THRUST AREA: Computational Nanoscience and Mathematical Modeling

Thrust Leader: Dr. Qi Wang (Math)  http://www.math.sc.edu/~qwang/
Faculty members: Dr. Peter Binev (Math), Dr. Sophya Garashchuk (Chem),  Dr. Andreas Heyden (Chem E.), Dr. Lili Ju (Math), Dr. Yuriy Pershin (Physics), Dr. Hong Wang (Math), Dr. Vitaly Rassolov, (Dept of Chem and BioChem), Dr. Xiaoming He, (Dept of Mech and Biomedical Eng.)
Postdoctoral Associates and Visiting Members: Dr. Eric Choate, Dr. Guanghua Ji, Dr. Brandon Lindley

The common theme of the members of this thrust area is to study complex phenomena in nanoscience research through mathematical modeling and  computation. The current research activities in the group include: algorithm development and analysis, pattern recognition and visualization, Monte Carlo, MD, Ab initio simulation of complex material systems, multiscale modeling and simulation of molecular structures, self-assembly phenomena, and mesoscale structure in complex fluids/soft matter, high performance computing, and GPU computing.

The Heyden’s Group:

• The Heydens group primary research interests are in the areas of nanomaterial science and heterogeneous catalysis.  Our goal is to use computer simulations to obtain a deeper - molecular - understanding of key issues in these areas, such as the self-assembly process in catalyst synthesis, the structure of small metal clusters on high-surface-area supports, and the structure-performance relationship of single-site heterogeneous catalysts. Ultimately, we aim to elucidate the physical effects that must be considered for the design and production of highly selective heterogeneous catalysts with a long lifetime.  Due to the high selectivity and activity of such catalytic materials, chemical processes can make better use of the world's limited resources and become more environmentally benign. Despite significant advances in computer algorithms and the increasing availability of computational resources, molecular modeling and simulation of large, complex systems at the atomic level remains a challenge and is currently limited to relatively simple, well-defined materials.  To enable simulations of complex systems that accurately reflect experimental observations, continued advances in modeling potential energy surfaces and statistical mechanical sampling are necessary.  While studying systems relevant for catalysis, we develop new theoretical and computational tools for the investigation of these complex chemical systems. Our tool development efforts are at the interface between engineering, chemistry, and physics, and are rooted in classical, statistical, and quantum mechanics with a special focus on novel multiscale modeling methods.

The Garashchuk’s Group:

Theoretical and computational chemistry including quantum effects in dynamics of nuclei, development of approximate quantum potential method applicable to large molecular systems and studies of reactivity of hyperthermal oxygen.

• Quantum effects in dynamics of nuclei. Quantum-mechanical effects in molecular dynamics are essential for accurate description and understanding of many chemical processes, such as those in surface reactions, photochemistry, in interactions of molecules with electric field, in chemistry of polymers, clusters and liquids. QM effects are the most pronounced in processes involving atomic and molecular hydrogen including reactions in enzymes, other biomolecular environments and nanomaterials. For example the isotope effects in water are manifested in such basic properties as melting point, which is 3.82C for deuterated water, and the temperature of maximum density in liquid state, which is 4C for water and 11.2C for deuterated water. The exact methods of solving the time dependent Schrodinger equation based on the grid or basis function representation are unfeasible for systems beyond 10-12 degrees of freedom, because of the exponential scaling of numerical efforts with the system size. In contrast, methods of molecular dynamics, based on classical trajectories are routinely applied to high-dimensional systems of hundreds of atoms, but they have two fundamental limitations: (i) the Born-Oppenheimer separation of motion of electrons and nuclei resulting in a single electronic surface dynamics and (ii) the classical motion of nuclei. Both issues can be resolved by doing dynamics simulation with quantum trajectories. Our theoretical work is guided by the ultimate goal -- to study dynamics of complex molecular systems using an accurate and efficient method which incorporates the quantum effects and is compatible with classical molecular dynamics. Possible applications include proton transfer processes in enzymes and other biomolecular environments and incoherent electron transport in open quantum systems, such as molecular electronic devices.

