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This paper addresses a first numerical simulation to the nonlinear dynamic system of equations that describes the prey-predator model at the predator mating period. Some male species accompany the females during the mating period. In this case, both male and female feed on the same prey. The presented work shows the numerical solution for this specific case of the prey-predator mathematical model via an exponential time differencing method. In addition, the paper provides the biological implication of the solution. [ABSTRACT FROM AUTHOR]

This article deals with the random sequential adsorption (RSA) of 2D disks of the same size on fractal surfaces with a Hausdorff dimension 1 < d < 2. According to the literature and confirmed by numerical simulations in the paper, the high coverage regime exhibits fractional dynamics, i.e., dynamics in t1/d where d is the fractal dimension of the surface. The main contribution this paper is that it proposes to capture this behavior with a particular class of nonlinear model: a driftless control affine model. [ABSTRACT FROM AUTHOR]

Using both analytical and numerical methods, nonlinear dynamic behaviours including chaotic motions and subharmonic bifurcations of an inclined beam subjected to harmonic excitation in temperature field are investigated in this paper. Based on the Galerkin method, the mathematical model of motion is derived. Melnikov method is adopted to give an analytical expression of conditions for chaotic motions of the inclined beam. The chaotic feature on the inclined angle is studied in detail. It is presented that there exists a unique excitation frequency |$\omega ^*$|⁠ , such that the critical value of chaos is the monotone decreasing function of the inclination angle when the excitation frequency |$\omega <\omega ^*$|⁠ ; whereas |$\omega>\omega ^*$|⁠ , it is the monotone increasing function of the inclination angle. The subharmonic bifurcations are also studied. It is obtained that subharmonic bifurcations of even orders or odd orders may occur for this system. With the techniques of elliptic functions, it is proved rigorously that this system may undergo chaos through finite subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold obtained by the analytical method. [ABSTRACT FROM AUTHOR]

The tip size of metal protrusions is an important factor affecting corona discharge, since it influences the electric filed, the ionization range and strength around the protrusion defect. Most existing studies on the influence of protrusion tip size on corona discharge are implemented by experimental methods. However, these studies are difficult to obtain the microphysical process of charged particles, which is related to the generation of current pulses and electromagnetic (EM) waves. In this paper, a hydrodynamic simulation model is proposed to study the effect of protrusion tip size on the microphysical process and current pulses of negative corona discharge. A mapping relationship between microscopic behaviors of charged particles and current pulses is established by this simulation method. Based on the comparison of microphysical quantities, the effect of defect tip size on the detailed parameters of current pulses is clearly explained. It shows that with the increase of tip size under a constant voltage, all the five parameters of current pluses increase. The rising time is related to the effective ionization coefficient, while the falling time is dependent on the velocities of positive and negative ions. The experiment and simulation results coincide in current waveforms and all five parameters. [ABSTRACT FROM AUTHOR]

In this paper, role of chaotic systems with perpendicular line equilibrium, line equilibrium, and no-equilibrium is investigated by employing Mittage-Leffler kernel. The fractal-fractionalized mathematical and dynamical models have been observed for quasi-periodicity chaos and hyperchaos as well as simple periodicity chaos and hyperchaos. Each chaotic systems type is simulated on the basis on comparative analysis through Atangana-Baleanu fractal differential operator versus Atangana-Baleanu fractional differential operator. The numerical simulations have been performed by means of Adams-Bashforth-Moulton method for observing the controversial role of chaotic systems on the basis of phase portrait. The nonsingularity associate to the fractal fractional differentiation of Atangana-Baleanu has been introduced. Finally, 3D and 2D phase portraits of chaotic system with perpendicular line equilibrium, line equilibrium and no-equilibrium have been underlined to capture the similarities and differences among the depicted phase portraits parametrically. [ABSTRACT FROM AUTHOR]

