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The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis R e f f (m) = 9 and effective reproduction numbers of pneumonia R e f f (p) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is m a x R e f f m , R e f f (p) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are α 1 , α 2 and π . Biologically, decrease in α 1 and increasing in π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical behavior of a mathematical model of cancer including tumor cells, immune cells, and normal cells is investigated when a delay term is induced. Though the model was originally proposed by De Pillis et al. (Math. Comput. Model. 37:1221–1244, 2003), to make the model more realistic, we have added a delay term into the model, and it has incorporated novelty in our present work. The stability of existing equilibrium points in the delay-induced system is studied in detail. Global stability conditions of the tumor-free equilibrium point have been found. It is shown that due to this delay effect, the coexisting equilibrium point may lose its stability through a Hopf bifurcation. The implicit function theorem is applied to characterize a complex function in a neighborhood of delay terms. Additionally, the presence of Hopf bifurcation is demonstrated when the transversality conditions are satisfied. The length of delay for which the solutions preserve the stability of the limit cycle is estimated. Finally, through a series of numerical simulations, the theoretical results are formally examined. [ABSTRACT FROM AUTHOR]

In this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We find that the fractional-order brushless DC motor system exhibits the character of chaos. For the proposed system, we show the largest exponent to be 0.711625. We calculate the equilibrium points of the model and discuss their local stability. We apply an iterative scheme by using the Laplace transform to find a special solution in this case. By taking into account the rule of trapezoidal product integration we develop two iterative methods to find an approximate solution of the system. We also study the existence and uniqueness of solutions. We take into account the numerical solutions for Caputo Liouville product integration and Atangana–Baleanu Caputo product integration. This scheme has an implicit structure. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results. [ABSTRACT FROM AUTHOR]

The article describes the simulation results of an unbalanced rotary machine with an automatic ball balancer with a deep chamber (ABB-DC) based on a mathematical model of such a system. The ABB chamber has a cylindrical shape and is filled with balls that can move freely in general motion. The model takes into account mutual collisions between the balls, as well as between the balls and the chamber. The model also includes friction forces and rolling resistance. The comparison of simulation results performed with two different construction types of the chamber, classic single-layer drum (ABB-SC) and ABB-DC, confirmed the better efficiency of the ABB-DC in the optimal range of the number of balls. The machine body movement was limited to planar motion. The correctness of such a limitation has been verified by analyzing waveforms of reaction forces of constraints and their moments. Waveforms were divided into transient and steady states. The results of the analysis indicate the additional constraints do not significantly affect machine body movements. However, this might affect the ball arranging process in the ABB chamber. The paper also presents details of performing numerical simulations based on the developed mathematical model and numerical tests to determine the optimal integration time-step. [ABSTRACT FROM AUTHOR]

The current paper attempts to develop a mathematical model to predict springback of thick sandwich panel made of steel/polyurethane (PUR)/steel in air bending process. Firstly, the behavior laws of sandwich panel components were experimentally obtained. Secondly, numerical simulations of the sandwich panel were conducted in bending process followed by springback for various process parameters. We found that the predicted springback agrees with experiment. Thirdly, three factors with three levels were considered in order to obtain a mathematical model to predict springback by using response surface method (RSM). Punch radius, die opening, and foam thickness are chosen as the main input parameters. The springback is considered as the output response. A relationship between the different factors and the response was obtained, and regression analysis has been done. The obtained results were analyzed with analysis of variance (ANOVA) in order to identify the factors' importance on the response. [ABSTRACT FROM AUTHOR]

