The crystallization and dynamics of water confined in model mesoporous silica particles (pore diameters ranging from 2.1 to 5 nm; pore length ≈ 1 μm) are studied in homogeneous aqueous suspensions by ...dielectric spectroscopy, differential scanning calorimetry, and nuclear magnetic resonance (NMR) techniques. We establish the phase diagram (T vs 1/d) of confined water covering a broad range of pore diameters. A linear dependence of the heterogeneous and the homogeneous nucleation temperatures on the inverse pore diameter is shown. The two lines converge at a pore diameter of ∼2.6 nm, below which formation of stable crystals is suppressed. By combining dielectric spectroscopy and different NMR techniques, we determine the dynamics of water within mesoporous silica over broad temperature and frequency ranges. Both techniques identify two dynamically distinguishable fractions of confined water coexisting within the pores. We attribute the two fractions to an interfacial water layer at the pore walls and confined water in the pore interior. Two alternative scenarios are proposed to rationalize the coexistence of two dynamically distinguishable water fractions. In the first scenario, two liquid fractions of water coexist under extreme confinement conditions for a range of temperatures; we discuss similarities with the two ultraviscous liquids (high-density liquid and low-density liquid) put forward for supercooled bulk water. In the second scenario, a liquid and a solid phase coexist; we conjecture that highly distorted and unstable crystal nuclei exist under extreme confinement that exhibit reorientation dynamics with time scales intermediate to the surrounding confined liquid and to bulk ice.
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IJS, KILJ, NUK, PNG, UL, UM
This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of ...susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized, and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F0∗,F1∗ ...of the proposed model are stated. Threshold parameter R0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative ρ and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The emergence of coronavirus disease (Covid-19) triggered a global pandemic with profound health, social, and economic impacts. Despite extensive governmental efforts, the virus remains a persistent ...worldwide threat. In this research, we introduce a nonlinear bi-susceptible model, also called bimodal dynamical system to study the dynamics of Covid-19. We delve into its transmission modes, risk factors, and potential long-term effects. Using analytical mathematical techniques, we ascertain the behaviors exhibited by the dynamic system at two main equilibrium states by imposing essential conditions on threshold parameter, thereby validating and affirming its inherent properties. To validate findings, we apply the nonstandard finite difference (NSFD) technique. By adjusting vaccination and hospitalization rates through constant control methods, we perform quantitative analysis and find that combining these measures with awareness expedites pandemic elimination. We identify influential parameters and formulate an optimal control problem with associated optimality conditions, determining effective time-dependent controls. Our study provides an evidence of the effectiveness of control strategies in achieving the desired outcome of reducing both financial costs and infection spread. The novelty of this research lies in utilizing a structure-preserving NSFD numerical scheme, backward in time, to analyze optimally the developed bi-susceptible Corona model.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
Flexible job shop scheduling problem (FJSSP) is a further expansion of the classical job shop scheduling problem (JSSP). FJSSP is known to be NP-hard with regards to optimization and hence poses a ...challenge in finding acceptable solutions. Genetic algorithm (GA) has successfully been applied in this regard since last two decades. This paper provides an insight into the actual complexity of selected benchmark problems through quantitative evaluation of the search space owing to their NP-hard nature. A four-layered genetic algorithm is then proposed and implemented with adaptive parameters of population initialization and operator probabilities to manage intensification and diversification intelligently. The concept of reinitialization is introduced whenever the algorithm is trapped in local minima till predefined number of generations. Results are then compared with various other standalone evolutionary algorithms for selected benchmark problems. It is found that the proposed GA finds better solutions with this technique as compared to solutions produced without this technique. Moreover, the technique helps to overcome the local minima trap. Further comparison and analysis indicate that the proposed algorithm produces comparative and improved solutions with respect to other analogous methodologies owing to the diversification technique.
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IZUM, KILJ, NUK, ODKLJ, PILJ, PNG, SAZU, UL, UM, UPUK
In this article, we develop a nonlinear SEIQHR fractional model with Atangana–Baleanu (ABC) derivative for the Corona virus disease (Covid-19). It is significant to mention that using a ...fractional-order derivative can provide more intricate insights into the complex dynamics of underlying models. We provide two unique equilibrium states of the model in order to analyze the problem. To explore the long-term dynamics of a disease, a threshold parameter for the model utilizing next-generation approach is computed. Local and global asymptotic behaviors of the proposed model at both the equilibrium states are established by imposing some necessary conditions on threshold parameter. To validate our obtained analytical results and to examine the importance of arbitrary order derivative, we implement a recently proposed Toufik–Atangana numerical technique. To reach our conclusions, we investigate a thorough quantitative analysis of the model through the adjustment of quarantine and hospitalization rates as a first constant control technique. Through numerical experiments, it is asserted that the Covid-19 pandemic may be eliminated more quickly if a human community selfishly adopted both of the necessary control measures at various coverage levels with appropriate awareness. The developed model is subjected to sensitivity analysis and the most sensitive parameters are identified. In addition, the bifurcation nature of the Covid-19 model is examined. Furthermore, we develop an optimal control problem along with the associated optimality conditions of Pontryagin type to discover the most effective controls for the both strategies, one for exposed and another for infected individuals. The goal is to reduce both the financial burden of executing these strategies as well as the number of exposed and infected people. The extremals are obtained numerically. The effectiveness and efficiency of the optimal control strategy are finally demonstrated by numerical simulations before and after the optimization. The importance of the current research work is the use of developed structure preserving Toufik-Atangana numerical scheme, backward in time, for the first time to analyze optimally the epidemic models, for example the proposed SEQIHR Covid-19 model.
