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A novel approach is presented for simulating non-spherical particles in the discrete element method (DEM). A particle's shape is described through a hierarchy of representations using spherical harmonic expansions. The expansion is computed at nodes, obtained by discretising the particle's surface. A low-degree expansion, i.e., one containing few terms, is sufficient to approximate a particle's overall shape without any surface texture. Expansions are computed to high degrees only at interparticle contacts, rather than for the entire particle, which reduces the computational cost. The advantages of this approach include the ability to simulate a wide range of particle shapes and adaptive resolution depending on spatial and temporal considerations. An additional unique benefit is that changes of particle shape due to chipping can be captured in DEM for the first time. This is accomplished by progressively omitting more of the highest-degree terms from the expansion to give an increasingly smooth surface.

Typical experimental setups for molecular systems must deal with a certain coupling to the external environment, that is, the system is open and exchanges mass, momentum, and energy with its surroundings. Instead, standard molecular simulations are mostly performed using periodic boundary conditions with a constant number of molecules. In this review, we summarize major development of simulation methodologies, which, contrary to standard techniques, open up the boundaries of a molecular system and allow for exchange of energy and matter with the environment, in and out of equilibrium. In particular, we construct the review around the open boundary simulation approaches based on the Adaptive Resolution Scheme (AdResS), which seamlessly couples different levels of resolution in molecular simulations. Ideas and theoretical concepts used in its development lie at the crossroad of different fields and disciplines and open many different directions for future developments in molecular simulation. We examine progress related to theoretical as well as novel modeling approaches bridging length scales from quantum to the continuum description and report on their application in various molecular systems. The outlook of the review is dedicated to the perspective of how to further incorporate rigorous theoretical approaches such as the Bergmann–Lebowitz and Emch–Sewell models into the molecular simulation algorithms and stimulate further development of open boundary simulation methods and their application.

We propose an open-boundary molecular dynamics method in which an atomistic system is in contact with an infinite particle reservoir at constant temperature, volume and chemical potential. In practice, following the Hamiltonian adaptive resolution strategy, the system is partitioned into a domain of interest and a reservoir of non-interacting, ideal gas, particles. An external potential, applied only in the interfacial region, balances the excess chemical potential of the system. To ensure that the size of the reservoir is infinite, we introduce a particle insertion/deletion algorithm to control the density in the ideal gas region. We show that it is possible to study non-equilibrium phenomena with this open-boundary molecular dynamics method. To this aim, we consider a prototypical confined liquid under the influence of an external constant density gradient. The resulting pressure-driven flow across the atomistic system exhibits a velocity profile consistent with the corresponding solution of the Navier-Stokes equation. In contrast to available computational methods in which external forces drive the system far from equilibrium, this approach conserves momentum and closely resembles experimental conditions. The presented method can be used to study various direct and indirect out-of-equilibrium conditions in complex molecular systems.

Molecular dynamics simulations are done to observe the behavior of the dynamics at microscopic level of systems during a period of nanoseconds. Advanced computation is done for a large number of degrees of freedom which belong to the atoms. The coarse-grained systems have larger components compared to the fine-grained systems. This article outlines an innovative version of the adaptive resolution scheme which connects the coarse-grained system with the fine-grained system based on a force interpolation scheme, taking into consideration a constant which maintains the temperature of the system around the value of 323 K degrees. The Hamiltonian derivation has been used for expressing the interactions which appear inside the system. The novel solution has been tested on the butane system and implemented in the GROMACS molecular dynamics software. The introduction of the constant in the Hamiltonian derivation lead to the creation of a thermostat for the butane system.

We consider the theoretical model of Bergmann and Lebowitz for open systems out of equilibrium and translate its principles in the adaptive resolution simulation molecular dynamics technique. We simulate Lennard-Jones fluids with open boundaries in a thermal gradient and find excellent agreement of the stationary responses with the results obtained from the simulation of a larger locally forced closed system. The encouraging results pave the way for a computational treatment of open systems far from equilibrium framed in a well-established theoretical model that avoids possible numerical artifacts and physical misinterpretations.