This paper proposes a new multi-objective day-ahead market clearing (DAMC) mechanism with demand response offers, considering realistic voltage-dependent load modeling. This paper presents several objectives such as Social Welfare Maximization including demand response offers (SWM), Load reduction Minimization ( $${P}_{\mathrm{red}}{M}$$ ), and Load Served Error (LSE) minimization. Energy and demand-side reserves are cleared through co-optimization process. The proposed approach is particularly suitable for stressed system conditions, where demand elasticity alone cannot yield a feasible optimal solution. The feasible solution is obtained by invoking demand-response offers. Here, multi-objective Strength Pareto Evolutionary Algorithm 2+ (SPEA 2+) has been used to solve the proposed DAMC problem. This paper emphasizes the requirement for selecting judiciously, a combination of objectives best suitable for the DAMC. The effectiveness of proposed DAMC scheme is confirmed with the results obtained from IEEE 30 bus system. It is assumed that all the generators and loads participate in DAMC. Two different cases-one with constant load modeling and the other with the voltage-dependent load modeling-have been simulated at stressed loading conditions. When loads are modeled as the voltage dependent, then it is shown that SWM and $${P}_{\mathrm{red}}{M}$$ are not valid single or multiple objectives with this load model, due to reduction in load served. With voltage-dependent load modeling, SWM and LSE minimization are best suited objectives to be optimized simultaneously. The obtained Pareto optimal front allows system operator to make a better decision regarding compromise between the conflicting objective functions. [ABSTRACT FROM AUTHOR]

In trustworthy service discovery for Mobile Social Networking in Proximity (MSNP), conventional trust computation faces a big challenging issue—relatively high latency. To cope with it, trustworthiness determination strategies were proposed in our previous study, aiming at avoiding trust computation under certain conditions, so as to reduce the latency. These strategies are conceived based on the assumption that data of a user's past experience and current profile could be used, and they are incorporated with a set of thresholds from the analysis result of these data. The settings of these thresholds directly affect service quality and user satisfaction on the MSNP service, which in turn becomes an optimization problem. In this paper, we focus on formulating this optimization problem and demonstrating the effectiveness of our proposed solution by designing a simulation experiment. In detail, we establish mathematical models and adjust parameters. We conduct simulations on MATLAB and analyze the results obtained under several different settings. We further compare our work with related works. The results show that our proposed solution is practically feasible and effective in reducing latency under certain conditions. [ABSTRACT FROM AUTHOR]

In this paper, a numerical technique is developed to discretize variable-order fractional Heston differential equation. The proposed strategy is followed by an optimization technology, genetic algorithm, for tuning the unknown parameters in the proposed model. The performance of the model is analyzed to profit and loss 500 close index from the US stock markets. Simulations illustrate the application of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper deals with adhesive frictionless normal contact between one elastic flat solid and one stiff solid with rough surface. After computation of the equilibrium solution of the energy minimization principle and respecting the contact constraints, we aim at studying the stability of this equilibrium solution. This study of stability implies solving an eigenvalue problem with inequality constraints. To achieve this goal, we propose a proximal algorithm which enables qualifying the solution as stable or unstable and that gives the instability modes. This method has a low computational cost since no linear system inversion is required and is also suitable for parallel implementation. Illustrations are given for the Hertzian contact and for rough contact. [ABSTRACT FROM AUTHOR]

In this paper, we consider a noncooperative finite multicriteria two-person game G. We study the problem of refinement of Pareto Nash equilibria of G and we propose an approach based on modeling the preferences of the players by two binary relations. This approach follows three main steps: first, we associate to G another game G¯ defined by the two sets of strategies and two binary relations over the set of the strategy profiles, where each binary relation expresses the preferences of the corresponding player. Second, we define a Noncooperative Equilibrium NCE for the game G¯ and we prove that every NCE of G¯ is a Pareto Nash equilibrium of G. Third, we propose a procedure for finding the set of NCE of G¯ independently of how the binary relations are constructed. Moreover, we give three ways to model the preferences of the players by using scalarization and the outranking methods ELECTRE I and PROMETHEE II. All the steps of the proposed approach are completely illustrated through an accompanying example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the flow of two immiscible fluids through a porous horizontal channel. The fluid in the upper region is the micropolar fluid/the Eringen fluid, and the fluid in the lower region is the Newtonian viscous fluid. The flow is driven by a constant pressure gradient. The presence of micropolar fluids introduces additional rotational parameters. Also, the porous material considered in both regions has two different permeabilities. A direct method is used to obtain the analytical solution of the concerned problem. In the present problem, the effects of the couple stress, the micropolarity parameter, the viscosity ratio, and the permeability on the velocity profile and the microrotational velocity are discussed. It is found that all the physical parameters play an important role in controlling the translational velocity profile and the microrotational velocity. In addition, numerical values of the different flow parameters are computed. The effects of the different flow parameters on the flow rate and the wall shear stress are also discussed graphically. [ABSTRACT FROM AUTHOR]

