Hierarchical growing cell structures: TreeGCS

We propose a hierarchical clustering algorithm (TreeGCS) based upon the Growing Cell Structure (GCS) neural network of Fritzke. Our algorithm refines and builds upon the GCS base, overcoming an inconsistency in the original GCS algorithm, where the network topology is susceptible to the ordering of the input vectors. Our algorithm is unsupervised, flexible, and dynamic and we have imposed no additional parameters on the underlying GCS algorithm. Our ultimate aim is a hierarchical clustering neural network that is both consistent and stable and identifies the innate hierarchical structure present in vector-based data. We demonstrate improved stability of the GCS foundation and evaluate our algorithm against the hierarchy generated by an ascendant hierarchical clustering dendogram. Our approach emulates the hierarchical clustering of the dendogram. It demonstrates the importance of the parameter settings for GCS and how they affect the stability of the clustering

Graphene-Based Nanostructures in Electrocatalytic Oxygen Reduction

Application of graphene-type materials in electrocatalysis is a topic of growing scientific and technological interest. A tremendous amount of research has been carried out in the field of oxygen electroreduction, particularly with respect to potential applications in the fuel cell research also with use of graphene-type catalytic components. This work addresses fundamental aspects and potential applications of graphene structures in the oxygen reduction electrocatalysis. Special attention will be paid to creation of catalytically active sites by using non-metallic heteroatoms as dopants, formation of hierarchical nanostructured electrocatalysts, their long-term stability, and application as supports for dispersed metals (activating interactions)

Hierarchical growing neural gas

“The original publication is available at www.springerlink.com”. Copyright Springer.This paper describes TreeGNG, a top-down unsupervised learning method that produces hierarchical classification schemes. TreeGNG is an extension to the Growing Neural Gas algorithm that maintains a time history of the learned topological mapping. TreeGNG is able to correct poor decisions made during the early phases of the construction of the tree, and provides the novel ability to influence the general shape and form of the learned hierarchy

Real time imaging of two-dimensional iron oxide spherulite nanostructure formation

The formation of complex hierarchical nanostructures has attracted a lot of attention from both the fundamental science and potential applications point of view. Spherulite structures with radial fibrillar branches have been found in various solids; however, their growth mechanisms remain poorly understood. Here, we report real time imaging of the formation of two-dimensional (2D) iron oxide spherulite nanostructures in a liquid cell using transmission electron microscopy (TEM). By tracking the growth trajectories, we show the characteristics of the reaction front and growth kinetics. Our observations reveal that the tip of a growing branch splits as the width exceeds certain sizes (5.5–8.5 nm). The radius of a spherulite nanostructure increases linearly with time at the early stage, transitioning to nonlinear growth at the later stage. Furthermore, a thin layer of solid is accumulated at the tip and nanoparticles from secondary nucleation also appear at the growing front which later develop into fibrillar branches. The spherulite nanostructure is polycrystalline with the co-existence of ferrihydrite and Fe3O4 through-out the growth. A growth model is further established, which provides rational explanations on the linear growth at the early stage and the nonlinearity at the later stage of growth. [Figure not available: see fulltext.]

Growth-Driven Percolations: The Dynamics of Community Formation in Neuronal Systems

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the simulation of neuronal development and the formation of neuronal communities. Starting from images of real neurons, geometrical measurements are obtained and used to construct probabilistic models which can be subsequently sampled in order to produce morphologically realistic neuronal cells. Such cells are progressively grown while monitoring their connections along time, which are analysed in terms of percolation concepts. However, unlike traditional percolation, the critical point is verified along the growth stages, not the density of cells, which remains constant throughout the neuronal growth dynamics. It is shown, through simulations, that growing beta cells tend to reach percolation sooner than the alpha counterparts with the same diameter. Also, the percolation becomes more abrupt for higher densities of cells, being markedly sharper for the beta cells.Comment: 8 pages, 10 figure

A model for hierarchical patterns under mechanical stresses

We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.Comment: To appear in Philosophical Magazine. 18 pages, 8 figure

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time