Molecular dynamics (MD) has become one of the most powerful tools of investigation in soft matter. Despite such success, simulations of large molecular environments are mostly run using the approximation of closed systems without the possibility of exchange of matter. Due to the molecular complexity of soft matter systems, an optimal simulation strategy would require the application of concurrent multiscale resolution approaches such that each part of a large system can be considered as an open subsystem at a high resolution embedded in a large coarser reservoir of energy and particles. This paper discusses the current capability and the future perspectives of multiscale adaptive resolution MD methods to satisfy the conceptual principles of open systems and to perform simulations of complex molecular environments in soft matter.

We investigate the role of the thermodynamic (TD) force, as an essential and sufficient technical ingredient for an efficient and accurate adaptive resolution algorithm. Such a force applied in the coupling region of an adaptive resolution Molecular Dynamics (MD) set-up, assures thermodynamic equilibrium between atomistically resolved and coarse-grained regions, allowing the proper exchange of molecules. We numerically prove that indeed for systems as relevant as liquid water and 1,3-dimethylimidazolium chloride ionic liquid, the combined action of the TD force and thermostat allows for computationally efficient and numerically accurate simulations, beyond the current capabilities of adaptive resolution set-ups, which employ switching functions in the coupling region., Accepted in Journal of Chemical Physics

Path integral-based methodologies play a crucial role for the investigation of nuclear quantum effects by means of computer simulations. However, these techniques are significantly more demanding than corresponding classical simulations. To reduce this numerical effort, we recently proposed a method, based on a rigorous Hamiltonian formulation, which restricts the quantum modeling to a small but relevant spatial region within a larger reservoir where particles are treated classically. In this work, we extend this idea and show how it can be implemented along with state-of-the-art path integral simulation techniques, including path-integral molecular dynamics, which allows for the calculation of quantum statistical properties, and ring-polymer and centroid molecular dynamics, which allow the calculation of approximate quantum dynamical properties. To this end, we derive a new integration algorithm that also makes use of multiple time-stepping. The scheme is validated via adaptive classical-path-integral simulations of liquid water. Potential applications of the proposed multiresolution method are diverse and include efficient quantum simulations of interfaces as well as complex biomolecular systems such as membranes and proteins.

Multiscale methods are the most efficient way to address the interlinked spatiotemporal scales encountered in soft matter and molecular liquids. In the literature reported hybrid approaches span from quantum to atomistic, coarse-grained, and continuum length scales. In this article, we present the hybrid coupling of the molecular dynamics (MD) and dissipative particle dynamics (DPD) methods, bridging the micro- and mesoscopic descriptions. The interfacing is performed within the adaptive resolution scheme (AdResS), which is a linear momentum conserving coupling technique. Our methodology is hence suitable to simulate fluids on the micro/mesoscopic scale, where hydrodynamics plays an important role. The presented approach is showcased for water at ambient conditions. The supramolecular coupling is enabled by a recently developed clustering algorithm SWINGER that assembles, disassembles, and reassembles clusters as needed during the course of the simulation. This allows for a seamless coupling between standard atomistic MD and DPD models. The developed framework can be readily applied to various applications in the fields of materials and life sciences, e.g., simulations of phospholipids and polymer melts, or to study the red blood cells behavior in normal and disease states.

Wang and Agarwal (Eur. Phys. J. Special Topics, this issue, 2015, doi: 10.1140/epjst/e2015-02411-2) discuss variants of Adaptive Resolution Molecular Dynamics Simulations (AdResS), and their applications. Here we comment on their report, addressing scaling properties of the method, artificial forcings implemented to ensure constant density across the full simulation despite changing thermodynamic properties of the simulated media, the possible relation between an AdResS system on the one hand and a phase transition phenomenon on the other, and peculiarities of the SPC/E water model.

The problem of resolving a weak broadband signal against the background of a strong broadband signal using adaptive superresolution algorithms for signals with distorted coherence is considered. The correlation matrix is estimated using not only time but also frequency accumulation with a differently formed focusing matrix. Imitative simulation has been carried out and the simulation results are analyzed.

