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The purpose of this paper is to experimentally validate the crack growth control based on the topological derivative of the famous Rice's integral.

Single edge notch tensile specimens with two configurations were tested. Displacement fields near notch were experimentally obtained using the digital image correlation method. These displacements were used to verify the minimization of the associated shape functional, which is defined in terms of the Rice's integral, when a set of controls (holes) positioned according to the topological derivative information, is inserted. Based on the Griffth's energy criterion, this minimization represents an improvement in the fracture toughness of cracked bodies.

The experimental tests confirmed that a decrease around 27% in the value of the associated shape functional can be obtained following this approach. Therefore, the results allow us to conclude that the predictive methodology for crack growth control based on the topological derivative is feasible.

This is the first work concerning experimental validation of crack growth control based on the topological derivative method.

The purpose of this paper is to study some evolving mechanisms for producing weighted networks, as well as to analyze the statistical properties of the networks.

A simple one‐parameter evolution model of weighted networks is proposed, in which the topological growth combines with the variation of weights. Based on weight‐driven dynamics, the model can generate scale‐free distributions of the degree, node strength and edge weight, as confirmed in many real networks.

The exponent of the edge weight can be widely tuned. The unique parameter p controls the edge weight dynamical growth. The authors also obtain the non‐trivial weighted clustering coefficient and the weighted average to the nearest neighbors' degree.

Accessibility and availability of data are the main limitations which apply to the figures.

The new evolving networks method may be beneficial for understanding real networks.

The paper proposes a new approach of explaining the evolving mechanisms of the real networks.

Accurate presentation of the rock microstructure is critical to the grain-scale analysis of rock deformation and failure in numerical modelling. 3D granite microstructure modelling has only been used in limited studies with the mineral pattern often remaining poorly constructed. In this study, the authors developed a new approach for generating 2D and 3D granite microstructure models from a 2D image by combining a heterogeneous material reconstruction method (simulated annealing method) with Voronoi tessellation.

More specifically, the stochastic information in the 2D image is first extracted using the two-point correlation function (TPCF). Then an initial 2D or 3D Voronoi diagram with a random distribution of the minerals is generated and optimised using a simulated annealing method until the corresponding TPCF is consistent with that in the 2D image. The generated microstructure model accurately inherits the stochastic information (e.g. volume fraction and mineral pattern) from the 2D image. Lastly, the authors compared the topological characteristics and mechanical properties of the 2D and 3D reconstructed microstructure models with the model obtained by direct mapping from the 2D image of a real rock sample.

The good agreements between the mapped and reconstructed models indicate the accuracy of the reconstructed microstructure models on topological characteristics and mechanical properties.

The newly developed reconstruction method successfully transfers the mineral pattern from a granite sample into the 2D and 3D Voronoi-based microstructure models ready for use in grain-scale modelling.

The purpose of this paper is to present a new immunization strategy for effectively solving the control of the spread of the virus.

Inspired by the idea of network partition, taking two optimization targets which are the scale of sub-network and the sum of the strengths of the sub-network's nodes into account at the same time, a new immunization strategy based on greedy algorithm in the scale-free network is presented. After specifying the number of nodes through the immunization, the network is divided into the scale of sub-network and the sum of the strength of the sub-network's nodes as small as possible.

The experimental results show that the proposed algorithm has the better performance than targeted immunization which is supposed to be highly efficient at present.

This paper proposes a new immunization strategy based on greedy algorithm in the scale-free network for effectively solving the control of the spread of the virus.

A robotic wheelchair system was designed to assist disabled people with disabilities to walk.

An anticipated sharing control strategy based on topological map is proposed in this paper, which is used to assist robotic wheelchairs to realize interactive navigation. Then, a robotic wheelchair navigation control system based on the brain-computer interface and topological map was designed and implemented.

In the field of robotic wheelchairs, the problems of poor use, narrow application range and low humanization are still not improved.

In the system, the topological map construction is not restricted by the environment structure, which helps to expand the scope of application; the shared control system can predict the users’ intention and replace the users’ decision to realize human-machine interactive navigation, which has higher security, robustness and comfort.

