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In Electro-Osmotic Pumps (EOPs), a micro fluid flow is formed by applying an external electric field via two electrodes immersed in the electrolyte. The immersed electrodes, due to lying in the fluid flow path, can consider an obstacle that can negatively affect the flow inside the microchannel. This issue is usually neglected in studies performed on the electroosmotic flows. Concerning this motivation, in this paper, a novel concept of a multi-stage EOP (introduced earlier by the researchers) was investigated numerically where the electrodes were attached to the wall of the micropump so as not to obstruct the fluid flow and to facilitate the serialization of micropumps. A two-dimensional numerical code is developed to analyze the steady-state performance of the multi-stage EOP. The governing equations for the fluid flow, internal and external electric fields, and ion concentration distribution are solved using the Finite Volume method. The results showed that in the multi-stage EOP consisting of multiple micropumps connected in series, the maximum pressure of EOP will enhances by increasing the number of micropumps. In contrast, the maximum flow rate remains approximately constant. The relationship between the maximum pressure, and the strength of the applied external electric field, was also investigated based on the electric field strength, and the results were expressed as a mathematical correlation. [ABSTRACT FROM AUTHOR]

This paper explores the integration and harmonization of an epidemic dynamics model and a resource production–inventory management model, aiming to identify optimal control strategies of epidemic containment. We begin with establishing a generalized optimal control model for epidemic dynamics, which offers a unified framework to verify the sufficient conditions for the existence of the optimal solutions to a class of epidemic optimal control models. Based on the model, a resource production–inventory dynamic model with learning ability is proposed to find optimal strategies of the medical resource management. Subsequently, we propose the optimal control model for a dynamics system of COVID-19 and explore the optimal strategies of the combined applications of vaccine and recommended treatment in comprehensive control of the epidemic. Finally, the viability of effective integration and coordination between the optimal control models of the epidemic dynamics and the resource production–inventory system is verified by numerical simulation and analytical analysis, and a new method is implemented for finding the optimal management strategy for epidemic control. Therefore, this study advances a more comprehensive understanding of the interplay between epidemic dynamics and resource management, illustrating the feasibility and efficacy of integrating multiple models to achieve optimal decisions in both theoretical and practical aspects of epidemic control. • Sufficient condition of optimal solution to a class of optimal control models is set. • New optimal control models of COVID-19 and production–inventory dynamics are set. • Vaccine and treatment based medical resource optimal management way is implemented. • A multi-model integrated approach of optimal epidemic control strategies is explored. [ABSTRACT FROM AUTHOR]

Passively mode-locked fiber laser has advantages of compactness, simplicity, flexibility and high quality of the output pulse, which provides an excellent research platform for the analysis of optical soliton characteristics. In this paper, the complex cubic Ginzburg–Landau equation (CGLE) is employed to simulate pulse propagation in passively mode-locked Er-doped fiber laser. We use barycentric interpolation collocation method to numerically solve the dark single soliton, dark two-soliton and bright two-soliton solutions, and study the effects of dispersion, nonlinear effects, gain and loss on optical pulse transmission. We discuss the dynamic characteristics of the bright two-solitons and dark two-solitons for the complex CGLE, respectively. The results is of great significance for the study of optical pulse transmission in fiber laser. • The cubic Ginzburg–Landau equation is employed to simulate pulse propagation in passively mode-locked Er-doped fiber laser. • The dark single soliton solution and bright two-soliton solution are numerically solved by barycentric interpolation collocation method. • The dynamic characteristics of the bright two-solitons and dark two-solitons for the cubic Ginzburg–Landau equation are of great significance for the study of optical pulse transmission in fiber laser. [ABSTRACT FROM AUTHOR]

We are concerned with dynamical behavior of the indirectly and locally memory-damped Timoshenko system. The polynomial/exponential decay results for the long-term dynamical behavior of the Timoshenko system are established when the memory kernels decay polynomially/exponentially. To obtain ideal asymptotic decay rates under basic conditions, we take some analysis processes specially designed for our issues. The obtained long-term dynamical behavior theorems, with the exact uniform decay rates for the solutions to the system, indicate that for the Timoshenko system with indirect memory damping, a local memory effect is enough to produce an entire dissipation mechanism and to ensure the same decay rates as in the case of global memory effect. Moreover, although our conditions on the memory kernels are weaker compared with the ones in the literature, we still derive stronger conclusions. Finally, we present some results of numerical simulation to illustrate quantitatively the behavior of the solution energies of our system, which agree with our theoretical results well. • Timoshenko system in the paper is controlled only by an indirect local memory damping. • Ideal asymptotic decay results are established for the long-term dynamical behavior of the Timoshenko system. • The obtained theorems indicate that for the Timoshenko system with indirect memory damping, a local memory effect is enough to produce an entire dissipation mechanism and to ensure the same decay rates as in the case of global memory effect. • Although our conditions on the memory kernels are weaker compared with the ones in the literature, we still derive stronger conclusions. • Numerical simulation results agree with our theoretical results well. [ABSTRACT FROM AUTHOR]

In this paper, we present a systematic renormalization group method to investigate a class of singularly perturbed delay differential equations. The uniformly valid approximate solution can be obtained, and we give a rigorous proof of the error estimate of the approximate solution. In addition, some numerical comparisons between the exact solution, the result by the averaging method and our result are given for two examples. • We present a systematic RG approach to deal with the singularly perturbed DDEs. • We complete the entire task by unifying the piecewise RG equations into a delay one. • By the numerical simulations, the uniformly valid of our result be proved. [ABSTRACT FROM AUTHOR]

• A Cournot-Bertrand duopoly mixed competition model is established. • The stability conditions of the system are analyzed by numerical calculation and numerical simulation. • The Arnold's tongues are studied. • The coexistence of attractors is analyzed by using the basin of attraction. • The contact bifurcation in the basin of attraction is studied by using the theory of critical curve and noninvertible map. In this paper, we consider the Cournot-Bertrand duopoly mixed competition model, which is characterized by different decision-making variables and different objective functions of the two enterprises. This form of competition is more consistent with the complex actual economic market. The general stability conditions of the four equilibria are given and analyzed with eigenvalues and Jury criterion, so that enterprise decision makers could choose appropriate parameters to determine the development of the enterprise. Under the specific parameter conditions, the stability conditions are analyzed and demonstrated in detail by using two-dimensional bifurcation diagrams, stable region diagrams and bifurcation curves. Many fractal Arnold's tongues are found in two-dimensional bifurcation diagrams. These tongues are associated with the Neimark-Sacker bifurcation of the fixed point and are arranged in accordance with the organization law of the periodic tree of the Stern-Brocot tree, which is helpful for us to analyze the transitions of system between period and chaos. With the help of the basin of attraction, the coexistence of attractors is analyzed, on which the decision maker can choose the initial conditions that are beneficial to the development of the enterprise. We also analyze the topology structure of basin of attraction and the formation mechanism of holes in the basin of attraction by using the theory of critical curve and noninvertible map. [ABSTRACT FROM AUTHOR]