Adaptive resolution techniques are powerful methods for the efficient simulation of soft matter systems in which they simultaneously employ atomistic and coarse-grained (CG) force fields. In such simulations, two regions with different resolutions are coupled with each other via a hybrid transition region, and particles change their description on the fly when crossing this boundary. Here we show that the relative entropy, which provides a fundamental basis for many approaches in systematic coarse-graining, is also an effective instrument for the understanding of adaptive resolution simulation methodologies. We demonstrate that the use of coarse-grained potentials which minimize the relative entropy with respect to the atomistic system can help achieve a smoother transition between the different regions within the adaptive setup. Furthermore, we derive a quantitative relation between the width of the hybrid region and the seamlessness of the coupling. Our results do not only shed light on the what and how of adaptive resolution techniques but will also help setting up such simulations in an optimal manner.

Simulating complex fluids or in general complex molecular systems requires approaches covering decades of time and length scales. This usually cannot be achieved within one simulation model. Over the years many different methods and models have been developed ranging from rather generic models, representing most efficiently the universal statistical mechanical properties of e.g. polymers, to all atom models and even quantum mechanical treatments. While these allow for scientifically very important studies in their own right, only a combination and close link between models of different levels allows for a truly quantitative description of materials and processes. In the present contribution we discuss an adaptive resolution approach where different levels of detail are treated within one simulation and the molecules are free to diffuse between different regions in space, where the molecules interact with different interaction potentials.

Hamiltonian adaptive resolution scheme (H-AdResS), which allows to simulate materials by treating different domains of the system at different levels of resolution, is a recently proposed atomistic/coarse-grained multiscale model. In this work, a scheme to calculate the dielectric functions of liquids on account of H-AdResS is presented. In the proposed H-AdResS dielectric-function calculation scheme (DielectFunctCalS), the corrected molecular dipole moments are calculated by multiplying molecular dipole moment by the weighting fraction of the molecular mapping point. As the widths of all-atom and hybrid regions show different degrees of influence on the dielectric functions, a prefactor is multiplied to eliminate the effects of all-atom and hybrid region widths. Since one goal of using the H-AdResS method is to reduce computational costs, widths of the all-atom region and the hybrid region can be reduced considering that the coarse-grained simulation is much more timesaving compared to atomistic simulati...

We describe TREEASPH, a new code to evolve self-gravitating fluids, both with and without a collisionless component. In TREEASPH, gravitational forces are computed from a hierarchical tree algorithm (TREEcode), while hydrodynamic properties are computed by using a SPH method that includes the ∇h correction terms appearing when the spatial resolution h(t,r) is not a constant. Another important feature, which considerably increases the code efficiency on sequential and vectorial computers, is that time-stepping is performed from a PEC scheme (Predic-Evaluate-Correct) modified to allow for individual timesteps. Some authors have previously noted that the ∇h correction terms are needed to avoid the introduction on simulations of a non-physical entropy. By using TREEASPH we show here that, in cosmological simulations, this non-physical entropy has a negative sign. As a consequence, when the ∇h terms are neglected, the density peaks associated to shock fronts are overestimated. This in turn results in an overestimated efficiency of star-formation processes.

In this paper, we investigate the equilibrium statistical properties of both the force and potential interpolations of adaptive resolution simulation (AdResS) under the theoretical framework of grand-canonical like AdResS (GC-AdResS). The thermodynamic relations between the higher and lower resolutions are derived by considering the absence of fundamental conservation laws in mechanics for both branches of AdResS. In order to investigate the applicability of AdResS method in studying the properties beyond the equilibrium, we demonstrate the accuracy of AdResS in computing the dynamical properties in two numerical examples: The velocity auto-correlation of pure water and the conformational relaxation of alanine dipeptide dissolved in water. Theoretical and technical open questions of the AdResS method are discussed in the end of the paper.

This paper describes the first successful steps towards the goal of minimizing the complexity of the coarse-grained (CG) part of adaptive resolution molecular dynamics(MD) simulations. The idea is motivated by the observation that in such simulations, when they aim at generating proper statistics in the atomistic resolution region, i.e., when they don't need to be dynamically accurate, the coarse-grained region is just there to provide an appropriate thermodynamic bath. In addition, the detailed behavior of particles passing into the atomistic region can still be manipulated considerably while they are passing the hybrid region. Thus, the authors ask why one should not use the simplest particle model available in the coarse-grained region, set up such that it provides the minimal statistical information needed to reliably drive the statistics in the atomistic subdomain. In a first realization of this approach, they adopt an ideal gas model that is void of any particle-particle interactions in the coarse-grained region, they discuss some subtleties that need attention to make it all work, and demonstrate convincing performance and reasonable to very good accuracy of this extreme variant of adaptive resolution modelling.