This paper is devoted to the theoretical and numerical study of a new topological sensitivity concerning the insertion of a small bolt connecting two parts in a mechanical structure. First, an idealized model of bolt is proposed which relies on a non-local interaction between the two ends of the bolt (head and threads) and possibly featuring a pre-stressed state. Second, a formula for the topological sensitivity of such an idealized bolt is rigorously derived for a large class of objective functions. Third, numerical tests are performed in 2D and 3D to assess the efficiency of the bolt topological sensitivity in the case of no pre-stress. In particular, the placement of bolts (acting then as springs) is coupled to the further optimization of their location and to the shape and topology of the structure for volume minimization under compliance constraint.

The methodology relies on the adjoint method and the variational formulation of the linearized elasticity equations in order to establish the topological sensitivity.

The numerical results prove the influence of the number and locations of the bolts which strongly influence the final optimized design of the structure.

This paper is the first one to study the topology optimization of bolted systems without a fixed prescribed number of bolts.

Our paper studies a central issue with a long history in economics: the relationship between population and economic growth. We analyze the joint dynamics of economic and demographic growth in 111 countries during the period 1960–2019.

Using the concept of economic regime, the paper introduces the notion of distance between the dynamical paths of different countries. Then, a minimal spanning tree (MST) and a hierarchical tree (HT) are constructed to detect groups of countries sharing similar dynamic performance.

The methodology confirms the existence of three country clubs, each of which exhibits a different dynamic behavior pattern. The analysis also shows that the clusters clearly differ with respect to the evolution of other fundamental variables not previously considered [gross domestic product (GDP) per capita, human capital and life expectancy, among others].

Our results indirectly suggest the existence of dynamic interdependence in the trajectories of economic growth and population change between countries. It also provides evidence against single-model approaches to explain the interdependence between demographic change and economic growth.

We introduce a methodology that allows for a model-free topological and hierarchical description of the interplay between economic growth and population.

Considers a systems model of changes in industrial structure, employment and income levels. A country subsidizes imported resources to augment its existing resource base and to develop an export promotion strategy. This is leveraged with borrowed money. According to neo‐classical economic theory, factors of production are paid in proportion to their output contribution. Economic growth occurs when the return from a higher rate of factor utilization exceeds the cost of subsidization. In the study of ordinary differential equations, simultaneous changes in variables can be treated as part of a dynamic system subject to constraints. At any moment resources are fixed, and we may assume D'Alembert's principle of virtual work with respect to the internal constraints of the system. Subsidized economic growth shares a paradigm with analytical dynamics, the stability of motion around the neighbourhood of a singular point. The classical analytical‐topological methods which describe asymptotic stability are used to investigate economic policy.

In this paper, the organism model for knowledge‐based enterprise is proposed. A dynamic capacity grey set is defined and analyzed based on the definition of the growth and development for knowledge‐based enterprise organism. The structure of the capacity whiten core, a subset of the capacity grey set, is optimized for different periods of the organism's life cycle. The organism grey topological structure model of knowledge‐based enterprise is described to possess the essential capacity grey set.

WeChat is the largest acquaintance social networking platform in China, in which users can view and reshare web pages shared by friends. This paper aims to analyze the spatio-temporal dynamics of web pages diffused in WeChat and advice on commercials.

A large number of web pages diffused in WeChat are collected and exclusively divided into four categories according to their titles, including advertisements, news bulletins, holiday greetings and emotional essays. For each web page, an information cascade (tree structure) is constructed to describe the diffusion trace. Based on the categories, the spatio-temporal popularity is characterized; the topological, temporal and spatial properties are examined; and the spatio-temporal diffusion velocity is explored.

Through comparative analysis, different categories of pages show diversity. For spatio-temporal popularity, there is no significant difference in cascade size; holiday greetings usually last for a relatively short time on average; emotional essays are more likely to spread to more provinces. For topological, temporal and spatial characteristics, the diffusion process of advertisements is more likely to be broadcasting than other categories; news bulletins and holiday greetings have an obvious bursty; the number of viewing behavior decreases from east to west in general. For spatio-temporal diffusion velocity, emotional essays diffuse the fastest in topological and spatio-temporal dimensions.

These findings contribute to promoting products and providing support for data driven modeling of information diffusion and human activity in spatio-temporal dimensions.