Inhomogeneous Region Research Articles

Local spin Hall conductivity

The spin Hall conductivity is usually calculated for periodic solids, while the knowledge of local contributions from inhomogeneous regions like interfaces or surfaces would be desirable. In this work we derive a local expression for the spin Hall conductivity of two-dimensional systems in analogy to the local anomalous Hall conductivity discussed recently. Our approach is applicable to heterogeneous fully bounded systems and nanoribbons with both open and periodic boundary conditions.

Local axisymmetry-breaking–induced transition of trapped-particle orbit and loss channels in quasi-axisymmetric stellarators

The transition of trapped-particle orbit topologies has been investigated in quasi-axisymmetric (QA) configurations, such as the Chinese First Quasi-axisymmetric Stellarator (CFQS). It is found that the axisymmetry-breaking phenomenon in QA configurations is of great significance at some specific locations, which could easily induce blocked particles to transit into localized particles. A novel aspect is presented to interpret the transition mechanism of trapped-particle orbit topologies in this paper, i.e., as the amplitudes of non-axisymmetric field increase along the radius direction, the region of large toroidal inhomogeneity is gradually generated, which makes the length of the trapped-particle trajectory substantially short, and hence, may restrict particles to a single helical field period. Meanwhile, at such locations the “pseudo-axisymmetric” field results in coupling of the maximum radial drift and the minimum poloidal drift, which enables the transition of trapped-particle orbit topologies considerably and forms specific loss channels, degrading plasma confinement. These results may shed light on the optimization of QA configurations via avoidance of such coupling with respect to energetic particle confinement. Moreover, this work is also relevant to the generation of inhomogeneity of particle flux deposition on the devertor plates.

Torsional complex impedance of pipe pile considering pile installation and soil plug effect

Torsional vibrations of pipe pile are more complicated compared to solid pile. In actual engineering, pile surrounding soil may be strengthened or weakened due to different pile installation methods, which is regarded as pile installation effect. At the same time, soil plug effect which describes the interaction between the soil plug and pile wall is also non-negligible in bearing analysis. Along the model of inhomogeneous medium, this paper subdivides the inhomogeneous soil region into certain sub-zones whose shear complex stiffness are derived by virtue of continuity conditions and plain strain model. To study the influence of soil plug effect, the additional mass model is raised and utilized in this paper. In this model, the pile-soil plug system is vertically split into infinite sections, and each pipe pile section and soil plug section is connected by distributed Voigt model. The analytical solution of torsional complex impedance is acquired and compared with results obtained from former studies to verify its rationality. Finally, a parametric research is presented to exhibit the influence of the pile installation and soil plug effect on the torsional complex impedance of pipe pile head.

A Two-Stage Evolutionary Fuzzy Clustering Framework for Noisy Image Segmentation

This article presents a two-stage evolutionary fuzzy clustering framework for noisy image segmentation. It is a bi-stage system comprising a multi-objective optimization stage and a fuzzy clustering segmentation stage. In the multi-objective optimization stage, the fuzzy clustering on pixels in inhomogeneous regions is converted into a multi-objective problem, which can preserve image details while restraining noise. The multi-objective problem is decomposed into several sub-problems by the Tchebycheff approach. A trade-off can be obtained by optimizing these sub-problems simultaneously. In the fuzzy clustering segmentation stage, fuzzy clustering with the trade-off between preserving image details and restraining noise is performed on the whole observed image. To deal with this fuzzy clustering problem, an adaptive evolutionary fuzzy clustering algorithm with spatial information is proposed. Experiment results on synthetic and real images illustrate the effectiveness of the proposed framework for noisy image segmentation.

Inhomogeneous Image Segmentation Using Hybrid Active Contours Model With Application to Breast Tumor Detection

The most fatal and frequent cancer amongst women is breast cancer. Mammography provides timely detection of lumps and masses in breast tissue, but effective diagnosis requires accurately identifying malignant tumor boundaries, which remains challenging, particularly for images with inhomogeneous regions. Therefore, we propose an active contour method based on a reformed combined local and global fitted function to address breast tumor segmentation. This combined function is strengthened by a proposed average energy driving function to capture obscure boundaries for regions of interest more precisely from inhomogeneous images. Including a p-Laplace term eliminates reinitialization requirements and suppresses false contours in the segmentation. Bias field signal, which causes image homogeneity corruption, is estimated by bias field initialization to ensure independence from the initial contour position. Local and global fitted models are incorporated by introducing bias fields within them. The proposed method was tested on the MIAS MiniMammographic Database, with quantitative analysis to calculate its accuracy, effectiveness, and efficiency. Experimentation confirmed the proposed method provided superior results compared with previous state-of-the-art methods.

