March 2013
Intermediate to advanced
406 pages
14h 48m
English
Content preview from Perturbation Theories for the Thermodynamic Properties of Fluids and Solids
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Overview of Computer Simulation Methods 41
where F
ij
is the force acting on particle i due to the interaction with particle j,
Equation 2.10, and we are assuming pairwise additive interactions. r
i
, p
i
, and t
are virtual variables defined for the extended system, whereas the real variables
of the actual system are r
i
= r
i
, p
i
= p
i
/s, and t
=
t
0
dt/s. The equations of
motion (3.29) can be expressed in terms of the real variables, but the resulting
equations are no longer canonical nor the transformed equation 3.28 is a Hamiltonian
(Nosé 1984b).
On the other hand, with the change dt
=dt/s, Equations 3.29 transform into
(Hoover 1985)
˙
r
i
=
p
i
ms
,
˙
p
i
= s
j=i
F
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