112,642 research outputs found
Nucleation and growth mechanism of polycarbazole deposited by electrochemistry
Polycarbazole (PCz) thin films have been deposited by electro-oxidation of carbazole in LiClO4 + anhydrous acetonitrile onto SnO2 coated glass substrates, by potentiostatic method and the nucleation and growth mechanism (NGM) were studied. The obtained current time transients (j-t) were fitted using a mathematical equation with three contributions: instantaneous nucleation with two-dimensional (IN2D) or three-dimensional (IN3D) growth, and also a progressive nucleation with three dimensional (PN3D) growth. At the beginning, the IN2D contribution is predominant but, quickly the IN3D processes become more important. At a deposition time t > 17 s the IN3D corresponds to 80 % of the total current. The visualization by scanning electron microscopy of the surface morphology of the PCz films is in agreement with the NGM proposed by the mathematical method. The film covers very rapidly the SnO2 under layer related to the 2D process, even if some heterogeneities randomly distributed in the films, issued from the 3D processes, are also visible. After two minutes of deposition, the roughness of the whole surface of the films corroborates the 3D processes domination. Therefore, the information directly obtained from the (j-t) transients is a suitable and very useful tool to predict the working conditions in order to control the type of morphology of the film prepared by electropolymerization
Minkowski Tensors of Anisotropic Spatial Structure
This article describes the theoretical foundation of and explicit algorithms
for a novel approach to morphology and anisotropy analysis of complex spatial
structure using tensor-valued Minkowski functionals, the so-called Minkowski
tensors. Minkowski tensors are generalisations of the well-known scalar
Minkowski functionals and are explicitly sensitive to anisotropic aspects of
morphology, relevant for example for elastic moduli or permeability of
microstructured materials. Here we derive explicit linear-time algorithms to
compute these tensorial measures for three-dimensional shapes. These apply to
representations of any object that can be represented by a triangulation of its
bounding surface; their application is illustrated for the polyhedral Voronoi
cellular complexes of jammed sphere configurations, and for triangulations of a
biopolymer fibre network obtained by confocal microscopy. The article further
bridges the substantial notational and conceptual gap between the different but
equivalent approaches to scalar or tensorial Minkowski functionals in
mathematics and in physics, hence making the mathematical measure theoretic
method more readily accessible for future application in the physical sciences
A computational framework for the morpho-elastic development of molluskan shells by surface and volume growth
Mollusk shells are an ideal model system for understanding the morpho-elastic
basis of morphological evolution of invertebrates' exoskeletons. During the
formation of the shell, the mantle tissue secretes proteins and minerals that
calcify to form a new incremental layer of the exoskeleton. Most of the
existing literature on the morphology of mollusks is descriptive. The
mathematical understanding of the underlying coupling between pre-existing
shell morphology, de novo surface deposition and morpho-elastic volume growth
is at a nascent stage, primarily limited to reduced geometric representations.
Here, we propose a general, three-dimensional computational framework coupling
pre-existing morphology, incremental surface growth by accretion, and
morpho-elastic volume growth. We exercise this framework by applying it to
explain the stepwise morphogenesis of seashells during growth: new material
surfaces are laid down by accretive growth on the mantle whose form is
determined by its morpho-elastic growth. Calcification of the newest surfaces
extends the shell as well as creates a new scaffold that constrains the next
growth step. We study the effects of surface and volumetric growth rates, and
of previously deposited shell geometries on the resulting modes of mantle
deformation, and therefore of the developing shell's morphology. Connections
are made to a range of complex shells ornamentations.Comment: Main article is 20 pages long with 15 figures. Supplementary material
is 4 pages long with 6 figures and 6 attached movies. To be published in PLOS
Computational Biolog
Automation Process for Morphometric Analysis of Volumetric CT Data from Pulmonary Vasculature in Rats
With advances in medical imaging scanners, it has become commonplace to generate large multidimensional datasets. These datasets require tools for a rapid, thorough analysis. To address this need, we have developed an automated algorithm for morphometric analysis incorporating A Visualization Workshop computational and image processing libraries for three-dimensional segmentation, vascular tree generation and structural hierarchical ordering with a two-stage numeric optimization procedure for estimating vessel diameters. We combine this new technique with our mathematical models of pulmonary vascular morphology to quantify structural and functional attributes of lung arterial trees. Our physiological studies require repeated measurements of vascular structure to determine differences in vessel biomechanical properties between animal models of pulmonary disease. Automation provides many advantages including significantly improved speed and minimized operator interaction and biasing. The results are validated by comparison with previously published rat pulmonary arterial micro-CT data analysis techniques, in which vessels were manually mapped and measured using intense operator intervention
Visual Reconstruction and Feature Analysis of the Three-Dimensional Surface of Earthworm
This paper demonstrates a method for visual reconstruction and feature analysis of the three-dimensional surface of earthworm in CATIA (Computer Aided Three Dimensional Interactive Application) and IDL (Interactive Data Language). The earthworm, with a relatively simple surface morphology and good capability in reducing soil adhesion and resistance, was selected to study the feasible methods in the visual reconstruction and feature analysis of the three-dimensional surface of living things. The digital measurements of surfaces of the earthworm were carried out using a three-dimensional laser scanner. Point clouds, the scanning digital data of the surface of the earthworm, were processed by screening unwanted data, reconstructing surface and analysing feature in CATIA. In order to get more detail information about the point clouds, IDL, which integrates a powerful, array-oriented language with numerous mathematical analysis and graphical display techniques, was adopted for the visual reconstruction and feature analysis of three- dimensional surface of the earthworm. Importing of point clouds and reconstruction of the surface of earthworm were conducted in CATIA. Analysis feature of the scanning data and reconstructing surface were carried out in IDL, which provides a high level of flexibility to access, analyse and visualize the data using different methods. Polynomial regression equation of the surface of earthworm in the longitudinal plane was derived. In addition, point clouds were more easily displayed and analysed by resizing, rotating and zooming in IDL. Methods and results presented in this paper prove to be potentially useful for analyzing the feature of biological prototype, optimizing the mathematical model and affording deformable physical model to bionic engineering, those works would have great implications to the research of biological coupling theory and technological creation in bionic engineering. Keywords: Visual Reconstruction; Feature Analysis; Three-Dimensional Surface; Earthworm; CATIA; ID
