Circular Boundary Research Articles

High order local farfield expansions absorbing boundary conditions for multiple scattering

In this paper, we derive high order and local absorbing boundary conditions (ABC) for two- and three-dimensional multiple acoustic scattering problems. For this purpose, we employ Karp and Wilcox farfield expansions, which are exact representations of purely outgoing waves in two- and three-dimensions, respectively. We seek solutions of multiple scattering problems for scatterers of arbitrary shape in both homogeneous and locally inhomogeneous media by assuming that each scatterer and its surrounding inhomogeneity (if any) can be well-separated by artificial boundaries from the other scatterers. As a consequence, the computational domain is reduced to the union of relatively small disjoint subdomains bounded in the interior by a scatterer boundary and in the exterior by a circular (2D) or spherical (3D) artificial boundary. The novel ABC is defined at these artificial boundaries by considering continuities of the scattered field and its derivatives at the artificial boundaries and by representing the scattered wave as a superposition of outgoing waves from each subdomain. Finally, we numerically solve the new bounded boundary value problem for numerous examples including complexly shaped obstacles, such as prototype submarines and aircrafts. Accurate results are obtained at relatively low computational cost for problems in both homogeneous and inhomogeneous media.

Experimental study on wave-induced seabed response and force on the pipeline shallowly buried in a submerged sandy slope

Waves on the submerged sloping seabed tend to transform and even break, inducing seabed response and exerting force on the shallowly-buried pipeline. In this study, a series of flume tests were carried out to characterize the wave propagation on a submerged sloping sandy seabed. Subsequently, seabed response considering the pipeline burial effect and ensuing force on the pipeline were investigated. Experimental results indicate that wave varies drastically on the sloping sandy seabed, accompanied with the nonlinearity strengthened. High-order nonlinear seabed response, at least the second order here, cannot be ignored. Pipeline presence, forming a smooth, impermeable and fixed circular boundary, makes the seabed response different from that without pipeline. The significance of the local hydrodynamics is highlighted after a heuristic investigation on the effect of pipeline relative water depth. For the pipeline buried in the shallow water, wave-induced horizontal force may be as important as the vertical force and should be taken into account in engineering. The relative burial depth and wave steepness at the toe are also found to affect the results obviously.

Buoyancy driven magnetohydrodynamic hybrid nanofluid flow within a circular enclosure fitted with fins

Various geometrical types of fins are used in numerous engineering and technological applications like semiconductor devices, gas turbines, electric transformers, automobile radiators, heat exchangers, hydrogen fuel cells, air-cooled engines, etc. Compared to conventional coolants, nanofluids explore superior thermal conductivities and thereby promote outstanding heat transport capabilities. Such unique noteworthy applications motivate the study of the hydrothermal fallouts of natural convective laminar magnetically influenced Ag-MgO-water hybrid nanofluid flows within a circular enclosure fitted with I-shaped rectangular fins of different lengths. The outer circular boundary is made cold, whereas the inner fitted fins remain heated. Requisite similarity variables have been incorporated to alter the dimensional equations into non-dimensional. After then, the Galerkin technique-based finite element strategy is chosen to run the entire numerical simulation. Various velocities, isotherms, streamlines, Nusselt number plots are generated to disclose the impact of different fins' lengths on the thermal control and flow behavior. Requisite plots are portrayed for the parametric variations of Rayleigh number (103 ≤ Ra ≤ 105), Hartmann number (2 ≤ Ha ≤ 6), and nanoparticle concentrations (0.00 ≤ ϕ2 ≤ 0.015). The higher intensity in isotherms, velocity, and streamlines is noted for AR = 1.1. Numerically higher heat transmission is realized for Rayleigh numbers, nanoparticle concentrations, and for AR = 1.1.Mathematics subject classification: 76W05

A Simple, Accurate and Semi-Analytical Meshless Method for Solving Laplace and Helmholtz Equations in Complex Two-Dimensional Geometries

A localized virtual boundary element–meshless collocation method (LVBE-MCM) is proposed to solve Laplace and Helmholtz equations in complex two-dimensional (2D) geometries. “Localized” refers to employing the moving least square method to locally approximate the physical quantities of the computational domain after introducing the traditional virtual boundary element method. The LVBE-MCM is a semi-analytical and domain-type meshless collocation method that is based on the fundamental solution of the governing equation, which is different from the traditional virtual boundary element method. When it comes to 2D problems, the LVBE-MCM only needs to calculate the numerical integration on the circular virtual boundary. It avoids the evaluation of singular/strong singular/hypersingular integrals seen in the boundary element method. Compared to the difficulty of selecting the virtual boundary and evaluating singular integrals, the LVBE-MCM is simple and straightforward. Numerical experiments, including irregular and doubly connected domains, demonstrate that the LVBE-MCM is accurate, stable, and convergent for solving both Laplace and Helmholtz equations.

