Arbitrary Geometrical Shape Research Articles

A dual spatial clustering method in the presence of heterogeneity and noise

AbstractThe detection of spatial clusters, taking into account both spatial proximity and attribute similarity, plays a vital role in spatial data analysis. Although several dual clustering methods are currently available in the literature, most of them have detected homogeneous spatially adjacent clusters suffering from between‐cluster inhomogeneity and noise, where those spatial points have been described in the attribute domain. This article aims to accommodate both spatial proximity and attribute similarity with the presence of heterogeneity and noise. In this algorithm, Delaunay triangulation with edge‐length constraints, with consideration of arbitrary geometrical shapes, different densities, and spatial noise, is first utilized to construct spatial proximity relationships among points. Then, a clustering strategy employing information entropy is designed to identify clusters having similar attributes. The attribute clustering can adaptively and accurately detect clusters under the consideration of heterogeneity and noise. The efficacy and practicability of the proposed algorithm are illustrated by experiments employing both simulated datasets and real spatial point events.

Faster and More Accurate Time Domain Electromagnetic Simulation Using Space Transformation

A novel finite difference time domain (FDTD) method based on space transformations is developed that overcomes the inherent obstacles of the conventional FDTD algorithm in a spatially complex domain. Our method leads to an adaptive mesh for the investigated structure based on its geometrical shape without adding additional numerical problems such as late-time instability. In this method, mesh boundaries can follow arbitrary geometrical shapes precisely meaning that discretization errors are minimized. Such errors can be considerable when dealing with large material differences or boundary conditions within the simulation domain. Different meshing and transformation techniques for a variety of different scenarios are presented. We show how boundaries discontinuity can be handled using our method without resulting artificial singularities or zeros. Unlike previous works no dispersive medium has been used so the simulation speed is similar to the standard FDTD method. The usability and superiority of this method in terms of simulation run time and accuracy are shown through a couple of scattering and plasmonic problems. Also, the result of any simulations are validated using finite element method.

A Study of the Structural Characteristics of Titanium Alloy Products Manufactured Using Additive Technologies by Combining the Selective Laser Melting and Direct Metal Deposition Methods.

Titanium alloy product manufacturing is traditionally considered to be a rather difficult task. Additive manufacturing technologies, which have recently become quite widespread, can ensure the manufacture of titanium alloys products of an arbitrary geometrical shape. During this study, we have developed a methodology for manufacturing titanium alloys products using additive technologies on FL-Clad-R-4 complex of laser melting of metals by combined Selective Laser Melting (SLM) and Direct Metal Deposition (DMD) methods. Ti–6Al–4V and Ti–6Al–4Mo–1V alloys were used for the manufacture of samples. We studied the microstructure of the obtained details and measured the microhardness of the samples. We discovered a gradient of the structure throughout the height of the details walls, which is connected with the peculiarities of thermal cycles of the technology used. This affected the microhardness values: in the upper part of the details, the microhardness is 10–25% higher (about 500 HV) than in the lower part (about 400 HV). Products made according to the developed technique do not have visible defects and pores. The obtained results indicate the competitiveness of the proposed methodology.

3D acoustic metasurface carpet cloak based on groove structure units

A 3D acoustic metasurface carpet cloak (AMCC) based on groove structure units is proposed and investigated. The key idea behind this acoustic invisibility is the phase compensation via local phase modulation, and thus a cloak with a thickness of only of a half wavelength could be designed for objects with arbitrary geometric shapes and sizes. We first demonstrate the cloaking effect of hiding a conical object numerically, and find that the working bandwidth of the designed AMCC is from 6200–7500 Hz. Further experimental results are in good agreement with the numerical simulations, verifying that the AMCC works well for the normal incident wave and the small-angled incident waves. As another example, we also confirm that the proposed AMCC can hide a semispherical object. The present AMCC is thin, has a simple geometrical structure, and is easy to implement, which benefits future realistic applications.

