In this study, we investigate and fabricate two-dimensional ordered lattice structure by breath figures method. The breath figures pattern was prepared with the solution of carbon disulfide (CS2) doped with 1% weight concentration of polystyrene. The temperature and the humidity were controlled at ~23¢J and ~60 %, respectively. The breath figures pattern began to expand while CS2 is under evaporation. We explored the relationship between self-assemble of the water droplet and ordered structure via the solution height, the temperature evolution, and the dynamical optical images in the formation process of breath figures pattern. It was found that the radius of the water droplets varying with time follows the power law, £l ~ t £go; £g0=0.76. The fast Fourier transformation and Voronoi Diagram were used to conform that the formation of the breath figures pattern varied form a disordered state to an ordered state with the evaporation of CS2. The understanding of the breath figures pattern provides us to fabricate the photonics with size from nano- to micro-scale and to improve the application of nano device.

В работе описаны процессы пластической деформации для наиболее распространённых металлов с ГПУ кристаллической решеткой, к числу которых относится титан, магний, цирконий. Рассматривается характеристика ГПУ металлов с точки зрения особенностей кристаллического строения и действующих механизмов пластической деформации, описана область применения. Описано поведение металлов с ГПУ решеткой при пластической деформации и при повышенных температурах, что накладывает требования к технологии производства изделий из данных металлов. Представлены основные условия текучести, применяемые для ортотропных металлов, отражающие различное поведение материала в разных направлениях. Методом конечных элементов выполнены расчеты и представлено сравнение параметров плоской прокатки циркониевого сплава Э125 при применении изотропного и ортотропного условий текучести. / The paper describes the processes of plastic deformation for the most common metals with an HCP crystal lattice, which include titanium, magnesium, and zirconium. The characteristics of HCP metals are considered from the point of view of the features of the crystal structure and the operating mechanisms of plastic deformation, and the scope is described. The behavior of metals with an HCP lattice under plastic deformation and at elevated temperatures is described, which imposes requirements on the technology for the production of products from these metals. The basic flow conditions used for orthotropic metals are presented, reflecting the different behavior of the material in different directions. The finite element method is used to perform calculations and compare the parameters of flat rolling of the E125 zirconium alloy using isotropic and orthotropic yield conditions.

While current approaches to digital image processing within the context of machine learning and deep learning are motivated by biological processes within the human brain, they are, however, also limited due to the current state of the art of input and output devices as well as the algorithms that are concerned with the processing of their data. In order to generate digital images from real-world scenes, the utilized digital images' underlying lattice formats are predominantly based on rectangular or square structures. Yet, the human visual perception system suggests an alternative approach that manifests itself within the sensory cells of the human eye in the form of hexagonal arrangements. As previous research demonstrates that hexagonal arrangements can provide different benefits to image processing systems in general, this contribution is concerned with the synthesis of both worlds in the form of the biologically inspired hexagonal deep learning for hexagonal image processing. This contribution is therefore concerned with the design, the implementation, and the evaluation of hexagonal solutions to currently developed approaches in the form of hexagonal deep neural networks. For this purpose, the respectively realized hexagonal functionality had to be built from the ground up as hexagonal counterparts to otherwise conventional square lattice format based image processing and deep learning based systems. Furthermore, hexagonal equivalents for artificial neural network based operations, layers, as well as models and architectures had to be realized. This also encompasses the related evaluation metrics for hexagonal lattice format based representations of digital images and their conventional counterparts in comparison. Therefore, the developed hexagonal image processing and deep learning framework Hexnet functions as a first general application-oriented open science framework for hexagonal image processing within the context of machine learning. To enable the evaluation of hexagonal approaches, a set of different application areas and use cases within conventional and hexagonal image processing – astronomical, medical, and industrial image processing – are provided that allow an assessment of hexagonal deep neural networks in terms of their classification capabilities as well as their general performance. The obtained and presented results demonstrate the possible benefits of hexagonal deep neural networks and their hexagonal representations for image processing systems. It is shown that hexagonal deep neural networks can result in increased classification capabilities given different basic geometric shapes and contours, which in turn partially translate into their real-world applications. This is indicated by a relative improvement in F1-score for the proposed hexagonal and square models, ranging from 1.00 (industrial image processing) to 1.03 (geometric primitives) with single classes even reaching a relative improvement of over 1.05. However, possible disadvantages are also given by the increased complexity of hexagonal algorithms. This is evident by the present potential in regard to runtime optimizations that have yet to be realized for certain hexagonal operations in comparison to their currently deployed square equivalents.:1 Introduction and Motivation 2 Fundamentals and Methods 3 Implementation 4 Test Results, Evaluation, and Discussion 5 Conclusion and Outlook