A new calculation method for hydrogeological parameters from unsteady-flow pumping tests with a circular constant water-head boundary of finite scale

Laboratory model experiments can be used to verify the applicability and accuracy of a new hydrogeological test method. The unsteady-flow pumping test is the most commonly used comparison method. The axisymmetrical circular aquifer model is frequently used in laboratory model experiments. However, the scale of the laboratory experiment model is always finite, which increases the influence on the test calculation results when using conventional Theis theory. Here, based on analytical analysis and laboratory experiments, a new calculation method is proposed for the circular constant water-head boundary of finite scale. The proposed method can eliminate the effect of the finite-scale circular constant water-head boundary on the unsteady pumping test results and can also be applied to large-scale circular constant water-head boundaries. Geotextiles are permeable fabrics; therefore, the hydraulic conductivity of a geotextile can be used to simulate the hydraulic conductivity of a fractured aquifer. A geotextile test, steady pumping test and slug test were conducted to verify the accuracy of the proposed calculation method, with all the results indicating that the proposed method can provide more accurate hydrogeological parameters from an unsteady pumping test with a circular constant water-head boundary of finite scale than conventional Theis theory for unsteady pumping tests.

Mathematical modeling of unsteady flow with uniform/non-uniform temperature and magnetic intensity in a half-moon shaped domain

The mathematical modeling of two-dimensional unsteady free convective flow and thermal transport inside a half-moon shaped domain charged in the presence of uniform/non-uniform temperature and magnetic effects with Brownian motion of the nanoparticles has been conducted. Thirty-two types of nanofluids in a combination of various nanoparticles and base fluids having different sizes, shapes, and solid concentrations of nanoparticles are chosen to examine the better performance of heat transfer. The circular boundary is cooled while the diameter boundary is heated with uniform/non-uniform temperature. An external uniform/non-uniform/periodic magnetic field is imposed along diameter. The powerful partial differential equations solver, finite element method of Galerkin type, has been engaged in numerical simulation. The numerical solution's heat transfer mechanism reaches a steady state from the unsteady situation within a very short dimensionless time of about 0.65. The thermal transport rate enhances for increasing buoyancy force whereas decreases with higher magnetic intensity. The uniform thermal condition along the diameter of half-moon gives a higher thermal transport rate compared to non-uniform heating conditions. The non-uniform magnetic field provides greater values of the mean Nusselt number than the uniform field. In addition, the outcomes also predict that a better rate of temperature transport for kerosene-based nanofluid than water-based, ethylene glycol-based, and engine oil-based nanofluid. The heat transfer rate is observed at about 67.86 and 23.78% using Co-Kerosene and Co-water nanofluids, respectively, with an additional 1% nanoparticles volume fraction. The blade shape nanoparticles provide a better heat transfer rate than spherical, cylindrical, brick, and platelet shapes. Small size nanoparticles confirm a higher value of average Nusselt number than big size. Mean Nusselt number increases 22.1 and 5.4% using 1% concentrated Cu-water and Cu-engine oil nanofluid, respectively than base fluid.

Packing of elastic rings with friction

We study the deformations of elastic filaments confined within slowly shrinking circular boundaries, under contact forces with friction. We perform computations with a spring-lattice model that deforms like a thin inextensible filament of uniform bending stiffness. Early in the deformation, two lobes of the filament make contact. If the friction coefficient is small enough, one lobe slides inside the other; otherwise, the lobes move together or one lobe bifurcates the other. There follows a sequence of deformations that is a mixture of spiralling and bifurcations, primarily the former with small friction and the latter with large friction. With zero friction, a simple model predicts that the maximum curvature and the total elastic energy scale as the wall radius to the − 3 / 2 and − 2 powers, respectively. With non-zero friction, the elastic energy follows a similar scaling but with a prefactor up to eight times larger, due to delayering and bending with a range of small curvatures. For friction coefficients as large as 1, the deformations are qualitatively similar with and without friction at the outer wall. Above 1, the wall friction case becomes dominated by buckling near the wall.

