Computational Physics

8.2 Molecular dynamics at constant energy 203 This form is most convenient because it is very stable with respect to errors due ...

204 Molecular dynamics simulations check whether their separation is larger thanrcut-off. In the same paper in which he introduc ...

8.2 Molecular dynamics at constant energy 205 we look at Header(IX,IY,IZ) and then move down from particle I to the following by ...

206 Molecular dynamics simulations and now the force and the potential are continuous. These adjustments to the potential can be ...

8.2 Molecular dynamics at constant energy 207 Continue simulation and determine physical quantities:Integration of the equations ...

208 Molecular dynamics simulations function beyondrcut-off: 〈U〉=〈U〉cut-off+ 2 π N(N− 1 ) V ∫∞ rcut-off r^2 drU(r)g(r) (8.18) whe ...

8.3 A molecular dynamics simulation program for argon 209 each of the momenta in order to make the total momentum zero. Now the ...

210 Molecular dynamics simulations Table 8.1. Molecular dynamics data for thermodynamic quantities of the Lennard–Jones liquid. ...

8.4 Integration methods: symplectic integrators 211 than the typical collision time (time of free flight), you should find 〈x^2 ...

212 Molecular dynamics simulations a steady increase or decrease, and thenoise, fluctuations on top of the drift. Drift is obvio ...

8.4 Integration methods: symplectic integrators 213 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0 5 10 15 20 25 30 35 40 45 Ener ...

214 Molecular dynamics simulations (8.27)and(8.28)does indeed scale ash^2. In the following we determine momenta according toEq. ...

8.4 Integration methods: symplectic integrators 215 The fact that this quantity is conserved can also be checked directly using( ...

216 Molecular dynamics simulations as we shall see below. Most important for molecular dynamics is the property that the total e ...

8.4 Integration methods: symplectic integrators 217 method in which a time-dependent friction parameter occurs, obeying a first ...

218 Molecular dynamics simulations It is convenient to introduce the combined momentum–position coordinatez = (p,x), in terms of ...

8.4 Integration methods: symplectic integrators 219 and similar forH(δzb). This leads to the form dδA dt ∣ ∣ ∣∣ t= 0 =−(LTδza)·( ...

220 Molecular dynamics simulations x p t Figure 8.3. The area conservation law for a symplectic flow. The integral ∮ pdx for any ...

8.4 Integration methods: symplectic integrators 221 increasing order of the integrator. Later Yoshida[21]and Forest[22]developed ...

222 Molecular dynamics simulations powers oftand equating equal powers ofton the left and right hand sides of the equality [30]. ...