Initial configuration

Fig. 10. Conformational flooding accelerates conformational transitions and makes them accessible for MD simulations. Top left snapshots of the protein backbone of BPTI during a 500 ps-MD simulation. Bottom left a projection of the conformational coordinates contributing most to the atomic motions shows that, on that MD time scale, the system remains in its initial configuration (CS 1). Top right Conformational flooding forces the system into new conformations after crossing high energy barriers (CS 2, CS 3,. . . ). Bottom right The projection visualizes the new conformations they remain stable, even when the applied flooding potentials (dashed contour lines) is switched off.

Fig. 8.15 Generation of an initial configuration of a polymer using periodic boundar]) conditions.

Figure 5.1 Initial configuration in a partially filled single blade internal mixer...

Step 2 an initial configuration representing the partially filled discretized domain is considered and an array consisting of the appropriate values of F - 1, 0.5 and 0 for nodes containing fluid, free surface boundary and air, respectively, is prepared. The sets of initial values for the nodal velocity, pressure and temperature fields in the solution domain are assumed and stored as input arrays. An array containing the boundary conditions along the external boundaries of the solution domain is prepared and stored. 

Figure 5.5 (a-d) Initial configuration and simulated material distribution within the twin-... 

Because mesoscale methods are so new, it is very important to validate the results as much as possible. One of the best forms of validation is to compare the computational results to experimental results. Often, experimental results are not available for the system of interest, so an initial validation calculation is done for a similar system for which experimental results are available. Results may also be compared to any other applicable theoretical results. The researcher can verify that a sulficiently long simulation was run by seeing that the same end results are obtained after starting from several different initial configurations. 

As described previously, the Leap-frog algorithm for molecular dynamics requires an initial configuration for the atoms and an initial set of velocity vectors. /2- These initial velocities can come... 

Some scales have a software feature whereby a certain geographical region is identified on initial configuration, and the software then makes the appropriate correction. Some high performance balances have built-in test weights for initial (and periodic) calibration. 

Time reversibility. Newton s equation is reversible in time. Eor a numerical simulation to retain this property it should be able to retrace its path back to the initial configuration (when the sign of the time step At is changed to —At). However, because of chaos (which is part of most complex systems), even modest numerical errors make this backtracking possible only for short periods of time. Any two classical trajectories that are initially very close will eventually exponentially diverge from one another. In the same way, any small perturbation, even the tiny error associated with finite precision on the computer, will cause the computer trajectories to diverge from each other and from the exact classical trajectory (for examples, see pp. 76-77 in Ref. 6). Nonetheless, for short periods of time a stable integration should exliibit temporal reversibility. 

The figure characterizes materials in some initial configuration, which is altered in time as a loading pulse sweeps over it. The shock-compression event is characterized by a transition zone in which significant changes are occurring. After the transition, the material is in a substantially different state, and, finally, the pressure is released. 

The most critical aspects of the process are those that occur in the transition zone, although it should be recognized that the initial configuration has direct influence on the subsequent processes in the transition zone. In Fig. 6.1, the four critical features are identified as (1) the configuration change (2) mechanical mixing (3) shock activation and (4) heating. 

To further characterize the event it is first necessary to identify critical features of the initial configuration that will strongly influence the process. For powder compacts, the most obvious features are the morphological characteristics of the powders, their microstructures, and the porosity of the compact. For solid density samples, the grain structure, grain boundaries, defect level, impurities, and inclusions are critical features. 

We go next to the analysis and failure analysis block in Figure 7-11. That is, we consider the initial configuration with a particular material or materials. Then, for the prescribed loads, we perform a set of structural analyses to get the various structural response parameters like stresses, displacements, buckling loads, natural frequencies, etc. Those analyses are all deterministic processes. That is, within the limits of accuracy of the available analysis techniques, we are able to predict a specific set of responses for a particular structural configuration. We must know how a particular structural configuration behaves so we can compare the actual behavior with the desired behavior, i.e., with the design requirements. 

The simulation starts usually from an initial configuration with lattice sites assigned spin values between 1 and 16 at random, although at lower... 

D. Initial Configurations, Symmetries and Reduction of Dependent Variables... 

To start minimization one needs an initial configuration which should contain the most important features of the investigated structures. This may substantially reduce the computation time. Here we present the initial configurations used in the minimization of structures with Im >m symmetries. 

The initial configuration is set up by building the field 0(r) for a unit cell first on a small cubic lattice, A = 3 or 5, analogously to a two-component, AB, molecular crystal. The value of the field 0(r) = at the point r = (f, 7, k)h on the lattice is set to 1 if, in the molecular crystal, an atom A is in this place if there is an atom B, 0, is set to —1 if there is an empty place, j is set to 0. Fig. 2 shows the initial configuration used to build the field 0(r) for the simple cubic-phase unit cell. Filled black circles represent atoms of type A and hollow circles represent atoms of type B. In this case all sites are occupied by atoms A or B. 

FiG. 2 The initial configuration used to create structures of symmetry of simple cubic phase. 

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