An isogeometric approach to flexoelectric effect in ferroelectric materials

Flexoelectricity is an electromechanical coupling effect between the polarization and strain gradient in all dielectrics regardless of point group symmetry. Due to its significant influence on material behavior at the nanoscale, the flexoelectric effect has attracted more and more attention in recent years. In this paper, a real space phase field model for the flexoelectric effect in ferroelectric materials is developed by using isogeometric analysis (IGA). The IGA employs the same smooth and high-order basis functions to describe both the geometry of material and the solution of phase field, which is able to give an accurate and efficient description of the flexoelectric effect in ferroelectrics with arbitrary geometrical shapes and boundary conditions. To this end, phase field simulations on the effect of flexoelectricity are conducted for nanoscale ferroelectrics with different geometrical shapes and boundary conditions. The simulation results show that the flexoelectric effect has significant influence on the domain structures and domain switching of ferroelectric materials at the nanoscale. For ferroelectric nanobeam under bending load, due to the flexoelectric effect, the mechanical bending can break the symmetry of hysteresis loop between electric field and polarization. As for ferroelectric nanodots, the flexoelectric effect increases the magnitude of spontaneous polarizations and results in the tilting of polarization vortex. In addition, out-of-plane components appear in the polarization vortex of ferroelectric nanodots due to the flexoelectric effect, which increases the coercive field for the switching of polarization vortex and changes the switching process significantly. The present work not only presents an effective nonlocal model for the domain evolution in ferroelectric materials with the consideration of the flexoelectric effect, but also asymmetric hysteresis loop between polarization and external electric field for ferroelectric beam, and new switching behavior of the polarization vortex in ferroelectric nanodots due to the flexoelectric effect.

Dynamic Formation Control Over Directed Networks Using Graphical Laplacian Approach

This paper investigates the dynamic formation control problem for multi-agent systems over directed networks, in which a desired spatial shape is time-varying instead of fixed one as usually assumed in the literature. Inspired by the fact that the existing approaches, including absolute positions based, relative positions based, inter-agent distances based, and inter-agent bearings based, for specifying a formation shape are not invariant under all three transformations: translations, rotations, and scalings, a novel specification for formation shapes is proposed that is invariant under translations, rotations, and scalings in two- and three-dimensional spaces, and thus more intrinsic. In doing so, a new notion, called matrix-valued Laplacian, for graphs is introduced in detail along with some useful properties. It is demonstrated that the matrix-valued Laplacian provides much flexibility. Subsequently, two controllers are designed for guaranteeing the achievement of a dynamic formation shape. It is proved that arbitrary dynamic geometric shape can be reached by the designed controllers. Finally, two numerical examples are provided for demonstrating the effectiveness of the theoretical results.

Continuum and Spectral Line Radiation from a Random Clumpy Medium

Abstract We present a formalism for continuum and line emission from random clumpy media together with its application to problems of current interest, including CO spectral lines from ensembles of clouds and radio emission from H ii regions, supernovae, and star-forming regions. For line emission, we find that the effects of clump opacity on observed line ratios can be indistinguishable from variations of intrinsic line strengths, adding to the difficulties in determining abundances from line observations. Our formalism is applicable to arbitrary distributions of cloud properties, provided the cloud volume filling factor is small; numerical simulations show it to hold up to filling factors of ∼10%. We show that irrespective of the complexity of the cloud ensemble, the radiative effect of clumpiness can be parameterized at each frequency by a single multiplicative correction to the overall optical depth; this multiplier is derived from appropriate averaging over individual cloud properties. Our main finding is that cloud shapes have only a negligible effect on radiation propagation in clumpy media; the results of calculations employing point-like clouds are practically indistinguishable from those for finite-sized clouds with arbitrary geometrical shapes.

Procena verovatnoće pogađanja cilja jednim hicem kao rezultat numeričkog rešavanja dvostrukih integrala pomoću Mathcad-a

A geometric interpretation of single shot hit probability (Phit) is a volume of 3D space enclosed above by the surface f(y,z) described the bivariate normal distribution and bounded from below by the YOZ plane with the target's contour (T-region). The Phit is proposed to estimate by a method based on the numerical integration of the double integral. Its integrand is the 2D normal distribution of Y, Z system of random variables. The dispersion characteristics and coordinates of the dispersion center are known in advance. Limits of first and second integrals are described by the analytic functions, which characterize the geometric shape of the Tregion. Implementation of the offered method: the selected shooting target is partitioned into N geometric subregions; for each of it, analytic formula(s) for the subregion's boundaries is determined and each double integral is defined. The Phit estimations are produced using a numerical integration in the computer software Mathcad. The results of the calculus of all Phits (for subregions) are added up (or subtracted) depending on the geometric relationships between them. The schema for numerically Phit solving makes it possible to calculate a likelihood for targets with arbitrary geometric shapes and not just rectangular-shaped silhouettes. For illustrating the operability of the proposed method, the Phit for two kinds of head-type shooting targets had been evaluated. The developed method had been compared with the already existing works.