When a tsunami occurred on a sea area, prediction of its arrival time is critical for evacuating people from the coastal area. There are many problems related to tsunami to be solved for reducing negative effects of this serious disaster. Numerical modeling of tsunami wave propagation is a computationally intensive problem which needs to accelerate its calculations by parallel processing. The method of splitting tsunami (MOST) is one of the well-known numerical solvers for tsunami modeling. We have developed a tsunami propagation code based on MOST algorithm and implemented different parallel optimizations for GPU and FPGA. In the latest study, we have the best performance of OpenCL kernel which is implemented tsunami simulation on AMD Radeon 280X GPU. This paper targets on design and evaluation on FPGA using OpenCL. The performance on FPGA design generated automatically by Altera offline compiler follows the results of GPU by several kernel modifications. [ABSTRACT FROM AUTHOR]

This study is mainly to explore gas transport process in heterogeneous media, which is to lay the foundation for oil-gas exploitation and development. Anomalous transport is observed to be ubiquitous in complex geological formations and has a paramount impact on petroleum engineering. Simultaneously, the random motion of particles usually exhibits obvious path- and history- dependent behaviors. This paper investigates the time-space fractional derivative models as a potential explanation for the time memory of long waiting time and the space non-locality of large regional-scale. A one-dimensional fractional advection-dispersion equation (FADE) based on fractional Fick’s law is firstly used to accurately describe the transport of Carbon dioxide (CO2) in complex media. The new fractional Darcy-advection-dispersion equation (FDADE) model has subsequently been proposed to make a comparison with FADE model and demonstrate its physical mechanism. Finally, the priori estimation of the parameters (fractional derivative index) in fractional derivative models and corresponding physical explanation are presented. Combined with experimental data, the numerical simulations show the fractional derivative models can well characterize the heavy-tailed and early breakthrough phenomenon of CO2 transport. [ABSTRACT FROM AUTHOR]

In this paper, the Hopf bifurcation control for a Lotka-Volterra predator-prey model with two delays is studied by using a hybrid control strategy. By analyzing the associated characteristic equation, its local stability and the existence of Hopf bifurcation with respect to both delays are established. In addition, the onset of an inherent bifurcation is delayed. Based on the normal form theory and the center manifold theorem, explicit formulas are derived to determine the direction of Hopf bifurcation and stability of the bifurcating periodic solution. Numerical simulation results confirm that the hybrid controller is efficient in controlling Hopf bifurcation. [ABSTRACT FROM AUTHOR]

A singular biological economic model which considers a prey-predator system with time delay and stage structure is proposed in this paper. The local stability at the equilibrium point and the dynamic behavior of the model are studied. Local stability analysis of the model without time delay reveals that there is a phenomenon of singularity-induced bifurcation due to the economic equilibrium. Furthermore, the phenomenon of Hopf bifurcation of the model at the boundary equilibrium point occurs as the time delay satisfies certain conditions. In order to apply variable structure control to eliminate the complex behaviors caused by singularity-induced bifurcation, the singular model is transformed into a single-input and single-output model with parameter varying within definite intervals. Then variable structure control with sliding mode based on a power reaching law is designed to stabilize the model. Numerical simulations are given to verify the effectiveness of the conclusions. [ABSTRACT FROM AUTHOR]

Huanglongbing (HLB) is one of the most common widespread vector-borne transmission diseases through psyllid, which is called a kind of cancer of plant disease. In recent years, biologists have focused on the role of cross protection strategy to control the spread of HLB. In this paper, according to transmission mechanism of HLB, a deterministic model with cross protection is formulated. A threshold value $R_{0}$ is established to measure whether or not the disease is uniformly persistent. The existence of a backward bifurcation presents a further sub-threshold condition below $R_{0}$ for the spread of the disease. We also discuss the effects of cross protection and removing infected trees in spreading the disease. Numerical simulations suggest that cross protection is a promotion control measure, and replanting trees is bad for HLB control. [ABSTRACT FROM AUTHOR]

