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Concept: Numerical analysis


Because of its optical and electrical properties, large surfaces, and compatibility with standard silicon processes, porous silicon is a very interesting material in photovoltaic and microelectromechanical systems technology. In some applications, porous silicon is annealed at high temperature and, consequently, the cylindrical pores that are generated by anodization or stain etching reorganize into randomly distributed closed sphere-like pores. Although the design of devices which involve this material needs an accurate evaluation of its mechanical properties, only few researchers have studied the mechanical properties of porous silicon, and no data are nowadays available on the mechanical properties of sintered porous silicon. In this work we propose a finite element model to estimate the mechanical properties of sintered meso-porous silicon. The model has been employed to study the dependence of the Young’s modulus and the shear modulus (upper and lower bounds) on the porosity for porosities between 0% to 40%. Interpolation functions for the Young’s modulus and shear modulus have been obtained, and the results show good agreement with the data reported for other porous media. A Monte Carlo simulation has also been employed to study the effect of the actual microstructure on the mechanical properties.

Concepts: Silicon, Materials science, Monte Carlo method, Porosity, Computer simulation, Young's modulus, Numerical analysis, Shear modulus


Automated cell imaging systems facilitate fast and reliable analysis of biological events at the cellular level. In these systems, the first step is usually cell segmentation that greatly affects the success of the subsequent system steps. On the other hand, similar to other image segmentation problems, cell segmentation is an ill-posed problem that typically necessitates the use of domain-specific knowledge to obtain successful segmentations even by human subjects. The approaches that can incorporate this knowledge into their segmentation algorithms have potential to greatly improve segmentation results. In this work, we propose a new approach for the effective segmentation of live cells from phase contrast microscopy. This approach introduces a new set of “smart markers” for a marker-controlled watershed algorithm, for which the identification of its markers is critical. The proposed approach relies on using domain-specific knowledge, in the form of visual characteristics of the cells, to define the markers. We evaluate our approach on a total of 1,954 cells. The experimental results demonstrate that this approach, which uses the proposed definition of smart markers, is quite effective in identifying better markers compared to its counterparts. This will, in turn, be effective in improving the segmentation performance of a marker-controlled watershed algorithm.

Concepts: Better, Microscope, Microscopy, Numerical analysis, Image processing, Phase-contrast imaging, Watershed, Segmentation


A computational toolkit (spektr 3.0) has been developed to calculate x-ray spectra based on the tungsten anode spectral model using interpolating cubic splines (TASMICS) algorithm, updating previous work based on the tungsten anode spectral model using interpolating polynomials (TASMIP) spectral model. The toolkit includes a matlab (The Mathworks, Natick, MA) function library and improved user interface (UI) along with an optimization algorithm to match calculated beam quality with measurements.

Concepts: Algorithm, Mathematics, Java, Numerical analysis, User interface, The MathWorks, MATLAB, Natick, Massachusetts


Soft actuators made from elastomeric active materials can find widespread potential implementation in a variety of applications ranging from assistive wearable technologies targeted at biomedical rehabilitation or assistance with activities of daily living, bioinspired and biomimetic systems, to gripping and manipulating fragile objects, and adaptable locomotion. In this manuscript, we propose a novel two-component soft actuator design and design tool that produces actuators targeted towards these applications with enhanced mechanical performance and manufacturability. Our numerical models developed using the finite element method can predict the actuator behavior at large mechanical strains to allow efficient design iterations for system optimization. Based on two distinctive actuator prototypes' (linear and bending actuators) experimental results that include free displacement and blocked-forces, we have validated the efficacy of the numerical models. The presented extensive investigation of mechanical performance for soft actuators with varying geometric parameters demonstrates the practical application of the design tool, and the robustness of the actuator hardware design, towards diverse soft robotic systems for a wide set of assistive wearable technologies, including replicating the motion of several parts of the human body.

Concepts: Engineering, Finite element method, Continuum mechanics, Human body, Design, Numerical analysis, Failure assessment, Linear actuator


This paper presents a novel reaction-diffusion (RD) method for implicit active contours that is completely free of the costly reinitialization procedure in level set evolution (LSE). A diffusion term is introduced into LSE, resulting in an RD-LSE equation, from which a piecewise constant solution can be derived. In order to obtain a stable numerical solution from the RD-based LSE, we propose a two-step splitting method to iteratively solve the RD-LSE equation, where we first iterate the LSE equation, then solve the diffusion equation. The second step regularizes the level set function obtained in the first step to ensure stability, and thus the complex and costly reinitialization procedure is completely eliminated from LSE. By successfully applying diffusion to LSE, the RD-LSE model is stable by means of the simple finite difference method, which is very easy to implement. The proposed RD method can be generalized to solve the LSE for both variational level set method and partial differential equation-based level set method. The RD-LSE method shows very good performance on boundary antileakage. The extensive and promising experimental results on synthetic and real images validate the effectiveness of the proposed RD-LSE approach.