The in-pipe robots are currently of significant interest, considering numerous recent publications on this subject. Such machines can use various locomotion principles: wheeled, tracked (caterpillar), walking (legged), screw-type, worm-type, snake-type, etc. In most cases, such robots are equipped with an active drive system transmitting the torque from a motor shaft to the corresponding locomotion mechanism (wheels, tracks, etc.). The present paper is devoted to the wheeled in-pipe robot that doesn't need a complex transmission. In such a case, the idea of implementing the vibratory locomotion system driven by an internal unbalanced mass is proposed. The corresponding kinematic diagram of the wheeled vibration-driven in-pipe robot is developed, and the differential equations describing the robot motion are deduced. In order to carry out the virtual experimental investigations, the robot's simulation model is designed in the SolidWorks software. The major scientific novelty of the present research consists in developing the theoretical foundation for designing and practical implementation of the in-pipe robots driven by the inertial vibration exciters and equipped with the unidirectionally rotating wheels and overrunning clutches. The results of numerical modeling and computer simulation of the robot motion substantiate the possibilities and expediency of implementing the proposed vibration-driven locomotion principles while creating novel designs of the in-pipe robots. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce a new concept for a hydraulic semi-active yaw damper (SAYD) for the improvement of the stability of a high-speed rail vehicle. This concept represents a further elaboration of Secondary Yaw Control but envisages the use of semi-active hydraulic dampers instead of full-active electromechanical dampers, simplifying the design of the system and facilitating the design of a safe and fault tolerant device. Two control algorithms are proposed for the semi-active damper: maximum power point tracking and skyhook with Karnopp approximation. A multi-physics model of the SAYD is introduced and used in co-simulation with a multi-body model of a high-speed vehicle. Using these models, numerical simulations are performed to assess the behaviour of the semi-active damper in terms of improving the running stability of the rail vehicle at very high speed, showing that the use of the SAYD in combination with any of the two control strategies considered allows to improve substantially the stability of the vehicle. The results of experimental investigations performed in the project will be reported in a companion paper. [ABSTRACT FROM AUTHOR]

In this paper, the dynamics of a modified Nicholson-Bailey model as a discrete dynamical system has been studied. Local dynamics in a neighborhood of boundary fixed points are investigated. It is also proved that the model has a unique positive fixed point and a Neimark-Sacker bifurcation emerges at this fixed point. Some numerical simulations are presented to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

This paper deals with the fractional mathematical model for the spread of polio in a community with variable size structure including the role of vaccination. The considered model has been extended with help of Atangana–Baleanu in the sense of the Caputo (ABC) fractional operator. The positivity and boundedness of solution (positively invariant region) are presented for the ABC-fractional model of polio. The fixed-point theory has been adopted to study the existing results and uniqueness of the solution for the concerned problem. We also investigate the stability result for the considered model using the Ulam–Hyers stability scheme by taking a small perturbation in the beginning. Numerical simulation is obtained with the help of the fractional Adams–Bashforth technique. Two different initial approximations for all the compartments have been tested for achieving stability to their same equilibrium points. The control simulation is also drawn at fixed infection and exposure rates at various fractional orders. The comparison at different available rates of infection and exposition is also plotted to show the decrease in the infection by decreasing these rates. Various graphical presentations are given to understand the dynamics of the model at various fractional orders. [ABSTRACT FROM AUTHOR]

A nonlinear energy-based controller and a Lyapunov-based model predictive control (MPC) technology are constructed in sequence for shipboard boom cranes, while taking full state constraints into account. The mathematical model is firstly transformed to ease the explicit influences of ship rollings on the desired positions and payload swings. Barrier Lyapunov functions (BLFs) are then involved in the energy-based controller to deal with different types of state constraints, in which constraints with positive bounds are also effectively tackled with a modified BLF. By adding a contractive constraint with the energy-based controller in traditional MPC framework, Lyapunov-based MPC is then established, in which the recursive feasibility and stability is ensured effectively and easily. Asymptotical stability of two controllers is analyzed and guaranteed in theory, respectively. Compared with the energy-based controller, control performance is improved and enhanced by the Lyapunov-based MPC through solving the optimal control problem. Simulations are finally implemented, and comparisons are also carried out to demonstrate the effectiveness and features of the established controllers in this paper. • An energy-based controller is independently developed for shipboard boom cranes. The asymmetrical constraints on all states are strictly respected and asymptotic stability is guaranteed by embedding BLFs in the Lyapunov function and controller. • To the best of our knowledge, Lyapunov-based MPC is firstly applied to shipboard boom cranes while tackling full state constraints. The recursive feasibility and asymptotic stability are ensured by taking energy-based controller as initial guesses and contractive constraints. • Two groups of numerical simulations are implemented to demonstrate the effectiveness. [ABSTRACT FROM AUTHOR]

