Two-phase flow analogy as an effective boundary condition for modelling liquids at atomistic resolution

A hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework based on the analogy with two-phase hydrodynamics has been extended to dynamically tracking the feature of interest at all-atom resolution. In the model, the hydrodynamics description is used as an effective boundary condition to close the molecular dynamics solution without resorting to standard periodic boundary conditions. The approach is implemented in a popular Molecular Dynamics package GROMACS and results for two biomolecular systems are reported. A small peptide dialanine and a complete capsid of a virus porcine circovirus 2 in water are considered and shown to reproduce the structural and dynamic properties compared to those obtained in theory, purely atomistic simulations, and experiment

Hybrid multiscale simulation reveals focusing of a diffusing peptide molecule by parallel shear flow in water

The hybrid Molecular Dynamics - Fluctuating Hydrodynamics model is extended for multi-resolution simulations of molecular diffusion in water under a steady shear flow. Cases of water self-diffusion and a small protein diffusion in water are considered. For the switched-off flow effect, the model is validated in comparison with the reference all-atom equilibrium molecular dynamics solution. With the flow effect included, the multiscale model correctly captures the mean flow velocity distribution as well as the difference between mean square deviations in different directions with respect to the flow in accordance with the diffusion theory. Results of the simulations are analysed in the context of using hydrodynamic flow gradients for molecular diffusion focusing

A hybrid molecular dynamics/fluctuating hydrodynamics method for modelling liquids at multiple scales in space and time

A new 3D implementation of a hybrid model based on the analogy with two-phase hydrodynamics has been developed for the simulation of liquids at microscale. The idea of the method is to smoothly combine the atomistic description in the molecular dynamics zone with the Landau-Lifshitz fluctuating hydrodynamics representation in the rest of the system in the framework of macroscopic conservation laws through the use of a single "zoom-in" user-defined function s that has the meaning of a partial concentration in the two-phase analogy model. In comparison with our previous works, the implementation has been extended to full 3D simulations for a range of atomistic models in GROMACS from argon to water in equilibrium conditions with a constant or a spatially variable function s. Preliminary results of simulating the diffusion of a small peptide in water are also reported

A generalised Landau-Lifshitz fluctuating hydrodynamics model for concurrent simulations of liquids at atomistic and continuum resolution

A new hybrid molecular dynamics-hydrodynamics method based on the analogy with two-phase flows is implemented that takes into account the feedback of molecular dynamics on hydrodynamics consistently. The consistency is achieved by deriving a discrete system of fluctuating hydrodynamic equations whose solution converges to the locally averaged molecular dynamics field exactly in terms of the locally averaged fields. The new equations can be viewed as a generalisation of the classical continuum Landau-Lifshitz fluctuating hydrodynamics model in statistical mechanics to include a smooth transition from large-scale continuum hydrodynamics that obeys a Gaussian statistics to all-atom molecular dynamics. Similar to the classical Landau-Lifshitz fluctuating hydrodynamics model, the suggested generalised Landau-Lifshitz fluctuating hydrodynamics equations are too complex for analytical solution; hence, a computational scheme for solving these equations is suggested. The scheme is implemented in a popular open-source molecular dynamics code GROMACS (GROningen MAchine for Chemical Simulations), and numerical examples are provided for liquid argon simulations under equilibrium conditions and under macroscopic flow effects.</p

A mult-retsolution particle/fluctuating hydrodynamics model for hybrid simulations of liquids based on the two-phase flow analogy

A triple-scale model of a molecular liquid, where atomistic, coarse-grained, and hydrodynamic descriptions of the same substance are consistently combined, is developed. Following the two-phase analogy method, the continuum and discrete particle representations of the same substance are coupled together in the framework of conservation laws for mass and momentum that are treated as effective phases of a nominally two-phase flow. The effective phase distribution, which governs the model resolution locally, is a user-defined function. In comparison with the previous models of this kind in the literature which used the classical Molecular Dynamics (MD) for the particulate phase, the current approach uses the Adaptive Resolution Scheme (AdResS) and stochastic integration to smoothen the particle transition from non-bonded atom dynamics to hydrodynamics. Accuracy and robustness of the new AdResS-Fluctuating Hydrodynamics (FH) model for water at equilibrium conditions is compared with the previous implementation of the two-phase analogy model based on the MD-FH method. To demonstrate that the AdResS-FH method can accurately support hydrodynamic fluctuations of mass and momentum, a test problem of high-frequency acoustic wave propagation through a small hybrid computational domain region is considered.</p

Coupling boundary conditions in continuum-particle approach for open systems: theoretical analysis and computational implementation

