Internal coordinate discontinuous

Note that left-hand side of this expression is, in fact, a continuity equation for which states that the multi-particle joint PDF is constant along trajectories in phase space. The term on the right-hand side of Fq. (4.32) has a contribution due to the Alp-particle collision operator, which generates discontinuous changes in particle velocities Up" and internal coordinates p", and to particle nucleation or evaporation. The first term on the left-hand side is accumulation of The remaining terms on the left-hand side represent... 

The cumulative distribution Fj(t) represents the probability that the quiescence time T is smaller than t. By assuming that the effect of the continuous change of the internal-coordinate vector is negligible, for the calculation of this probability, and by including also collision and aggregation as an additional discontinuous event, the following expression is obtained ... 

The first term in (12.4.1-9) represents physical transport. The second and third terms account for the continuous evolution of the particle internal coordinates, the second of the velocity, the third of the other particle internal coordinates. A ", and represent the rate of change in the phase space of the properties, A[" and A " of the i-component of the velocity of the iP particle, and of the property Discontinuous changes in the particle internal coordinates are due to collisions and are described by the source terms Bn Dyv), 5 represents "birth" and D "destruction" processes. 

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