• The mathematical model on the grounding resistance of the vertical electrode is proposed. • Accuracy of the mathematical model is proved by computer simulation analysis and the field measurement examination in this paper. • The mathematical model can be used in the design of vertical grounding electrode effectively. In this paper, a mathematical model on the grounding resistance of vertical electrode is proposed. The proposed mathematical model is modeled with consideration of the effects of parameters such as the length and diameter of vertical electrode, the soil resistivity and the embedding depth. This mathematical model can be applied effectively to the design of grounding system using vertical electrode in harmonious soil with the resistivity values less than 900Ω∙m. The accuracy of proposed model is proved by the simulation analysis and measurement examination of the electric field in this paper. [ABSTRACT FROM AUTHOR]

At the end of 2019, the world knew the propagation of a new pandemic named COVID-19. This disease harmed the exercises of humankind and changed our way of life. For modeling and studying infectious illness transmission, mathematical models are helpful tools. Thus, in this paper, taking into account the effect of the intensity of the noises, we define a threshold value Π s of the model, which determines the extinction and persistence of the COVID-19 pandemic. We give numerical simulations to illustrate the analytical results. [ABSTRACT FROM AUTHOR]

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them the computation of shortest paths and the design of efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we generalize the dynamics to the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterizations of the optimum solution. [ABSTRACT FROM AUTHOR]

In this paper, we develop an in-host mathematical model of snakebite envenoming that includes tissue, red blood and platelet cells of humans as specific targets of different kinds of toxins in the snake venom. The model is use to study some harmful effects of cytotoxic and hemotoxic snake venom on their target cells under the influence of snake antivenom. The model has two equilibrium points, namely, trivial and venom free. It has been shown that both the equilibrium points are globally asymptotically stable and numerical simulations illustrate the global asymptotic stability of the venom free equilibrium point. Furthermore, simulations reveal the importance of administering antivenom to avert the possible damage from venom toxins on the target cells. It is also shown through simulation that administering the required dose of antivenom can lead to the elimination of venom toxins within one week. Therefore, we recommend the administration of an adequate dose of antivenom therapy as it helps in deactivating venom toxins faster and consequently enhances the recovery time. [ABSTRACT FROM AUTHOR]

Describes the above-named upcoming special issue or section. May include topics to be covered or calls for papers. [ABSTRACT FROM AUTHOR]

The idea behind the neutrosophic set is we can connect the concept by dynamics of opposite interacts and its neutral that are uncertain and get common parts. Automata theory is beneficial to solve computational complexity problem and also it is an in uential mathematical modeling tool in computer science. Inspired by the concepts of neutrosophic sets and automata theory, here, we are introducing and discussing the algebraic concept of neutrosophic finite automata based on the paper [10]. Generally, composite machines can be achieved by the output of the one machine that will be used as input for another machines. This paper introduced the concept of composite automata under the environment of the neutrosophic set and also examined the box function between the composite neutrosophic finite automata. [ABSTRACT FROM AUTHOR]

This paper proposes new mathematical models of representation, which can describe the dynamic behavior of large-scale nonlinear systems, such as an extended mathematical model of Volterra series, interconnected Hammerstein structures, and interconnected Wiener structures. In this research, we focus on the class of large-scale nonlinear systems, which are composed of several interconnected nonlinear subsystems. In this context, a discrete nonlinear mathematical model with unknown time-varying parameters, mono-variable, characterizes each interconnected subsystem operating in a deterministic or stochastic environment. An illustrative numerical simulation example of two interconnected nonlinear processes is provided to prove the validity and the performance of the developed theoretical results. [ABSTRACT FROM AUTHOR]

The paper presents the results of work leading to the construction of a spatial hybrid model based on finite element (FE) and Monte Carlo (MC) methods allowing the computer simulation of physical phenomena accompanying the steel sample testing at temperatures that are characteristic for soft-reduction process. The proposed solution includes local density variations at the level of mechanical solution (the incompressibility condition was replaced with the condition of mass conservation), and at the same time simulates the grain growth in a comprehensive resistance heating process combined with a local remelting followed by free/controlled cooling of the sample tested. Simulation of grain growth in the entire computing domain would not be possible without the support of GPU processors. There was a 59-fold increase in the computing speed on the GPU compared to single-threaded computing on the CPU. The study was complemented by examples of experimental and computer simulation results, showing the correctness of the adopted model assumptions. [ABSTRACT FROM AUTHOR]