Contracting Electromagnetic Full-Wave Inversion of 2-D Inhomogeneous Objects With Irregular Shapes Based on the Hybrid SESI Forward Solver

An efficient two-dimensional (2-D) electromagnetic (EM) full-wave inversion (FWI) method based on the hybrid spectral-element spectral-integral (SESI) forward solver is proposed. In the forward scattering computation, the scalar Helmholtz equation is discretized and solved by the spectral element method (SEM). Its computational domain is truncated by a circle on which a 2-D surface integral equation is performed and the spectral-integral method (SIM) is used to accelerate its solution. Transmitters and receivers are placed outside the circular boundary and they are connected to the equivalent current on the circle by Green’s functions. In each iteration of FWI, the sensitivity matrix is updated by the electric field values solved by SESI only in the internal nodes inside the computation domain. Then the conjugate gradient (CG) method is used to solve for the relative permittivity and conductivity values in the corresponding interior elements. Meanwhile, the structural consistency constraint (SCC) algorithm is adopted to gradually compress the inversion domain and guarantee the inversion accuracy. Several numerical experiments are carried out not only to show the computation efficiency of the SESI forward solver but also to verify the correctness of the iterative inversion procedure as well as the effectiveness of SCC.

On optimal cloaking-by-mapping transformations

A central ingredient of cloaking-by-mapping is the diffeomorphism which transforms an annulus with a small hole into an annulus with a finite size hole, while being the identity on the outer boundary of the annulus. The resulting meta-material is anisotropic, which makes it difficult to manufacture. The problem of minimizing anisotropy among radial transformations has been studied in Griesmaier and Vogelius [Inverse Prob. 30 (2014) 17]. In this work, as in Griesmaier and Vogelius [Inverse Prob. 30 (2014) 17], we formulate the problem of minimizing anisotropy as an energy minimization problem. Our main goal is to provide strong evidence for the conjecture that for cloaks with circular boundaries, non-radial transformations do not lead to lower degree of anisotropy. In the final section, we consider cloaks with non-circular boundaries and show that in this case, non-radial cloaks may be advantageous, when it comes to minimizing anisotropy.

CBFMCycleGAN-VC: Using the Improved MaskCycleGAN-VC to Effectively Predict a Person’s Voice After Aging

One task of nonparallel speech conversion is to convert the source speaker’s speech samples to the target speaker’s speech samples, keeping the content unchanged. In view of the advantages of MaskCycleGAN-VC in nonparallel speech conversion, such as small model size and superior performance, our paper uses the basic structure of MaskCycleGAN-VC to improve it and proposes a cyclic boundary method filling in the frame MaskCycleGAN-VC (CBFMCycleGAN-VC) model, which predicts the voice of a person as he ages by using voice samples of his younger self. First, this paper adds speech preprocessing modules, including the Chebyshev low-pass filter and adaptive filter, which increases the robustness of the system. Second, our paper considers the time-domain difference in the weight parameters, which makes it easier to grasp the mapping law of the time-domain structure, with a faster convergence speed. Last, the circular boundary method is introduced to avoid the ringing effect, to enhance the connection between the filled frame and the adjacent frame, and to obtain a better generator. The simulation results show that the CBFMCycleGAN-VC model is more suitable for the speech conversion task of predicting the voices of elderly people, and the convergence speed is faster. The converted voice is also closer to the voice of the target speaker in the time domain and frequency domain. Under the condition that the accuracy rate is similar to that of MaskCycleGAN-VC, the MOS score is 17.5% higher than that of MaskCycleGAN-VC.

Progressive Domain Adaptive Network for Crater Detection

Existing crater detection methods are typically carried out in the same domain where the training and testing data are drawn from an identical distribution. However, this means that when we apply a trained crater detector to a new scene probably caused by changes in sensors, lighting or other factors will lead to a significant performance drop. In this work, we aim to improve the accuracy of the domain (scene) adaptive crater detection which will reduce labor costs caused by annotation. Firstly, we proposed a progressive domain adaptive network (PDAN) which can progressively learn the knowledge from the source domain to the target domain by the projected intermediate domain features generated by the subspace along the geodesic on the Grassmann manifold. Secondly, in order to further extract the domain agnostic feature and utilize the characteristics of craters, we proposed a low-level feature enhancement module (LFEM) and a circular boundary enhancement module (CBEM). Thirdly, a weighted instance-level alignment network (WIAN) is presented to adaptively align the instance level feature further reduce the differences between two domains, and enhance the performance. To evaluate the effectiveness of the proposed method, based on our previous Mars day crater dataset (MDCD), we present a domain adaptive crater detection (DACD) dataset which contains 1000 images in two domains and more than 20000 craters. The extensive experiments based on the DACD and open datasets demonstrated that the proposed network could effectively eliminate the impact of domain shift and achieve state-of-the-art results.