• Quantum or Bohmian trajectories. The time-dependent Schrodinger equation can be recast in terms of the wavefunction amplitude and phase associated with the trajectories evolving in time according to Hamilton's equations of motion. All quantum effects are expressed through the action of quantum potential dependent on the amplitude and its derivatives, acting on a trajectory in addition to the external "classical'' potential. For general problems, the exact determination of the quantum potential is at least as difficult as the solution of the standard Schrodinger equation, but the quantum trajectory formulation provides a convenient starting point for approximation of the "quantum'' quantities, which are small in the semiclassical limit of heavy particles such as nuclei. We develop global approximations to the quantum potential, which capture dominant quantum effects, such as zero-point energy, tunneling, wavepacket bifurcation, in a computationally efficient manner (currently tested for up to 40 degrees of freedom). Long-time (picoseconds) zero-point energy description is of special importance in condensed phase (system interacting with the environment). New work on stabilization of the energy flow including error-balancing and approximations on subspaces is underway. Reactivity of hyperthermal oxygen. Reactions of oxygen colliding with various gas phase molecules and surfaces at energies of several eV are studied using quasi-classical and quantum trajectories in conjunction with experiments. Conceptual issues of interest are effects of intersystem crossing and zero-point energy redistribution on reactivity.

The Wang’s Group:

Research interests of our group include (1). fluid dynamics and rheology of complex fluids, especially, flows of liquid crystal polymers, biaxial liquid crystals, phase transition, pattern formation and defect dynamics of liquid crystal polymers; (2). polymer blends, multiphase flows, and flowing nanocomposites; (3). multiscale theory, kinetic theory and tensor based continuum theory for flows of complex fluids of microstructures  and rheology of flowing nanocomposite  materials; (4). characterization of mechanical and electric properties of nanocomposite materials; (5) modeling and computation of of biomaterials, biofluids, and  cell dynamics; (6). parallel computation of complex systems and high performance computing; and (7). wave propagation in anisotropic media.

Our currently funded projects are listed below.

• Modeling of polymer particulate nanocomposites (PNC) and inhomogeneous liquid crystal polymers. We develop multiscale kinetic theory for inhomogeneous flowing PNC systems to study their phase, morphology and rheological properties in various flow conditions and under external electric and magnetic fields. Large-scale computational efforts are carried out to resolve the inhomogeneous mesoscopic material structures in sheared liquid crystal flows and PNCs.

• Multiscale modeling and simulation of complex biological system. A paradigm of multiscale kinetic theories is developed to model biofilm-flow interaction and biofilm-substrate interaction. In these theories, the biofilm is modeled as a mixture of extracellular polymeric substance, bacteria, nutrients, antibacterial agents, and solvent, etc.. A system of mesoscopic equations are then used to describe the dynamics of various components in the flow. Finite difference and spectral methods are employed to resolve the solutions of the differential equation system. We also use phase field models rooted in the kinetic theory to study cell motility and cell-substrate interaction.

• High performance computing and time-domain paralelization. Time and spatial domain parallelization methodologies are developed to speed up and refine our numerical computations for numerical partial differential equations and molecular dynamic simulation tools.

• Liquid crystal systems and suspension flows. Mesoscopic domain theory and kinetic theory for biaxial liquid crystal polymers and suspension flows in general are developed to study their phase, rheological and material properties. Wave propagation in the biaxial liquid crystal polymers subject to active electric and/or magnetic field is also our research object.

Recent publications:

S. Garashchuk and V. A. Rassolov. "Stabilization of Quantum Energy Flows within the Approximate Quantum
Trajectory Approach". J. Phys. Chem. A 111, 10251 (2007)

S. Garashchuk. "Computation of correlation functions and wave function projections in the contex t of
quantum trajectory dynamics". J. Chem. Phys. 126, 154104 (2007).

S. Garashchuk, V. A. Rassolov and G. C. Schatz. Semiclassical nonadiabatic dynamics based on quantum
trajectories for the O(3P, 1D)+H2 system. J. Chem. Phys. 124, 244307 (2006)

Garashchuk, S. and V. A. Rassolov. "Modified quantum trajectory dynamics using a mixed wavefunction
representation." J. Chem. Phys. 121, 8711 (2004).

Garashchuk, S. and V. A. Rassolov. Quantum dynamics with Bohmian trajectories: energy conserving
approximation to the quantum potential." Chem. Phys. Lett. 376(3-4), 358 (2003).

Garashchuk, S. and V. A. Rassolov. "Semiclassical dynamics with quantum trajectories: Formulation and
comparison with the semiclassical initial value representation propagator. J. Chem. Phys. 118(6), 2482
(2003).
Garashchuk, S. and V. A. Rassolov. Semiclassical dynamics based on quantum trajectories. Chem. Phys.
Lett. 364(5-6), 562 (2002).

