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This paper explores the synergy between fuzzy set theory and genetic algorithms in the domain of epidemic modeling, shedding light on the broader challenges inherent in infectious diseases. In response to the evolving landscape of epidemiology, the study advocates for sophisticated modeling techniques to better understand and predict dynamic scenarios. The research thoroughly investigates the global stability of equilibrium solutions within a fuzzy epidemic model, accompanied by an inventive parameter estimation methodology. Utilizing Lyapunov functions, the paper establishes global stability outcomes for both disease-free and endemic equilibria. The novel approach, integrating continued fraction theory and a genetic algorithm, is applied to fit real-world epidemic data, offering insights crucial for public health planning and control measures. By addressing unexplored facets and bridging gaps in previous research, the paper contributes to a more comprehensive understanding of epidemic dynamics, providing a foundation for effective public health strategies in the face of infectious diseases.

The main buffet suppression techniques of aircrafts include active and passive flow control, aiming to reduce the impact of the fluctuating loads on the airfoil. These techniques are remedies after the airfoil design. The buffet suppression is not always considered in the aerodynamic optimization in the state of airfoil design because it is difficult to extract an appropriate key objective variable to indicate the flow stability. In this paper, the damping rate of disturbance, which is computed by the global stability analysis, can be used to indicate flow stability. Based on the global stability analysis, a transonic buffet suppression methodology by airfoil optimization is proposed. The objective is to improve the aerodynamic performance as well as the flow stability in the desired flight state. The RAE2822 airfoil is chosen as the initial airfoil. A benchmark of the unsteady aerodynamic configuration optimization design considering buffet suppression is developed. First, the numerical methods are verified and the damping rate of disturbance is chosen as a constraint in the aerodynamic optimization to extend the buffet onset. Then, the surrogate models constructed by the radial basis function interpolation are used to replace the computational fluid dynamics (CFD) solver. The teaching- and learning-based optimization (TLBO) is used. Finally, the aerodynamic and the flow stability characteristics of the airfoil before and after optimization are compared and analyzed. The proposed optimization framework can not only improve the aerodynamic characteristics in the cruise state but can also suppress the transonic buffet on higher angles of attack. [ABSTRACT FROM AUTHOR]

Staphylococcus aureus has been increasing globally, which negatively affects food safety, human and veterinary medicine. It colonizes about 30% of the world population, causing superficial skin and soft tissue infections. The dynamics of direct (human-to-human) and indirect (environment-to-human) transmission, shedding, and treatment failure of the disease remains an open epidemiological challenge. Therefore, this study introduces a mathematical model that incorporates both direct and indirect transmission cycle, effect of shedding, treatment failure and time-dependent control parameters. We derive an expression for the basic reproduction number, R0s, under different scenarios. Using comparison, Lyapunov and center manifold theories, we establish that the non-optimal control model is globally asymptotically stable whenever R0s

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier-Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft. [ABSTRACT FROM AUTHOR]

In the paper, the two main approaches to calculating the Jacobian of the Navier–Stokes equations, namely, the continuum (CA) and discrete (DA) approaches, have been directly compared for the first time. The DA to calculating this Jacobian was implemented based on in-house finite-volume code for hydrodynamics simulation (in addition to the already existing CA). The DA was successfully verified by comparison between the obtained numerical result and that of solving the transient Navier–Stokes equations. The comparison of these approaches was carried out using the example of a laminar flow past a cylinder by a perfect gas at the near-critical Reynolds numbers (Re = 50 and 60). It was established that the CA predicted the growth rate of perturbations more accurately, while the DA did their frequency and amplitude in toto. The results obtained allow to assert that both CA and DA are equivalent in terms of accuracy, and the choice of a particular approach for analyzing the stability may be determined by other criteria, e. g., ease of implementation, computational work and so on.