Magnetoresistance anisotropy in ErB12 antiferromagnetic metal: The evidence for dynamic charge stripes

The nature of charge transport and magnetization anisotropy was investigated in the ErB12 antiferromagnetic metal with both cooperative Jahn-Teller distortions of the fcc crystal structure and electronic instability (dynamic charge stripes). A butterfly pattern of the H-φ magnetic phase diagram in the (1 1 0) plane was reconstructed, including a large number of different magnetic phases separated from each other by radial and circular boundaries. It is argued that fluctuations of electron density are responsible for the suppression of the indirect Ruderman-Kittel-Kasuya-Yoshida (RKKY) exchange between the nearest neighbored Er3+ ions located along the 〈110〉 directions producing the magnetic phase diversity in ErB12.

Large mass rigidity for a liquid drop model in2D with kernels of finite moments

Motivated by Gamow’s liquid drop model in the large mass regime, we consider an isoperimetric problem in which the standard perimeter P(E) is replaced by P(E)-γP ε (E), with 0<γ<1 and P ε a nonlocal energy such that P ε (E)→P(E) as ε vanishes. We prove that unit area minimizers are disks for ε>0 small enough. More precisely, we first show that in dimension 2, minimizers are necessarily convex, provided that ε is small enough. In turn, this implies that minimizers have nearly circular boundaries, that is, their boundary is a small Lipschitz perturbation of the circle. Then, using a Fuglede-type argument, we prove that (in arbitrary dimension n≥2) the unit ball in ℝ n is the unique unit-volume minimizer of the problem among centered nearly spherical sets. As a consequence, up to translations, the unit disk is the unique minimizer. This isoperimetric problem is equivalent to a generalization of the liquid drop model for the atomic nucleus introduced by Gamow, where the nonlocal repulsive potential is given by a radial, sufficiently integrable kernel. In that formulation, our main result states that if the first moment of the kernel is smaller than an explicit threshold, there exists a critical mass m 0 such that for any m>m 0 , the disk is the unique minimizer of area m up to translations. This is in sharp contrast with the usual case of Riesz kernels, where the problem does not admit minimizers above a critical mass.

Energy and Entropy Production of Nanofluid within an Annulus Partly Saturated by a Porous Region.

The flow and heat transfer fields from a nanofluid within a horizontal annulus partly saturated with a porous region are examined by the Galerkin weighted residual finite element technique scheme. The inner and the outer circular boundaries have hot and cold temperatures, respectively. Impacts of the wide ranges of the Darcy number, porosity, dimensionless length of the porous layer, and nanoparticle volume fractions on the streamlines, isotherms, and isentropic distributions are investigated. The primary outcomes revealed that the stream function value is powered by increasing the Darcy parameter and porosity and reduced by growing the porous region’s area. The Bejan number and the average temperature are reduced by the increase in , porosity , and nanoparticles volume fractions . The heat transfer through the nanofluid-porous layer was determined to be the best toward high rates of Darcy number, porosity, and volume fraction of nanofluid. Further, the local velocity and local temperature in the interface surface between nanofluid-porous layers obtain high values at the smallest area from the porous region (), and in contrast, the local heat transfer takes the lower value.

WiFi Fingerprint Localization With Circular Boundary

For the issues (heterogeneity, heavy initial training, etc.) in WiFi fingerprinting-based positioning technology, a circular boundary is proposed in this letter. First, the correctness of the boundary is proved by theoretical derivation. Then, for the fact that only the information of reference points (RPs) is known in real environment, objective functions are set and the relationship between the center and radius is explored to solve the expression of circular boundary. Finally, the AP-Sequence algorithm is adopted to estimate users' location. Experimental results show that the proposed algorithm with low-overhead fingerprinting achieving an average localization error of 5-8 m outperforms other state-of-the-art approaches based on AP-Sequence (e.g. FreeLoc, SBL.).

Emergence of a smooth interface from growth of a dendritic network against a mechanosensitive contractile material.

