**Acknowledgements**

corresponding to Г (1, 200). In case of crystalline order state, the amplitude of vibrating particle decreases significantly and it converts completely in square waveform. It is interesting to note that the fundamental behavior of dust particles is different and it shows decaying trends in nonideal gases state, sinusoidal form in liquid state and square wave form in crystalline state at fixed screening value. Figures show that the results of *S*(*k*,ω) depend on the plasma parameters (*κ*, Г), as expected. Furthermore, it is investigated that in the ideal form of dusty plasma with high temperatures (low coupling values) the dust particles are exponentially decaying from high to low amplitude. One of justification is the dust particles transferred their energy to the surrounding particles that at high plasma temperature values. Furthermore, in panels (b) represent the EMD results of *S*(*k*,ω) in the liquefied state of dusty plasma. In this regime, dust particles comparatively less transfer their energy to the system. At this regime amplitude is maximum for simulation box size (*L* = max) and frequency of oscillating of dust particles is low and in the sinusoidal waveform. The frequency and amplitude of oscillating dust particles increase with increasing wave numbers *k =* 2, 3 and exhibit in the periodic wave form. Panels (c) show the results of *S*(*k*,ω) of dusty plasma in the nearly crystalline states. We have analyzed that in this regime the particles are tightly bound. In this case, the dust particles have small amplitude as compared to the gaseous and liquefy forms of dusty plasma.

It is observed from each panel of **Figures 1**–**4**, the dynamic of dust particles increases with increasing wave number. It is to be noted that the values of amplitude of the *S*(*k,ω*) are 3 = 0.7406, 0.6662, 0.8004 and 0.7902 respectively, for four wave numbers (*k* = 0, 1, 2, and 3) at the same values of *κ*, Г and *N*. It is observed that the dynamical structure factor of SCCDPs depends on plasma parameters (*κ*, Г). The frequency mode of *S*(*k,ω*) is high at low *κ* for SCCDPs. It is observed that *κ* is equally affecting on the dynamic of dust particles either the

We have employed EMD simulations for the investigations of *S*(*k,ω*) over a wide range of Coulomb and Debye screening parameters (*κ*, Г). It has been shown that the presented EMD technique and previous numerical methods have equivalent performance for the wide range of plasma state points, both yielding satisfactory data for plasma *S*(*k,ω*). New simulations provide more consistent and inclusive results for the plasma *S*(*k,ω*) over a complete range of Г (1, 200) and *κ* (1.4, 4) than the previously known numerical results. Our investigations show that the dynamic of dust particles are exponentially decayed, sinusoidal form and crystalline form, respectively, in the gaseous, liquefy regime and crystalline states of SCCDPs. Moreover, the dynamical spectra of dusty plasma do not observe at very high values of Г and low values of *κ*. Moreover, our results indicate that the dynamical structure factor in SCCDPs depends on *κ*, Г and *k.* It has been shown that the presented simulation has comparable performance with the earlier simulation of *S*(*k,ω*) over the wide domain of plasma states. For future work, it is suggested that presented EMD technique based Ewald summation can be used to investigate and explore dynamical structure factor behaviors in other simple liquid, dipolar and

dusty plasma in any phase (gaseous, liquid and crystalline).

140 Plasma Science and Technology - Basic Fundamentals and Modern Applications

**4. Summary**

ionic materials.

The authors are grateful to the National Advanced Computing, National Center of Physics (NCP), Pakistan, and National High Performance Computing Center of X'ian Jiaotong. The authors thank the University, P.R. China, for allocating computer time to test and run our MD code.