The paper is concerned with a delayed diffusive predator-prey system where the growth of prey population is governed by Allee effect and the predator population consumes the prey according to Beddington-DeAngelis type functional response. The situation of bi-stability and the existence of two coexisting equilibria for the proposed model system are addressed. The stability of the steady state together with its dependence on the magnitude of time delay has been obtained. The conditions that guarantee the occurrence of the Hopf bifurcation in presence of delay are demonstrated. Furthermore, the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Finally, some numerical simulations have been carried out in order to validate the assumptions of the model. [ABSTRACT FROM AUTHOR]

Discrete hard fault is always tested in existing node selection methods for analog circuit diagnosis. Actually, analog component parameter changes continuously and output node voltages distribute in a continuous voltage interval. In this paper, an novel test node selection method is proposed for continuous parameter shifting (CPS) fault. Firstly, CPS faults are sampled by parameter scan simulation in a single test frequency. Collected node voltages are seen as a data set in a statistical distribution. Secondly, ambiguous faults are identified according to the independent distributions of all CPS faults. The independence of CPS fault sample is deduced by Kruskal-Wallis non-parametric testing. Then, new fault dictionaries are generated for each test node according to ambiguous interval. The proposed fault dictionary represents the mutual independence of each pair of CPS faults. Finally, as fault dictionaries are considered as connected graphs, the optimal test nodes are selected based on an improved depth first search (DFS) algorithm. The effectiveness of method is verified by testing linear and nonlinear circuits. [ABSTRACT FROM AUTHOR]

The dynamic behavior of a servomechanism must be studied as a whole without distinction between its parts, in order to assess correctly the overall performance of the system. For this reason, in many cases of practical interest, it may be useful to analyze the dynamics of a mechatronic device using a mathematical model and a computer simulation software, in order to verify the consequences arising from the modification of a particular parameter of the system. Following this methodological approach, this paper proposes a model for the dynamic analysis of a typical industrial servomechanism characterized by elasticity and backlash in the transmission. The model has been implemented into a software application and it can be used to test, from a theoretical point of view, the dynamic behavior of the device under user-defined operating conditions. The numerical simulations, which can be performed in a short time, may help the designer to optimize the dynamic performance of the servomechanism without performing experimental activities. On the basis of the simulation results, he can then evaluate, for example, whether the presence of the backlash still allows to obtain acceptable acceleration values. The software also allows to verify the effects resulting from different settings of the position regulator, and therefore, it can be helpful to assist the designer during the calibration procedures. [ABSTRACT FROM AUTHOR]

This paper characterizes the error in distance relay operation due to the existence of asynchronous frequency components when a fault in a line with series compensation occurs. The distance relay model and the impact of non-filtered frequency components using the conventional digital filters is presented, an error will appear in voltage and current fundamental frequency phasors estimation and, by consequence an error, in apparent impedance estimation. Then, the proposed distance relay algorithm using the Prony method as a filter and its application considerations are described. Next, the line series compensation effects in distance relay estimation are presented, showing the importance of the estimation of the fundamental frequency phasor. Afterward, the effect of series compensation in distance relay performance is characterized by evaluating a simulated fault event. Finally, the proposed algorithm is evaluated in reach and operation time of the simulated and real fault events using a 3D operation characteristic of the relay. [ABSTRACT FROM AUTHOR]

In this paper, a predator-prey system with Michaelis-Menten functional response on time scales is investigated. First of all, we generalize the semi-cycle concept to time scales. Second, we obtain the uniformly ultimate boundedness of solutions of this system. Our results demonstrate that when the death rate of the predator is rather small without prey, whereas the intrinsic growth rate of the prey is relatively large, the species could coexist in the long run. In particular, if $\mathbb{T}=\mathbb{R}$ or $\mathbb{T}=\mathbb{Z}$ , some well-known results have been generalized. In addition, for the continuous case, we provide a new idea to prove its permanence. Finally, a numerical simulation is given to support our main results. [ABSTRACT FROM AUTHOR]

