Genetic algorithms for determining the topological structure of metallic clusters

Quantum Molecular Dynamics Studies of the Structure and Dynamics of Metal Clusters

A linear network is a type of wireless sensor network in which sparse nodes are deployed along a virtual line; for example, on streetlights or columns of a bridge, tunnel, and pipelines. The typical deployment of Linear Wireless Sensor Net-work (LWSN) creates an energy hole around the sink node since nodes near the sink nodes deplete their energy faster than others. Optimal network topology is one of the key factors that can help improve LWSN performance and lifetime. Finding optimal topology becomes tough in large network where total possible combinations is very high. We propose an Optimal Topology Generation (OpToGen) framework based on genetic algorithm for LWSN. Network deployment tools can use OpToGen to configure and deploy LWSNs. Through a discrete event simulator, we demonstrate that the use of genetic algorithm accomplishes fast convergence to optimal topologies as well as less computational overhead as compared to brute force search for optimal topology. We have evaluated OpToGen on the number of generations it took to achieve the best topology for various sized LWSNs. The trade-off between energy consumption and different network sizes is also reported.

The dependence of the properties of small copper clusters on their size, and their relationships to the properties of the bulk metal have been studied through ab initio SCF calculations (with the emphasis on the clusters Cu8 and Cu13). The basis set used is of double-zeta quality for the valence shells 3d and 4s. The analysis focuses on the following properties of the clusters: geometrical structure, binding energy, and distribution of energy levels. For the 13-atom cluster, the icosahedron is found more stable than the cubo-octahedron corresponding to the fcc structure of the bulk metal. The binding energy per atom increases almost linearly with the number of atoms of the cluster. From the orbital energy values, the sets of 3d and 4s levels are well separated for Cu8 and just begin to overlap for Cu13. This situation looks rather different from the one for the bulk metal where the s band totally overlaps the d band. The relationship between the orbital energies from the ab initio SCF calculations and the ionization potentials is discussed. For the 13-atom cluster, the relaxation effect is probably small enough that the above conclusions, based on Koopmans’ theorem and the use of orbital energies, should not be altered by including it. On the whole, the ab initio results contradict the conclusion of the SCF–Xα–SW calculations that the electronic structure of small metal clusters and of the bulk metal are not fundamentally different and that not many atoms are needed in a cluster to have a resemblance to the bulk. This idea was based on the analysis of the orbital energy values from the Xα calculations, which showed that the ’’d band’’ was completely overlapped by the ’’s band.’’ However, this represents probably a spurious effect, since the Xα eigenvalue differs from the corresponding ionization potential by a ’’self-interaction term,’’ with rather different values for the orbitals of the 3d type and of the 4s type.

The structure and dynamics of model metal clusters containing 13–55 atoms are investigated by molecular dynamics with regular quenching along the trajectory. The atoms interact via Sutton–Chen many-body potentials suitable for describing surface and bulk properties of gold and silver. The features of the potential energy surfaces of the clusters are elucidated by structural analysis of the quenched configurations and by eigenvector-following to find connecting transition states, and these features are related to the dynamical behavior. The observation of time-scale coexistence is shown to be strongly dependent upon cluster size as well as potential parameters. The Sutton–Chen silver and gold clusters have very different structural properties, with the silver potential stabilizing the icosahedral geometry, and the gold potential favoring glasslike structures. The results are compared with the available experimental observations.

Structural topology constraints in topology optimization are an important research topic. The structural topology is characterized by the topological invariance of the number of holes. The holes of a structure in 3D space can be classified as internally enclosed holes and external through-holes (or tunnels). The genus is the number of tunnels. This article proposes the quotient set design variable method (QSDV) to implement the inequality constraint on the maximum genus allowed in an optimized structure for 3D structural topology optimization. The principle of the QSDV is to classify the changing design variables according to the connectivity of the elements in a structure to obtain the quotient set and update the corresponding elements in the quotient set to meet the topological constraint. Based on the standard relaxation algorithm discrete variable topology optimization method (DVTOCRA), the effectiveness of the QSDV is illustrated in numerical examples of a 3D cantilever beam.

During the last 20 years, structural optimization has become one of the most important topics of engineering applications. Design optimization of structure has been an interesting area of research in the field of engineering design for its ability to short the design cycle and to enhance product quality. Significant research activity has occurred in the area of structural optimization in the last decade. Especially for topology optimization of structure, many new theoretical, algorithmic, and computational contributions have resulted by researchers and engineers. Topology optimization is a powerful tool for global and multi-scale design of macrostructures, microstructures, and the cell of prescribed composite materials. The population based evolutionary algorithms have emerged as powerful mechanism for finding optimum solutions of complex optimization problems in engineering during the last two decades. Evolutionary computation is the study of computational systems which use ideas and get inspiration from natural evolution and adaptation [1]. The thinking has wide application in various engineering fields, such as computer science, artificial intelligence, operations research. Genetic algorithm is another kind of bio-inspired optimization method and it is playing an increasingly important role in studies of complex adaptive systems. Its application ranges from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices and structures, such as aircraft turbines and integrated circuits [2]. Optimization of structures can be classified into three categories: sizing, shaping, and topology optimization. In the topology optimization, it is concerned with the structure members and connectivity between members. In general, it is easily represented by discrete variables rather than by those used for continuous optimization problems. Topology optimization is the most difficult and complex among three categories and it is special useful in developing innovative conceptual designs. Structural optimization, in particular the topology optimization, has been identified as one of the most challenging tasks in structural design. Various techniques and approaches have been established during the last two decades. Topology optimization usually referred to as layout optimization or general shape optimization [3]. It lets engineers get the optimal topology of structure or new configurations during product design phase, as they are implementing the design of the size