The main buffet suppression techniques of aircrafts include active and passive flow control, aiming to reduce the impact of the fluctuating loads on the airfoil. These techniques are remedies after the airfoil design. The buffet suppression is not always considered in the aerodynamic optimization in the state of airfoil design because it is difficult to extract an appropriate key objective variable to indicate the flow stability. In this paper, the damping rate of disturbance, which is computed by the global stability analysis, can be used to indicate flow stability. Based on the global stability analysis, a transonic buffet suppression methodology by airfoil optimization is proposed. The objective is to improve the aerodynamic performance as well as the flow stability in the desired flight state. The RAE2822 airfoil is chosen as the initial airfoil. A benchmark of the unsteady aerodynamic configuration optimization design considering buffet suppression is developed. First, the numerical methods are verified and the damping rate of disturbance is chosen as a constraint in the aerodynamic optimization to extend the buffet onset. Then, the surrogate models constructed by the radial basis function interpolation are used to replace the computational fluid dynamics (CFD) solver. The teaching- and learning-based optimization (TLBO) is used. Finally, the aerodynamic and the flow stability characteristics of the airfoil before and after optimization are compared and analyzed. The proposed optimization framework can not only improve the aerodynamic characteristics in the cruise state but can also suppress the transonic buffet on higher angles of attack.

The friction performance and compression properties of geotextile bags under different degrees of consolidation are researched through the slope sliding test, direct shear test, and unconfined compression test in this study. The geotextile bags are made up of geotextile and tailings sands obtained from a construction site of a prototype tailings dam in Yunnan Province. The slope sliding test is considered as an easy method to study the friction performance of geotextile bags with different degrees of consolidation. Through the test, the friction coefficients between the bags were obtained. Given the geotextile bags can withstand the vertical load in practical engineering, the direct shear test is also proposed and conducted. The ultimate bearing capacity of the geotextile bags with different consolidation degrees is studied in the unconfined compression test. The test reveals that the ultimate bearing capacity of geotextile bags, although featured with different moisture contents before the test, stays the same under the condition of slow loading. Finally, a stability analysis method based on the limit equilibrium theory is developed to simulate the stability of the tailings dam using geotextile bags (TDGB). According to the test results, the TDGB has demonstrated an improved stability compared with the general tailings dam. [ABSTRACT FROM AUTHOR]

In this work, a numerical framework for global stability analysis of rigid-body-motion fluid–structure-interaction problems is presented. The Jacobian matrices which arise in the linearization procedure are derived numerically via the first-order finite difference scheme. The linearized fluid–structure coupled equations are solved using an immersed boundary method. The linear stability solver is first tested on two canonical cases, i.e., the flow past a stationary cylinder and the flow past an isolated elastically mounted cylinder. An excellent agreement between the results obtained here and those from available published research is achieved. The solver is then used to study the linear stability of the flow past two elastically mounted cylinders in tandem arrangement. The variations in growth rate and frequency of two leading modes with reduced velocity are examined. The mechanisms of lock-in and galloping phenomena observed in nonlinear simulation are elucidated from the perspective of linear instabilities in the leading modes. [ABSTRACT FROM AUTHOR]

This article analyzes the global stability of synchronous reference frame phase-locked loops (SRF-PLLs) from a large signal viewpoint. First, a large-signal model of SRF-PLL is accurately established, without applying any linearization method. Then, according to the phase portrait and Lyapunov argument, the global performance of SRF-PLL is discussed in the nonlinear frame. Compared with the small-signal analysis methods, the proposed analysis, not relying on the small-signal model and linearization method, provides a global discussion of the SRF-PLL performance. The contributions of this article are as follows. First, it is found that SRF-PLL has infinite equilibrium points, including stable points and saddle points. Second, it provides a way to divide the global region of SRF-PLL into many small regions. In each small region, the SRF-PLL only has one stable equilibrium point. And for any initial states $(\tilde{\theta }(t_0),\tilde{\omega }(t_0))$ in a small region, all states $(\tilde{\theta }(t),\tilde{\omega }(t)),t>t_0$ will remain in this small region, and SRF-PLL will converge to the unique stable equilibrium point of this small region. Third, by dividing the global region of SRF-PLL into many small regions, it is found that when the frequency of grids varies largely, the SRF-PLL will converge to a new equilibrium point that is far away from the original equilibrium point. It is the reason why the frequency convergence of SRF-PLL has many oscillations and SRF-PLL has a rather slow dynamic, when the frequency changes largely. The experimental results are provided to verify the proposed global stability analysis of SRF-PLL. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle's stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis. [ABSTRACT FROM AUTHOR]