Understanding Genomic Evolution of Olfactory Receptors through Fractal and Mathematical Morphology
Fractals and Mathematical Morphology are immensely used to study many problems in different branches of science and technology including the domain of Biology. There are many more unrevealed facts and figures of genes and genome in Computational Biology. In this paper, our objective is to explore how the evolutionary network is associated among Human, Chimpanzee and Mouse with regards to their genomic information. We are about to explore their genomic evolution through the quantitative measures of fractals and morphology. We have considered olfactory receptors for our case study. These olfactory receptors do function in different species with subtle differences in the structures of DNA sequences. Those subtle differences can be exposed through intricate details of Fractals and Mathematical Morphology
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Accuracy of generic mesh conformation: the future of facial morphological analysis
Three-dimensional (3D) analysis of the face is required for the assessment of changes following surgery, to monitor the progress of pathological conditions and for the evaluation of facial growth. Sophisticated methods have been applied for the evaluation of facial morphology, the most common being dense surface correspondence. The method depends on the application of a mathematical facial mask known as the generic facial mesh for the evaluation of the characteristics of facial morphology. This study evaluated the accuracy of the conformation of generic mesh to the underlying facial morphology. The study was conducted on 10 non-patient volunteers. Thirty-four 2-mm-diameter self-adhesive, non-reflective markers were placed on each face. These were readily identifiable on the captured 3D facial image, which was captured by Di3D stereophotogrammetry. The markers helped in minimising digitisation errors during the conformation process. For each case, the face was captured six times: at rest and at the maximum movements of four facial expressions. The 3D facial image of each facial expression was analysed. Euclidean distances between the 19 corresponding landmarks on the conformed mesh and on the original 3D facial model provided a measure of the accuracy of the conformation process. For all facial expressions and all corresponding landmarks, these distances were between 0.7 and 1.7 mm. The absolute mean distances ranged from 0.73 to 1.74 mm. The mean absolute error of the conformation process was 1.13 ± 0.26 mm. The conformation of the generic facial mesh is accurate enough for clinical trial proved to be accurate enough for the analysis of the captured 3D facial images
A two-fluid model for tissue growth within\ud a dynamic flow environment
We study the growth of a tissue construct in a perfusion bioreactor, focussing on its response to the mechanical environment. The bioreactor system is modelled as a two-dimensional channel containing a tissue construct through which a flow of culture medium is driven. We employ a multiphase formulation of the type presented by G. Lemon, J. King, H. Byrne, O. Jensen and K. Shakesheff in their study (Multiphase modelling of tissue growth using the theory of mixtures. J. Math. Biol. 52(2), 2006, 571–594) restricted to two interacting fluid phases, representing a cell population (and attendant extracellular matrix) and a culture medium, and employ the simplifying limit of large interphase viscous drag after S. Franks in her study (Mathematical Modelling of Tumour Growth and Stability. Ph.D. Thesis, University of Nottingham, UK, 2002) and S. Franks and J. King in their study (Interactions between a uniformly proliferating tumour and its surrounding: Uniform material properties. Math. Med. Biol. 20, 2003, 47–89).\ud
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The novel aspects of this study are: (i) the investigation of the effect of an imposed flow on the growth of the tissue construct, and (ii) the inclusion of a mechanotransduction mechanism regulating the response of the cells to the local mechanical environment. Specifically, we consider the response of the cells to their local density and the culture medium pressure. As such, this study forms the first step towards a general multiphase formulation that incorporates the effect of mechanotransduction on the growth and morphology of a tissue construct. The model is analysed using analytic and numerical techniques, the results of which illustrate the potential use of the model to predict the dominant regulatory stimuli in a cell population
Multiscale Modeling and Simulation of Organic Solar Cells
In this article, we continue our mathematical study of organic solar cells
(OSCs) and propose a two-scale (micro- and macro-scale) model of heterojunction
OSCs with interface geometries characterized by an arbitrarily complex
morphology. The microscale model consists of a system of partial and ordinary
differential equations in an heterogeneous domain, that provides a full
description of excitation/transport phenomena occurring in the bulk regions and
dissociation/recombination processes occurring in a thin material slab across
the interface. The macroscale model is obtained by a micro-to-macro scale
transition that consists of averaging the mass balance equations in the normal
direction across the interface thickness, giving rise to nonlinear transmission
conditions that are parametrized by the interfacial width. These conditions
account in a lumped manner for the volumetric dissociation/recombination
phenomena occurring in the thin slab and depend locally on the electric field
magnitude and orientation. Using the macroscale model in two spatial
dimensions, device structures with complex interface morphologies, for which
existing data are available, are numerically investigated showing that, if the
electric field orientation relative to the interface is taken into due account,
the device performance is determined not only by the total interface length but
also by its shape
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