Two-dimensional wave equation solved by generalized alternating flux based local discontinuous Galerkin method

The wave propagation is often carried out in complex geological structures. Solving the wave propagation problem effectively in inhomogeneous medium is of great interest and has many applications in physics and engineering. In this paper, the local discontinuous Galekin (LDG) method is applied to the numerical solution of the second-order wave equation. Firstly, the auxiliary variables are introduced, and the second-order wave equations are written as a system of first-order partial differential equations. Then the discontinuous Galerkin format is applied to the corresponding linearized wave equations and adjoint equations. We consider the triangulation in this paper. In order to ensure that the discrete format satisfies the energy conservation, the generalized alternating flux is chosen on the element boundary. We proves that the LDG method satisfies the energy conservation. The exponential integral factor method is used in time discretization. In order to improve the computational efficiency, the Krylov subspace method is used to approximate the product of the exponential matrix and the vector. Numerical examples with exact solutions are given in numerical experiments. The numerical results verify the numerical precision and energy conservation of the LDG method. In addition, the calculation of inhomogeneous medium and complex computational regions are considered. The results show that the LDG method is suitable for simulation of complex structures and propagation in multi-scale structured medium.

Spatial Resolution in GNSS-R Under Coherent Scattering

Global Navigation Satellite Systems Reflectometry can be understood as a multistatic radar using satellite navigation signals as signals of opportunity. The scattered signals over sea ice, flooded areas, even under dense vegetation, and in some cases, over land show a significant coherent component. Under coherent scattering conditions, it is usually stated that the coherent signal component comes from an area equal to the first Fresnel zone. This letter analyzes in more detail the spatial resolution in this forward scattering configuration, showing that, when coherent scattering is nonnegligible, the spatial resolution is mostly determined by the geometry and not by typical surface roughness values. As the scattering area around the specular reflection point increases and encompasses the first Fresnel zone, the received power increases and then it fluctuates as higher order Fresnel zones are included (rapid phase changes due to the spherical waves). These contributions may explain in part the large scattering encountered over inhomogeneous land regions, as these different contributions add or subtract, depending on the phase of the electric field, and are weighted by different scattering coefficients (i.e., changes in the dielectric constant and/or surface roughness, such in water ponds or some agricultural fields). Finally, over homogeneous targets, when all Fresnel zones are included, the received power tends asymptotically to the value obtained using the free-space propagation with a total path length equal to the sum of the path lengths, weighted by the reflection coefficient. This value can also be interpreted as coming from an effective region that is actually ~0.6 times the first Fresnel zone.

Hybrid Active Contour Based on Local and Global Statistics Parameterized by Weight Coefficients for Inhomogeneous Image Segmentation

Image inhomogeneity often occurs in real-world images and may present considerable difficulties during image segmentation. Therefore, this paper presents a new approach for the segmentation of inhomogeneous images. The proposed hybrid active contour model is formulated by combining the statistical information of both the local and global region-based energy fitting models. The inclusion of the local region-based energy fitting model assists in extracting the inhomogeneous intensity regions, whereas the curve evolution over the homogeneous regions is accelerated by including the global region-based model in the proposed method. Both the local and global region-based energy functions in the proposed model drag contours toward the accurate object boundaries with precision. Each of the local and global region-based parts are parameterized with weight coefficients, based on image complexity, to modulate two parts. The proposed hybrid model is strongly capable of detecting region of interests (ROIs) in the presence of complex object boundaries and noise, as its local region-based part comprises bias field. Moreover, the proposed method includes a new bias field (NBF) initialization and eliminates the dependence over the initial contour position. Experimental results on synthetic and real-world images, produced by the proposed model, and comparative analysis with previous state-of-the-art methods confirm its superior performance in terms of both time efficiency and segmentation accuracy.

Markov Chain Monte Carlo Solution of Poisson’s Equation in Axisymmetric Regions

The advent of the Monte Carlo methods to the field of EM have seen floating random walk, fixed random walk and Exodus methods deployed to solve Poisson’s equation in rectangular coordinate and axisymmetric solution regions. However, when considering large EM domains, classical Monte Carlo methods could be time-consuming because they calculate potential one point at a time. Thus, Markov Chain Monte Carlo (MCMC) is generally preferred to other Monte Carlo methods when considering whole-field computation. In this paper, MCMC has been applied to solve Poisson’s equation in homogeneous and inhomogeneous axisymmetric regions. The MCMC results are compared with the analytical and finite difference solutions.

