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      The droplet formation-dissolution transition in different ensembles: Finite-size scaling from two perspectives

      1 , 2 , 1 , 3 , 1
      SciPost Physics
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          Abstract

          The formation and dissolution of a droplet is an important mechanism related to various nucleation phenomena. Here, we address the droplet formation-dissolution transition in a two-dimensional Lennard-Jones gas to demonstrate a consistent finite-size scaling approach from two perspectives using orthogonal control parameters. For the canonical ensemble, this means that we fix the temperature while varying the density and vice versa. Using specialised parallel multicanonical methods for both cases, we confirm analytical predictions at fixed temperature (rigorously only proven for lattice systems) and corresponding scaling predictions from expansions at fixed density. Importantly, our methodological approach provides us with reference quantities from the grand canonical ensemble that enter the analytical predictions. Our orthogonal finite-size scaling setup can be exploited for theoretical and experimental investigations of general nucleation phenomena – if one identifies the corresponding reference ensemble and adapts the theory accordingly. In this case, our numerical approach can be readily translated to the corresponding ensembles and thereby proves very useful for numerical studies of equilibrium cluster formation, in general.

          Most cited references49

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          Phase-change materials for rewriteable data storage.

          Phase-change materials are some of the most promising materials for data-storage applications. They are already used in rewriteable optical data storage and offer great potential as an emerging non-volatile electronic memory. This review looks at the unique property combination that characterizes phase-change materials. The crystalline state often shows an octahedral-like atomic arrangement, frequently accompanied by pronounced lattice distortions and huge vacancy concentrations. This can be attributed to the chemical bonding in phase-change alloys, which is promoted by p-orbitals. From this insight, phase-change alloys with desired properties can be designed. This is demonstrated for the optical properties of phase-change alloys, in particular the contrast between the amorphous and crystalline states. The origin of the fast crystallization kinetics is also discussed.
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            Multicanonical algorithms for first order phase transitions

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              String method in collective variables: minimum free energy paths and isocommittor surfaces.

              A computational technique is proposed which combines the string method with a sampling technique to determine minimum free energy paths. The technique only requires to compute the mean force and another conditional expectation locally along the string, and therefore can be applied even if the number of collective variables kept in the free energy calculation is large. This is in contrast with other free energy sampling techniques which aim at mapping the full free energy landscape and whose cost increases exponentially with the number of collective variables kept in the free energy. Provided that the number of collective variables is large enough, the new technique captures the mechanism of transition in that it allows to determine the committor function for the reaction and, in particular, the transition state region. The new technique is illustrated on the example of alanine dipeptide, in which we compute the minimum free energy path for the isomerization transition using either two or four dihedral angles as collective variables. It is shown that the mechanism of transition can be captured using the four dihedral angles, but it cannot be captured using only two of them.
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                Author and article information

                Journal
                SciPost Physics
                SciPost Phys.
                Stichting SciPost
                2018
                December 13 2018
                : 5
                : 6
                Affiliations
                [1 ]Leipzig University
                [2 ]Bernstein Center for Computational Neuroscience Göttingen
                [3 ]Max Planck Institute for Dynamics and Self Organization
                Article
                10.21468/SciPostPhys.5.6.062
                3b5a29a7-fc96-47c9-82a9-ee40ad7a3663
                © 2018

                This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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