatures and high-symmetry orientations of the applied magnetic field. It is important to discriminate between ferrimagnets with grossly unequal sublattices (when the moments differ by a factor of 2 or more) and those whose sublattice moments are relatively close, i.e., differ by less than a factor of 2. In the former case, as many as 10 different curve shapes are possible; in the latter case, only 9. For a given compound and field direction, the shape is determined by the system’s locus in the coordinate plane of reduced anisotropy parameters. For any ratio of the sublattice moments, such a diagram is obtainable by means of analytic expressions.

Study on Ultrasonic P-Scan Imaging Technology for Rotary Parts Used in Coal Mine Machinery

Aiming at implementing numeralization, automatization and imaging of ultrasonic testing in rotary parts used in coal mine machinery, ultrasonic P-scan imaging technology of rotary parts is studied in this paper. Searching pixel units according to the incident direction of ultrasonic, and correcting non-isotropic resolution images to isotropic ones with linear interpolation algorithm to, multi-layer B-/C-/D-scan and 3-D projection view imaging are achieved. Experimental results show P-scan image could accurately reflect the localization, quantification and orientation of flaws.

A new boundary integral equation formulation for plane orthotropic elastic media

A new boundary integral equation formulation for solving plane elasticity problems involving orthotropic media is presented in this paper. Based on the real variable fundamental solutions of the considered problems, a limit theorem for the transformation from domain integral equations into boundary integral equations (BIEs) and a novel decomposition technique to the fundamental solutions, the regularized BIEs with indirect unknowns, which do not involve the direct calculation of CPV and HFP integrals, are established. The limiting process is done in global coordinates and no separate numerical treatment for strong and weak singular integrals was necessary. The current method does not need to transform the considered problems into isotropic ones as is normally done in the existing literature, so no inverse transform is required. The numerical implementation is carried out using both discontinuous quadratic elements and exact elements, which is developed to model its boundary with negligible error. The validity of the proposed scheme is demonstrated by three numerical examples. Excellent agreement between the numerical results and exact solutions was obtained even with using small amounts of element.

A novel boundary element approach for solving the anisotropic potential problems

This presentation is mainly devoted to the research on the regularization of indirect boundary integral equations (IBIEs) for anisotropic potential problems. Based on a new idea, a novel regularization technique is pursued, in which the regularized IBIEs excluding the CPV and HFP integrals are established. The proposed method has many advantages. First, it does not need to calculate multiple integral as the Galerkin method, so it is simple and easy for programming. Second, it can compute boundary quantities ∂u/ ∂x i ( i=1,2). Third, the anisotropic problems can be solved directly without transforming them into isotropic ones so that no inverse transform is required. Finally, the gradient BIEs are independent of the potential BIEs and they can provide variously useful equations. Numerical examples show that a better precision and high computational efficiency can be achieved by the present method.

Exact solutions for free vibrations of orthotropic rectangular Mindlin plates

Exact closed-form solutions are obtained for free vibrations of orthotropic rectangular Mindlin plates by using the separation of variables method although it is difficult to solve them. The plates have two opposite edges simply supported and all possible combinations of classical boundary conditions at the other two edges. The exact solutions of orthotropic rectangular Mindlin plates are compared with those of isotropic ones and their differences are discussed. The exact solutions are validated through both mathematical proof and numerical comparisons with available p-Ritz solutions and the differential quadrature finite element method solutions calculated by the authors.

Accurate formula for determination of natural frequencies of FGM plates basing on frequencies of isotropic plates

The functionally graded materials (FGM) have many advantages especially in thermal environments, and in the recent years they have been used in many engineering applications. A FGM plate is an inhomogeneous composite made of two constituents (usually ceramic and metal), with both the composition and the material properties varying smoothly through the thickness of the plate. The FGM plate vibrations have a strong bending-stretching coupling effect. Large computational efforts are required for calculating by numerical methods the natural frequencies of such plates with different volume fractions of containing materials. Basing on the investigation of tendencies in frequency variation due to different volume fraction, the present study derives an empiric accurate formula that gives a correlation between the frequencies of FGM plate and isotropic ones made of containing materials, even with different Poisson ratio. The formula gives immediately accurate results for different vibrational modes and for various volume fractions of containing materials without expending much computational effort. Numerical example is presented in order to demonstrate the accuracy, applicability and convenience of using the suggested formula. The natural frequencies calculated with the presented formula are compared with those obtained through other numerical method for thick FGM annular plates.

