Search

The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes 'h'. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease. [ABSTRACT FROM AUTHOR]

Whooping cough is a highly transmitted disease around the world. According to the World Health Organization (WHO), 0.15 million cases had reported globally in 2018. Most of the Asian and African states are infected regions. Through the study, we investigated the whole population into the four classes susceptible (S), exposed (E), infected (I), and vaccinated or recovered (R). The transmission dynamics of whooping cough disease are studied analytically and numerically. Analytical analyses are positivity, boundedness, reproduction number, equilibria, and local and global stabilities. In numerical analysis, we developed an implicit numerical integration scheme consistent with the biological problem's properties. The analysis of the implicit method for the said model is dynamically consistent, positive, and bounded. Furthermore, an implicit numerical integration scheme is suitable for studying a particular epidemic model such as the whooping cough disease. [ABSTRACT FROM AUTHOR]

In this work, the heat transfer features and stagnation point flow of Magnetohydrodynamics (MHD) hybrid second-grade nanofluid through a convectively heated permeable shrinking/stretching sheet is reported. The purpose of the present investigation is to consider hybrid nanofluids comprising of Alumina Al 2 O 3 and Copper Cu nanoparticles within the Sodium Alginate (SA) as a host fluid for boosting the heat transfer rate. Also, the effects of free convection, viscous dissipation, heat source/sink, and nonlinear thermal radiation are considered. The converted nonlinear coupled fuzzy differential equations (FDEs) with the help of triangular fuzzy numbers (TFNs) are solved using the numerical scheme bvp4c. The numerical results are acquired for various engineering parameters to study the Nusselt number, skin friction coefficient, velocity, and temperature distribution through figures and tables. For the validation, the current numerical results were found to be good as compared to existing results in limiting cases. It is also inspected by this work that with the enhancement of the volume fraction of nanoparticles, the heat transfer rate also increases. So, it may be taken as a fuzzy parameter for a better understanding of fuzzy variables. For the comparison, the volume fraction of nanofluids and hybrid nanofluid are said to be TFN [0, 0.1, 0.2]. In the end, we can see that fuzzy triangular membership functions (MFs) have not only helped to overcome the computational cost but also given better accuracy than the existent results. Finding from fuzzy MFs, the performance of hybrid nanofluids is better than nanofluids. [ABSTRACT FROM AUTHOR]

This study presents a structure preserving nonstandard finite difference scheme to analyze a susceptible-infected-treatment-recovered (SITR) dynamical model of coronavirus 2019 (covid-19) with bimodal virus transmission in susceptible population. The underlying model incorporates the possible treatment measures as the emerging scenario of covid-19 vaccines. Keeping in view the fact that the real time data for covid-19 is updated at discrete time steps, we propose a new structure preserving numerical scheme for the proposed model. The proposed numerical scheme produces realistic solutions of the complex bi-modal SITR nonlinear model, converges unconditionally to steady states and reflects dynamical consistency with continuous sense of the model. The analysis of the model reveals that the model remains stable at the steady state points. The basic reproduction number R covid falls less than 1 when treatment rate is increased and disease will die out. On the other hand, it predicts that human population may face devastating effects of pandemic if the treatment measures are not strictly implemented. [ABSTRACT FROM AUTHOR]

In this work the chaotic dynamics of flexible curvilinear Euler–Bernoulli micro‐beams embedded into a stationary temperature field is investigated. The temperature field is modelled based on a the Duhamel–Neumann theory and is free from the restrictions on the temperature field distribution along beam thickness. The von Kármán geometric strain–stress relations are employed. The governing nonlinear PDEs are yielded by the Hamilton principle with an account of the modified couple stress theory. The finite dimension problem is truncated to a finite system of nonlinear ODEs using the finite difference method (FDM) and then the Cauchy problem is solved with a help of the Runge–Kutta method. Action of the 2D thermal field is defined by solution to the heat transfer PDE which is also solved by FDM of the second order of accuracy. The so‐called charts of vibration regimes (amplitude‐frequency planes) are constructed. In particular, novel features of nonlinear (chaotic) dynamics versus the change of the magnitude of the size (length) dependent parameter are reported. The carried out numerical analysis is supported by the monitoring of frequency power spectra based on the fast Fourier transform (FFT), phase space projections, Poincaré maps and LLEs (largest Lyapunov exponents). We have also analyzed system chaotic dynamics of the classical and size‐dependent beam models versus series of values of the two control parameters, i.e. beam curvature and its size‐dependent length. Moreover, we have detected and illustrated the novel scenarios of transition form regular to chaotic vibrations of the studied beams, governed by non‐linear PDEs. [ABSTRACT FROM AUTHOR]