A New Concept for a Flat Lens Design Using Dielectric Cylinders

A new design method called the array scattering method for a flat lens made of dielectric cylinders is presented. The method reconstructs the far-field radiation pattern of a 2-D arbitrary geometrical shape dielectric scatterer. Since the method has no restrictions on the near field, it allows us to alter the polarization currents distribution in order to obtain a better far-field performance for a periodic structure with a given unit cell size. The method also allows us to perform a simple parametric study on the limits of the unit cell size, taking into account the scatterer geometrical dimensions. This parameter (unit cell size) does not appear in the formulation if we use a method that assumes an infinite array of cylinders. The realization is done using the multiple scattering method, which is one of the most accurate methods to deal with arrays scattering. Nevertheless, the method is almost entirely analytic, not iterative and does not require multiple simulations in order to obtain the required objective.

Changes in intrinsic functional connectivity and group relevant salience: The case of sport rivalry.

Studies have shown that attending to salient group relevant information could increase the BOLD activity across distributed neural networks. However, it is unclear how attending to group relevant information changes the functional connectivity across these networks. We investigated this issue combining resting states and task-based fMRI experiment. The task involved football fans learning associations between arbitrary geometric shapes and the badges of in-group, the rival and the neutral football teams. Upon learning, participants viewed different badge/shape pairs and their task was to judge whether the viewed pair was a match or a mismatch. For whole brain analyses increased activity was found in the IFG, DLPFC, AI, fusiform gyrus, precuneus and pSTS (all in the left hemisphere) for the rival over the in-group mismatch. Further, the ROI analyses revealed larger beta-values for the rival badge in the left pSTS, left AI and the left IFG. However, larger beta-values were found in the left pSTS and the left IFG (but not AI) for the in-group shape. The intrinsic functional connectivity analyses revealed that compare to the pre-task, post task functional connectivity was decreased between the left DLPFC and the left AI. In contrast, it was increased between the left IFG and the left AI and this was correlated with the difference in RT for the rival vs. in-group team. Our findings suggest that attending to group relevant information differentially affects the strength of functional coupling in attention networks and this can be explained by the saliency of the group relevant information.

Gravity Anomaly of Polyhedral Bodies Having a Polynomial Density Contrast

We analytically evaluate the gravity anomaly associated with a polyhedral body having an arbitrary geometrical shape and a polynomial density contrast in both the horizontal and vertical directions. The gravity anomaly is evaluated at an arbitrary point that does not necessarily coincide with the origin of the reference frame in which the density function is assigned. Density contrast is assumed to be a third-order polynomial as a maximum but the general approach exploited in the paper can be easily extended to higher-order polynomial functions. Invoking recent results of potential theory, the solution derived in the paper is shown to be singularity-free and is expressed as a sum of algebraic quantities that only depend upon the 3D coordinates of the polyhedron vertices and upon the polynomial density function. The accuracy, robustness and effectiveness of the proposed approach are illustrated by numerical comparisons with examples derived from the existing literature.

SIMULATION OF SURFACE HEATING FOR ARBITRARY SHAPE’S MOVING BODIES/SOURCES BY USING R-FUNCTIONS

The purpose of this article is to propose an efficient algorithm for determining the place of an action of a heat source with a given motion law for a body of an arbitrary shape using methods of analytical geometry. The solution to this problem is an important part of a modeling of a laser, plasma, ion beam treatment. In addition, it can also be used for mass transfer problems, such as simulation of coating, sputtering, painting etc. The problem is solved by the method of R-functions to define the shape of the test body and the heat source and the analytical determination zone shadowing. As an example, we consider the problem of using the method of ion cleaning parameters optimization considering temperature limitations. Application of the R-functions can significantly reduce the amount of computation with usage of the ray tracing algorithm. The numerical realization of the proposed method requires an accurate creation of a numerical mesh. The best results in terms of accuracy of determination the scope of the source can be expected when applying adaptive tunable meshes. In case of integration of the R-functions into the CAD system, the use of the proposed method would be simple enough. The proposed method allows to determine the range of the source by the expression, which is constructed only once for the body and the source of arbitrary geometric shapes moving in any law. This distinguishes the proposed approach against all known algorithms for ray tracing. The proposed method can also be used for time-dependent multisource with arbitrary shapes, which move in different directions.