One-Dimensional Non-Uniform Dielectric Structure as Tunable Resonator

The paper presents research on the composite dielectric resonators. This type of resonator consists of dielectric parts, which can move with respect to each other using an external actuator. The air discontinuity between dielectric parts perturbs the electromagnetic field of the resonator and as a result, shifts resonance frequency. As an analytical solution for this kind of structure does not exist, most practical techniques resort to approximate numerical solutions. The electromagnetic field problem for an inhomogeneous dielectric structure consisting of two infinite plates separated by a dielectric layer with a different dielectric constant is solved rigorously. The problem is reduced to a nonlinear eigenvalues and vectors problem. The eigenvalues determine the resonant frequencies, and the vectors represent the electromagnetic field of the resonance structure. It is shown, that the resonant frequency of the basic LM -mode has a high sensitivity to the change of the air layer between dielectric plates. Displacement of the plates in a few percent of its thickness leads to a change in the resonant frequency by tens of percent, depending on the dielectric constant of the plate. The sensitivity of the resonant frequency shift and the tuning range increases as the dielectric constant grows up and the plate thickness decreases. Another factor affected on resonant frequency tuning sensitivity and range is the distribution of the electromagnetic field along the dielectric plate plane. The increase of the electromagnetic field variation in such directions leads to growing sensitivity but reducing the tuning range. Resonant frequencies of LE -mode are less sensitive to a displacement of resonator's parts. The main reason for such a difference is the direction of E -field in inhomogeneity regions. E -field of LM -modes is directed normally to the border between the dialectic plate and air, but the E -field of LE -modes is located parallel to the border. The correlation characteristics of the tuning with the geometric and electrophysical parameters of the plates were established. It has been shown, that resonance frequency tuning occurs without degradation of the resonator's unloaded Q -factor. Moreover, the Q -factor increases due to the redistribution of electromagnetic field energy into the air region where the loss is almost absent. It has been demonstrated, that the regularities for a one-dimensional inhomogeneous structure are valid for inhomogeneous cylindrical dielectric resonators.

Hyperspectral Unmixing with Gaussian Mixture Model and Spatial Group Sparsity

In recent years, endmember variability has received much attention in the field of hyperspectral unmixing. To solve the problem caused by the inaccuracy of the endmember signature, the endmembers are usually modeled to assume followed by a statistical distribution. However, those distribution-based methods only use the spectral information alone and do not fully exploit the possible local spatial correlation. When the pixels lie on the inhomogeneous region, the abundances of the neighboring pixels will not share the same prior constraints. Thus, in this paper, to achieve better abundance estimation performance, a method based on the Gaussian mixture model (GMM) and spatial group sparsity constraint is proposed. To fully exploit the group structure, we take the superpixel segmentation (SS) as preprocessing to generate the spatial groups. Then, we use GMM to model the endmember distribution, incorporating the spatial group sparsity as a mixed-norm regularization into the objective function. Finally, under the Bayesian framework, the conditional density function leads to a standard maximum a posteriori (MAP) problem, which can be solved using generalized expectation-maximization (GEM). Experiments on simulated and real hyperspectral data demonstrate that the proposed algorithm has higher unmixing precision compared with other state-of-the-art methods.

Active contour model based on LIF model and optimal DoG operator energy for image segmentation

In order to solve the problem that the region-based active contour model is sensitive to the initial contour position, the convergence is poor, and the active contour model can not obtain good segmentation results when segmenting complex background images and severe intensity inhomogeneous images. In this paper, an active contour model which combines Local Image Fitting (LIF) and Difference of Gaussian (DoG) operator energy for image segmentation is proposed. Firstly, an optimal DoG operator is obtained by using the edge energy term, it can enhance the edge while smoothing inhomogeneous regions. Then, using the DoG energy term which is obtained in the first step and the LIF energy term to construct the total function energy terms. In this process, the regularization term is also established, it can control the smoothness of evolution curve, avoiding over-segmentation and re-initialization step. Finally, the variational method and gradient descent flow method are adopted to minimize the total energy functional for segmentation. Compared with other region-based active contour models, the experimental results show that the proposed method can achieve a better segmentation performance with less iterations and high calculation efficiency while segmenting the synthetic and real images with intensity inhomogeneity.

