Kinetic and scaling behavior of collective motion in biomaterials

Abstract

Collective motion in biomaterials is one of primordial phenomenon which can described the dynamical properties of such complex system. Many cells are coordinately and synchronously moving with an interfacial molecular mobility. These biological systems exhibit different behaviors; they may change configurations. Hence, we study numerically the kinetic and scaling behavior of these organisms under the noise effect. Previous researches use the Vicsek model to study the collectif motion in biomaterials. As an originality, our study is developed by using the Langevin dynamic, as a stochastic differential equation, which gives us important results. Effectively, in our paper we simulate the evolution of biomaterials as an example of complex system. In our work, the attention is drawn to use a new approach to study and discuss numerically the dynamic evolution and scaling behavior of self-propelled particles in biomaterials. The results show that the mean velocity of cells increases in time to reach an equilibrium phase. The individuals move as a single consistent structure from disordered state to order one. The originality of our work is to study the variation of the characteristic length. This later, is as a crucial parameter, separates the cells clusters may describe the system morphology. The time evolution of this parameter exhibits two different regimes separated by characteristic time which decrease exponentially with noise. We used the dynamical scaling to determine the scaling exponents which characterize the scaling behavior of the considered biomaterials.