This paper considers a noncooperative m-player best-choice game with complete information about the quality parameters of incoming candidates. Collective decision-making is based on voting. The optimal threshold strategies and payoffs of the players are found depending on the voting threshold. The results of numerical simulation are presented. [ABSTRACT FROM AUTHOR]

In this paper, we study a predator-prey-mutualist system with digestion delay. First, we calculate the threshold value of delay and prove that the positive equilibrium is locally asymptotically stable when the delay is less than the threshold value and the system undergoes a Hopf bifurcation at the positive equilibrium when the delay is equal to the threshold value. Second, by applying the normal form method and center manifold theorem, we investigate the properties of Hopf bifurcation, such as the direction and stability. Finally, some numerical simulations are carried out to verify the main theoretical conclusions. [ABSTRACT FROM AUTHOR]

The designing of twist drill flutes (as well as that of end mills and of some combined tools) cannot be separated from the way they are manufactured. The aim of this paper is to present an intuitive direct method for modelling, simulation and manufacturing of the drill flutes with different shapes using conical grinding wheels with standardized shapes. The mathematical approach is described, which enables us to determine the flute profile in a section perpendicular to its axis as well as the manufacturing parameters. The grinding wheel has an initial position with respect to the cylindrical work piece, which is described using four parameters (Denavit Hartenberg parameters). We have presented algorithms in pseudocode that produce the flute shape and that compute the optimum parameters of the wheel position in the manufacturing process. Subsequently, a software application based on the aforementioned model is able to create visualizations of the flute shape. The analysis of the flute shape has enabled us to understand the influence of the geometrical parameters and the position of the grinding wheel on the resulting product in the grinding process. The order in which these parameters are to be set is also specified. We have built atlases of maps presenting the influence of the geometrical parameters and the position of the grinding wheel in the grinding process upon the shape of the flute. The validity of the method is proven by the agreement of the computed values with the input and output data produced by experiment. The proposed method allows helical flutes to be generated solely by using cylindrical and conical grinding wheels of standard shapes. [ABSTRACT FROM AUTHOR]

Finite element simulations are being more and more applied when studying the crash-worthiness of vehicles during impact. This paper deals with setting up such a simulation and discusses several ways to simplify and verify a simulated crash. For this purpose, a notch impact-testing machine will be released from a certain angle and crash into a model constructed with three different wall thicknesses. The plastic and elastic deformation is measured in the front of the model and is then used for validation of the simulation. In the end, the simulation was found to be in good agreement with the real crash data. [ABSTRACT FROM AUTHOR]

This paper presents a numerical simulation of the flow resulting from transverse jet injection into a supersonic flow through a slot nozzle at different pressures in the injected jet and the crossflow. Calculations on grids with different resolutions use the Spalart-Allmaras turbulence model, the k- ε model, the k- ω model, and the SST model. Based on a comparison of the calculated and experimental data on the wall pressure distribution, the length of the recirculation area, and the depth of jet penetration into the supersonic flow, conclusions are made on the accuracy of the calculation results for the different turbulence models and the applicability of these models to similar problems. [ABSTRACT FROM AUTHOR]

Material constitutive model is one of the basic scientific fundamentals for simulation accuracy of high-speed cutting (HSC). A high-speed orthogonal cutting method (HS-OCM) based on the shear slip distance, aided by split Hopkinson pressure bar (SHPB) experiments, is proposed in this paper to obtain the shear slip deformation characteristics in the HSC of 6061-T6 aluminum alloy. The Johnson-Cook (JC) model was modified in three ways according to the variation tendencies of the effect curves of strain hardening, strain rate strengthening, and thermal softening, and an improved material constitutive model was obtained. The simulation validations of the obtained material constitutive models were executed. It was found that the modified JC model improves simulation accuracy, i.e., the maximum simulation errors of the cutting force and cutting temperature are 18.5 and 12.2 %, respectively. The HS-OCM avoids the cutting speed limitation (<700 m/min) of the quick-stop test usually used in conventional OCM and the difficulty of predicting tendency inflection points of the inverse identification method employing a finite element simulation model, and allows the experimental measurement of the deformation characteristics of 6061-T6 aluminum alloy in high-speed (2000 m/min) cutting. During HSC of 6061-T6 aluminum alloy, the shear stress, shear strain rate, and deformation temperature in the primary deformation zone increase with increasing cutting speed, whereas the shear strain decreases. [ABSTRACT FROM AUTHOR]

