C01 - Adaptive coupling of scales in molecular dynamics and beyond to fluid dynamics
Head(s): Prof. Dr. Luigi Delle Site (FU Berlin), Prof. Dr. Felix Höfling (FU Berlin), Prof. Dr.-Ing. Rupert Klein (FU Berlin)
Project member(s): Roya Ebrahimi Viand, Abbas Gholami Poshtehani, Gottfried Hastermann
Participating institution(s): FU Berlin
The project concerns the construction of a well-founded statistical mechanics framework, with a corresponding mathematical formalisation, for the Adaptive Resolution Simulation (AdResS) technique in the field of molecular dynamics (MD) and its generalisation to multi-scale fluid flow modelling. AdResS adaptively couples an atomistically resolved subsystem to an environment that is represented by a coarse-grained (CG) model. Prior to the first funding period, basic work, developed in Berlin, had anticipated the possibility of re-framing the AdResS idea within the principles of the grand-canonical (GC) ensemble. Starting from this point and as an initial step in the first funding period, we reformulated the method first within the frame of the GC ensemble and next in more general terms of systems with open boundaries. Such results go well beyond the specific technical implementation of AdResS and are general enough to be extended to all techniques of MD that treat systems composed by a region of space embedded in a larger reservoir of energy and particles.
In this context, the Bergman–Lebowitz (BL) formalism for systems with open boundaries was used to justify the definition and calculation of observables in AdResS’ atomistic subsystem, such as time correlation functions. Under certain asymptotic conditions concerning length scales, an underlying Hamiltonian structure was found. In conclusion, the computational atomistic/coarsegrained coupling strategy of AdResS, developed earlier following intuitive principles, has been transformed into a theoretically well-founded method for open systems (GC-AdResS) in this project. The potential of the method was demonstrated by calculating the molecular dipole– dipole time correlation function, e.g., in water, which gives access to the spatially local IR spectrum of molecular systems.
For the next funding period, as its ultimate goal, the project foresees the seamless coupling of the particle-based GC-AdResS to a grid-based finite volume continuum hydrodynamics solver to make large-scale and non-equilibrium systems accessible to simulations within this framework. One reference application for this technology concerns the physics of colloidal microswimmers. These nanoparticles are set in motion within a fluid at low Reynolds number by the interplay of non-equilibrium molecular surface processes and long-ranged hydrodynamic fields. Another advanced application concerns molecular transport in nano-porous materials, such as metalorganic frameworks (MOFs), within the context of species separation or storage to be investigated in cooperation with Dr. Sebastian Matera’s Junior Research Group at FU Berlin.
The challenge in this development is to build an efficient and well-justified framework that consistently links regions in space with atomistic, coarse-grained, and continuum representations of the pertinent processes through coupling conditions that properly reflect the scale-dependent physics at the respective interfaces. Depending on the application, different scaling regimes must be allowed for. These include molecular subsystems in or close to thermodynamic equilibrium as well as systems in full non-equilibrium, coupled to continuum models for deterministic or fluctuating hydrodynamics.
The project’s central goals for the coming funding period are (i) to extend the technical capabilities of the AdResS scheme to a larger scale range by transferring its successful paradigm also to coarse-grained/continuum interfaces, (ii) to systematically map out the rather rich landscape of different possible scaling regimes as a basis for the judicious choice of atomistic, coarse-grained, and continuum model components for concrete applications, and (iii) to contribute to our understanding of nano-fluidic applications, such as micro-swimmers and flows near nano-porous materials.