A Multiscale Factorization Method for Simulating Mesoscopic Systems with Atomic Precision

Mesoscopic $N-$atom systems derive their structural and dynamical properties from processes coupled across multiple scales in space and time. An efficient method for understanding these systems in the friction dominated regime from the underlying N-atom formulation is presented. The method integrates notions of multiscale analysis, Trotter factorization, and a hypothesis that the momenta conjugate to coarse-grained variables can be treated as a stationary random process. The method is demonstrated for Lactoferrin, Nudaurelia Capensis Omega Virus, and Cowpea Chlorotic Mottle Virus to assess its accuracy and scaling with system size.Comment: This is the latest version with improved convergence analysi

ProtoMD: A Prototyping Toolkit for Multiscale Molecular Dynamics

ProtoMD is a toolkit that facilitates the development of algorithms for multiscale molecular dynamics (MD) simulations. It is designed for multiscale methods which capture the dynamic transfer of information across multiple spatial scales, such as the atomic to the mesoscopic scale, via coevolving microscopic and coarse-grained (CG) variables. ProtoMD can be also be used to calibrate parameters needed in traditional CG-MD methods. The toolkit integrates `GROMACS wrapper' to initiate MD simulations, and `MDAnalysis' to analyze and manipulate trajectory files. It facilitates experimentation with a spectrum of coarse-grained variables, prototyping rare events (such as chemical reactions), or simulating nanocharacterization experiments such as terahertz spectroscopy, AFM, nanopore, and time-of-flight mass spectroscopy. ProtoMD is written in python and is freely available under the GNU General Public License from github.com/CTCNano/proto_md

Scaling Behavior of Quantum Nanosystems: Emergence of Quasi-particles, Collective Modes, and Mixed Exchange Symmetry States

Quantum nanosystems such as graphene nanoribbons or superconducting nanoparticles are studied via a multiscale approach. Long space-time dynamics is derived using a perturbation expansion in the ratio of the nearest-neighbor distance to a nanometer-scale characteristic length, and a theorem on the equivalence of long-time averages and expectation values. This dynamics is shown to satisfy a coarse-grained wave equation (CGWE) which takes a Schr\"odinger-like form with modified masses and interactions. The scaling of space and time is determined by the orders of magnitude of various contributions to the N-body potential. If the spatial scale of the coarse-graining is too large, the CGWE would imply an unbounded growth of gradients; if it is too short, the system's size would display uncontrolled growth inappropriate for the bound states of interest, i.e., collective motion or migration within a stable nano-assembly. The balance of these two extremes removes arbitrariness in the choice of the scaling of space-time. Since the long-scale dynamics of each fermion involves its interaction with many others, we hypothesize that the solutions of the CGWE have mean-field character to good approximation, i.e., can be factorized into single-particle functions. This leads to a Coarse-grained Mean-field (CGMF) approximation that is distinct in character from traditional Hartree-Fock theory. A variational principle is used to derive equations for the single-particle functions. This theme is developed and used to derive an equation for low-lying disturbances from the ground state corresponding to long wavelength density disturbances or long-scale migration. An algorithm for the efficient simulation of quantum nanosystems is suggested.Comment: Copyright 2011 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics; Keywords: Quantum nanosystems, coarse-grained wave equation, mean field theory, multiscale analysi

SIMULATION-ENHANCED FRACTURE DETECTION: RESEARCH AND DEMONSTRATION IN U.S. BASINS

Remote detection and characterization of fractured reservoirs is facilitated in this project by developing a revolutionary software system. The Model-Automated Geo-Informatics (MAGI) software integrates basin modeling, seismic data, synthetic seismic wave propagation and well data via information theory. The result is a seismic inversion cast in terms of fracture and other reservoir characteristics. The MAGI software was fully tested on synthetic data to verify program accuracy and robustness to data error. In Phase II, we (1) collected geological information (stratigraphic, structural, thermal, geochemical, fracturing and other information across the study area) (Task 4.1); (2) created a GIS database that is compatible with the input requirements of MAGI (Task 4.1); (3) implemented a web-based interface for user friendly access (Task 4.2); (4) gathered and preprocessed seismic data for input into MAGI; (5) developed two- and three-dimensional wave propagation simulators (in time domain) for fluid saturated porous media and implemented matching layer methodology for absorbing boundary conditions (Task 4.3); (6) developed parallel version of the seismic simulators (Task 4.3); (7) proposed an information theory framework that allows for the integration of multiple data types of a range of quality (Task 4.4); (8) developed and implemented highly efficient, parallel, Gauss-Newton seismic waveform inversion code based on reciprocity theorem (Task 4.5); (9) verified and demonstrated the accuracy and efficiency of the wave propagation and seismic waveform inversion codes (Tasks 4.3 and 4.5); and (10) identified the requirements for seismic data to allow seismic inversion (Task 4.6). With these accomplishments, we are prepared to carry out a demonstration in the Illinois Basin. A database of the proposed study area and the web-based system to facilitate geologic and seismic data input are ready for this demonstration as are mapping tools for comparison and observations