We consider a model for insect-pathogen interaction where the insect population is divided into two groups, one group susceptible to disease and other resistant to disease. An individual born susceptible to or resistant to disease depends on the local population levels at the start of each generation. Here we consider density-dependent models of transmission because we characterize diseases that spread through environmental propagules or through random contact among individuals. We consider the case where the fraction of resistant individuals increases as the total population increases. White and Wilson ( Theor. Popul. Biol. 56, 163 ()) have reported the results of density-dependent monotonic increase of resistance class by choosing a particular type of function. In this paper, we have chosen a class of monotonic density-dependent resistance functions and studied their effects on insect-pathogen dynamics. In particular, we have investigated the effects of different types of monotonic density-dependent resistance on the bistable nature of the model. Numerical simulation results are presented and interpreted. [ABSTRACT FROM AUTHOR]

In this paper, we study periodic solutions for a seasonally forced SIR model with impact of media coverage. Usually, media reports, information processing, and individuals' alerted responses to the information can only arise as the number of infected individuals reaches and exceeds a certain level. The piecewise smooth righthand side is introduced to describe the impact of this kind of media coverage. Using Leray-Schauder degree theory, we establish new results on the existence of at least one positive periodic solution for a seasonally forced SIR model with impact of media coverage. Some numerical simulations are presented to illustrate the effectiveness of such media coverage. [ABSTRACT FROM AUTHOR]

Assembly modeling and simulation are two important activities in product development. The former makes an assembly model by specifying mating constraints between parts. The latter visually simulates the process of forming an assembly model through sequencing and finding paths of parts. In practice applications, the sequence of assembling parts in assembly modeling cannot be directly utilized to facilitate path finding and sequencing in assembly simulation, and specifying mating constraints in assembly modeling and finding/sequencing paths of parts in assembly simulation are usually accomplished manually, which are tedious and error-prone. One responsible reason is that when creating part models, designers know how they will interact with each other, but this information is not stored in part models. To alleviate the problems, this paper introduced the concept of assembly feature pair (AFP) and proposed a framework method to integrate assembly modeling and simulation. An AFP consists of form feature pairs on two parts together with assembly behaviors. Correspondingly, the mating constraints between parts and the information of assembly process can be captured to facilitate assembly modeling and assembly simulation. Based on AFP, the framework method can integrate assembly modeling and simulation from three aspects: (1) AFPs will be embedded into part models at part modeling stage, storing designers' knowledge of how parts will interact with each other, (2) the laborious work of applying mating constraints between parts in assembly modeling will be replaced by instantiating the embedded AFP in part models, and the instantiation sequence of AFPs will be directly used in assembly simulation, and (3) the manual work of planning and sequencing paths of parts in assembly simulation will also be replaced by instantiating the embedded AFP in part models based on the randomized motion planning theory. To demonstrate the theoretical framework, an implementation sample was presented. [ABSTRACT FROM AUTHOR]

Accurate prediction of cutting force plays an important role in simulation and application of orthogonal turn-milling operation. However, the existing cutting force models for this operation are limited to the case with flat-end cutters, which is not enough in practice. The objective of this paper is to extend the simulation of cutting forces in orthogonal turn-milling into the case with round insert cutters. To achieve this goal, the basic kinematic relationship between the tool and the part is discussed firstly in detail. Then, the approaches to determine two vital factors, namely undeformed chip thickness and the tool-part engagement region are presented. With the real swept surface of the cutting edge replaced by the geometry envelop of the tool, the analytical formulation of the undeformed chip thickness is derived. The engagement region is determined by judging the positions of discretized cutting edge elements and the in-process workpiece surface, which is described by the mapped grids. Using the cutting coefficients calibrated through experiments, cutting forces are calculated. Validation experiments under different conditions were conducted on a turn-mill machine tool with rotating cutting force dynamometer used. The results prove that the proposed model is capable of predicting cutting forces accurately both in shape and magnitude. [ABSTRACT FROM AUTHOR]

