Head(s): Prof. Dr. Luigi Delle Site (FU Berlin), Prof. Dr.-Ing. Rupert Klein (FU Berlin)
Project member(s): Roya Ebrahimi Viand, Abbas Gholami Poshtehani, Gottfried Hastermann, Dr. Arthur Straube, Sara Panahian Jand, Dr. Zahra Nourbakhsh
Participating institution(s): FU Berlin

Project SummarIn molecular liquids the study of local events, e.g., molecular solvation, requires a detailed microscopic sampling in the region of interest. Instead the rest of the system plays the role of a
macroscopic thermodynamic bath for which the microscopic sampling is not relevant. In molecular simulation the possibility of treating simultaneously different regions at different levels of resolution would imply a high degree of numerical efficiency. In this perspective the core of this project is the physico-mathematical formalization and corresponding improvement and generalization of the Adaptive Resolution Simulation scheme (AdResS). This method enables the adaptive coupling of regions within which particle interactions are represented at different levels of detail, e.g., atomistic and coarse-grained. The project aims at the mathematical formalization and at related improvements and generalizations of the technique. Key results of the second funding period are (i) a drastic simplification of AdResS that replaces system-specific coarse-grained models for the region represented with lower resolution by a generic reservoir of passive tracers; (ii) a hierarchical Liouville-type mathematical model for open many-particle
systems derived directly from the Liouville equation for the “universe” (open system plus large-scale environment); (iii) a generalization of AdResS to non-equilibrium open systems; and (iv) a first embedding of this updated scheme in a one-dimensional fluctuating hydrodynamics (FHD) simulation. The innovations (iii) and (iv) strongly rely on insights gained from the new mathematical model (ii) and from the generalizations enabled by the passive tracer representation in the low-resolution region (i).
With the achievements so far, the project is ready to target its long-term goal, i.e., the full particle-continuum coupling utilizing an advanced AdResS approach. Specifically the following developments are foreseen: Theoretical developments based on the new Liouville hierarchy for open systems will include (1) a boundary layer analysis that addresses mutual feedbacks between the open system and its environment for both short- and long-range particle interactions and (2) a study of the continuum limit for the large-scale environment of an open system. In parallel, the project will extend the current one-dimensional AdResS-FHD model to multiple space dimensions, and it will investigate physically interesting application problems that demonstrate the capabilities of the simulation technology as it evolves.

Publications C01