We analyse epidemic model in this article, with incubation delay under the effect of pollution, where disease transmission follows saturated incidence rate and quadratic treatment has also been considered. Boundedness and presence of endemic equilibrium point (Q) as well as point of infection-free equilibrium (Q*) for the model has been established. We investigate the stability analysis of the model around Q and Q*. R0 as a basicreproduction number has been calculated. When R0 < 1, the model is stable for Q, but when R0 > 1, it shifts from a stable to an unstable environment for ϱ > 0. Using center manifold theory, it was shown that at R0 = 1, the model exhibits backward bifurcation, when the bifurcating constant a > 0, while if a < 0, then the bifurcation is forward. We analyse the presence of Hopf bifurcation for endemic equilibrium point Q* by taking time delay as the critical parameter. Considering the normal form theory, we obtain the direction and the stability of Hopf Bifurcation. We establish the global stability of Q* using Lyapunov Lasalle theorem. Our results indicate that pollution affects the disease transmission dynamics of the model. We observe that in the diseased model with pollution the survival of the species is significantly less as compared when there is only disease and no pollution. Numerical simulations are performed to validate our logical findings. [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]

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In this paper we consider a system of second order rational difference equations. We mainly discuss the boundedness and persistence, existence of fixed point, and uniqueness of positive fixed point, local and global behavior of positive fixed point and rate of convergence of every positive solution of the system under discussion. It will be shown that the system under discussion exhibits some special dynamics such as same mathematical condition for existence of fixed point and its global stability. Finally, some numerical examples are provided for verification of theoretical results.

abstract: Current practices in structural engineering demand ever-increasing knowledge and expertise concerning stability of structures from professionals in this field. This paper implements standardized procedures for geometrically nonlinear analysis of steel and reinforced concrete structures, with the objective of comparing methodologies with one another and with a geometrically exact finite element analysis performed with Ansys 14.0. The following methods are presented in this research: Load Amplification Method, from NBR 8800:2008; the γ z coefficient method, from NBR 6118:2014; the P-Delta iterative method and the α c r coefficient method, prescribed in EN 1993-1-1:2005. A bibliographic review focused on standardized approximate methods and models for consideration of material and geometric nonlinearities is presented. Numerical examples are included, from which information is gathered to ensure a valid comparison between methodologies. In summary, the presented methods show a good correlation of results when applied within their respective recommended applicability limits, of which, Eurocode 3 seems to present the major applicability range. The treated approximate methods show to be more suitable for regular framed structures subjected to regular load distributions.

In this article, we study the non-standard finite difference (NSFD) schemes for the diabetes mellitus with tuberculosis infection. We have classified diabetes mellitus into two categories such as diabetes without complications and with complications and studied diabetes with tuberculosis infection. We have modelled diabetes with tuberculosis infection with linear and nonlinear model and studied the local and global asymptotic stability analysis using the NSFD scheme.

In this paper, a hybrid SEIAM model for infectious disease with a continuous age structure is established, where combined dynamic effects of media coverage and multi-staged infected progression on threshold dynamics are discussed. Sufficient conditions for uniform persistence of the solution are studied by using the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability analysis of endemic equilibrium is investigated based on Lyapunov–LaSalle’s stability theorem. In order to minimize costs incurred due to applied controls and infectious disease burden, an optimal cost-effective control strategy associated with disease treatment and media coverage is discussed. Numerical simulations are carried out to show consistency with theoretical analysis.

Q fever (query fever) is classified as one of the likely zoonosis that is transmissible to humans from farm animals. The disease may lead to significant economic losses to livestock owners. The deterministic dynamics of direct transmission, different shedding rates, treatment, the effect of relapse, and seasonality of disease remains an open problem. Therefore, this study introduces direct transmission cycle, different shedding rates, treatment, the effect of relapse, and time-dependent parameters. We obtain control reproduction expressions for the model under different scenarios. Using Lyapunov functions, we establish that the non-seasonal model is globally asymptotically stable. The extension of the model to include seasonal trends shows that there exists a positive periodic solution. The global sensitivity method used shows that imperfect treatment reduces the rate of indirect transmission, but, leads to an increase in direct transmission by symptomatic cattle herds. Optimal control model is also utilized to explore the impact of time-dependent treatment, disinfectant, and separate facilities for animal birthing. We show the control efficacies; and also calculated the average cost-effectiveness ratio, and the incremental cost-effectiveness ratio. We hope that this study further enlightens farm owners on the use of other interventions in controlling Q fever disease in livestock.