In their paper, Delgado-Buscalioni et al. (Eur. Phys. J. Special Topics, this issue, 2015, doi: 10.1140/epjst/e2015-02415-x) discuss a methodology for implementing open boundaries in molecular dynamics simulations through an outer “boundary layer” that manipulates exiting and entering particles to enforce the targeted statistical properties in the main simulation domain. Here we comment on the relation of the approach to the adaptive resolution technology “AdResS”, on the respective roles of volume and area averages in flux coupling techniques, and on the possibility of coupling MD simulations to a fluctuating hydrodynamics code.

We would like to thank R. Klein for providing valuable comments [1] on our recent paper [2]. The questions raised therein will be replied in the following.

Artículo escrito por un elevado número de autores, solo se referencian el que aparece en primer lugar, el nombre del grupo de colaboración, si le hubiere, y los autores pertenecientes a la UAM, Adaptive resolution schemes allow the simulation of a molecular fluid treating simultaneously different subregions of the system at different levels of resolution. In this work we present a new scheme formulated in terms of a global Hamiltonian. Within this approach equilibrium states corresponding to well-defined statistical ensembles can be generated making use of all standard molecular dynamics or Monte Carlo methods. Models at different resolutions can thus be coupled, and thermodynamic equilibrium can be modulated keeping each region at desired pressure or density without disrupting the Hamiltonian framework, This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. P. E. thanks the Institute for Biocomputation and Physics of Complex Systems (BIFI) for continued support, and the Ministry of Science and Innovation for support through Project No. FIS2010- 22047-C05-03. R.D.B. also thanks FIS2010-22047-C05- 01 and the support of the ‘‘Comunidad de Madrid’’ via Project No. MODELICO-CM (S2009/ESP-1691). D. D. acknowledges funding from the Max Planck Society under the MPRG program

We have conducted a triple-scale simulation of liquid water by concurrently coupling atomistic, mesoscopic, and continuum models of the liquid. The presented triple-scale hydrodynamic solver for molecular liquids enables the insertion of large molecules into the atomistic domain through a mesoscopic region. We show that the triple-scale scheme is robust against the details of the mesoscopic model owing to the conservation of linear momentum by the adaptive resolution forces. Our multiscale approach is designed for molecular simulations of open domains with relatively large molecules, either in the grand canonical ensemble or under non-equilibrium conditions., triple-scale simulation, molecular dynamics, continuum, water

We present a dual-resolution molecular dynamics (MD) simulation of liquid water employing a recently introduced Adaptive Resolution Scheme (AdResS). The spatially adaptive molecular resolution procedure allows for changing from a coarse-grained to an all-atom representation and vice-versa on-the-fly. In order to find the most appropriate coarse-grained water model to be employed with AdResS we first study the accuracy of different coarse-grained water models in reproducing the structural properties of the all-atom system. Typically, coarse-grained molecular models have a higher diffusion constant than the corresponding all-atom models due to the reduction in degrees of freedom (DOFs) upon coarse-graining that eliminates the fluctuating forces associated with those integrated-out molecular DOFs. Here, we introduce the methodology to obtain the same diffusional dynamics across different resolutions. We show that this approach leads to the correct description of essential thermodynamic, structural and dynamical properties of liquid water at ambient conditions., 12 pages, 16 figures

Quantum effects due to the spatial delocalization of light atoms are treated in molecular simulation via the path integral technique. Among several methods, Path Integral (PI) Molecular Dynamics (MD) is nowadays a powerful tool to investigate properties induced by spatial delocalization of atoms; however, computationally this technique is very demanding. The above mentioned limitation implies the restriction of PIMD applications to relatively small systems and short time scales. One of the possible solutions to overcome size and time limitation is to introduce PIMD algorithms into the Adaptive Resolution Simulation Scheme (AdResS). AdResS requires a relatively small region treated at path integral level and embeds it into a large molecular reservoir consisting of generic spherical coarse grained molecules. It was previously shown that the realization of the idea above, at a simple level, produced reasonable results for toy systems or simple/test systems like liquid parahydrogen. Encouraged by previous results, in this paper, we show the simulation of liquid water at room conditions where AdResS, in its latest and more accurate Grand-Canonical-like version (GC-AdResS), is merged with two of the most relevant PIMD techniques available in the literature. The comparison of our results with those reported in the literature and/or with those obtained from full PIMD simulations shows a highly satisfactory agreement.

