A simulation-based study of the variability of remnant polarization <inline-formula> <tex-math notation="LaTeX">({P}_{r}) </tex-math></inline-formula> in a multigranular 3-D ultrathin ferroelectric ...(FE) capacitor is presented in this article. The Poisson-Voronoi tessellation (PVT) algorithm is used for the nucleation of grains in the FE region, which corresponds to the physical growth mechanism. The PVT algorithm implemented in MATLAB is coupled with TCAD simulations, to trace the FE hysteresis loop. The impact of both, area and thickness scaling on the variability of <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula>, is considered. It is found that amount of variability in <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula> increases as FE thickness decreases. In addition, FE with the smaller surface area exhibits a higher variability in <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula> compared to a larger surface area FE capacitor. Furthermore, the impact of dielectric content in the FE grains is analyzed. It is seen that the dielectric grains cause a very large amount of variability in the FE hysteresis loop. An increase in the dielectric grains also leads to a loss in the retentivity of the hysteresis loop.
The inability of simulating the grain shapes of granular media accurately has been an outstanding issue preventing particle-based methods such as discrete element method from providing meaningful ...information for relevant scientific and engineering applications. In this study we propose a novel statistical method to generate virtual 3D particles with realistically complex yet controllable shapes and further pack them effectively for use in discrete-element modelling of granular materials. We combine the theory of random fields for spherical topology with a Fourier-shape-descriptor based method for the particle generation, and develop rigorous solutions to resolve the mathematical difficulties arising from the linking of the two. The generated particles are then packed within a prescribed container by a cell-filling algorithm based on Constrained Voronoi Tessellation. We employ two examples to demonstrate the excellent control and flexibility that the proposed method can offer in reproducing such key characteristics as shape descriptors (aspect ratio, roundness, sphericity, presence of facets, etc.), size distribution and solid fraction. The study provides a general and robust framework on effective characterization and packing of granular particles with complex shapes for discrete modelling of granular media.
It is a great challenge to evaluate the network performance of cellular mobile communication systems. In this paper, we propose new spatial spectrum and energy efficiency models for Poisson-Voronoi ...tessellation (PVT) random cellular networks. To evaluate the user access to the network, a Markov chain based wireless channel access model is first proposed for PVT random cellular networks. On that basis, the outage probability and blocking probability of PVT random cellular networks are derived, which can be computed numerically. Furthermore, taking into account the call arrival rate, the path loss exponent and the base station (BS) density in random cellular networks, spatial spectrum and energy efficiency models are proposed and analyzed for PVT random cellular networks. Numerical simulations are conducted to evaluate the network spectrum and energy efficiency in PVT random cellular networks.
Superpixels are perceptually meaningful atomic regions that can effectively capture image features. Among various methods for computing uniform superpixels, simple linear iterative clustering (SLIC) ...is popular due to its simplicity and high performance. In this paper, we extend SLIC to compute content-sensitive superpixels, i.e., small superpixels in content-dense regions with high intensity or colour variation and large superpixels in content-sparse regions. Rather than using the conventional SLIC method that clusters pixels in R 5 , we map the input image Ito a 2-dimensional manifold M ⊂ R 5 , whose area elements are a good measure of the content density in I. We propose a simple method, called intrinsic manifold SLIC (IMSLIC), for computing a geodesic centroidal Voronoi tessellation (GCVT)-a uniform tessellation-on M, which induces the content-sensitive superpixels in I. In contrast to the existing algorithms, IMSLIC characterizes the content sensitivity by measuring areas of Voronoi cells on M. Using a simple and fast approximation to a closed-form solution, the method can compute the GCVT at a very low cost and guarantees that all Voronoi cells are simply connected. We thoroughly evaluate IMSLIC and compare it with eleven representative methods on the BSDS500 dataset and seven representative methods on the NYUV2 dataset. Computational results show that IMSLIC outperforms existing methods in terms of commonly used quality measures pertaining to superpixels such as compactness, adherence to boundaries, and achievable segmentation accuracy. We also evaluate IMSLIC and seven representative methods in an image contour closure application, and the results on two datasets, WHD and WSD, show that IMSLIC achieves the best foreground segmentation performance.
Stochastic models are valuable tools to study the mechanical behaviour of foams whose characteristic features include random cellular morphology and cells of different size (polydispersity). Random ...Laguerre tessellations, additively weighted generalisations of Voronoi tessellations, possess these features which makes them natural models for foams. This work studies how well a random foam can be represented by a Laguerre tessellation. For this means the Surface Evolver is used to simulate random, polydisperse soap froths which are subsequently reconstructed by Laguerre tessellations. By design, the resulting Laguerre approximations resemble the cellular morphology of the underlying froth. The Young’s modulus of low-density solid foams with open cells is then calculated for random, polydisperse foams based on Laguerre approximations and simulated soap froths. For the special case of monodisperse foams, we compare Laguerre approximated foams with the well known Kelvin and Weaire–Phelan foams.
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•Laguerre approximations provide realistic models for low-density open-cell foams.•Laguerre approximations are at most 5% stiffer than simulated monodisperse foams.•Laguerre approximations provide a nonparametric approach to model foams.
