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Given the friction and drag reduction effects observed in various biological hexagonal structures in nature, a new design was implemented on the rubber surface of the stator of a submersible screw pump. This design featured a multilayer concentric hexagonal groove structure. Furthermore, a composite multilayer hexagonal structure integrating grooves and pits was also developed and applied. This study investigated the influence of groove layer number, groove depth, pit depth, and multilayer hexagonal groove texture arrangement on the rubber surface flow characteristics. Additionally, the pressure field state, the degree of influence on the oil film-bearing capacity, and the biomimetic and hydrodynamic lubrication theories were tested using the finite element analysis method. Tribological experiments were conducted on nanosecond laser-processed rubber textures under simulated liquid lubrication conditions, reflecting actual shale oil well experiments. These experiments aimed to investigate the influence of multilayer hexagonal shape parameters on the tribological characteristics of the stator-rotor friction pair of a submersible screw pump. The results indicated that with a constant overall size, a multilayer hexagonal structure with ~0.1 mm groove depth enhanced the oil film-bearing capacity, providing significant friction and drag reduction. For composite textures, a deeper pit depth within the study area enhanced the oil film-bearing capacity. Furthermore, a gradient arrangement of groove textures featuring wider outer grooves and shallower depth exhibited superior performance in terms of bearing capacity. [ABSTRACT FROM AUTHOR]

The effects of complex well conditions in shale oil wells on the swelling and tribological properties of high-acrylonitrile stator rubber used in screw pumps were investigated in this study. Tests were conducted considering the combined effects of immersion medium, temperature, and duration. The key parameters measured included mass change rate, volume change rate, hardness, elongation at break, tensile strength, surface micro-morphology of the rubber after thermal expansion and swelling, friction coefficient, and wear quantity. The results indicated that in the actual well fluids, the mass change rate of high-acrylonitrile rubber ranged from −1.08% to 1.29%, with a maximum volume change rate of 2.78%. In diesel oil, the greatest mass change rate of the rubber was 4.68%, and the volume change rate did not exceed ±1%, indicating superior swelling resistance. In both actual well fluids and diesel oil, the maximum decreases in hardness were 8.7% and 9.5%, respectively. Tensile strength and elongation at break decreased with increasing immersion temperature, with elongation at break in 80 °C diesel oil decreasing by over 50%, indicating a significant decline in the tensile properties of the rubber. The average friction coefficient of rubber specimens immersed in actual well fluids at three temperatures, as well as in diesel oil at 25 and 50 °C, decreased compared with the high-acrylonitrile rubber without thermal expansion and swelling. However, the average friction coefficient of rubber specimens immersed in diesel oil at 80 °C increased. The wear quantity of the rubber increased following immersion in both media. Additionally, the friction coefficient and wear quantity of the rubber increased with increasing immersion temperatures. The results of the study can offer valuable insights into assessing the durability of properties in high-acrylonitrile stator rubber under complex well conditions. [ABSTRACT FROM AUTHOR]

The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the population when encountering predators and ignores the role of individual prey. To address this issue, we contemplate the dynamics of a stochastic prey–predator model with Smith growth rate and cooperative defense. The population density of prey is measured by mass, and the growth limitations are based on the proportion of unused available resources. Additionally, the grazing pattern of the predator incorporates cooperative characteristics into the functional response. We carry out existence and uniqueness analysis for the global positive solution. Then, we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solutions for investigating whether prey and predator populations continue to survive. Numerical examples indicate that the Smith growth rate, cooperative defense and environmental disturbance play crucial roles in the coexistence of interacting populations. [ABSTRACT FROM AUTHOR]

This paper investigates Turing instability and Hopf bifurcation for a diffusive plankton system with time delay and cell size. To determine the effects of diffusion and cell size on the dynamics of the system, we first study the system without time delay, where the conditions of stability of coexisting equilibrium and Turing instability are obtained through Routh-Hurwitz criterion. Then we give the existence of Hopf bifurcation using time delay as bifurcation parameter by analyzing the distribution of eigenvalues, and derive the property of Hopf bifurcation by applying the centre manifold theory. Finally, numerical simulation shows that different cell size increases the variety of dynamics for diffusive plankton system. [ABSTRACT FROM AUTHOR]