The adaptive resolution scheme (AdResS) for efficient hybrid particle-based atomistic/mesoscale molecular dynamics (MD) simulations recently introduced by us, [J. Chem. Phys. 123, 224106 (2005)] is extended to high density molecular liquids with spherical boundaries between the atomistic and mesoscale regions. The key feature of this approach is that it allows for a dynamical change of the number of molecular degrees of freedom during the course of a MD simulation by an on-the-fly switching between the atomistic and mesoscopic levels of detail. Pressure and density variations occurring at the atomistic/mesoscale boundary in the original version are considerably reduced employing the improved methodology presented here.

The last few years have seen enormous progress in the availability of computational resources, so that the size and complexity of physical systems that can be investigated numerically has increased substantially. The physical mechanisms behind the processes creating life, such as those in a living cell, are of foremost interest in biophysical research. A main challenge here is that complexity not only emerges from interactions of many macro-molecular compounds, but is already evident at the level of a single molecule. An exciting recent development in this context is, therefore, that detailed atomistic level characterization of large-scale dynamics of individual bio-macromolecules, such as proteins and DNA, is starting to become feasible in some cases. This has contributed to a better understanding of the molecular mechanisms of, e.g. protein folding and aggregation, as well as DNA dynamics. Nevertheless, simulations of the dynamical behaviour of complex multicomponent cellular processes at an all-atom level will remain beyond reach for the foreseeable future, and may not even be desirable. Ultimate understanding of many biological processes will require the development of methods targeting different time and length scales and, importantly, ways to bridge these in multiscale approaches. At the scientific programme Dynamics of biomolecular processes: from atomistic representations to coarse-grained models held between 27 February and 23 March 2012, and hosted by the Nordic Institute for Theoretical Physics, new modelling approaches and results for particular biological systems were presented and discussed. The programme was attended by around 30 scientists from the Nordic countries and elsewhere. It also included a PhD and postdoc 'winter school', where basic theoretical concepts and techniques of biomolecular modelling and simulations were presented. One to two decades ago, the biomolecular modelling field was dominated by two widely different and largely independent approaches. On the one hand, computationally convenient and highly simplified lattice models were being used to elucidate the fundamental aspects of biomolecular conformational transitions, such as protein folding. On the other hand, these generic coarse-grained approaches were complemented by atomistic representations of the biomolecules. Physico-chemical all-atom models, often with an explicit representation of the surrounding solvent, were applied to specific protein structures to investigate their detailed dynamical behaviour. Today the situation is strikingly different, as was evident during the programme, where several new efforts were presented that try to combine the atomistic and the generic modelling approaches. The aim is to develop coarse-grained models at an intermediate-level resolution that are detailed enough to study specific biomolecular systems, and yet remain computationally efficient. These attempts are accompanied by the emergence of systematic coarse-graining techniques which bridge the physics of different lengths and timescales in a single simulation dynamically by applying appropriate representations of the associated degrees of freedom. Such adaptive resolution schemes represent promising candidates to tackle systems with an intrinsic multiscale nature, such as hierarchical chains and networks of biochemical reactions on a cellular level, calling for a very detailed description on an atomistic particle (or even quantum) level but simultaneously allowing the investigation of large-scale structuring and transport phenomena. The presentations and discussions during the programme also showed that the numerical evidence from (multiscale) simulations needs to be complemented by analytical and theoretical investigations to provide, eventually, a combined and deepened insight into the properties of biomolecular processes. The contributions from this scientific programme published in this issue of Physica Scripta highlight some of these new developments while also addressing related issues, such as the challenge of achieving efficient conformational sampling for chain molecules, and the interaction of nano-particles with biomolecules. The latter topic is especially timely as nano-particles are currently being considered for use as drug delivery devices, and present concerns about the general safety of their use might be resolved (or substantiated) by studies of this kind. This scientific programme and the contributions presented here were made possible by the financial and administrative support of the Nordic Institute for Theoretical Physics.