Estimates of rape against women had been usually taken from two main sources till the early 1980s; The national crime victimization study and the Uniform Crime Report’s official statistics. Scholars argued, however, that the true incidence of rape was greatly underestimated by those data sources. For example, a uniform crime report focuses on recorded incidents, but several violations are not reported to the police. Two methodological causes have contributed to the underestimation of rape by national crime surveys. First, its definition of rape was considered too limited because it covered only carnal information and, thus, omitted many actions, such as offenses other than penile-vaginal penetration, from the scope of contemporary rape laws. Second, critics argued that the national crime survey was inappropriately structured for interviewees who had previously been assaulted to generate allegations of abuse. The crux of this critique was that there was no clear concern about rape in the national crime survey. How to establish evaluation methods that would show the real nature of rape was the crucial question. As a result of this, we are inspired to design a new mathematical model in this paper to study the dynamics of rape in our societies. Several characteristics of the established model, such as model formulation, boundedness, equilibrium solutions, basic reproduction number, global stability analysis are derived. The existence and characterization of the optimal control function are carried out. For sensitivity analysis as well as to show the significance of the control strategies, several simulation results are given. To get a deep insight into the dynamical behavior of the model, numerical simulations are performed and consequently we obtain the graphical results based on parameters taken as variables. The Euler technique is employed to do the job.

In this paper, we study the dynamics of a vector-borne disease model with two transmission paths: direct transmission through contact and indirect transmission through vector. The direct transmission is considered to be a nonmonotone incidence function to describe the psychological effect of some severe diseases among the population when the number of infected hosts is large and/or the disease possesses high case fatality rate. The system has a disease-free equilibrium which is locally asymptotically stable when the basic reproduction number ( R 0 ) is less than unity and may have up to four endemic equilibria. Analytical expression representing the epidemic growth rate is obtained for the system. Sensitivity of the two transmission pathways were compared with respect to the epidemic growth rate. We numerically find that the direct transmission coefficient is more sensitive than the indirect transmission coefficient with respect to R 0 and the epidemic growth rate. Local stability of endemic equilibrium is studied. Further, the global asymptotic stability of the endemic equilibrium is proved using Li and Muldowney geometric approach. The explicit condition for which the system undergoes backward bifurcation is obtained. The basic model also exhibits the hysteresis phenomenon which implies diseases will persist even when R 0 < 1 although the system undergoes a forward bifurcation and this phenomenon is rarely observed in disease models. Consequently, our analysis suggests that the diseases with multiple transmission routes exhibit bistable dynamics. However, efficient application of temporary control in bistable regions will curb the disease to lower endemicity. Additionally, numerical simulations reveal that the equilibrium level of infected hosts decreases as psychological effect increases. [ABSTRACT FROM AUTHOR]

Several variants of the SARS-CoV-2 virus have been detected during the COVID-19 pandemic. Some of these new variants have been of health public concern due to their higher infectiousness. We propose a theoretical mathematical model based on differential equations to study the effect of introducing a new, more transmissible SARS-CoV-2 variant in a population. The mathematical model is formulated in such a way that it takes into account the higher transmission rate of the new SARS-CoV-2 strain and the subpopulation of asymptomatic carriers. We find the basic reproduction number R0 using the method of the next generation matrix. This threshold parameter is crucial since it indicates what parameters play an important role in the outcome of the COVID-19 pandemic. We study the local stability of the infection-free and endemic equilibrium states, which are potential outcomes of a pandemic. Moreover, by using a suitable Lyapunov functional and the LaSalle invariant principle, it is proved that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. Our study shows that the new more transmissible SARS-CoV-2 variant will prevail and the prevalence of the preexistent variant would decrease and eventually disappear. We perform numerical simulations to support the analytic results and to show some effects of a new more transmissible SARS-CoV-2 variant in a population.

The stable operation and control of the proposed terrestrial multi-terminal Voltage Source Converter (VSC) medium voltage DC (MVDC) distribution network is a remarkable motivation towards developing the future universal DC grid interconnecting the low voltage DC systems on one side and the high voltage DC systems on the other. The small-signal stability analysis are important in designing these power electronic based systems (PEBS). In this study, small-signal stability approaches for PEBS are reviewed with the aim of identifying suitable methods for the proposed MVDC distribution network. It is established that the impedance-based methods are suitable for local stability analysis complementing very well with the state-space modelling-eigenvalue analysis method best for global stability analysis. The Lyapunov linearisation method offers simple, adaptable, and accurate small-signal and large-signal stability study. On the other hand, the bifurcation analysis is an emerging non-linear approach with promising efficiency and precision. In conclusion, there is no single small-signal stability criterion that encompass an acceptable level of accuracy, adaptability, and efficiency. Thus, the impedance-based methods combined with state-space modelling-eigenvalue analysis, Lyapunov linearisation, and bifurcation theory can be suitable small-signal stability approaches for the multi-terminal MVDC distribution network.