Adaptive Resolution Simulation (AdResS) is a multi-resolution method with open system characteristics for modelling atomistic-level systems. In AdResS, a high-resolution open system is in contact with a reservoir of particles and energy, and the system is recreating the thermodynamics and physics of the full atomistic system of reference. In this thesis, the fundamental characteristics of the AdResS method are studied to provide a better understanding of the statistical mechanics undergoing within open system. Among the most relevant results, it is worth underlining the equivalence of the grand potential, determined theoretically, with the pressure, calculated numerically for the same volume of the atomistically resolved region. Moreover, such analysis led to a straightforward calculation of the chemical potential of the liquid under investigation for a wide range of thermodynamic conditions. It has been shown that the pressure difference resulting from the abrupt change of resolutions is compensated by the energy provided by the external force (thermodynamic force) in AdResS. Moreover, the chemical potential of AdResS is related to the chemical potential of the full-atomistic simulation of reference by calculating different contributions corresponding to the abrupt change of resolutions. Next, a fluctuating hydrodynamics (FHD) solver is designed to capture the small-scale fluctuations in the continuum simulations by adding a stochastic flux term to the Navier-Stokes equation of the compressible flow. Then, this continuum solver is coupled to the previously developed AdResS simulator through a small interface region by employing a novel coupling algorithm according to the non-equilibrium AdResS simulation. To this aim, a set of pre-calculated thermodynamic forces is prepared and the information on the continuum side transfers to the particle subdomain by interpolating proper thermodynamic force. The AdResS-FHD coupling system is developed and tested for various cases with different conditions and showed satisfactory agreement with the results of the reference continuum and fully atomistic simulations.Die Adaptive Resolution Simulation (AdResS) ist eine Mehrfachauflösungsmethode mit Eigenschaften eines offenen Systems zur Modellierung von Systemen auf atomistischer Ebene. Bei AdResS steht ein hochaufl¨osendes offenes System in Kontakt mit einem Reservoir von Teilchen und Energie, und das System bildet die Thermodynamik und Physik des vollständigen atomistischen Bezugssystems nach. In dieser Arbeit werden die grundlegenden Eigenschaften der AdResS-Methode untersucht, um ein besseres Verständnis der statistischen Mechanik in einem offenen System zu ermöglichen. Zu den wichtigsten Ergebnissen gehört die Aquivalenz zwischen dem theoretisch ermittelten Großkanonischen Potential und dem numerisch berechneten Druck. Darüber hinaus führte diese Analyse zu einer einfachen Berechnung des chemischen Potenzials der untersuchten Flüssigkeit für ein breites Spektrum thermodynamischer Bedingungen. Es wurde gezeigt, dass der Druckunterschied, der sich aus der abrupten Anderung der Auflösung ergibt, durch die Energie kompensiert wird, die von der Äußeren Kraft (thermodynamische Kraft) in AdResS bereitgestellt wird. Als Nächstes wird ein fluktuierender hydrodynamischer (FHD) Solver entwickelt, um die kleinräumigen Fluktuationen in den Kontinuumssimulationen zu erfassen, indem ein stochastischer Flussterm zur Navier-Stokes-Gleichung der kompressiblen Strömung hinzugefügt wird. Anschließend wird dieser Kontinuumslöser mit dem zuvor entwickelten AdResS-Simulator durch eine kleine Schnittstellenregion gekoppelt, indem ein neuartiger Kopplungsalgorithmus entsprechend der Nicht-Gleichgewichts AdResS-Simulation eingesetzt wird. Zu diesem Ziel wird ein Satz von vorberechneten thermodynamischen Kräften vorbereitet und die Informationen auf der Kontinuumsseite werden durch Interpolation geeigneter thermodynamischer Kräfte auf das Partikel-Subdomain transferieren. Das AdResS-FHD-Kopplungssystem wurde für verschiedene Fälle mit unterschiedlichen Bedingungen entwickelt und getestet und zeigte zufriedenstellende Übereinstimmung mit den Ergebnissen der Referenzkontinuums- und vollständig atomistischen Simulationen

A Thermostat-Consistent Fully Coupled Molecular Dynamics-Generalized Fluctuating Hydrodynamics Model

The previously developed multiscale method for concurrently coupling atomistic and continuum hydrodynamic representations of the same chemical substance is extended to consistently incorporate the Langevin‐type thermostat equations in the model. This allows not only to preserve the mass and momentum conservation laws based on the two‐phase flow analogy modeling framework but also to capture the correct local fluctuations and temperature in the pure atomistic region of the hybrid model. Numerical results for the test problem of equilibrium isothermal fluctuations of SPC/E water are presented. Advantages of using local thermostat equations adjusted for the multiresolution model for accurately capturing of the local water density in the atomistic part of the hybrid simulation domain are discussed. Comparisons with the reference pure all‐atom molecular dynamics simulations in GROMACS show that the suggested hybrid models are by a factor of 5–20 faster depending on the simulation domain size

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Comment: 95 pages, 48 figure

Molecular Dynamics Simulation of Open Systems far from Equilibrium

Open systems have been the subject of interest in science for a long time because many complex molecular systems are open systems embedded in a large environment that serves as a reservoir of particles and energy. In order to test the methods' accuracy and applicability, simulations of open systems exposed to different non-equilibrium conditions are performed, and the results are compared to the results of full resolution simulations and the range of applicability of the method is investigated. Furthermore, a study on fluid flow through regular bead packings as a model of a porous medium was conducted to investigate the flow--pressure relation in these media and its dependence on geometry and porosity of the medium. These simulations are also done with AdResS for extension to open boundaries. The results presented in this thesis help to understand the capabilities of our simulation method to simulate open systems out of equilibrium. We found that by choosing proper boundary conditions and reservoir states, simulations of open systems embedded in large reservoirs of particles and energy can be done with low computational cost. The findings of this thesis pave the way for future research on applications in which a more realistic system is subjected to non-equilibrium conditions and flows of heat and mass