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We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonicallike version (GC-AdResS) [Wang et al. Phys.Rev.X 3, 011018 (2013)], to calculate the excess chemical potential, $μ^{ex}$, of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS the procedure to calculate $μ^{ex}$ corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, $μ^{ex}$, for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed.
In this paper, we investigate the conformational dynamics of alanine dipeptide under an external electric field by nonequilibrium molecular dynamics simulation. We consider the case of a constant and of an oscillatory field. In this context, we propose a procedure to implement the temperature control, which removes the irrelevant thermal effects of the field. For the constant field different time-scales are identified in the conformational, dipole moment, and orientational dynamics. Moreover, we prove that the solvent structure only marginally changes when the external field is switched on. In the case of oscillatory field, the conformational changes are shown to be as strong as in the previous case, and nontrivial nonequilibrium circular paths in the conformation space are revealed by calculating the integrated net probability fluxes.
Applications of the cross-entropy method to importance sampling and optimal control of diffusions
(2014)
We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.
Linear response theory and optimal control for a molecular system under nonequilibrium conditions
(2013)
In this paper, we propose a straightforward generalization of linear
response theory to systems in nonequilibrium that are subject to
nonequilibrium driving. We briefly revisit the standard linear response
result for equilibrium systems, where we consider Langevin dynamics
as a special case, and then give an alternative derivation using a
change-of-measure argument that does not rely on any stationarity or
reversibility assumption. This procedure moreover easily enables us
to calculate the second order correction to the linear response formula
(which may or may not be useful in practice). Furthermore, we outline
how the novel nonequilibirum linear response formula can be used to
compute optimal controls of molecular systems for cases in which one
wants to steer the system to maximize a certain target expectation
value. We illustrate our approach with simple numerical examples.