Background: Collaborative computer simulations are available on some online platforms which support students at distributed locations to synchronously collaborate on the simulations to learn sciences. However, how students collaborate with each other in collaborative simulations is not clear. Objectives: The aim of this study was to investigate whether functional interdependency would influence learning. Methods: Two collaborative learning models with different functional interdependencies were examined (the synchronous model and the distributed accountability model). Multiple data sources obtained from 64 students were collected and analyzed. We discuss the collaborative learning with two levels of factors: the individual‐level factors (i.e., individual perceptions of teamwork quality, visual attention and learning performance before and after a simulation activity) and the pair‐level factors (i.e., discourse data and joint attention). Given that the pair‐level factors in the collaborative learning environment may affect the individual‐level factors, we further discuss the interactions of the two levels of factors in different collaborative learning models with hierarchical linear modeling (HLM) analysis. Results and Conclusions: The analytical results of the individual‐level factors found participants in the distributed accountability model demonstrated more frequent and longer attention to the learning activity. Furthermore, the results indicated that the two simulation learning activities would enhance the participants' learning performance except in Q2. For the pair‐level factors, the results demonstrated that the participants in the distributed accountability model showed more active discourse segments but similar joint attention patterns in the learning activity. The results of the HLM analysis indicated that the students in the distributed accountability model had to collaborate with their partners through more constructive dialogue, and focused on the same areas of interest to enhance their learning performance, as the complexity of the distributed accountability design was implemented in a simulation learning activity. Major takeaways: We found that the increase of functional interdependency cannot guarantee students' learning effect in collaborative learning and may hinder the communication that is needed during collaboration. Researcher may need to consider other collaboration tools to enhance the reciprocal reflection. Lay Description: What is already known about this topic: Collaborative simulations are helpful in making the learning process cohesive.The learning effects of functional interdependence in collaborative learning are under debate. What this paper adds: We examined collaborative learning models with different functional interdependencies.We discuss the collaborative learning with the individual‐, the pair‐level factors and their interactions Implications for practice and/or policy: The importance of decreasing cognitive load induced by simulation with high functional interdependency.It is necessary to increase participants' transactive and constructive engagement in collaborative models. [ABSTRACT FROM AUTHOR]

To get a better understanding of HIV/TB co-infection, we've constructed and tested a mathematical model. This model includes a set of first order non-linear Ordinary Differential Equations with six exclusive compartments; for example, people infected with TB (TB-infected), HIV (HIV-infected), or people infected with both (co-infected) (A). Compartment transitions have been shown. It's worth pointing out that the paper mentions the existence of a positive invariant area and positive solution. The researchers were able to support their conclusions by employing MATLAB and in-depth computer simulations. [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]

The present paper deals with the performance evaluation of an M / M / 1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that have dealt with retrial queues by considering all the above-mentioned aspects (collisions, transmission errors and unreliable server). This queue can be used as a mathematical model of several computer systems and telecommunication networks. We apply the generating function method to derive the joint distribution of the server state and the orbit length in the steady state, and we obtain some performance measures. Finally, we provide numerical illustrations to show the effectiveness and the applicability of the model. [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]

This paper considers an optimal control problem of large-scale gas supply systems. Solving this problem, we must take into account line packing in systems modeling. For unsteady-state gas flow modeling, a lumped-parameter model is proposed. On the base of this model the paper elaborates a system of ordinary differential equations to imitate unsteady-state gas flow in pipeline system of selectable configuration and provides the integration algorithm using the global gradient method. Adduced an example of calculating a circuitous gas supply system demonstrates the adequacy of the proposed model. The paper includes the mathematical formulation of a technical diagnostics problem of large pipeline system equipment in case of unsteady-state gas flow. The estimation of technical state is reduced to the constrained optimization problem. On the base of the lumped parameters model, we propose an algorithm of the solution of this problem and use it for identification of the gas supply system of selectable configuration. The numerical experiments demonstrate that the algorithm converges with good speed. The paper contains a description of an optimal control concept of large-scale pipeline system. Stated ideas can be applied in case of the system collapse. • For unsteady-state gas flow modeling a lumped-parameter model is proposed. • A method for integrating this system is recommended. • A method for estimating parameters of gas transportation system model is proposed. • A concept of large pipeline system control is described. [ABSTRACT FROM AUTHOR]

