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Edge-based and face-based smoothed finite element methods (ES-FEM and FS-FEM, respectively) are modified versions of the finite element method allowing to achieve more accurate results and to reduce sensitivity to mesh distortion, at least for linear elements. These properties make the two methods very attractive. However, their implementation in a standard finite element code is nontrivial because it requires heavy and extensive modifications to the code architecture. In this article, we present an element-based formulation of ES-FEM and FS-FEM methods allowing to implement the two methods in a standard finite element code with no modifications to its architecture. Moreover, the element-based formulation permits to easily manage any type of element, especially in 3D models where, to the best of the authors' knowledge, only tetrahedral elements are used in FS-FEM applications found in the literature. Shape functions for non-simplex 3D elements are proposed in order to apply FS-FEM to any standard finite element.
Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations.
In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric 2x2 matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach.
The characterization of the degradation kinetics of biodegradable polymers is mandatory with regard to their proper application. In the present work, polymer-modified electrolyte–insulator–semiconductor (PMEIS) field-effect sensors have been applied for in-situ monitoring of the pH-dependent degradation kinetics of the commercially available biopolymer poly(d,l-lactic acid) (PDLLA) in buffer solutions from pH 3 to pH 13. PDLLA films of 500 nm thickness were deposited on the surface of an Al–p-Si–SiO2–Ta2O5 structure from a polymer solution by means of spin-coating method. The PMEIS sensor is, in principle, capable to detect any changes in bulk, surface and interface properties of the polymer induced by degradation processes. A faster degradation has been observed for PDLLA films exposed to alkaline solutions (pH 9, pH 11 and pH 13).
An application of a scanning light-addressable potentiometric sensor for label-free DNA detection
(2013)
This work is an attempt to answer the question: How to use convex programming in shakedown analysis of structures made of materials with temperature-dependent properties. Based on recently established shakedown theorems and formulations, a dual relationship between upper and lower bounds of the shakedown limit load is found, an algorithmfor shakedown analysis is proposed. While the original problem is neither convex nor concave, the algorithm presented here has the advantage of employing convex programming tools.