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This study aims to propose and evaluate a searching scheme for a bichromatic reverse k-nearest neighbor (BRkNN) that has objects and queries in spatial networks. In this proposed scheme, the author’s search for the BRkNN of the query using an influence zone for each object with a network Voronoi diagram (NVD).

The author’s analyze and evaluate the performance of the proposed searching scheme.

The contribution of this paper is that it confirmed that the proposed searching scheme gives shorter processing time than the conventional linear search.

A future direction of this study will involve making a searching scheme that reduces the processing time when objects move automatically on spatial networks.

In BRkNN, consider two groups in a convenience store, where several convenience stores, which are constructed in Groups A and B, operate in a given region. The author’s can use RNN is RkNN when k = 1 (RNN) effectively to set a new store considering the Euclidean and road distances among stores and the location relationship between Groups A and B.

In the proposed searching scheme, the author’s search for the BRkNN of the query for each object with an NVD using the influence zone, which is the region where an object in the spatial network recognizes the nearest neighbor for the query.

The purpose of this paper is to fill a gap between experimental and abstract‐theoretic models of reaction‐diffusion computing. Chemical reaction‐diffusion computers are amongst leading experimental prototypes in the field of unconventional and nature‐inspired computing. In the reaction‐diffusion computers, the data are represented by concentration profiles of reagents, information is transferred by propagating diffusive and phase waves, computation is implemented in interaction of the traveling patterns, and results of the computation are recorded as a final concentration profile.

The paper analyzes a possibility of co‐algebraic representation of the computation in reaction‐diffusion systems using reaction‐diffusion cellular‐automata models.

Using notions of space‐time trajectories of local domains of a reaction‐diffusion medium the logic of trajectories is built, where well‐formed formulas and their truth‐values are defined by co‐induction. These formulas are non‐well‐founded set‐theoretic objects. It is demonstrated that the logic of trajectories is a co‐algebra.

The paper uses the logic defined to establish a semantical model of the computation in reaction‐diffusion media.

The work presents the first ever attempt toward mathematical formalization of reaction‐diffusion processes and is built building up semantics of reaction‐diffusion computing. It is envisaged that the formalism produced will be used in developing programming techniques of reaction‐diffusion chemical media.

This research aims to provide optimization and route safety planning employing the fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) technique.

This research combines the use of graphical, communication tools and simulated models based on building information modeling (BIM) technology and agent-based modeling (ABM) to identify a safe evacuation route. Adopting the multi-criteria decision-making (MCDM) approach, the proposed rescue plan can reduce potential hazards along the evacuation route by selecting a safe route for evacuating residents and entering firefighters to the scene of the incident.

The results show that the use of simulated models along with MCDM methods in the selection of safe routes improves the performance of safe evacuation operations for both relief groups and residents.

The introduced model can improve the performance management of different groups at the time of the incident and reduce casualties and property losses using the information received from sensors at the scene. Moreover, the proposed rescue plan prevents group and individual reactivation at the time of the incident.

Despite many advances in the architecture, engineering and construction (AEC) industry, the number of victims of fire incidents in buildings is increasing compared to other natural disasters. Improving decision management based on effective parameters at the time of incident reduces casualties of residents and rescue workers.

Additive manufacturing (AM), a rapidly evolving paradigm, has shown significant advantages over traditional subtractive processing routines by allowing for the custom creation of structural components with enhanced performance. Numerous studies have shown that the technical qualities of AM components are profoundly affected by the discovery of novel metastable substructures in diverse alloys. Therefore, the purpose of this study is to determine the effect of cell structure parameters on its mechanical response.

Initially, a methodology was suggested for testing porous materials, focusing on static tensile testing. For a qualitative evaluation of the cellular structures produced, computed tomography (CT) was used. Then, the CT scanner was used to analyze a sample and determine its actual relative density, as well as perform a detailed geometric analysis.

The experimental research demonstrates that the mechanical properties of a cell’s structure are significantly influenced by its shape during formation. It was also determined that using selective laser melting to produce cell structures with a minimum single-cell size of approximately 2 mm would be the most appropriate method.

Further studies of cellular structures for testing their static tensile strength are planned for the future. The study will be carried out for a larger number of samples, taking into account a wider range of cellular structure parameters. An important step will also be the verification of the results of the static tensile test using numerical analysis for the model obtained by CT scanning.

The fabrication of metallic parts with different cellular structures is very important with a selective laser melted machine. However, the determination of cell size and structure with mechanical properties is quiet novel in this current investigation.

A simplified approach for estimating weld lines, vent locations and fill times for resin transfer molding applications in non‐planar geometry is presented. The molding parts are treated as polyhedral spaces for which the concept of Voronoi diagram and shortest paths is utilized to predict the formation of weld lines, location of vents and filling times. The approach is based purely on geometrical considerations and on previously established observations that it is possible to treat the resin flow inside the mold as partly radial and partly channel‐like. The proposed procedure is geared towards software implementation, but it enables one to gain more insight into the process before detailed and time‐consuming calculations are attempted.

The total capacity of ambulances in metropolitan cities is often less than the post-disaster demand, especially in the case of disasters such as earthquakes. However, because earthquakes are a rare occurrence in these cities, it is unreasonable to maintain the ambulance capacity at a higher level than usual. Therefore, the effective use of ambulances is critical in saving human lives during such disasters. Thus, this paper aims to provide a method for determining how to transport the maximum number of disaster victims to hospitals on time.