Geometrically constrained isogeometric parameterized level-set based topology optimization via trimmed elements

In this paper, an approach based on the fast point-in-polygon (PIP) algorithm and trimmed elements is proposed for isogeometric topology optimization (TO) with arbitrary geometric constraints. The isogeometric parameterized level-set-based TO method, which directly uses the non-uniform rational basis splines (NURBS) for both level set function (LSF) parameterization and objective function calculation, provides higher accuracy and efficiency than previous methods. The integration of trimmed elements is completed by the efficient quadrature rule that can design the quadrature points and weights for arbitrary geometric shape. Numerical examples demonstrate the efficiency and flexibility of the method.

Approach to solution of coupled heat transfer problem on the surface of hypersonic vehicle of arbitrary shape

In this paper, an approach to solve conjugate heat- and mass-transfer problems is considered to be applied to hypersonic vehicle surface of arbitrary shape. The approach under developing should satisfy the following demands. (i) The surface of the body of interest may have arbitrary geometrical shape. (ii) The shape of the body can change during calculation. (iii) The flight characteristics may vary in a wide range, specifically flight altitude, free-stream Mach number, angle-of-attack, etc. (iv) The approach should be realized with using the high-performance-computing (HPC) technologies. The approach is based on coupled solution of 3D unsteady hypersonic flow equations and 3D unsteady heat conductance problem for the thick wall. Iterative process is applied to account for ablation of wall material and, consequently, mass injection from the surface and changes in the surface shape. While iterations, unstructured computational grids both in the flow region and within the wall interior are adapted to the current geometry and flow conditions. The flow computations are done on HPC platform and are most time-consuming part of the whole problem, while heat conductance problem can be solved on many kinds of computers.

2D full-waveform modeling of seismic waves in layered karstic media

We have developed a new propagator-matrix scheme to simulate seismic-wave propagation and scattering in a multilayered medium containing karstic voids. The propagator matrices can be found using the boundary element method. The model can have irregular boundaries, including arbitrary free-surface topography. Any number of karsts can be included in the model, and each karst can be of arbitrary geometric shape. We have used the Burton-Miller formulation to tackle the numerical instability caused by the fictitious resonance due to the finite size of a karstic void. Our method was implemented in the frequency-space domain, so frequency-dependent [Formula: see text] can be readily incorporated. We have validated our calculation by comparing it with the analytical solution for a cylindrical void and to the spectral element method for a more complex model. This new modeling capability is useful in many important applications in seismic inverse theory, such as imaging karsts, caves, sinkholes, and clandestine tunnels.

Development of an Anthropomorphic Gripping Manipulator: The Analysis of Implementation Methods

The object of the article is the study of implementation methods for the development of hardware-software engineering solutions in the field of the creation of a universal anthropomorphic gripper. Such technical solutions are intended to enable the adaptation and extensive use of advanced robotic systems in the natural environmental conditions formed by people through equipping them with anthropomorphic universal grippers able to grip, hold and manipulate objects with arbitrary geometric shapes. During the study the anatomical structure of the hand was analyzed. The design and construction of anthropomorphic grippers represented in scientific articles and patents were considered. Also the structure of servomotors and sensor systems were analyzed which provide feedback and adaptability of control. As a result of conducted research trends in the technology of anthropomorphic gripping manipulators were identified. Before the development of a working prototype a comprehensive virtual simulation of a gripper is planned to be conducted. For this purpose Matlab as well as Gazebo, GraspIt and MoveIt included in the Robotic Operation System (ROS) were selected. Using Matlab a mathematical model was created which describe the dynamics and kinematics of the future prototype. For the visualization of the modeling process and the creation of a virtual surround space a mathematical model in Gazebo was developed. Concurrent simulations in these environments allows for the development of algorithms and control software. Motion simulation of the hand in conditions close to real usage allows for the optimization of kinematic and mechanical design.

