Academic literature on the topic 'Discrete Kinetic System'

The kinetics associated with the reaction of aromatic and aliphatic diamines with phthalic anhydride in glacial acetic acid was studied. This model system was intended to simulate the synthesis of polyimides from diamines and dianhydrides in molten benzoic acid. The reaction proceeds in two discrete steps, the first acylation occurs by the reaction of the diamine with phthalic anhydride followed by cy-clodehydration of the corresponding bis-(o-carboxyamides). The focus of the work was on the influence of chemical composition and basicity of the diamines on the kinetics. Kinetic and thermodynamic characteristics of model reactions were determined. It was established that acylation of aromatic and aliphatic diamines in acid medium proceeds as a reversible second-order reaction catalyzed by acid medium. On the basis of kinetic data obtained, an explanation is given for the observed phenomenon of reactivity leveling of diamines regardless of the basicity.

Following some general ideas on the discrete kinetic and stochastic game theory proposed by one of the authors in a previous work, this paper develops a discrete velocity mathematical model for vehicular traffic along a one-way road. The kinetic scale is chosen because, unlike the macroscopic one, it allows to capture the probabilistic essence of the interactions among the vehicles, and offers at the same time, unlike the microscopic one, the opportunity of a profitable analytical investigation of the relevant global features of the system. The discretization of the velocity variable, rather than being a pure mathematical technicality, plays a role in including the intrinsic granular nature of the flow of vehicles in the mathematical theory of traffic. Other important characteristics of the model concern the gain and loss terms of the kinetic equations, namely the construction of a density-dependent table of games to model velocity transitions and the introduction of a visibility length to account for nonlocal interactions among the vehicles.

The conventional modeling method of the marine steam turbine rotational speed control system (MSTRSCS) is based on Newton’s second law, constructing the mechanical equations between the rotational acceleration and the resultant torque. The disadvantages of this are nonlinearity, a complex structure and an infinite point of discontinuity in the rotational acceleration when the rotational speed is close to 0. Taking the kinetic energy of MSTRSCS as the output variable by using the kinetic energy theorem in this paper, we convert the complex nonlinear model of MSTRSCS into a linear one, since kinetic energy and rotational speed are homeomorphic. Model predictive control (MPC) adopts a discrete-time model, whereas the real system is time-continuous. Hence, poor performance is obtained in the real system when the time-discrete control law is applied to the MSTRSCS through the actuator. In case of high requirements for system accuracy and control performance, conventional MPC (CMPC) cannot meet the engineering requirements. In order to lessen the impact of this phenomenon, this paper proposes a novel MPC with actuator dynamic compensation (ADCMPC), in which the dynamics of the actuator are quantified and the system performance is improved. Compared with other control techniques such as CMPC, the performance of the ADCMPC strategy in MSTRSCS is successfully validated.

Kinetic models of discrete opinion dynamics are studied on directed Barabási–Albert networks by using extensive Monte Carlo simulations. A continuous phase transition has been found in this system. The critical values of the noise parameter are obtained for several values of the connectivity of these directed networks. In addition, the ratio of the critical exponents of the order parameter and the corresponding susceptibility to the correlation length have also been computed. It is noticed that the kinetic model and the majority-vote model on these directed Barabási–Albert networks are in the same universality class.