With the rapid development of smart grids, the strategic behavior evolution in user-side electricity market transactions has become increasingly complex. To explore the dynamic evolution mechanisms in this area, this paper systematically reviews the application of evolutionary game theory in user-side electricity markets, focusing on its unique advantages in modeling multi-agent interactions and dynamic strategy optimization. While evolutionary game theory excels in explaining the formation of long-term stable strategies, it faces limitations when dealing with real-time dynamic changes and high-dimensional state spaces. Thus, this paper further investigates the integration of deep reinforcement learning, particularly the deep Q-learning network (DQN), with evolutionary game theory, aiming to enhance its adaptability in electricity market applications. The introduction of the DQN enables market participants to perform adaptive strategy optimization in rapidly changing environments, thereby more effectively responding to supply–demand fluctuations in electricity markets. Through simulations based on a multi-agent model, this study reveals the dynamic characteristics of strategy evolution under different market conditions, highlighting the changing interaction patterns among participants in complex market environments. In summary, this comprehensive review not only demonstrates the broad applicability of evolutionary game theory in user-side electricity markets but also extends its potential in real-time decision making through the integration of modern algorithms, providing new theoretical foundations and practical insights for future market optimization and policy formulation.

Magnetorheological fluid (MRF), as a novel intelligent composite material, possesses unique controllable properties in the presence of a magnetic field, thereby opening up new possibilities for its engineering applications. This study proposes a novel parametric model to predict the nonlinear hysteresis behavior of MRF using micron-scale carbonyl iron particles. Experiments with large-amplitude shear tests (10% strain amplitude, 0.1 Hz and 1 Hz frequencies) were conducted at five current levels (0 A, 0.5 A, 1 A, 1.5 A, and 2 A) to identify model parameters via a genetic optimization algorithm. The proposed model, with fewer parameters and no differential operators, outperforms existing models (e.g. Bouc–Wen and hyperbolic tangent models) in capturing MRF’s nonlinear behavior. This research provides a robust theoretical framework for predicting the nonlinear hysteresis in automotive dampers and semi-active suspension control.

In the context of increasing global efforts to mitigate climate change, effective carbon emission reduction is a pressing issue. Governments and power companies are key stakeholders in implementing low-carbon strategies, but their interactions require careful management to ensure optimal outcomes for both economic development and environmental protection. This paper addresses this real-world challenge by utilizing evolutionary game theory (EGT) to model the strategic interactions between these stakeholders under a low-carbon trading mechanism. Unlike classical game theory, which assumes complete rationality and perfect information, EGT allows for bounded rationality and learning over time, making it particularly suitable for modeling long-term interactions in complex systems like carbon markets. This study builds an evolutionary game model between the government and power companies to explore how different strategies in carbon emission reduction evolve over time. Using payoff matrices and replicator dynamics equations, we determine the evolutionarily stable equilibrium (ESE) points and analyze their stability through dynamic simulations. The findings show that in the absence of a third-party regulator, neither party achieves an ideal ESE. To address this, a third-party regulatory body is introduced into the model, leading to the formulation of a tripartite evolutionary game. The results highlight the importance of regulatory oversight in achieving stable and optimal low-carbon strategies. This paper offers practical policy recommendations based on the simulation outcomes, providing a robust theoretical framework for government intervention in carbon markets and guiding enterprises towards sustainable practices.

In this paper, an automatic-recovery inertial switch is presented which for the first time adopts gallium–indium (EGaIn) as the switching metal droplet. The device consists of a glass substrate with patterned sensing electrodes, a PDMS microfluidic chip with microchannels and microvalves and a metal droplet. Here, we used EGaIn as the conductive element of the switch because it has several advantages compared with other conductive materials such as water or mercury. Specifically, the proposed device has the ability to automatically recover and can be used repeatedly. In the initial off-state, the droplet is stored in the reservoir. During the working state, the metal droplet passes through the channel and connects the sensing electrodes when the acceleration exceeds the designed threshold level. After that, the EGaIn will return to its original position by a subtle use of its structural characteristics.

Dimensionless numbers are often used to characterize the various modes of droplet breakup processes. However, the current methods of calculating these dimensionless numbers are not uniform—consequently, the calculation results are different, resulting in different phase diagrams of droplet separation. This paper first summarizes the methods of calculating the Weber number. The maximum transient velocity at the center of a nozzle is then used as the characteristic velocity for calculating the Weber number, and this formulation is used to solve certain scenarios in which the traditional Weber number cannot be applied, such as the strange phenomenon of the upward flight of separated droplets. A mathematical model is established to simulate the various separation forms of droplets, and the experimental study is also carried out. This upward flight of droplets is found to be the result of competition between the liquid inertial force, surface tension force, and suction effect of the nozzle mouth. The final velocity of the droplets depends on the existence of a stagnation surface and the corresponding sweep effect. Finally, the phase diagram of different droplet separation modes is drawn in the Ohnesorge–Weber number space.