Adaptive-resolution particle methods reduce the computational cost for problems that develop a wide spectrum of length scales in their solution. Concepts from self-organization can be used to determine suitable particle distributions, sizes, and numbers at runtime. If the spatial derivatives of the function strongly depend on the direction, the computational cost and the required number of particles can be further reduced by using anisotropic particles. Anisotropic particles have ellipsoidal influence regions (shapes) that are locally aligned with the direction of smallest variation of the function. We present a framework that allows consistent evaluation of linear differential operators on arbitrary distributions of anisotropic particles. We further extend the concept of particle self-organization to anisotropic particles, where also the directions and magnitudes of anisotropy are self-adapted. We benchmark the accuracy and efficiency of the method in a number of 2D and 3D test cases.

We extend the use of the adaptive resolution method (AdResS) in its Grand Canonical-like version (GC-AdResS) to the molecular dynamics simulation of 1,3-dimethylimidazolium chloride. We show that the partitioning of the total system in a subsystem of interest with atomistic details and a reservoir of coarse-grained particles leads to satisfactory results. The challenging aspect of this study, compared to previous AdResS simulations, is the presence of charged particles and the necessity of addressing the question about the minimal physical input needed to model the coarse-grained particles in the reservoir. We propose two different approaches and show that in both cases they are sufficient to capture the decisive physical characteristics that allow a valid system-reservoir coupling. The technical satisfactory result paves the way for multiscale analysis of ionic liquids and for truly open boundary molecular simulations., Comment: published on: Phys. Chem. Chem. Phys., 2017,19, 4701-4709

We develop a multiscale hybrid scheme for simulations of soft condensed matter systems, which allows one to treat the system at the particle level in selected regions of space, and at the continuum level elsewhere. It is derived systematically from an underlying particle-based model by field theoretic methods. Particles in different representation regions can switch representations on the fly, controlled by a spatially varying tuning function. As a test case, the hybrid scheme is applied to simulate colloid-polymer composites with high resolution regions close to the colloids. The hybrid simulations are significantly faster than reference simulations of a pure particle-based model, and the results are in good agreement.

This article deals with the molecular dynamics simulation of open systems that can exchange energy and matter with a reservoir; the physics of the reservoir and its interactions with the system are described by the model introduced by Bergmann and Lebowitz. Despite its conceptual appeal, the model did not gain popularity in the field of molecular simulation and, as a consequence, did not play a role in the development of open system molecular simulation techniques, even though it can provide the conceptual legitimation of simulation techniques that mimic open systems. We shall demonstrate that the model can serve as a tool to devise both numerical procedures and conceptual definitions of physical quantities that cannot be defined in a straightforward way by systems with a fixed number of molecules. In particular, we discuss the utility of the Bergmann-Lebowitz model for the calculation of equilibrium time correlation functions within the Grand Canonical Adaptive Resolution method (GC-AdResS) and report numerical results for the case of liquid water.

We use the Grand Canonical Adaptive Resolution Molecular Dynamics Technique (GC-AdResS) to examine the essential degrees of freedom necessary for reproducing the structural properties of the imidazolium class of ionic liquids. In this technique, the atomistic details are treated as an open sub-region of the system while the surrounding environment is modelled as a generic coarse-grained model. We systematically characterize the spatial quantities such as intramolecular, intermolecular radial distribution functions, other structural and orientational properties of ILs. The spatial quantities computed in an open sub-region of the system are in excellent agreement with the equivalent quantities calculated in a full atomistic simulation, suggesting that the atomistic degrees of freedom outside the sub-region are negligible. The size of the sub-region considered in this study is 2 nm, which is essentially the size of a few ions. Insight from the study suggests that a higher degree of spatial locality seems to play a crucial role in characterizing the properties of imidazolium based ionic liquids.