Micro Model Simulate Active Incompressible Fluid

Active matter is a new interdisciplinary science with a wealth of dynamic phenomena and phase transition behavior as a typical non-equilibrium system and it plays an important role in the life system. Especially, the study about active incompressible system has attracted many physist's attention last two years, our purpose in this letter is to release active incompressible system, then observe the type of phase transition through measuring critical exponents, and prove whether the velocity correlation function follows the special rule or not, which is predicted by incompressible active fluids theory.The main research work and innovation point of this treatise as follows:1. We introduce the development and situation of active matter systematically from the view of experiment, simulation and theory. Experiments on active incompressible systems are still lacking at present. We elucidate the continuum theory of active compressible and incompressible system, and give some important predictions.2. We study the simulation work of Vicsek model and like Vicsek model, and make a list about achievement and methods of Vicsek T., Chate H., et al, such as order parameter and its probability distribution, Binder cumulant, number fluctuation,critical exponents and "hysteresis" and so on, using these methods to analyze phase transition, finit size effect and giant fluctuation etc. All their methods and discussion are compared with ourselves research work.3. We achieve the active incompressible system through special particle interactions based on micro model, which are proposed as D interaction and V alignment. We build the model which is called as D Vicsek through combining discrete Vicsek model with D interaction, and also build the other model which is called as DV Vicsek through combining continue Vicsek with D interaction and V alignment. As for D Vicsek model, although Band structure disappears and the distribution of density is uniform in order phase, it is still a discontinue phase transition. Because there is always the existence of giant number fluctuation, and it is caused by the increment of noise or the competition between D interaction and alignment in the system, where D can suppress the unsteady of density effectively.What's notable is that it is a coexistence of metastable state and stable state in ordered phase at the range of ?? [0.45,0.48] without noise for smaller velocity. DV Vicsek model conquers successfully some terrible drawbacks in D Vicsek model which are the present of direction noise and the competition between D interaction and alignment. We realize the active incompressible system in two dimension. Although the giant fluctuation disappears and the density is evenly distributed, the particles can not accumulate to form the Band structure, but we find the presence of the velocity field Band, which causes the system to remain discontinuous phase transition. We measure the exponential relationship between the velocity correlation function and the distance satisfying, and the exponent is about -1.0, and there is a significant difference from the predicted results in continuum theory. We observe that there is a linear relationship between the transformation point and the parameter b, and the slope of the linear relationship is exponentially related to the random force f: ac? -fv·b,where v? 2.0. In addition, there is a power exponential relationship between the transformation point and the random force f , the index changes with the parameters b.4. Although the behavior of phase transition in active incompressible system has been studied by M.F.Laguna et al[28] through numerical solution of fluid equation,we achieve active incompressible system through special interaction based on micro model firstly. Although M.F.Laguna et al[28] studied the phase transition behavior of the active incompressible system by numerical solution of the fluid equation, the research results of this system have not been realized from the microscopic model level. We construct the microscopic model of active incompressible system for the first time by constructing novel particle action types.