A parametric pendulum excited by a discrete wave-modulated step function of length is subjected to a mathematical analysis and numerical modeling. We observe an existence of almost periodic solutions of ordinary differential equations with linear boundary value conditions. An exemplary oscillator subject to both an almost periodic step elongation and forcing synchronizes with the forcing, tending to almost periodic motions like stable limit cycles. Conditions for that synchronization as well as trajectories of numerical solutions on time history plots and phase planes are shown to confirm correctness of the analytical derivations and dedicated numerical modeling. [ABSTRACT FROM AUTHOR]

Mathematical modeling, theoretical/numerical analysis, and experimental verification of wear processes occurring on the contact surface of friction linings of a mechanical friction clutch are studied. In contrast to many earlier papers we take into consideration wear properties and flexibility of friction materials being in friction contact. During mathematical modeling and numerical simulations we consider a general nonlinear differential model of wear (differential wear model) and a model of wear in the integral form (integral wear model). Equations governing contact pressure and wear distributions of individual friction linings, decrease of distance between clutch shields, and friction torque transmitted by the clutch are derived and compared with experimental data. Both analytical and numerical analyses are carried out with the qualitative and quantitative theories of differential and integral equations, including the Laplace transform approach to ODEs. We show that theoretical results and numerical simulations agree with the experimental data. Finally, a numerical analysis of the proposed mathematical models was carried out in a wider range of parameters of the considered system. [ABSTRACT FROM AUTHOR]

The dynamic response of a nonlinear system with three degrees of freedom, which is excited by nonideal excitation, is investigated. In the considered system the role of a nonideal source is played by a direct current motor, where the central axis of the rotor is not coincident with the axis of rotation. This translation generates a torque whose magnitude depends on the angular velocity. During the system operation a general coordinate assigned to the nonideal source grows rapidly as a result of rotation. We propose the decomposition of the equations of motion in such a way to extract the solution which is directly related to the rotation of an unbalanced rotor. The remaining part of the solution describes pure oscillation depending on the dynamical behaviour of the whole system. The decomposed equations are solved numerically. The influence of selected system parameters on the rotor vibration is examined. The presented approach can be applied to separate vibration and rotation of motions in many other engineering systems. [ABSTRACT FROM AUTHOR]

Thermal processes occurring in the mechanical clutch or brake systems have a great influence on the strength of elements of these systems as well as on their dynamics. The contact problems exhibited by such systems include heat generated by dry friction contact surfaces. The contact dynamics in general depends on many system parameters, and it attracted attention of many researches focused on analysis of the mentioned phenomena in different kinds of mechanical systems like clutches, brakes, and others. In this work a mathematical model describing the processes of heat generation and its propagation in the mechanical friction clutch is presented. The presented model takes into account the unequal distribution of flux density of produced heat in the clutch, the thermal conductivity of materials of friction linings, and the heat transfer between the friction linings of clutch and its environments. The analyzed object is described by a set of algebraic linear homo- and heterogeneous equations, and it is derived using a computer numerical method. Many interesting numerical and experimental results are obtained, illustrated and discussed. Presented numerical results coincide with experimental data. [ABSTRACT FROM AUTHOR]

In this paper, for the first time, the complete set of Tangens hyperbolicus approximations of model of dry friction coupled with rolling resistance for circular contact area between interacting bodies is proposed. The developed approximations are compared with corresponding Padé approximants of the first and second order well known from the literature and with the numerical solution of the exact integral model as well. It is shown that Tangens hyperbolicus approximants are closest to the exact solution. Then the approximated models are applied to the celtic stone dynamics, however with the significant simplifying assumption of circular contact between stone and the table, presenting differences between them again. Certain specific approximations and regularizations of the friction and rolling resistance models enabling and facilitating their application to the real problem are shown. The analysis of the response dependence on initial conditions is performed by the use of a special kind of diagram. [ABSTRACT FROM AUTHOR]

Complex vibration of flexible elastic shells subjected to transversal and sign-changeable local load in the frame of nonlinear classical theory is studied. A transition from partial to ordinary differential equations is carried out using the higher-order Bubnov-Galerkin approach. Numerical analysis is performed applying theoretical background of nonlinear dynamics and qualitative theory of differential equations. Mainly the so-called Sharkovskiy periodicity is studied. [ABSTRACT FROM AUTHOR]

Abstract: By using Tichonov theorem for singularly perturbed differential equations, we study the relationship between dynamics of discontinuous differential equations and their continuous approximations along periodic solutions. [Copyright &y& Elsevier]