Transmissivity of electromagnetic wave propagating in magnetized plasma sheath using variational method

A variational method is introduced to analyze the transmissivity of an electromagnetic wave propagating in the magnetized plasma sheath. The plasma density is modeled by two parabolic inhomogeneous regions separated by one homogeneous region. The Lagrangian density of the system is constructed based on the fluid energy density and the electromagnetic energy density. The total variation of the Lagrangian density is derived. The fluid and electromagnetic fields are numerically solved by expansion in piecewise polynomial function space. We investigate the effect of an external magnetic field on the transmissivity of the electromagnetic wave. It is found that the transmissivity is increased when an external magnetic field is applied. The dependence of transmissivity on the collision frequency between the electrons and the neutral particles has also been studied. We also show that the external magnetic field causes a shift in the critical frequency of the plasma sheath.

Regularities of microdefect formation in silicon during heat treatment for internal getter synthesis

Gettering is defined as a process by which metal impurities in the device region are reduced by localizing them in predetermined, passive regions of the silicon wafer. Internal or intrinsic gettering is an effective way to reduce the contamination in active regions. The generation of internal getters is based on the decomposition of the supersaturated oxygen solid solution in silicon, which favours the formation of a complex defect system in silicon that consists of various precipitate/dislocation agglomerates. Regularities of microdefect formation during oxygen solid solution decomposition in silicon have been studied. We show that actual solid solution supersaturation, temperature and heat treatment duration determine the structure of the solid solution. Combining these factors, including heat treatment parameters, one can control solid solution decomposition rate and SiOx precipitate sizes and quantity. The methods of X-ray diffuse scattering and transmission electron microscopy have shown high efficiency for studying the effect of heat treatment in crystals. For annealing at 450 °C, solid solution decomposition occurs at high supersaturation degrees, and concentration inhomogeneity regions may form at an early decomposition stage over the actual annealing time (up to 40 h). With an increase in the temperature of subsequent annealing to 650 °C, local regions with above-average oxygen supersaturation degrees increase the efficiency of oxygen solid solution decomposition. Further, an increase in annealing temperature to T > 1000 °С results in a more intense generation of the largest precipitates at the expense of the smaller ones. Once the precipitate sizes become sufficiently large, the elastic stresses start to relax, leading to partial incoherence and the generation of dislocations around the particles. This type of defect structure seems to be the most efficient getter.

Chan\u2013Vese Reformulation for Selective Image Segmentation

Selective segmentation involves incorporating user input to partition an image into foreground and background, by discriminating between objects of a similar type. Typically, such methods involve introducing additional constraints to generic segmentation approaches. However, we show that this is often inconsistent with respect to common assumptions about the image. The proposed method introduces a new fitting term that is more useful in practice than the Chan–Vese framework. In particular, the idea is to define a term that allows for the background to consist of multiple regions of inhomogeneity. We provide comparative experimental results to alternative approaches to demonstrate the advantages of the proposed method, broadening the possible application of these methods.

Development of a method for triangulation of inhomogeneous regions represented by functions

In the process of designing structures from inhomogeneous materials, there is the need to build discrete models that consider the peculiarities of the geometrical shape of subdomains from different materials. The first stage in the modeling of such structures is the construction of a geometric model. In order to describe the shapes of inhomogeneous structures, we have proposed a functional approach, based on the use of systems of implicit functions and R-functions. The first implicit function defines the shape of a structure. The implicit functions starting from a second one determine the shapes of the subdomains whose boundaries must be considered when building a discrete model. Each implicit function within the system exceeds zero at inner points of the respective domain or subdomain, is equal to zero at the border, and is less than zero at outer points. The result is a possibility to describe the shapes of domains and subdomains of arbitrary complexity.We have constructed a method for the triangulation of structures from inhomogeneous materials, whose shape is assigned functionally. The devised method makes it possible to consider the shape of subdomains from different materials used in the structure. The basic idea of the method implies consistent correction of coordinates for the nodes from the primary triangulation of the domain. Primary triangulation can be arbitrary, but it must fully capture the structure. At each step, the boundary of the structure or a subdomain from a particular material is approached by the node closest to the respective boundary. Following the displacement of each node, the coordinates of neighboring nodes are computed by minimizing the functional of exponents in the planes of incident elements. At the same time, for the elements that are incident at nodes and whose coordinates were changed, meeting the Delaunay condition is checked; if necessary, the operation «flip» is performed to change the diagonal. Upon removing the outer nodes, one would obtain a discrete model in which the boundaries of the structure and subdomains from different materials are approximated by nodes and edges of elements.

