Kinetic energy in a system of particles with a nonreciprocal interaction

Abstract

We present a theoretical model for the description of the heating mechanism and the redistribution of kinetic energy in a system of particles with nonreciprocal interactions that occur in disperse systems of different nature. To verify the theory, we carried out the numerical simulations of two-particle systems with a nonreciprocal “quasi-dipole–dipole” interaction that is similar to the interaction due to the effect of ion focusing in a laboratory complex plasma under experimental conditions. The proposed model of heating can explain various features of dust dynamics in anisotropic complex plasma.

Motion of a self-propelled particle with rotational inertia

“…In the inertialess limit of rotation, applying the correlation method 79–81 to eqn (1) and (5), we get (see Appendix A)where V 0 = F 0 / Mν fr . Eqn (7) looks like the ones obtained in ref.…”

“…〈 x 2 ( t )〉 can be derived by applying the correlation method 79–81 to eqn (6), taking into account the initial conditions of the problem and eqn (8) and (9). Since 〈 F ( x ) ran F ( x ) 0 〉 = 0, the solution is independent for two random processes, i.e.…”

“…In the inertialess limit of rotation, applying the correlation method [79][80][81] to eqn (1) and ( 5), we get (see Appendix A)…”

“…B. Mean-square displacement hx 2 (t)i can be derived by applying the correlation method [79][80][81] to eqn (6), taking into account the initial conditions of the problem and eqn ( 8) and ( 9). Since hF (x) ran F (x) 0 i = 0, the solution is independent for two random processes, i.e., hx 2 (t)i hx T 2 (t)i for F (x) 0 = 0, and hx 2 (t)i hx P 2 (t)i for F (x) ran = 0.…”

“…Assuming F ran = 0, the mean-square velocity of the particle due to self-propulsion, V P 2 , can be derived by applying the correlation method. [79][80][81] The system of eqn (1) and ( 5) can be rewritten in the vector form as…”