A methodology for obtaining the optimal structure and distribution for the gradient properties of a material in order to reduce the stress level in a soldered joint was constructed. The developed methodology was based on a combination of topological optimization methods (the moving asymptotes method) and the finite elements method; it was first implemented to solve problems of optimizing soldered joints. Using the proposed methodology, a number of problems were solved, allowing one to obtain optimal structural characteristics, in which a decrease in stress is revealed. Designing compounds using this technique will provide more robust designs. The proposed technique can be applied to a wide class of practical problems. [ABSTRACT FROM AUTHOR]

• Magnetic pendulum system is analysed numerically and experimentally. • Model of the system is discretised into states with one- and two-well potential. • Pulsating excitation signal parameters are obtained for one-side oscillations. • The same oscillations are possible for different duty cycles and the same frequency. • Multiperiodic solutions may arise from localized forcing in kick-exited systems. This paper presents a theoretical and numerical analysis of one-side oscillation in a single magnetic pendulum. The system is composed of a physical pendulum with a neodymium magnet fixed to the end of the rod. The pendulum is driven by a pulsating, repulsive magnetic field generated by an electric coil placed underneath. The pendulum pivot is damped by an elastic element. The excitation current signal has a pulsating rectangular waveform with a controlled frequency and duty cycle. In general, magnetic interaction weakens with increasing distance between the magnet and the coil, making excitation in this system not only time-dependent but also position-dependent. The specific type of solution, referred to as "one-side oscillation" is analysed in terms of a frequency and a duty cycle of the current signal. By one-side oscillations, we mean oscillations of the pendulum characterized by the same sign of angular displacement, without passing through the lowest and the highest vertical equilibrium positions. The analysis is based mainly on the assumption that outside some "active zone" the influence of magnetic interaction on the pendulum dynamics is negligible, and the system can be discretized into two states: with and without magnetic force. The results were confirmed by experimental data showing the different periodicity of one-side oscillations. Limitations of the proposed analysis were found in the case of some variants of the analysed solution type. An overview of the system dynamics is presented in the form of bifurcation diagrams obtained numerically and verified by experimental estimates, which show the existence of chaotic behaviour and multiperiodicity for various values of the frequency of the current signal. [ABSTRACT FROM AUTHOR]

The aim of the work is to develop and test simple mathematical models suitable for fast and realistic simulations of bifurcation dynamics of systems with a double potential well generated by a pair of repulsive magnets positioned transversely to the direction of motion, where there are motion resistances typical for rolling guides found in industry. Mathematical modelling of a harmonically forced one-degree-of-freedom oscillator with magnetically modified elasticity generating a double symmetrical minimum of potential was carried out. The system is composed of a cart moving along a linear rolling bearing with inertial excitation by means of a stepper motor with an unbalanced disc. The stiffness is realized by a pair of neodymium magnets of axes perpendicular to the direction of motion, in a position corresponding to the static equilibrium position of the oscillator, with additional mechanical linear springs, which generate a system similar to the Duffing system. Different models of the interaction force between cylindrical neodymium magnets were developed. The model parameters are estimated based on experimental data. Then the model is validated through additional experimental and numerical bifurcation analysis of the system. A very good agreement between numerical simulations and experimental data is obtained. • Experimental and mathematical models of 1DOF oscillator with magnetically modified stiffness. • Good agreement between numerical simulations and experimental data is obtained. • Bifurcation dynamics is investigated by experimental and numerical methods. [ABSTRACT FROM AUTHOR]

• Experimental and mathematical models of 2DOF oscillator with magnetic springs are presented. • Good agreement between numerical simulations and experimental data is obtained. • Regular and chaotic dynamics is investigated by numerical methods. In this paper, oscillations in the physical model consisting of two carts mounted on a guide are considered. The movement of the carts is restricted by the repelling permanent magnets. The interaction between carts is provided by a linear spring. The harmonic external loading is applied to one of the carts. According to the experimental studies, the period doubling cascade leading to the creation of a chaotic attractor occurs with an increase in the forcing frequency in the system. Chaotic attractor crises, quasi-periodic regimes, and finite periodic doubling cascade are revealed as well. To describe system's dynamics, the nonlinear mathematical model is developed. Based on the experimental data, the procedure of model validation is introduced. The numerical and qualitative analysis of the mathematical model allows one to identify bifurcation types, reveal unstable modes, and discover phenomena existing beyond the main period doubling cascade. [ABSTRACT FROM AUTHOR]