Simulated annealing energy function

This criterion resumes all the a priori knowledge that we are able to convey concerning the physical aspect of the flawed region. Unfortunately, neither the weak membrane model (U2 (f)) nor the Beta law Ui (f)) energies are convex functions. Consequently, we need to implement a global optimization technique to reach the solution. Simulated annealing (SA) cannot be used here because it leads to a prohibitive cost for calculations [9]. We have adopted a continuation method like the GNC [2]. 

The time for classical simulated annealing increases exponentially as a function of the ratio of the energy scales /AU. However, for 5 > 1 the situation is qualitatively different. As a result of the weak temperature dependence in the barrier crossing times, the time for simulated annealing increases only weakly as a power law. 

A particularly important application of molecular dynamics, often in conjunction with the simulated annealing method, is in the refinement of X-ray and NMR data to determine the three-dimensional structures of large biological molecules such as proteins. The aim of such refinement is to determine the conformation (or conformations) that best explain the experimental data. A modified form of molecular dynamics called restrained moleculai dynarrdcs is usually used in which additional terms, called penalty functions, are added tc the potential energy function. These extra terms have the effect of penalising conformations... 

Fig. 31. Decrease of energy during simulated annealing. The temperature is exponentially lowered from kT=l to 0. The insert shows a cross section through the energy landscape as a function of the number of stochastic 1-spin-flips...

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