Quasi-2D Monte Carlo simulations of phase transitions and internal aggregate structures in a highly dense suspension composed of magnetic plate-like particles

The phase transitions and the internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis have been investigated by means of the Monte Carlo method. The present study considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and the magnetic field strength on particle aggregations and phase transitions. The internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation functions, orientational pair correlation functions, nematic and polar order parameters. The main results obtained here are summarized as follows. When the influence of the magnetic interaction between particles is of the same order of that of the perpendicular magnetic field strength, the particles form column-like clusters, and the internal structure of the suspension shows solid-like structures. For the case of a strong applied magnetic field, the internal structure is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under the situation of a strong applied magnetic field, and the internal structure exhibits solid-like ones. The brick wall-like structures also appear for a relatively weak magnetic field applied along the in-plane direction despite a slightly smaller volumetric fraction compared with the case of the perpendicular applied magnetic field.

Dimensionality imprint of electrical anisotropy in magnetotelluric responses

Dimensionality analysis of magnetotelluric data is a common procedure for inferring the main properties of the geoelectric structures of the subsurface such as the strike direction or the presence of superficial distorting bodies, and enables the most appropriate modeling approach (1D, 2D or 3D) to be determined. Most of the methods currently used assume that the electrical conductivity of individual parts of a structure is isotropic, although some traces of anisotropy in data responses can be recognized. In this paper we investigate the imprints of anisotropic media responses in dimensionality analysis using rotational invariants of the magnetotelluric tensor. We show results for responses generated from 2D synthetic anisotropic models and for field data that have been interpreted as showing the effects of electrical anisotropy in parts of the subsurface structure. As a result of this study we extend the WAL dimensionality criteria to include extra conditions that allow anisotropic media to be distinguished from 2D isotropic ones. The new conditions require the analysis of the strike directions obtained and take into account the overall behavior of different sites in a survey.

Designing optical elements from isotropic materials by using transformation optics

By taking advantage of a conformal mapping technique, we propose designs for various optical elements such as directional antennas, flat lenses, or bends. In contrast to most of the existing design approaches, the elements can be implemented with isotropic materials, thus strongly facilitating their fabrication. We furthermore generalize the concept and show that under certain conditions previously suggested devices consisting of anisotropic materials may be replaced by isotropic ones using an appropriate transformation. The designs are double-checked by full-wave simulations. A comparison with their anisotropic counterparts reveals a similar performance.

SPHERICALLY SYMMETRIC STELLAR CLUSTERS WITH ANISOTROPY AND CUTOFF ENERGY IN MOMENTUM DISTRIBUTION. II. THE RELATIVISTIC REGIME

We numerically construct models of spherically symmetric relativistic stellar clusters with anisotropic distribution functions. Newtonian solutions obtained in Paper I are generalized as isotropic Maxwellian ones with energy cutoff in their distribution function. We consider distributions with different levels of anisotropy and discuss some general characteristics of the models.

磁性扁平粒子からなる高濃度サスペンションの相転移と内部構造発現現象に関する擬2次元モンテカルロ・シミュレーション(流体工学,流体機械)

We have investigated phase transitions and internal aggregate structures of a highly dense suspension composed of magnetic plate-like particles with a magnetic moment normal to the particle axis, by means of the Monte Carlo method. In the present study, we have considered a quasi-2D system in order to clarify the influences of the volumetric fraction of particles and magnetic field strength on particle aggregations and phase transitions. Internal structures of particle aggregates have been discussed quantitatively in terms of pair correlation and orientational pair correlation functions. The main results obtained here are summarised as follows. When the influence of magnetic interactions between particles is of the same order of the magnetic field strength, the particles form column-like clusters, and the internal structure of a dispersion shows solid-like structures. As the magnetic field strength becomes strong, the internal structure of a dispersion is transformed from solid-like structures into isotropic ones. However, as the volumetric fraction increases, the particles form brick wall-like structures under circumstances of a strong applied magnetic field, and the internal structure of a dispersion exhibits solid-like ones.