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Molecular Simulations for Nanofluids
Published in Victor M. Starov, Nanoscience, 2010
Higher-density systems present a particular challenge to MC because the likelihood of randomly finding a “hole” in the volume diminishes rapidly once the density exceeds twice the critical value (Frenkel and Smit 2002), making insertion events rare and, hence, exploration of the phase space very slow. A number of biased MC methods have been developed to address this and similar problems, including cavity-biased GCMC, force-biased NVT MC, and virial-biased NPT MC—once again, details of all these long-standing MC methods are available in the texts mentioned above.A technique for improving sampling of the phase space that has become popular in recent years with the rise of parallel computers is parallel tempering (or replica exchange; Frenkel and Smit 2002; Earl and Deem 2005), where configurations from MC simulations running in parallel at different thermodynamic states (usually temperature) are swapped with a probability related to their energy differences.
Formulation Design and Optimization Using Molecular Dynamics
Published in Davide Fissore, Roberto Pisano, Antonello Barresi, Freeze Drying of Pharmaceutical Products, 2019
Roberto Pisano, Andrea Arsiccio
Among the different possible approaches, the so-called parallel-tempering replica exchange molecular dynamics (REMD) is often used (Hansmann 1997; Sugita and Okamoto 1999). REMD simulations enhance the sampling by running several independent replicas of the system of interest at different temperatures, and periodically exchanging the coordinates between the replicas with the following acceptance probability, α=min(1,e(1kBTj−1kBTi)[Uj−Ui]),where we have imagined an exchange between two replicas at temperatures Ti and Tj and having energies Ui and Uj. Typically, the set of replicas is constructed so that the replica at the lowest temperature represents the ensemble from which sampling is wanted, while the highest temperature is chosen so that the barriers in the energy landscape will be crossed over accessible simulation time scales.
Application of enhanced sampling approaches to the early stages of mineralization
Published in Elaine DiMasi, Laurie B. Gower, Biomineralization Sourcebook, 2014
With the convention that i < j, if the potential energy of con guration xj is less than or equal to that of con guration xi, the swap is always accepted. However, in the event that U(xj) > U(xi), the swap may still be accepted provided that e- is greater than a random number generated on the interval [0, 1]. This procedure ensures that the simulation does not get trapped in a local energy minimum and that the lowest energy con gurations are continually promoted toward lower temperature replicas as they are encountered. In practice, swaps are usually only attempted between neighboring replicas because the probability of accepting a swap between nonadjacent pairs diminishes rapidly. For a simple example of parallel tempering and how it enhances the exploration of energy landscapes, refer to Figure 18.9. In Figure 18.9a, a 1D energy surface, U(x), is presented that displays several degenerate local energy minima, which are separated by barriers that increase in magnitude as x tends toward higher values. First, consider the behavior of a particle operating on U(x) at several increasing temperatures from T1 to T5. Also let the initial position of the particle at each temperature be the minimum centered at x = -1.25. If an ordinary Monte Carlo simulation is performed in the canonical ensemble with T = T1, the particle is unable to overcome many of the barriers on the landscape and according to the probability distribution, P(x), shown in Figure 18.9b, resides only in the two leftmost wells throughout the run. However, if T = T5, the particle easily traverses the full potential. The parallel tempering method harnesses the ability of the higher-temperature simulations to easily traverse barriers to overcome the sampling deficiency that exists at lower temperatures. Figure 18.9c shows the corresponding probability distributions that are obtained at each temperature from parallel tempering. In contrast to those obtained from standard sampling, the distributions show that all the potential wells are sampled at every temperature. Moreover, the probability of finding the particle in any one of the energy wells is approximately the same because all the wells are at the same energy level, and since parallel tempering ensures proper sampling of the Boltzmann distribution, the system properties determined from ensemble averages taken at each temperature are also valid. If the sampling is thorough enough, it is even possible to obtain the energy landscape directly from any one of the finite temperature probability distributions (i.e., A(x) = - -1 ln P(x)), particularly the high-temperature ones; however, at lower temperatures P(x) is more sparse in the high energy
Routing and wavelength assignment with protection: A quadratic unconstrained binary optimization approach enabled by Digital Annealer technology
Published in IISE Transactions, 2023
Oylum Şeker, Merve Bodur, Hamed Pouya
While being grounded in SA, DA’s algorithm differs from it in some key aspects. First, it uses a parallel trial scheme, where it evaluates all possible moves in parallel at each iteration, as opposed to the classic way of considering one random move only. When more than one flip is eligible for acceptance, one of them is chosen uniformly at random. Second, it utilizes a dynamic offset mechanism to escape from local optima, such that if no flip is accepted in the current iteration, the acceptance probabilities in the subsequent iteration are artificially increased. Specifically, when no candidate variable to flip can be found, a positive offset value is added to the objective function, equivalent to multiplying the acceptance probabilities with a coefficient that is a function of the current temperature and the magnitude of the offset. Otherwise, the offset value is set to zero. Third, DA has the parallel tempering option, also referred to as the replica exchange method, where multiple independent search processes (replicas) are initiated in parallel with a different temperature each, and states (solutions) are probabilistically exchanged between them. This way, each replica performs a random walk in the temperature space, helping to avoid being stuck at a local minimum (Hukushima and Nemoto, 1996; Aramon et al., 2019; Matsubara et al., 2020). In our computational experiments, we utilize DA in parallel tempering mode.
Nucleation on a sphere: the roles of curvature, confinement and ensemble
Published in Molecular Physics, 2018
Jack O. Law, Alex G. Wong, Halim Kusumaatmaja, Mark A. Miller
To improve computational efficiency further, replica exchange (also known as parallel tempering) is employed [45,46]. During simulations aimed at locating the coexistence curve, exchange moves are made between temperatures. When using umbrella sampling, exchange moves are made between sizes of the target nucleus (see Section 2.5). To improve the efficiency of the canonical simulations, collective moves are used. These are based on the scheme of [47], modified to include the fluctuating pseudo-temperature described by Whitelam and Geissler [48].
The characteristics of molten globule states and folding pathways strongly depend on the sequence of a protein
Published in Molecular Physics, 2018
M.J.J. Dijkstra, W.J. Fokkink, J. Heringa, E. van Dijk, S. Abeln
Parallel tempering is used in order to improve the sampling within the simulation of inaccessible regions in the configurational space [52]. The simulation was set to attempt 1,000,000 replica swaps in total, attempting one every 10,000 moves. Acceptance of a replica swap is governed by the acceptance rule below. In total 30 temperatures are sampled, linearly spaced on the interval .