•Experiments were conducted to investigate the NiTi dynamic fracture behaviors.•The micro features of the fracture surface under an impact loading were revealed by the electron microscope.•A novel ...constitutive model based on the Boyd and Lagoudas formulation was proposed.•The dynamic fracture behaviors of NiTi can be well predicted by using the constitutive model and cohesive elements.•The effects of grain size on intergranular fracture toughness were characterized.
The mechanical behaviors of NiTi shape memory alloy under the impact loading raised many interests in the fields of engineering and science, whereas its fracture process has not been well understood so far. In this work, multi-scale experiments and numerical simulations were conducted to comprehensively study the dynamic fracture performances of NiTi alloy. The impact crack experiments were carried out with the utilization of split Hopkinson compression bar, which showed the variation of crack propagation rate versus impact velocity. The Scanning Electron Microscope (SEM) and Transmission Electron Microscope (TEM) were employed to observe the fracture surfaces. The micro images revealed that the fracture behaviors were manifested as quasi-brittle fracture features. By taking the plastic evolution into consideration, a novel constitutive model based on Boyd and Lagoudas phase transition formulation was proposed, which overcomes the limitation of simultaneously describing super-elastic and plastic behaviors of NiTi. With the novel constitutive model, the crack propagation process was accurately reproduced with numerical results in good agreements with our experimental observations. Furthermore, the representative volume element (RVE) with Voronoi tessellation was employed to numerically study the grain size effect on intergranular fracture toughness. It was demonstrated that the reduction of grain size promoted the hinderance effect of intergranular fracture, which led to an evident improvement of intergranular fracture toughness in model with a smaller grain size.
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In this study, the Voronoi tessellation method has been used to design novel bone like three dimension (3D) porous scaffolds. The Voronoi method has been processed with computer ...design software to obtain 3D virtual isotropic porous interconnected models, exactly matching the main histomorphometric indices of trabecular bone (trabecular thickness, trabecular separation, trabecular number, bone volume to total volume ratio, bone surface to bone volume ratio, etc.). These bone like models have been further computed for mechanical (elastic modulus) and fluid mass transport (permeability) properties. The results show that the final properties of the scaffolds can be controlled during their microstructure and histomorphometric initial design stage. It is also shown that final properties can be tuned during the design stage to exactly match those of trabecular natural bone. Moreover, identical total porosity models can be designed with quite different specific bone surface area and thus, this specific microstructural feature can be used to favour cell adhesion, migration and, ultimately, new bone apposition (i.e. osteoconduction). Once the virtual models are fully characterized and optimized, these can be easily 3D printed by additive manufacturing and/or stereolitography technologies.
The significance of this article goes far beyond the specific objectives on which it is focussed. In fact, it shows, in a guided way, the entire novel process that can be followed to design graded porous implants, whatever its external shape and geometry, but internally tuned to the exact histomorphometric indices needed to match natural human tissues microstructures and, consequently, their mechanical and fluid properties, among others.
The significance is even more relevant nowadays thanks to the available new computing and design software that is easily linked to the 3D printing new technologies. It is this transversality, at the frontier of different disciplines, the main characteristic that gives this article a high scientific impact and interest to a broaden audience.
The recently introduced multidimensional archive of phenotypic elites (MAP-Elites) is an evolutionary algorithm capable of producing a large archive of diverse, high-performing solutions in a single ...run. It works by discretizing a continuous feature space into unique regions according to the desired discretization per dimension. While simple, this algorithm has a main drawback: it cannot scale to high-dimensional feature spaces since the number of regions increase exponentially with the number of dimensions. In this paper, we address this limitation by introducing a simple extension of MAP-Elites that has a constant, predefined number of regions irrespective of the dimensionality of the feature space. Our main insight is that methods from computational geometry could partition a high-dimensional space into well-spread geometric regions. In particular, our algorithm uses a centroidal Voronoi tessellation (CVT) to divide the feature space into a desired number of regions; it then places every generated individual in its closest region, replacing a less fit one if the region is already occupied. We demonstrate the effectiveness of the new "CVT-MAP-Elites" algorithm in high-dimensional feature spaces through comparisons against MAP-Elites in maze navigation and hexapod locomotion tasks.
Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we ...study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.
Topology optimization using polytopes Gain, Arun L.; Paulino, Glaucio H.; Duarte, Leonardo S. ...
Computer methods in applied mechanics and engineering,
08/2015, Letnik:
293
Journal Article
Recenzirano
Odprti dostop
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of ...polyhedral meshes such as its unstructured nature and the connectivity of faces between elements makes them specially attractive for topology optimization applications. Numerical anomalies in designs such as the single node connections and checkerboard pattern can be naturally circumvented with polyhedrons. In the current work, we solve the governing three-dimensional elasticity state equation using the Virtual Element Method (VEM) approach. The main characteristic difference between VEM and standard finite element methods (FEM) is that in VEM the canonical basis functions are not constructed explicitly. Rather the stiffness matrix is computed directly utilizing a projection map which extracts the linear component of the deformation. Such a construction guarantees the satisfaction of the patch test (used by engineers as an indicator of optimal convergence of numerical solutions under mesh refinement). Finally, the computations reduce to the evaluation of matrices which contain purely geometric surface facet quantities. The present work focuses on the first-order VEM in which the degrees of freedom are associated with the vertices. The features of the current optimization approach are demonstrated using numerical examples for compliance minimization and compliant mechanism problems.
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