The transportation-related disaster management problem is complex and dynamic. The practical solution needs decomposition and a fast algorithm for determining the next mission of a vehicle. The suggested method is a synthesis of mathematical modeling, scheduling theory, heuristic methods and the Voronoi diagram of geometry. This study presents new elements for the treatment, including new mathematical theorems and algorithms. In the proposed method, each hospital is responsible for a region determined by the Voronoi diagram. The region may change if a hospital becomes full. The ambulance vehicles work for hospitals. For every patient, there is an estimated deadline by which the person must reach the hospital to survive. The second part of the concept is the way of scheduling the vehicles. The objective is to transport the maximum number of patients on time. In terms of scheduling theory, this is a problem whose objective function is to minimize the sum of the unit penalties.

The Voronoi diagram can be effectively used for decomposing the complex problem. The mathematical model of transportation to one hospital is the P‖ΣU_j problem of scheduling theory. This study provides a new mathematical theorem to describe the structure of an algorithm that provides the optimal solution. This study introduces the notion of the partial oracle. This algorithmic tool helps to elaborate heuristic methods, which provide approximations to the precise method. The realization of the partial oracle with constructive elements and elements proves the nonexistence of any solution. This paper contains case studies of three hospitals in Tehran. The results are close to the best possible results that can be achieved. However, obtaining the optimal solution requires a long CPU time, even in the nondynamic case, because the problem P‖ΣU_j is NP-complete.

This research suggests good approximation because of the complexity of the problem. Researchers are encouraged to test the proposed propositions further. In addition, the problem in the dynamic environment needs more attention.

If a large-scale earthquake can be expected in a city, the city authorities should have a central control system of ambulances. This study presents a simple and efficient method for the post-disaster transport problem and decision-making. The security of the city can be improved by purchasing ambulances and using the proposed method to boost the effectiveness of post-disaster relief.

The population will be safer and more secure if the recommended measures are realized. The measures are important for any city situated in a region where the outbreak of a major earthquake is possible at any moment.

This paper fulfills an identified need to study the operations related to the transport of seriously injured people using emergency vehicles in the post-disaster period in an efficient way.

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 typical approach of modeling the aerodynamics of an aircraft is to develop a complete database through testing or computational fluid dynamics (CFD). The database will be huge if it has a reasonable resolution and requires an unacceptable CFD effort during the conceptional design. Therefore, this paper aims to reduce the computing effort required via establishing a general aerodynamic model that needs minor parameters.

The model structure was a preconfigured polynomial model, and the parameters were estimated with a recursive method to further reduce the calculation effort. To uniformly disperse the sample points through each step, a unique recursive sampling method based on a Voronoi diagram was presented. In addition, a multivariate orthogonal function approach was used.

A case study of a flying wing aircraft demonstrated that generating a model with acceptable precision (0.01 absolute error or 5% relative error) costs only 1/54 of the cost of creating a database. A series of six degrees of freedom flight simulations shows that the model’s prediction was accurate.

This method proposed a new way to simplify the model and recursive sampling. It is a low-cost way of obtaining high-fidelity models during primary design, allowing for more precise flight dynamics analysis.

1) The OE-MLPG penalty meshfree method is developed to solve cracked structure.(2) Smartening the numerical meshfree method by combining the particle swarm optimization (PSO) optimization algorithms and Voronoi computational geometric algorithm. (3). Selection of base functions, finding optimal penalty factor and distribution of appropriate nodal points to the accuracy of calculation in the meshless local Petrov–Galekrin (MLPG) meshless method.

Using appropriate shape functions and distribution of nodal points in local domains and sub-domains and choosing an approximation or interpolation method has an effective role in the application of meshless methods for the analysis of computational fracture mechanics problems, especially problems with geometric discontinuity and cracks. In this research, computational geometry technique, based on the Voronoi diagram (VD) and Delaunay triangulation and PSO algorithm, are used to distribute nodal points in the sub-domain of analysis (crack line and around it on the crack plane).

By doing this process, the problems caused by too closeness of nodal points in computationally sensitive areas that exist in general methods of nodal point distribution are also solved. Comparing the effect of the number of sentences of basic functions and their order in the definition of shape functions, performing the mono-objective PSO algorithm to find the penalty factor, the coefficient, convergence, arrangement of nodal points during the three stages of VD implementation and the accuracy of the answers found indicates, the efficiency of V-E-MLPG method with Ns = 7 and ß = 0.0037–0.0075 to estimation of 3D-stress intensity factors (3D-SIFs) in computational fracture mechanics.

The present manuscript is a continuation of the studies (Ref. [33]) carried out by the authors, about; feasibility assessment, improvement and solution of challenges, introduction of more capacities and capabilities of the numerical MLPG method have been used. In order to validate the modeling and accuracy of calculations, the results have been compared with the findings of reference article [34] and [35].

We describe a new mathematical approach for deriving and solving covolume models of the three‐dimensional, incompressible Navier—Stokes flow equations. The approach integrates three technical components into a single modelling algorothm: automatic grid generation; covolume equation generation; dual variable reduction.