The stable operation and control of the proposed terrestrial multi-terminal Voltage Source Converter (VSC) medium voltage DC (MVDC) distribution network is a remarkable motivation towards developing the future universal DC grid interconnecting the low voltage DC systems on one side and the high voltage DC systems on the other. The small-signal stability analysis are important in designing these power electronic based systems (PEBS). In this study, small-signal stability approaches for PEBS are reviewed with the aim of identifying suitable methods for the proposed MVDC distribution network. It is established that the impedance-based methods are suitable for local stability analysis complementing very well with the state-space modelling-eigenvalue analysis method best for global stability analysis. The Lyapunov linearisation method offers simple, adaptable, and accurate small-signal and large-signal stability study. On the other hand, the bifurcation analysis is an emerging non-linear approach with promising efficiency and precision. In conclusion, there is no single small-signal stability criterion that encompass an acceptable level of accuracy, adaptability, and efficiency. Thus, the impedance-based methods combined with state-space modelling-eigenvalue analysis, Lyapunov linearisation, and bifurcation theory can be suitable small-signal stability approaches for the multi-terminal MVDC distribution network. [ABSTRACT FROM AUTHOR]

In this article, we study the non-standard finite difference (NSFD) schemes for the diabetes mellitus with tuberculosis infection. We have classified diabetes mellitus into two categories such as diabetes without complications and with complications and studied diabetes with tuberculosis infection. We have modelled diabetes with tuberculosis infection with linear and nonlinear model and studied the local and global asymptotic stability analysis using the NSFD scheme. [ABSTRACT FROM AUTHOR]

Abstract The stability properties of basic states are often elucidated by examining the evolution of small disturbances. Such studies have recently been successfully applied to mean turbulent states, obtained through averaging of experimental measurements or Large-Eddy Simulations (LES), for both wall-bounded as well as free shear flows. Typically, the equations are employed using the disturbance form of the equations. To circumvent the necessity to linearize the governing equations, an especially tedious task for viscous and turbulent closure terms, Touber and Sandham (2009) [21] , proposed an approach that achieves the same purpose by solving the full Navier–Stokes (NS) equations, with a forcing term to maintain mean flow invariance. The method places no restrictions, such as slow streamwise variations, on the underlying basic state. The goals of the current work are to first verify this mean flow perturbation (NS-MFP) technique and then apply it to the problem of jet noise. For the first thrust, we show that when the basic state is appropriately constrained, the technique reverts to Linear, Parabolized and Global stability methods. The method is then verified by reproducing the growth of unstable modes in an inviscid Mach 6 entropy layer. The application to jet noise considers subsonic Mach 0.9 and perfectly expanded supersonic Mach 1.3 round jets. The results are compared with those from Parabolized Stability Equations (PSE) and LES solutions, respectively, considering monochromatic and multi-frequency perturbations. The NS-MFP method successfully reproduces key features of the modal response, including Strouhal number dependent directivity of noise radiation. Aspects related to the manner in which the mean basic state is obtained, whether from LES or Reynolds-averaged Navier–Stokes (RANS) equation are also explored. In particular, the sensitivity of the perturbation to whether the eddy viscosity is included or not, is examined in reference to maximum intensity of pressure fluctuation, directivity of noise radiation and the rate of fall-off of the spectra at higher Strouhal numbers. The results indicate that a closer match on the noise-radiation characteristics is obtained when effects of eddy-viscosity on the disturbances are neglected. [ABSTRACT FROM AUTHOR]

We present a global stability analysis of a Curzon–Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability.