In this paper, we identify the unknown source which depends only on spatial variable for a fractional diffusion equation using the Fourier method. Not alike the previous literature, we propose to choose the regularization parameter by an a posteriori rule, with which we can obtain error estimate of Hölder type between the exact solution and the regularized approximation. Numerical simulations show that the proposed scheme is effective and stable. [ABSTRACT FROM AUTHOR]

In this paper, three nonlinear differential-difference equations (NDDEs) from the same hierarchy are investigated using the generalised perturbation (n,N-n)-fold Darboux transformation (DT) technique. The dark multisoliton solutions in terms of determinants for three equations are obtained by means of the discrete N-fold DT. Propagation and elastic interaction structures of such soliton solutions are shown graphically. The details of their evolutions are studied through numerical simulations. Numerical results show the accuracy of our numerical scheme and the stable evolutions of such dark multisolitons without a noise. We find that the solutions of lower-order NDDEs in the same hierarchy are more robust against a small noise than their corresponding higher-order NDDEs. The discrete generalised perturbation (1,N-1)-fold DT is used to derive some discrete rational and semirational solutions of the first equation, and a few mathematical features are also discussed. Results in this paper might be helpful for understanding some physical phenomena. [ABSTRACT FROM AUTHOR]

In this paper we develop a stochastic mathematical model of cholera disease dynamics by considering direct contact transmission pathway. The model considers four compartments, namely susceptible humans, infectious humans, treated humans, and recovered humans. Firstly, we develop a deterministic mathematical model of cholera. Since the deterministic model does not consider the randomness process or environmental factors, we converted it to a stochastic model. Then, for both types of models, the qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction numbers are obtained for both models and compared. From the comparison, we obtained that the basic reproduction number of the stochastic model is much smaller than that of the deterministic one, which means that the stochastic approach is more realistic. Finally, we performed sensitivity analysis and numerical simulations. The numerical simulation results show that reducing contact rate, improving treatment rate, and environmental sanitation are the most crucial activities to eradicate cholera disease from the community. [ABSTRACT FROM AUTHOR]

Link prediction in a complex network is a problem of fundamental interest in network science and has attracted increasing attention in recent years. It aims to predict missing (or future) links between two entities in a complex system that are not already connected. Among existing methods, local similarity indices are most popular that take into account the information of common neighbours to estimate the likelihood of existence of a connection between two nodes. In this paper, we propose global and quasi-local extensions of some commonly used local similarity indices. We have performed extensive numerical simulations on publicly available datasets from diverse domains demonstrating that the proposed extensions not only give superior performance, when compared to their respective local indices, but also outperform some of the current, state-of-the-art, local and global link-prediction methods. [ABSTRACT FROM AUTHOR]

Acknowledging many effects on humans, which are ignored in deterministic models for COVID-19, in this paper, we consider stochastic mathematical model for COVID-19. Firstly, the formulation of a stochastic susceptible–infected–recovered model is presented. Secondly, we devote with full strength our concentrated attention to sufficient conditions for extinction and persistence. Thirdly, we examine the threshold of the proposed stochastic COVID-19 model, when noise is small or large. Finally, we show the numerical simulations graphically using MATLAB. [ABSTRACT FROM AUTHOR]

The emergence and evolution of real-world systems have been extensively studied in the last few years. However, equally important phenomena are related to the dynamics of systems' collapse, which has been less explored, especially when they can be cast into interdependent systems. In this paper, we develop a dynamical model that allows scrutinizing the collapse of systems composed of two interdependent networks. Specifically, we explore the dynamics of the system's collapse under two scenarios: in the first one, the condition for failure should be satisfied for the focal node as well as for its corresponding node in the other network; while in the second one, it is enough that failure of one of the nodes occurs in either of the two networks. We report extensive numerical simulations of the dynamics performed in different setups of interdependent networks, and analyze how the system behavior depends on the previous scenarios as well as on the topology of the interdependent system. Our results can provide valuable insights into the crashing dynamics and evolutionary properties of interdependent complex systems. [ABSTRACT FROM AUTHOR]