We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by 'multiscale modelling', formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a detailed mathematical model describing the dynamics of a prey-predator model under the influence of an SIS infectious disease by using nonlinear differential equations. We use the functional response of ratio-dependent Michaelis-Menten type to describe the predation strategy. In the presence of the disease, prey and predator population are divided into two disjointed classes, namely infected and susceptible. The first one is governed through due predation interaction, and the second one is governed through the propagation of disease in the prey and predator population via predation. Our aim is to analyze the effect of predation on the dynamic of the disease transmission. Important mathematical results resulting from the transmission of the disease under influence of predation are offered. First, results concerning boundedness, uniform persistence, existence and uniqueness of solutions have been developed. In addition, many thresholds have been computed and used to investigate local and global stability analysis by using Routh-Hurwitz criterion and Lyapunov principle. We also establish the Hopf bifurcation to highlight periodic fluctuation with persistence of the disease or without disease in the prey and predator population. Finally, numerical simulations are carried out to illustrate the feasibility of the theoretical results. [ABSTRACT FROM AUTHOR]

Modelling the human cardiorespiratory system using computer simulation tools can serve to help physicians to comprehend the causes and development of cardiorespiratory diseases. The objective of this paper is to develop an integrated model of the cardiovascular and respiratory systems, along with their intrinsic control mechanisms, by combining analogous hydraulic-electric and diffusion-electric circuits, respectively. This modelling task is performed in object-oriented language in SIMSCAPE using the physical interconnected components to define the underlying dynamic equations. Simulation steady state results under rest and under variable physical exercise conditions, as well as under limiting conditions show a high qualitative agreement with clinical observations reported in literature. This object-oriented modelling approach, based on the combined use of electrical analogies, proves to be avaluable tool as a test bench for different strategies aimed to qualitative prediction of the effects of cardiorespiratory interactions during exercise, thus avoiding the formulation of complex mathematical models. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fractional-order prey-predator model with infection on both populations. First, we prove some important results such as existence, uniqueness, non-negativity and boundedness of the solutions of the fractional-order dynamical system. Next, we discuss the local stability and global stability of the fractional-order prey-predator model. Numerical simulations are presented with several examples. [ABSTRACT FROM AUTHOR]

In the power control process of the range extender, both the engine and the generator are at risk of reaching the torque output limit. The limitation not only comes from the restriction of their own torque output capacity, but also comes from the additional constraints that are established to avoid power reverse undershoot. In order to improve the system performance under time-varying torque constraints, a real-time model predictive controller (MPC) that manipulates the torque commands of the engine and the generator to track the reference power is designed. Different from the traditional penalty function method, the quadratic function is taken as the penalty function in this paper, which greatly improves the efficiency of solving the optimal solution. Meanwhile, the steady-state torque command in the feasible region is taken as the extreme point of the quadratic penalty function, which avoids the penalty coefficient tending to infinity. By adjusting the penalty coefficients of different constraints, the overall optimal solution approaches the boundary of the active inequality constraints. And according to the Karush-Kuhn-Tucker (KKT) condition, it is proved that the optimal solution of the original problem can be obtained through iteration. The effectiveness and practicability of the proposed strategy are evaluated through numerical simulations on Simulink and experiments on a range extender. [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]

In this paper, we have developed a mathematical model of diabetes (type-2 diabetes) in a deterministic approach. We have described our model in the population dynamics with four compartments. Namely, Susceptible, Imbalance Glucose Level (IGL), Treatment and Restrain population. Our model exhibits two nonnegative equilibrium points namely Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The expression for the Treatment reproduction number R T is computed. We have proved that the equilibrium points of the model are locally and globally asymptotically stable under some conditions. Numerical simulation is performed to verify our analytical findings such as stability of DFE and EE. The simulations show better results based on the required conditions. We tried to fit our model with the data given by the International Diabetes Federation (IDF) [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)] and it suits well with the data. It has been found that our model shows the decrease in diabetes-affected population compared with the data given by the IDF [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)]. [ABSTRACT FROM AUTHOR]

