Computational Physics

8.7 Long-range interactions 243 We have not yet made any progress as we have only replaced the infinite sum overRby another infi ...

244 Molecular dynamics simulations In a careful treatment of the Ewald technique, the sum is carried out formally by taking a la ...

8.7 Long-range interactions 245 ........... Figure 8.6. Hierarchical subdivision of the full simulation space (a square) into ch ...

246 Molecular dynamics simulations N N NN N N N N IIII I I I II I II I I I II I I I II II II I S Figure 8.7. Interaction list of ...

8.8 Langevin dynamics simulation 247 whereKis the average size of the interaction list, which is at most 27.KandM are fixed numb ...

248 Molecular dynamics simulations because of their large mass, they will change their momenta only after many col- lisions with ...

8.8 Langevin dynamics simulation 249 subject to the following conditions. As the average effect of the collisions is already ab ...

250 Molecular dynamics simulations The expectation value ofv^2 is determined in a similar way. Using(8.151)and (8.144)we find 〈[ ...

8.9 Dynamical quantities: nonequilibrium molecular dynamics 251 The systematic interaction force between the particles in the so ...

252 Molecular dynamics simulations There exists a relation between time correlation functions and transport coeffi- cients via t ...

Exercises 253 Exercises 8.1 [C] For coding the leap-frog method(Eq. (8.7))two arrays are needed, one containing the velocities a ...

254 Molecular dynamics simulations velocities have very peculiar values). The collision time for pairi,jis found by |rij+tvij|=σ ...

Exercises 255 (b) Find a necessary condition to writeADasJ∇zHD. Show that this condition is equivalent to that found in (a). (c) ...

256 Molecular dynamics simulations att+handt−hafter such a translation can cause severe errors: this should be done beforemoving ...

Exercises 257 (a) Using the leap-frog/Verlet algorithm, show that pi(t+h/ 2 )=pi(t)+hFi/2. The refreshed momentapi(t)are drawn f ...

258 Molecular dynamics simulations simply by shifting the bits ofNXandNYone position to the right (least significant direction) ...

References 259 then simply the opposite of this, as the sum of all the interparticle forces adds up to zero. (a) [C] Write routi ...

260 Molecular dynamics simulations [10] J. G. Powles, W. A. B. Evans, and N. Quirke, ‘Non-destructive molecular dynamics simulat ...

References 261 [34] S. Nosé, ‘A unified formulation of constant temperature molecular-dynamics methods,’J. Chem. Phys., 81 (1984 ...

262 Molecular dynamics simulations [57] J. Barnes and P. Hut, ‘A hierarchicalO(NlogN)force-calculation algorithm,’Nature, 324 (1 ...