The synchronisation between two floating memristor-based Colpitts oscillators is studied in this paper. Firstly, the mathematical and circuit models of Colpitts oscillator based on a floating memristor with a diode bridge structure are built. On this basis, numerical simulations on the features of both the independent memristor and the floating memristor are conducted and compared using MATLAB software. Secondly, circuit simulation is made on the synchronisation of two floating memristor-based systems by using MULTISIM software. Finally, the physical circuit on the synchronisation of the two coupling Colpitts systems based on the diode bridge memristors is implemented by using the linear error feedback scheme and improved by the capacitor coupling scheme and the adaptive nonlinear feedback control scheme, respectively. The experimental results by the oscilloscope and simulation results show that approximate synchronisation is achieved. [ABSTRACT FROM AUTHOR]

In this paper, by taking two important network environment factors (namely point-to-group worm propagation and benign worms) into consideration, a mathematical model with multiple delays to model the worm prevalence is presented. Sufficient conditions for the local stability of the unique endemic equilibrium and the existence of a Hopf bifurcation are demonstrated by choosing the different combinations of the three delays and analyzing the associated characteristic equation. Directly afterward, the stability and direction of the bifurcated periodic solutions are investigated by using center manifold theorem and the normal form theory. Finally, special attention is paid to some numerical simulations in order to verify the obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, two kinds of novel non-ideal voltage-controlled multi-piecewise cubic nonlinearity memristors and their mathematical models are presented. By adding the memristor to the circuit of a three-dimensional jerk system, a novel memristive multiscroll hyperchaotic jerk system is established without introducing any other ordinary nonlinear functions, from which 2N+2-scroll and 2M+1-scroll hyperchaotic attractors are achieved. It is exciting to note that this new memristive system can produce the extreme multistability phenomenon of coexisting infinitely multiple attractors. Furthermore, the dynamical behaviours of the proposed system are analysed by phase portraits, equilibrium points, Lyapunov exponents and bifurcation diagrams. The results indicate that the system exhibits hyperchaotic, chaotic and periodic dynamics. Especially, the phenomenon of transient chaos can also be found in this memristive multiscroll system. Additionally, the MULTISIM circuit simulations and the hardware experimental results are performed to verify numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies a class of asymptotically almost periodic recurrent neural networks involving mixed delays. By utilizing differential inequality analysis, some novel assertions are gained to validate the asymptotically almost periodicity of the addressed model, which generalizes and refines some recent literature works. In the end, an example with its numerical simulations is carried out to validate the analytical results. [ABSTRACT FROM AUTHOR]

In this paper we present a mathematical model of malaria transmission. The model is an autonomous system, constructed by considering two models: a model of vector population and a model of virus transmission. The threshold dynamics of each model is determined and a relation between them established. Furthermore, the Lyapunov principle is applied to study the stability of equilibrium points. The common basic reproduction number has been determined using the next generation matrix and its implication for malaria management analyzed. Hence, we show that if the threshold dynamics quantities are less than unity, the mosquitoes population disappears leading to malaria disappearance; but if they are greater than unity, mosquitoes population persists and malaria also.Finally, numerical simulations are carried out to support our mathematical results. [ABSTRACT FROM AUTHOR]

A two-species commensal symbiosis model involving Allee effect and one party can not survive independently is proposed and studied in this paper. Sufficient conditions which ensure the local and global stability of the boundary equilibrium and the positive equilibrium are obtained, respectively. Numeric simulations show that with the increasing of Alee effect, the system takes much longer time to reach its stable steady-state solution, though the Allee effect has no influence on the final density of the species. The Allee effect has instable effect on the system, however, such effect is controllable. [ABSTRACT FROM AUTHOR]

This paper deals with a Neumann boundary value problem in a d-dimensional box Td=(0,π)d (d=1,2,3) for a nonlinear diffusion chemotaxis model with logistic source. By using the embedding theorem, the higher-order energy estimates and bootstrap arguments, the condition of chemotaxis-driven instability and the nonlinear evolution near an unstable positive constant equilibrium for this chemotaxis model are proved. Our result provides a quantitative characterization for early spatial pattern formation on the positive constant equilibrium. Finally, numerical simulations are carried out to support our theoretical nonlinear instability results. [ABSTRACT FROM AUTHOR]