In this paper, we study a stochastic nutrient‐phytoplankton‐zooplankton model with cell size that represents the interaction between internal mechanism of species and external environment. We first investigate the existence and uniqueness of the global positive solution with positive initial values. Then we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solution. Once more, we find that large noise intensities cause the extinctions of phytoplankton and zooplankton. Finally, numerical simulations are given to verify the correctness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the linear quadratic regulator optimal leader-following consensus for multiagent systems in a single-integrator form. Substantially different from the existing related works, the cost function, a global one, and the topology structure are both pregiven, and the optimal protocol to be sought is distributed (which merely depends on relative state information). This violates the optimal protocol design based on the algebraic Riccati equation, although a centralized protocol can be derived. To solve the problem, a novel design strategy of distributed optimal protocol is proposed for the multiagent systems over the digraph of a directed tree. Specifically, the dynamics of the consensus error is explicitly obtained, by which an online-implementable algorithm is given to achieve the parameterization of the cost function. Namely, the completely explicit formula with respect to the gain parameters of all agents is derived for the cost function. Based on this, the existence of optimal gain parameters is rigorously proven, which means the existence of the desired distributed optimal protocol. Furthermore, the optimal gain parameters are derived by minimizing the explicit formula. Two simulation examples are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, finite-time consensus tracking is investigated via time-varying feedback for uncertain nonlinear multi-agent systems (NMASs). The presence of inherent uncertainties and disturbances in the NMASs highlights the main novelty : (1) The inherent uncertainties imply that more serious unknowns and time-variations are allowed in the nonlineartities and the control coefficients of the NMASs. (2) The inherent disturbances mean that the upper bound of the disturbances is unknown. To compensate the inherent uncertainties and disturbances, time-varying protocols are proposed by integrating time-varying technique and sliding mode method. Based on the proposed protocols, the finite-time leader-following consensus and finite-time containment are achieved under directed graph. Finally, the validation of the proposed protocols is verified by two examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the almost sure consensus via time-varying feedback for a class of uncertain stochastic nonlinear multiagent systems. A remarkable feature of the systems is that the nonlinearities allow serious unknowns and time-variations. Moreover, there exists no known bound for the unknown control coefficients. To handle the unknowns and time-variations, a time-varying consensus scheme is developed. The main idea of the scheme is to incorporate a delicate function of time into consensus protocols such that the unknowns and time-variations can be compensated as time increases. Based on the proposed protocols, the almost sure leaderless consensus and almost sure leader-following consensus are achieved. Finally, two simulation examples are provided to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the adaptive leader-following consensus for first- and second-order uncertain nonlinear multi-agent systems (NMASs) with single- and double-integrator leader, respectively. Remarkably, the control coefficients of the followers need not belong to any known finite interval, which makes the systems in question essentially different from those in the related works. Moreover, parameterized unknowns exist in the nonlinearities of the followers, and unknown control input is imposed on the leader, which make the problems difficult to solve. To compensate for these uncertainties/unknowns, the leader-following consensus protocols are constructed by employing adaptive technique for the first-order and the second-order NMASs. Under the designed adaptive consensus protocols and the connected graph, the leader-following consensus is achieved. Finally, two examples are given to show the effectiveness of the proposed leader-following consensus protocols. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effect of water temperature on phytoplankton–zooplankton dynamics with Holling type III functional response. Remarkably, growth rate, capture rate, handling time, death rate and Holling parameter are considered to be temperature dependent, which makes the model different from those in the existing related literatures. First, the relationships between model parameters and water temperature are presented. Then we give the positivity and boundedness of the solutions. And parameters dependent equilibrium analysis and stability analysis are obtained, respectively. It shows that when the water temperature is lower or higher than the optimal temperature, the equilibrium density of phytoplankton increases with decreasing capture rate and increasing handling time. Meanwhile, we show that the decrease of capture rate and increase of handing time cause the density of zooplankton also increases without the optimal temperature, while the population of zooplankton tends to decrease with decrease of growth rate. In addition, sensitivity of coexisting equilibrium to the parameters of the phytoplankton–zooplankton model is analyzed. Finally, one parameter bifurcation analysis is done. [ABSTRACT FROM AUTHOR]