Effective breaking of the action-reaction principle using spatial solitons

We discuss a class of interactions between self-confined optical beams breaking the action-reaction principle. The effective force intertwining the beams does not satisfy momentum conservation, paving the way to the potential existence of situations where both beams are pushed in the same direction, in turn leading to the so-called diametric drive. In our theoretical proposal the interaction between the two light beams is enabled by optical nonlinearity. The nonlinearity is assumed to change sign with the light polarization, in turn allowing the two light beams to be attracted or repelled by an inhomogeneous region according to the photon polarization. We demonstrate that this exotic type of nonlinear spin-orbit-like interaction can be achieved in nematic liquid crystals (NLCs). In fact, depending on the input polarization, in NLCs a change in temperature corresponds to a focusing or defocusing index change. For the polarization seeing a thermal defocusing response (corresponding to the extraordinary component), the self-confinement is ensured by the simultaneous action of reorientational nonlinearity.

Huygens’ principle may reveal Rayleigh scattering

Rayleigh scattering is an elastic scattering. The scattering particles do not change the amplitude of the incident light wave, so they must affect the phase of the light wave. In this paper, the microscopic dielectric sphere is used as the scattering particle model to study the modulation of the phase of the light wave by the scattering particles. The paper analyzes the influence of micro-particles on the optical path, and obtains the phase of the light wave according to the wavelength of the incident light and the particle parameters. According to the Huygens principle, the light scattering of the particles is studied by diffraction method, and the scattered light intensity is proportional to the particle volume and inversely proportional to the fourth power of the light wavelength. In view of the uneven refractive index of the actual optical medium, this paper uses the graded index microsphere model for equivalent. The modulation of the phase of the light-wave by the graded-index particles and the influence on the optical path are studied. Finally, using the Huygens principle, the scattering properties of the refractive index inhomogeneous region are obtained. The work of this paper provides a new method for light scattering research.

Guided wave based nondestructive analysis of localized inhomogeneity effects in an advanced sandwich composite structure

In this paper, we present a nondestructive analysis of localized inhomogeneity effects on guided wave propagation in an advanced sandwich composite structure. In the process, guided wave dispersion curves were semi-analytically determined for the structure to accurately identify different wave modes in experimental and numerical analysis signals. Finite element simulation of wave propagation in the target structure was then carried out in ABAQUS and validated with the experiment. Significant influences on the wave mode amplitudes were observed due to the presence of a localized inhomogeneity in the structure. An inhomogeneity identification strategy was prepared based on the amplitude changes in the registered guided wave signals from a predefined piezoelectric transducer network. The influence of varying elastic modulus and mass-density of the inhomogeneous region on the wave mode amplitudes and the corresponding inhomogeneity-index magnitudes were also studied.

The modelling of the time-dependency of interfacial properties due to chemical equilibrium reactions in demixed liquid systems

The interfacial properties between demixed liquid phases are of crucial importance in chemical engineering. This holds especially true considering extraction based processes inhabiting a chemical reaction due to the time-dependency of all thermodynamic properties that comes with it. The purpose of this work is to predict the dynamic interfacial properties in the demixed liquid system water + 1-hexanol + hexylacetate + acetic acid, which is overlaid by the auto-catalyzed chemical equilibrium esterification reaction 1-hexanol + acetic acid ↔ hexylacetate + water. In order to predict the interfacial properties for these reactive mixtures as function of time, the incompressible version of the density gradient theory (inc-DGT) was combined to the first time with differential rate equations describing the kinetics of this reaction by activities instead of concentrations. The quaternary phase equilibrium, the reaction kinetics, the reaction equilibrium as well as the inhomogeneous region of the interface were thereby described with an activity coefficient model, namely the NRTL-model. Particular attention is directed to the time-dependency of the interfacial tension while the system strives towards the thermodynamic equilibrium. It could be demonstrated that the prediction of the interfacial tension of the supposed model is very close to experimental data obtained also in this study using spinning-drop tensiometry. Furthermore, the time-dependency of the mole fraction profiles inside the inhomogeneous region of the interface due to a chemical reaction could be made visible for the first time.