•A new fractional model for the lethal Covid-19 with ABC operator is developed.•Necessary and sufficient conditions for the stability of disease free & endemic states are established.•Simulations utilizing an efficient Toufik-Atangana scheme confirm the derived analytical results.•The most sensitive parameters in the model are determined through sensitivity and bifurcation analysis.•Mathematical analysis to assess the impact of constant & optimally designed measures is performed.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this paper, existing classical Korteweg‐de Vries (KdV) equations are converted into the corresponding time‐fractional KdV equations by using Caputo‐Fabrizio fractional derivative and then solved ...with appropriate initial conditions by implementing semi‐numerical technique, that is, Laplace transform together with an iterative scheme. The obtained solutions are novel, and previous literature lacks such derivations. The stability of implemented technique is analyzed by applying Banach contraction principle and S‐stable mapping. Efficiency of Caputo‐Fabrizio fractional derivative is exhibited through graphical illustrations, and fractional results are drafted in tabular form for specific values of fractional parameter to validate the numerical investigation.
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FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SAZU, SBCE, SBMB, UL, UM, UPUK
The aim of this paper is to investigate stability of an isothermal glass tube drawing process through control parameters by the method of linear stability analysis. We want to see how the process ...parameters effect stability of the physical system being considered. For this purpose, we not only prove the existence and uniqueness of the solutions of steady state isothermal tube drawing model but also determine its numerical solution. To perform linear stability analysis, steady state numerical solution is incorporated in the eigenvalue problem, formulated by linearizing the isothermal model. The eigenvalue problem is then solved numerically to determine the critical draw ratio which indicates the onset of instabilities. To the end, stability of the process is analyzed using three different values of space step size. We also observe and discuss the effect of density, viscosity and pressure on stability of the isothermal tube drawing model.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Automotive-engine control and fault diagnostics largely depend upon the accuracy of the nonlinear models used. The structure of these nonlinear models is generally agreed upon. However, the model ...parameters are mostly difficult to obtain. This paper presents the development of second-order sliding-mode technique with real twisting algorithm for estimation of more than one parameter from a single dynamical equation of the nonlinear model. The system under study is a mean-value engine model of a naturally breathing gasoline engine. The parameters estimated are throttle body's discharge coefficient, load torque, and indicated torque as a function of inlet manifold pressure. The estimated variables are used to compensate for the unmodeled dynamics, modeling inaccuracies, and approximations which arise from the assumptions made for the development of mathematical model of a real-world system. The resulting model is a better description of the actual engine dynamics and gives good agreement to real engine data. The data are acquired from a production model vehicle equipped with an electronic control unit compliant to OBD-II standard. The observer designed is simple enough for implementation, and estimated parameters can also be used for engine-controller design and fault-diagnosis work.
Measles is a global threat due to its high contagion and rapid spread, especially in low-vaccination areas. Despite advancements in vaccination programs, Measles outbreaks still occur. Cross-border ...transmission emphasizes the need for global immunization and collaboration to prevent resurgence of this disease. In this paper, our main goal is to be able to understand the transmission dynamics and control of Measles using an SVEITR model. Various fundamental properties of the model are established analytically such as existence of a unique, bounded and positive solution. We demonstrate the stability of the model at two main equilibria by imposing essential criteria to a threshold parameter, computed using next generation matrix method. We implement Non-Standard Finite Difference (NSFD) scheme to approximate solutions for the continuous system and validate our analytical results. With the goal of potentially eradicating the disease from the population, we evaluate the effectiveness of two control measures through simulations that remain constant over time and are tailored for both the susceptible and infected individuals. Sensitivity analysis is performed to identify responsive parameters. We introduce optimal control strategies by incorporating time-dependent vaccination and treatment, with the aim of minimizing infections, reducing disease severity, and improving public health. The novelty of the present work lies in employing NSFD scheme especially for optimal control problem solving, with the aim of managing and properly controlling the disease. This work not only enhances theoretical understanding but also provides practical insights for policymakers and public health officials striving to control and eradicate Measles globally. This motivation emphasizes the importance of the research in the context of public health, the innovative aspects of the methodology, and the potential practical applications of the findings.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
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