Wir untersuchen globale dynamische Phänomene, die sich von dem Zusammenspiel zwischen Netzwerktopologie und Dynamik der einzelnen Elementen ergeben. Im ersten Teil untersuchen wir relativ kleine strukturierte Netzwerke mit überschaubarer Komplexität. Als geeigneter theoretischer Rahmen für erregbare Systeme verwenden wir das Kuramoto und Shinomoto Modell der sinusförmig-gekoppelten "aktiven Rotatoren" und studieren das Kollektivverhalten des Systems in Bezug auf Synchronisation. Wir besprechen die Einschränkungen, die durch die Netzwerktopologie auf dem Fluss im Phasenraum des Systems gestellt werden. Insbesondere interessieren wir uns für die Stabilitätseigenschaften von Fluss-invarianten Polydiagonalen und die Entwicklungen von Attraktoren in den Parameterräume solcher Systeme. Wir untersuchen zweidimensionale hexagonale Gitter mit periodischen Randbedingungen. Wir untersuchen allgemeine Bedingungen auf der Adjazenzmatrix von Netzwerken, die die Watanabe-Strogatz Reduktion ermöglichen, und diskutieren verschiedene Beispiele. Schließlich präsentieren wir eine generische Analyse der Bifurkationen, die auf der Untermannigfaltigkeit des Watanabe-Strogatz reduzierten Systems stattfinden. Im zweiten Teil der Arbeit untersuchen wir das globale dynamische Phänomen selbstanhaltender Aktivität (self-sustained activity / SSA) in neuronalen Netzwerken. Wir betrachten Netzwerke mit hierarchischer und modularer Topologie , umfassend Neuronen von verschiedenen kortikalen elektrophysiologischen Zellklassen. Wir zeigen, dass SSA Zustände mit ähnlich zu den experimentell beobachteten Eigenschaften existieren. Durch Analyse der Dynamik einzelner Neuronen sowie des Phasenraums des gesamten Systems erläutern wir die Rolle der Inhibierung. Darüber hinaus zeigen wir, dass beide Netzwerkarchitektur, in Bezug auf Modularität, sowie Mischung aus verschiedenen Neuronen, in Bezug auf die unterschiedlichen Zellklassen, einen Einfluss auf die Lebensdauer der SSA haben. / In this work we study global dynamical phenomena which emerge as a result of the interplay between network topology and single-node dynamics in systems of excitable elements. We first focus on relatively small structured networks with comprehensible complexity in terms of graph-symmetries. We discuss the constraints posed by the network topology on the dynamical flow in the phase space of the system and on the admissible synchronized states. In particular, we are interested in the stability properties of flow invariant polydiagonals and in the evolutions of attractors in the parameter spaces of such systems. As a suitable theoretical framework describing excitable elements we use the Kuramoto and Shinomoto model of sinusoidally coupled “active rotators”. We investigate plane hexagonal lattices of different size with periodic boundary conditions. We study general conditions posed on the adjacency matrix of the networks, enabling the Watanabe-Strogatz reduction, and discuss different examples. Finally, we present a generic analysis of bifurcations taking place on the submanifold associated with the Watanabe-Strogatz reduced system. In the second part of the work we investigate a global dynamical phenomenon in neuronal networks known as self-sustained activity (SSA). We consider networks of hierarchical and modular topology, comprising neurons of different cortical electrophysiological cell classes. In the investigated neural networks we show that SSA states with spiking characteristics, similar to the ones observed experimentally, can exist. By analyzing the dynamics of single neurons, as well as the phase space of the whole system, we explain the importance of inhibition for sustaining the global oscillatory activity of the network. Furthermore, we show that both network architecture, in terms of modularity level, as well as mixture of excitatory-inhibitory neurons, in terms of different cell classes, have influence on the lifetime of SSA.