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R0, the basic reproduction number, is less than unity. When R0 > 1 and under some conditions, then our system has a unique positive ω-periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level. [ABSTRACT FROM AUTHOR]

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimens- ional control input created by an electromagnetic actuator located on the cylinder surface, adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number repre- senting the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926 D and 0.822 D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode transformation. All of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force. [ABSTRACT FROM AUTHOR]

We perform two-dimensional unsteady Navier–Stokes simulation and global linear stability analysis of flow past a heated circular cylinder to investigate the effect of aided buoyancy on the stabilization of the flow. The Reynolds number of the incoming flow is fixed at 100, and the Richardson number characterizing the buoyancy is varied from 0.00 (buoyancy-free case) to 0.10 at which the flow is still unsteady. We investigate the effect of aided buoyancy in stabilizing the wake flow, identify the temporal and spatial characteristics of the growth of the perturbation, and quantify the contributions from various terms comprising the perturbed kinetic energy budget. Numerical results reveal that the increasing Ri decreases the fluctuation magnitude of the characteristic quantities monotonically, and the momentum deficit in the wake flow decays rapidly so that the flow velocity recovers to that of the free-stream; the strain on the wake flow is reduced in the region where the perturbation is the most greatly amplified. Global stability analysis shows that the temporal growth rate of the perturbation decreases monotonically with Ri , reflecting the stabilization of the flow due to aided buoyancy. The perturbation grows most significantly in the free shear layer separated from the cylinder. As Ri increases, the location of maximum perturbation growth moves closer to the cylinder and the perturbation decays more rapidly in the far wake. The introduction of the aided buoyancy alters the base flow, and destabilizes the near wake shear layer mainly through the strain-induced transfer term and the pressure term of the perturbed kinetic energy, whereas the flow is stabilized in the far wake as the strain is alleviated. [ABSTRACT FROM AUTHOR]

In this paper, we propose and analyze a mathematical model for the dynamics of visceral leishmaniasis with seasonality. Our results show that the disease-free equilibrium is globally asymptotically stable under certain conditions when R 0 , the basic reproduction number, is less than unity. When R 0 > 1 and under some conditions, then our system has a unique positive ω -periodic solution that is globally asymptotically stable. Applying two controls, vaccination and treatment, to our model forces the system to be non-periodic, and all fractions of infected populations settle on a very low level.

The structural instabilities of base flow in hypersonic wake flow over sphere are investigated by numerical simulation in this paper. Numerical simulation method is second-order accuracy NND scheme in spatial direction and Second-order Runge-Kutta scheme in temporal direction. Wakes flow of sphere at M∞ =2, Re =1.71E+6(based on the sphere radius) and at M ∞ =6, Re =1.71E+6 are simulated. Stable solutions are obtained and there are a primary separation and a secondary separation zone in flow over sphere at M∞ =2 and M∞ =6. Later, without any arbitrary disturbance imposed, the structural instability still occurs after a certain critical time. The evolving process of the structure of flow over sphere is a periodic behavior in the forepart, but it evolves into a non-periodic behavior after a critical time at M∞ =2. In the period time, the topological structures of the flow field over sphere and their evolving process at M∞ =6 are similar to that of M∞ =2, but there is non-periodic behavior observed at M∞ =6 in spite of long calculation time. In the case of sphere, the results by global stability theory, numerical results and results of power spectrum are compared each other. The global stability analysis method can give a good prediction result. This study result indicates that the present numerical simulation method and global stability analysis method can be used for the study of the stability of base flow and confirms that hypersonic flow at the base is also instability. [ABSTRACT FROM AUTHOR]

We present a global stability analysis of a Curzon-Ahlborn heat engine considering different regimes of performance. The stability theory is used to construct the Lyapunov functions to prove the asymptotic stability behavior around the steady state of internal temperatures. We provide a general analytic procedure for the description of the global stability by considering internal irreversibilities and a linear heat transfer law at the thermal couplings. The conditions of the global stability are explored for three regimes of performance: maximum power (MP), efficient power (EP) and the so-called ecological function (EF). Moreover, the analytical results were corroborated by means of numerical integrations, which fully validate the properties of the global asymptotic stability. [ABSTRACT FROM AUTHOR]

We examine a mathematical model for the transmission of Streptococcus Pneumoniae amongst young children when the carriage transmission coefficient depends on the serotype. Carriage means pneumococcal colonization. There are two sequence types (STs) spreading in a population each of which can be expressed as one of two serotypes. We derive the differential equation model for the carriage spread and perform an equilibrium and global stability analysis on it. A key parameter is the effective reproduction number R e. For R e ≤ 1,  there is only the carriage-free equilibrium (CFE) and the carriage will die out whatever be the starting values. For R e > 1, unless the effective reproduction numbers of the two STs are equal, in addition to the CFE there are two carriage equilibria, one for each ST. If the ST with the largest effective reproduction number is initially present, then in the long-term the carriage will tend to the corresponding equilibrium. [ABSTRACT FROM PUBLISHER]