A Review of Digital Watermarking by Bruce

By Bruce

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QN 1 N! (N − n)! 3) (n) n The quantity ρN (r ) dr n yields the probability of finding n particles of the system with coordinates in the volume element dr n , irrespective of the positions of the remaining particles and irrespective of all momenta. The particle densities and the closely related, equilibrium particle distribution functions, defined below, provide a complete description of the structure of a fluid, while knowledge of the low-order particle distribution functions, (2) in particular of the pair density ρN (r1 , r2 ), is often sufficient to calculate the equation of state and other thermodynamic properties of the system.

1). As ρ → 0, it follows from earlier definitions that z → 0, ρ/z → 1 and Ξ → 1. 22). 23). 12) Unlike the energy and pressure equations, the applicability of this relation does not rely on the assumption of pairwise additivity of the interparticle forces. 12) that χTid = β/ρ, in agreement with the result obtained by differentiation of the ideal-gas equation of state. 7 COMPUTER SIMULATION: MOLECULAR DYNAMICS AND MONTE CARLO As we briefly mentioned at the end of Chapter 1, the behaviour of liquids, solids and dense gases at the microscopic level can be simulated in one of two ways: by the method of molecular dynamics or by the Monte Carlo method.

In a molecular-dynamics simulation a local disturbance will F IG . 2. Periodic boundary condition used in computer simulations. The circle represents the truncation sphere drawn around a black particle in the central cell. See text for details. COMPUTER SIMULATION: MOLECULAR DYNAMICS AND MONTE CARLO 37 move through the periodic system and reappear at the same place, albeit in attenuated form, after a recurrence time of order L/c, where c is a speed of propagation that can be roughly equated to the speed of sound.

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