Time-dependent motion

Molecular dynamics simulations can overcome energy barriers and provide information about the time-dependent motion of molecu lar system s. You can use various strategies to set up an d run a molecular dynamics simulation, depending on your objective. Th IS section defines man y of these strategies and discusses specific consideration s in settingup a simulation. 

In static stability studies, we do not look for detailed timed-dependent motion of the parcel following the displacement (as the associated accelerations are considered negligible). 

Time-Dependent Motion The time-dependent motion of particles is computed by application of Newton s second law, equating the... 

The averaged Eulerian-Eulerian multi-fluid model denotes the averaged mass and momentum conservation equations as formulated in an Eulerian frame of reference for both the dispersed and continuous phases describing the time-dependent motion. For multiphase isothermal systems involving laminar flow, the averaged conservation equations for mass and momentum are given by ... 

In the preceding sections of this chapter, we have considered several examples of transient unidirectional flows. In each case, it was assumed that the flow started from rest with the abrupt imposition of either a finite pressure gradient or a finite boundary velocity, and we saw that the flow evolved toward steady state by means of diffusion of momentum with a time scale tc = i2Jv. Here we consider a final example of a transient unidirectional flow problem in which time-dependent motion is produced in a circular tube by the sudden imposition of a periodic, time-dependent pressure gradient ... 

Molecular dynamics aims to reproduce the time-dependent motional behavior of a molecule. The method has been detailed at length in a number of reviews. 

Currently there exist computers with sufficient storage capacity and speed to allow computation of these time-dependent motions for rather simple flows with finite difference meshes sufficiently fine to resolve the larger eddies of the motion. Even with such computations, however, it is necessary to model the effects of the eddies that are too small to be resolved. It is believed that since the transport of properties is governed by the larger eddies, the modeling process is less critical in these computations than where the entire turbulence is modeled. These turbulence simulations are still too costly for routine engineering computations and are used primarily to study the physics of particular turbulent flows. In fact, the results provide much more information than an engineer may ever want or need. 

Because of their large molecular size, complex bonding patterns, the presence of side chains, and other characteristics, polymers exhibit a number of phenomena in the solid state that are much less common in crystalline solids. In the study of bulk polymers, the time, temperature, and other variable-related characteristics have come to be classed as either relaxations or transitions. As a general definition, a relaxation can be considered a time-dependent motion in a polymer system in which the molecules return to an equUibrium from which they have been displaced by the action of some external force. For example, if a polymer sample is compressed under some external load that forces the molecules to rearrange to attain a new equUibrium state and the force is then removed, the material will, with time, relax or return to its original state (before compression). 

Molecular dynamics differs from lattice dynamics because the particles are effectively involved in time-dependent motion. Its major appeal is that it is an intuitive way of modeling time-dependent phenomena, such as diffusion but as noted above the drawback is that it is CPU time-consuming and can be computationally expensive. To a large extent, this has been offset with the development of more efficient simulation packages and the advancement of computer technology. This makes it possible to undertake MD simulations on a desktop PC. 

The second term on the right side of (6.29) expresses the effects of viscoelastic, time-dependent motions of the polymeric network on the moisture absorption process, while the third term represents the role of free volume on diffusion. 

---