Structures and machines require smoothening of raw materials. Self-organized smoothening guides cell and tissue morphogenesis and is relevant to advanced manufacturing. Across the syncytial Drosophila embryo surface, smooth interfaces form between expanding Arp2/3-based actin caps and surrounding actomyosin networks, demarcating the circumferences of nascent dome-like compartments used for pseudocleavage. We found that forming a smooth and circular boundary of the surrounding actomyosin domain requires Arp2/3 in vivo. To dissect the physical basis of this requirement, we reconstituted the interacting networks using node-based models. In simulations of actomyosin networks with local clearances in place of Arp2/3 domains, rough boundaries persisted when myosin contractility was low. With addition of expanding Arp2/3 network domains, myosin domain boundaries failed to smoothen, but accumulated myosin nodes and tension. After incorporating actomyosin mechanosensitivity, Arp2/3 network growth locally induced a surrounding contractile actomyosin ring that smoothened the interface between the cytoskeletal domains, an effect also evident in vivo. In this way, a smooth structure can emerge from the lateral interaction of irregular active materials.

An Analytical Method for Plane Elasticity Problems Involving Circular Boundaries

Complex structure with circular boundaries is commonly used in engineering practice, and it is essential to conduct a detailed analysis of the interior stress field of the structure. The Michell stress function is a well-known general solution for plane elasticity problems in the polar coordinates, particularly when circular boundaries are involved. This work presents an analytical method with the assistance of the Michell solution, which could be seamlessly combined with Fourier analysis. Using the expansion of Fourier series, problems with arbitrarily distributed loads can be handled via a standard procedure. A complete analytical solution is elaborated for an arbitrarily loaded circular ring, and a classical elastic solution is provided for verification.

A dynamic shell model for diagnostics of rotating machinery under periodic excitation

In this paper, a generalized dynamic model of a shell structure has been developed and utilized for diagnostics purposes. The dynamic model is three-dimensional, includes the effects of rotary inertia and shear deformation, and can handle moving loads in radial, tangential and axial directions. The model is utilized to determine in-plane radial displacements of the shell structure under concentrated radial loads for different boundary conditions. The periodic loads are constructed using harmonics obtained through the Fourier series expansion method. The modal expansion technique is implemented for calculation of the steady state forced response of the shell structure. A simplified acoustic radiation model is also implemented in conjunction with the dynamic shell model to predict the noise radiated from a rotating circular cylindrical shell structure under different kinematic, loading and boundary conditions. Moreover, forced vibration response and acoustic radiation predicted will be employed to reveal patterns in the signals that can potentially be used for diagnostics of rotating machinery applications. The shell model is derived using a comprehensive approach and thus can be used to model prevalent engineering applications ranging from electric motors to gears and bearings.

Optimal Design of Thinned Array Using a Hybrid Genetic Algorithm

In this paper, a hybrid genetic algorithm (GA) is proposed for thinning a two-dimensional planar array by combining the conventional GA with moving least squares (MLS). This enhances the convergence rate and the global search performance. The MLS method is used to estimate local interpolation functions from non-uniform sample data (the population and the value of the objective function in the GA), and to find new and better populations from the interpolated functions. By incorporating these improved populations into the next generation, the MLS-GA achieves improved search performance of the global optimum and a faster convergence rate compared to conventional GA alone. Moreover, a nonlinear chirp function is used for an efficient thinning design. To verify the proposed MLS-GA, it is applied to a test function and the results are compared to that of the GA. The algorithm is then applied to thin an array with a rectangular grid and circular boundary. The design objectives are to minimize the peak side-lobe level and gain loss while satisfying a given thinning coefficient and to compare the results with the GA.

Dynamic anti-plane behavior of rare earth giant magnetostrictive medium with a circular cavity defect in semi-space

An analytical solution to the anti-plane dynamics problem of semi-space rare earth giant magnetostrictive media with circular cavity defects near the horizontal boundary under the action of SH wave is studied. Based on the Helmholtz theorem and the theory of complex function, the elastic-magnetic dynamic equation of magnetostrictive medium is established, and the semi-space incident wave field is written. In addition, based on the theory of complex function and the method of wave function expansion, the expression of the wave function of the scattered displacement field and the corresponding magnetic potential of the scattered wave under the condition of no stress and magnetic insulation of the horizontal boundary are obtained. Then, based on the conditions of free boundary stress, continuous magnetic induction intensity and continuous magnetic potential around the circular cavity, the infinite linear algebraic equations are established. Finally, the analytical expressions of dynamic stress concentration factor and magnetic field intensity concentration factor around circular cavity in semi-space rare earth giant magnetostrictive medium are obtained. Numerical examples show that the analysis results depend on the following parameters: permeability, dimensional-piezomagnetic coefficient, frequency of the incident wave, incident angle, distance between the circular cavity and horizontal boundary. These results have certain reference value for the study of non-destructive testing and failure analysis of rare earth giant magnetostrictive materials.