Concepts: Mathematics, Level set, Partial differential equation, Numerical analysis, Level set method, Finite difference, Finite difference method, Finite differences


An approximate expression for Henry’s function, describing the electrophoretic mobility of a spherical colloidal particle in the limit of low surface potentials, is developed through a physical analogy to a colloidal particle with a linearly slipping surface (i.e. satisfies the Navier slip condition). The resulting expression reproduces Henry’s function with a relative error of no more than 0.1%. This approach is generalized for the electrophoretic mobility of a particle regardless of surface potential though necessary data for rigorous testing is lacking.

Concepts: Function, Colloid, Topology, Derivative, Numerical analysis, Potential, Colloidal chemistry, Zeta potential


The topological study of the electronic charge density is useful to obtain information about the kinds of bonds (ionic or covalent) and the atom charges on a molecule or crystal. For this study, it is necessary to calculate, at every space point, the electronic density and its electronic density derivatives values up to second order. In this work, a grid-based method for these calculations is described. The library, implemented for three dimensions, is based on a multidimensional Lagrange interpolation in a regular grid; by differentiating the resulting polynomial, the gradient vector, the Hessian matrix and the Laplacian formulas were obtained for every space point. More complex functions such as the Newton-Raphson method (to find the critical points, where the gradient is null) and the Cash-Karp Runge-Kutta method (used to make the gradient paths) were programmed. As in some crystals, the unit cell has angles different from 90°, the described library includes linear transformations to correct the gradient and Hessian when the grid is distorted (inclined). Functions were also developed to handle grid containing files (grd from DMol® program, CUBE from Gaussian® program and CHGCAR from VASP® program). Each one of these files contains the data for a molecular or crystal electronic property (such as charge density, spin density, electrostatic potential, and others) in a three-dimensional (3D) grid. The library can be adapted to make the topological study in any regular 3D grid by modifying the code of these functions. © 2012 Wiley Periodicals, Inc.

Concepts: Electric charge, Mathematics, Fundamental physics concepts, Atom, Chemical bond, Dimension, Euclidean space, Numerical analysis


The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.

Concepts: Mathematics, Function, Set theory, Graph theory, Level set, Numerical analysis, Image processing, Level set method


PURPOSE: To develop and test a new algorithm for fast direct Fourier transform (DrFT) reconstruction of MR data on non-Cartesian trajectories composed of lines with equally spaced points. THEORY AND METHODS: The DrFT, which is normally used as a reference in evaluating the accuracy of other reconstruction methods, can reconstruct images directly from non-Cartesian MR data without interpolation. However, DrFT reconstruction involves substantially intensive computation, which makes the DrFT impractical for clinical routine applications. In this article, the Chirp transform algorithm was introduced to accelerate the DrFT reconstruction of radial and Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction (PROPELLER) MRI data located on the trajectories that are composed of lines with equally spaced points. The performance of the proposed Chirp transform algorithm-DrFT algorithm was evaluated by using simulation and in vivo MRI data. RESULTS: After implementing the algorithm on a graphics processing unit, the proposed Chirp transform algorithm-DrFT algorithm achieved an acceleration of approximately one order of magnitude, and the speed-up factor was further increased to approximately three orders of magnitude compared with the traditional single-thread DrFT reconstruction. CONCLUSION: Implementation the Chirp transform algorithm-DrFT algorithm on the graphics processing unit can efficiently calculate the DrFT reconstruction of the radial and PROPELLER MRI data. Magn Reson Med, 2012. © 2012 Wiley Periodicals, Inc.

Concepts: Nuclear magnetic resonance, Parallel computing, Fourier transform, Numerical analysis, 3D computer graphics, Laplace transform, Lp space, Orders of approximation


Suggestions for improving the Basin-Hopping Monte Carlo (BHMC) algorithm for unbiased global optimization of clusters and nanoparticles are presented. The traditional basin-hopping exploration scheme with Monte Carlo sampling is improved by bringing together novel strategies and techniques employed in different global optimization methods, however with the care of keeping the underlying algorithm of BHMC unchanged. The improvements include a total of eleven local and nonlocal trial operators tailored for clusters and nanoparticles that allow an efficient exploration of the potential energy surface, two different strategies (static and dynamic) of operator selection, and a filter operator to handle unphysical solutions. In order to assess the efficiency of our strategies, we applied our implementation to several classes of systems, including Lennard-Jones and Sutton-Chen clusters with up to 147 and 148 atoms, respectively, a set of Lennard-Jones nanoparticles with sizes ranging from 200 to 1500 atoms, binary Lennard-Jones clusters with up to 100 atoms, (AgPd)_55 alloy clusters described by the Sutton-Chen potential, and aluminum clusters with up to 30 atoms described within the density functional theory framework. Using unbiased global search our implementation was able to reproduce successfully the great majority of all published results for the systems considered, and in many cases with more efficiency than the standard BHMC. We were also able to locate previously unknown global minimum structures for some of the systems considered. This revised BHMC method is a valuable tool for aiding theoretical investigations leading to a better understanding of atomic structures of clusters and nanoparticles.

Concepts: Better, Improve, Kinetic energy, Monte Carlo, Computational physics, Optimization, Numerical analysis, Stochastic optimization