Garashchuk, S. and D. J. Tannor. Semiclassical calculation of chemical reaction dynamics Via wavepacket
correlation functions. Annu. Rev. Phys. Chem. 51 (2000).

Garashchuk, S. and D. J. Tannor. Semiclassical calculation of cumulative reaction probabilities. PCCP
Phys. Chem. Chem. Phys. 1(6), 1081 (1999).

Garashchuk, S., F. Grossmann and D. Tannor. Semiclassical approach to the hydrogen-exchange reaction: Reactive and transition-state dynamics. J Chem. Soc. - Faraday, T. - 93(5), 781 (1997).

 Z. Cui, M. C. Calderer, Q. Wang, "A kinetic theory for flows of cholesteric liquid crystal polymers," Discrete and Continuous Dynamical Systems-Series B, 6 (2) (2006), pp 291-310.

 Z. Cui and Q. Wang, "A continuum mechanics model for flows of chiral nematic polymers and permeation flows," J. of Non-Newtonian Fluid Mechanics, 128 (1) (2006), pp. 44-61.

G. Ji, Q. Wang, P. Zhang, H. Zhou, “Study of phase transition in homogeneous, rigid extended nematics and magnetic suspensions using an order-reduction method,” Physics of Fluids, 18 (2006), pp. 1-17.

M. G. Forest, S. Sircar, Q. Wang, and R. Zhou, “Monodomain dynamics for rigid rod & platelet suspensions in strongly coupled coplanar linear flow and magnetic fields II: Kinetic theory “, Physics of Fluids, 18 (10) 2006, pp. 103102 (1-14).  

   A. Kataoka, B. C. W. Tanner, J. M. Macpherson, X. Xu, Q. Wang, M. Reginier, T. Daniel and Chase   P. B. Chase, “Spatially explicit, nanomechanical models of the muscle half sarcomere: Implications for mechanical tuning in atrophy and fatigue,” Acta Astronautica, 60 (2) (2007), pp 111-118. 

  H. Zhou, H. Wang, Q. Wang, and M. G. Forest, “Characterization of stable kinetic equilibria of rigid, dipolar rod ensembles for coupled dipole-dipole and excluded-volume potentials,” Nonlinearity, 20 (2007), 27-297.

  M. G. Forest, Q. Wang, and R. Zhou,  “Monodomain dynamics for rigid rod & platelet suspensions in strongly coupled coplanar linear flow and magnetic,” J. Rheology, 51 (2007), pp. 1-21.

 M. G. Forest, R. Zhou, and Q. Wang, “Nano-rod suspension flows:  a 2D Smoluchowski-Navier-Stokes solver”, International Journal of Numerical Analysis and modeling, 4 (3-4) (2007), pp. 478-488.

  H. Zhou, H. Wang, and Q. Wang, “Nonparallel solutions of extended nematic polymers under an external field,” Discrete and Continuous Dynamical Systems-Series B, 7 (4) (2007), pp. 907-929.   

 H.  Zhou, M. G. forest, and Q. Wang, “Anchoring-induced texture & flow feedback of nematic polymers in shear cells,” to appear Discrete Dynamical Systems Series B, 8 (3) (2007), pp. 707-733.

  M. G. Forest, R. Zhou, and Q. Wang, “Spatial coherence, rheological chaotic dynamics, and hydrodynamic feedback of nematic polymers in plate-driven shear,” Siam Journal on Multiscale Modeling and Simulation, MMS, 6 (3) (2007), pp. 858-878. 

G Ji, Q. Wang, P. Zhang, H. Wang, and H. Zhou, “Steady states of homogeneous, rigid, extended nematic polymers under imposed magnetic fields and their stability,” in press Communication in Mathematical Sciences, 5(4) (2007), pp. 917-950.

 T. Y. Zhang, N. Cogan, and Q. Wang, “Phase Field Models for Biofilms. II. 2-D Numerical Simulations of Biofilm-Flow Interaction,” Communications in Computational Physics, 4 (2008), pp. 72-101.

 Xiaofeng Yang, Zhenlu Cui, M. G. Forest, Qi Wang, and Ruhai Zhou, Dimensional Robustness & Instability of Sheared Semi-dilute, Nano-rod Dispersions,   Siam Journal on Multiscale Modeling and Simulation, to appear 2008.

T. Y. Zhang, N. Cogan, and Q. Wang, “Phase Field Models for Biofilms. I. Theory and 1-D simulations,” Siam Journal on Applied Math, to appear 2008.