**4. Conclusion**

An equilibrium MD simulation has been performed to report the velocity autocorrelation function (VACF) and self-diffusion coefficient (*D*) of three-dimensional (3D) electrorheological complex (dusty) plasmas (ER-CDPs) for the analysis of diffusion motion of dust particles. The interactions and forces between dust particles were modeled by Yukawa potential and Quadrupole interactions of charged dust particles. This paper highlights the outcomes of VACF and *D* for 3D

*Studies of Self Diffusion Coefficient in Electrorheological Complex Plasmas… DOI: http://dx.doi.org/10.5772/intechopen.98854*

### **Figure 6.**

*VACF as a function of molecular dynamics simulation time scale for constant plasma screening parameter* (κ *= 3.0). MD simulations results obtained for* N *= 500 simulated dust particles with the variation of uniaxial external electric field (0.0 <* MT ≤ *1.30) and four different plasma regimes (a)* Γ *= 30, (b)* Γ *= 75, (c)* Γ *= 250 and (d)* Γ *= 500.*

ER-CDPs in the presence of a uniaxial electric field (*MT*). We used Green-Kubo expression to calculate VACF and *D* over a wide range of CDPs Coulomb coupling (*Γ*) and Debye screening (*κ*) parameters. The VACF and *D* are significantly dependent on the plasma parameters (*κ*, *Γ*) and *MT*. The calculated results are highly consistent with other MD data in the absence of *MT.* It was observed that *D* decreased with increasing the *Γ*. The *MT* significantly affects the diffusion motion in ER-CDPs from intermediate to higher values of *Γ* and does not affect low *Γ*. The *D* increases with increasing the *MT* and *κ.* A new investigation gives more comprehensive and reliable data for VACF and *D* over given plasma parameters. It has been demonstrated that the presented numerical results for a given range of plasma parameters (*Γ*, *κ*) and the number of particles are good performances. The proposed numerical model is suitable for liquid-like and solid-like states for 3D CDPs. We can be concluded that the developed MD simulations approach will be employed to investigate the thermophysical properties of ER-CDPs.

## **Acknowledgements**

The support provided by the National Science Fund for Distinguished Young Scholars of China (No. 51525604), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 51721004) for the completion of the present work is gratefully acknowledged. The authors would also like to thank Dr. X. D. Zhang at the Network Information Center of Xi'an Jiaotong University for supporting the HPC platform and the National Centre for Physics (NCP) Islamabad allocation computational power to check and run the MD code.