Fabrication of free-standing casein devices with micro- and nanostructured regular and bioimprinted surface features

This work introduces a novel process for the fabrication of free-standing biodegradable casein devices with micro- and nanoscale regular and biomimetic surface features. Fabrication of intermediate polydimethylsiloxane (PDMS) moulds from photoresist masters and liquid-casting of casein is used to transfer arbitrary geometrical shapes onto the surface of casein devices. Casein film composition was optimized for mechanical stability and pattern resolution. It was found that 15% casein in 0.2% NaOH solution, mixed with 10% glycerol, and cross-linked by addition of 2% glutaraldehyde produced the best pattern transfer results. Biomimetic cell-like shapes were transferred onto casein by use of bioimprinting of two-dimensional cell-cultures into PDMS. To demonstrate this process, C2C12 mouse myoblasts were cultured on microscope slides, replicated into PDMS and casein using liquid casting and drying. Recessed alignment grids were integrated into the microscope glass slides to facilitate direct comparison of original cells and their bioimprints on PDMS and casein. Optical microscopy and atomic force microscopy confirmed the transfer of micron-scale morphological features, such as cell outlines, nuclei and larger lamellipodia, into the casein surface. Nanoscale feature resolution in casein was found to be limited compared to the PDMS intermediate moulds, which was attributed to limited wetting of the aqueous casein solution. Strategies to increase resolution of the casein transfer step, as well as degradation behavior of the fabricated devices in cell culture media are currently underway. Substrates fabricated with this process have applications in stem cell engineering, regenerative medicine, and implantable devices.

Conditional discriminations, symmetry, and semantic priming

Psychologists interested in the study of symbolic behavior have found that people are faster at reporting that two words are related to one another than they are in reporting that two words are not related – an effect called semantic priming. This phenomenon has largely been documented in the context of natural languages using real words as stimuli. The current study asked whether laboratory-generated stimulus–stimulus relations established between arbitrary geometrical shapes would also show the semantic priming effect. Participants learned six conditional relations using a one-to-many training structure (A1-B1, A1-C1, A1-D1, A2-B2, A2-C2, A2-D2) and demonstrated, via accurate performance on tests of derived symmetry, that the trained stimulus functions had become reversible. In a lexical decision task, subjects also demonstrated a priming effect as they displayed faster reaction times to target stimuli when the prime and target came from the same trained or derived conditional relations, compared to the condition in which the prime and target came from different trained or derived conditional relations. These data suggest that laboratory-generated equivalence relations may serve as useful analogues of symbolic behavior. However, the fact that conditional relations training and symmetry alone were sufficient to produce the effect suggests that semantic priming like effects may be the byproduct of simpler stimulus–stimulus relations.

Estimation of the Area of a Reverberant Plate Using Average Reverberation Properties

This paper aims to present an original method for the estimation of the area of thin plates of arbitrary geometrical shapes. This method relies on the acquisition and ensemble processing of reverberated elastic signals on few sensors. The acoustical Green's function in a reverberant solid medium is modeled by a nonstationary random process based on the image-sources method. In that way, mathematical expectations of the signal envelopes can be analytically related to reverberation properties and structural parameters such as plate area, group velocity, or source-receiver distance. Then, a simple curve fitting applied to an ensemble average over N realizations of the late envelopes allows to estimate a global term involving the values of structural parameters. From simple statistical modal arguments, it is shown that the obtained relation depends on the plate area and not on the plate shape. Finally, by considering an additional relation obtained from the early characteristics (treated in a deterministic way) of the reverberation signals, it is possible to deduce the area value. This estimation is performed without geometrical measurements and requires an access to only a small portion of the plate. Furthermore, this method does not require any time measurement nor trigger synchronization between the input channels of instrumentation (between measured signals), thus implying low hardware constraints. Experimental results obtained on metallic plates with free boundary conditions and embedded window glasses will be presented. Areas of up to several meter-squares are correctly estimated with a relative error of a few percents.

Generalization of the extended optical theorem for scalar arbitrary-shape acoustical beams in spherical coordinates

The extended optical theorem is generalized for scalar acoustical beams of arbitrary character with any angle of incidence interacting with an object of arbitrary geometric shape and size, and placed randomly in the beam's path with any scattering angle. Analytical expressions for the extinction, absorption, and scattering cross sections are derived, and the connections with the axial (i.e., along the direction of wave propagation) torque and radiation force calculations are discussed. As examples to illustrate the analysis for a viscoelastic object, the extinction, absorption, and scattering cross sections are provided for an infinite plane progressive wave, infinite nondiffracting Bessel beams, a zero-order spherical quasi-Gaussian beam, and a Bessel-Gauss vortex beam emanating from a finite circular aperture, which reduces to a finite high-order Bessel beam, a finite zero-order Bessel beam, and a finite piston radiator vibrating uniformly with appropriate selection of beam parameters. The similarity with the asymptotic quantum inelastic cross sections is also mentioned.