In this paper the computational methodology for evaluating vibro-isolation properties of the vibration reduction systems is discussed. The proposed procedure supports selecting the non-linear dynamic behaviour of passive systems and helps to perform the controller synthesis of active systems. Primarily, the mathematical model of a vibration reduction system is developed for the purpose of simulating its dynamic behaviour under different operating conditions. In the next step, the selected vibro-isolation criteria are determined numerically that are related to the opposed requirements of modern vibration reduction systems. Finally, an application of the Pareto-optimal approach is employed to find a trade-off regarding the high efficiency of vibration attenuation at the lowest suspension travel. [ABSTRACT FROM AUTHOR]

This paper reports a unified asymmetric memristive diode-bridge (UAMD) emulator with the current constraints for each pair of parallel bridge arms, which is implemented by an asymmetric diode-bridge cascaded with a parallel resistor and capacitor (RC) filter. The mathematical model is established and its pinched property is confirmed by multisim circuit analysis, MATLAB numerical simulation and hardware experiment. Besides, the UAMD emulator is expanded to the general cases and four diodes on symmetric bridge arms owning two situations are taken as two expanding examples. [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 so-called "raspberry" model refers to the hybrid lattice-Boltzmann and Langevin molecular dynamics scheme for simulating the dynamics of suspensions of colloidal particles, originally developed by Lobaskin and Dünweg [New J. Phys. 6, 54 (2004)], wherein discrete surface points are used to achieve fluid-particle coupling. This technique has been used in many simulation studies on the behavior of colloids. However, there are fundamental questions with regards to the use of this model. In this paper, we examine the accuracy with which the raspberry method is able to reproduce Stokes-level hydrodynamic interactions when compared to analytic expressions for solid spheres in simple-cubic crystals. To this end, we consider the quality of numerical experiments that are traditionally used to establish these properties and we discuss their shortcomings. We show that there is a discrepancy between the translational and rotational mobility reproduced by the simple raspberry model and present a way to numerically remedy this problem by adding internal coupling points. Finally, we examine a non-convex shape, namely, a colloidal dumbbell, and show that the filled raspberry model replicates the desired hydrodynamic behavior in bulk for this more complicated shape. Our investigation is continued in de Graaf et al. [J. Chem. Phys. 143, 084108 (2015)], wherein we consider the raspberry model in the confining geometry of two parallel plates. [ABSTRACT FROM AUTHOR]

In this paper we discuss the mathematical and computer modeling of non-isothermal two-phase flows with suspended particles. Natural convection between an outer cubical cavity and an inner hot sphere is investigated. To simulate heat fluxes loaded with particles, a thermal model of the lattice Boltzmann equation in combination with the interpolated bounce back method (TLBM-IBB) has been developed. In TLBM-IBB, IBB is used to process liquid-solid interfaces, and TLBM is used to simulate the heat flow of a fluid. The momentum exchange method is used to calculate the hydrodynamic force on the particle surface. Simulation performed for a range of Rayleigh numbers (105 - 106. The accuracy and efficiency of the existing method is demonstrated by the example of solving the test problem of natural convection around a stationary particle and three-dimensional compressible natural convection in a square cavity filled with air, which has a hot wall on the left and a cold wall on the right, and two horizontal walls are adiabatic. The results obtained are in good agreement with the experimental and numerical results of other authors. [ABSTRACT FROM AUTHOR]

As a new efficient rock-breaking technology, harmonic impact drilling technology has received great attention, but the research on its rock-breaking mechanism is insufficient, which limits its development. Based on the theory of vibration, a simplified model of high-frequency harmonic vibration impact system is established in this paper. The numerical model was solved by Matlab and the motion equations of drill bit and rock at different stages of motion are obtained, respectively. Based on the factor analysis of the mathematical model, the dynamic characteristics of the impact system under harmonic excitation are studied. Finally, numerical simulations are carried out to further analyze the drilling effect of harmonic impact drilling and verify the correctness of the simplified model. The results show that when the excitation frequency equals the resonance frequency of rock, the vibration displacement of rock reaches the peak value. The drilling speed is greatly increased by harmonic impact drilling compared with conventional drilling. [ABSTRACT FROM AUTHOR]