Composite materials offer a wide range of advantages in terms of strength, weight, and versatility, making them a popular choice for structural applications. The performance of composite structures depends not only on the material constituents but also on the topology and arrangement of these components. However, designing an optimal configuration that maximizes the desired performance metrics can be a challenging task due to the large design space and complex interactions between the components. It presents a novel approach for optimizing the multi-component topology and material orientation design of composite structures using artificial intelligence (AI) techniques. The objective is to develop an automated and efficient methodology that can identify the most optimal configuration for a given set of performance requirements. The proposed methodology combines AI algorithms, such as genetic algorithms and machine learning, with advanced computational modeling techniques. The genetic algorithms are employed to explore the design space and search for the best combination of topology and material orientations. Concurrently, machine learning techniques are utilized to model the complex relationships between the design variables and performance metrics, enabling the identification of design patterns and accelerating the optimization process.
 To achieve this, a comprehensive framework is established, encompassing the generation of an initial population of candidate designs, evaluation of their performance using numerical simulations or experimental testing, application of genetic algorithms to iteratively evolve the population by selecting the fittest designs and introducing variations, and utilization of machine learning models to predict the performance of new designs and guide the optimization process. The effectiveness of the proposed methodology is demonstrated through a case study involving the design of a composite aerospace structure. The results reveal that the AI-based optimization approach significantly outperforms traditional trial-and-error methods, leading to improved performance metrics such as strength, stiffness, and weight.
 The findings have significant implications for the design and manufacturing of composite structures in various industries, including aerospace, automotive, and civil engineering. The automated optimization process enabled by AI techniques can efficiently explore the design space, identify innovative solutions, and ultimately enhance the overall performance of composite structures.

Permanent magnet synchronous motors (PMSM) are widely used in various fields of application of electric drives of industrial enterprises. For each application of the electric drive, it is necessary to accept technical requirements, such as the maximum torque of the electric motor and the fulfillment of the required conditions for the strength characteristics of the rotor and stator.PMSM has a number of advantages over other types of engines. Asynchronous motors have developed resource rational energy efficiency, while synchronous motors are more energy efficient without modifications. PMSM have smaller weight and size parameters, which allows them to be used in a wider field of application, for example, in household appliances, robots and many other drives.TARGET. The aim is to develop a methodology for topological complex optimization of the engine design, based on a genetic algorithm.METHODS. The genetic algorithm is more accurate than traditional analytical methods, the method used in the analysis of AC machines, takes less time than the usual trial and error design procedure based on the finite element method. The main optimization criterion is an increase in torque while maintaining the mass of the most expensive material (permanent magnets). This feature is important for the manufacture of a designed engine in production.RESULTS. A program has been written in Python, which made it possible to carry out a comprehensive topological optimization for the engine under consideration.CONCLUSION. Topological optimization based on the method of modifying the rotor design using a genetic algorithm with the additions necessary for correct operation with synchronous motors is presented.

Atomically precise metal clusters have demonstrated significant advantages in homogeneous catalysis, heterogeneous catalysis, electronic catalysis, and photocatalysis. As much, electrocatalytic reduction of nitrate pollution into valuable compounds is a low‐energy consumption and environmentally friendly route, which combines environmental and economic advantages by efficiently eliminating pollutant and recycling waste. This review systematically summarizes the current researches on atomically precise metal clusters in the electroreduction of nitrate to produce high‐valued chemicals such as ammonia, urea, cyclohexanone oxime, and amino acids. The emphasis on the complexed reaction pathways and key intermediates involved in the conversion of nitrate into different target products is studied. The relationship between the structure of metal clusters and catalytic properties is delved into. This review aims to provide valuable insights for the design of high‐performance metal cluster catalysts to achieve efficient conversion from nitrate to high‐value‐added chemicals.

Stability and structure of metal clusters: Be13 and Be55

Thermodynamical size effect and the structure of metallic clusters

Smoothing topology optimization results using pre-built lookup tables

Topology optimization with closed B-splines and Boolean operations

According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.

During the tenure of the DOE grant DE-FG05-87EI145316 we have concentrated on equilibrium geometries, stability, and the electronic structure of transition metal-carbon clusters (met-cars), clusters designed to mimic the chemistry of atoms, and reactivity of homo-nuclear metal clusters and ions with various reactant molecules. It is difficult to describe all the research the authors have accomplished as they have published 38 papers. In this report, they outline briefly the salient features of their work on the following topics: (1) Designer Clusters: Building Blocks for a New Class of Solids; (2) Atomic Structure, Stability, and Electronic Properties of Metallo-Carbohedrenes; (3) Reactivity of Metal Clusters with H{sub 2} and NO; and (4) Anomalous Spectroscopy of Li{sub 4} Clusters.