Research Activities

The thrust consists of active research faculty members from a host of departments from science, engineering and mathematics. Their research spans a spectrum of disciplines and specialized areas. However, the central themes of their research activities can be roughly grouped into four sub-areas:

  • Modeling and computation of transport phenomena and material properties from nanoscale to macroscopic materials systems.
  • Numerical analysis, algorithmic development and high performance computing.
  • Image processing and visualization.
  • Computational and theoretical modeling of biological systems:

Numerical investigations of transport and morphology in multiphase complex fluids systems

This project focuses on mathematical constructs and numerical simulations for multiphase complex fluids (MCFs).  We use the term "complex fluid" for fluids, which require some description and modeling of microstructure to accurately predict behavior in even the simplest of experiments. We focus on two representative MCF systems, one arising from materials science and the other from biology.  The two MCF systems we are studying are the flowing polymer nanoparticulate composites (PNC) and biofilm flows. PNCs are  made from nano-sized particles (clays, silicates, metals, etc.) dispersed in polymer melts or polymer solutions often exhibiting significantly enhanced material properties when the particles are well dispersed and exfoliated. This enhancement is due to the conformational, electrical, thermal, or barrier properties of the inclusion molecules or nanoparticles, making them ideal substitutes for traditional high performance  materials in various demanding applications. It has been shown that a small fraction of clay particles added to a polymer matrix can change the physical properties of the material dramatically. Biofilms on the other hand are prevalent in human body and in nature. Understanding how biofilms develop, transport, and interact with the environment and drugs (or disinfectants) will be extremely important for biological science, environmental sciences, and medicine.

We adopt a common computational paradigm that lays the foundation for generic MCF mixtures:  computations based on kinetic theories.  Kinetic theories allow the coupling of the molecular dynamics to the macroscopic or averaged dynamics providing mesoscopic resolution to the MCF system.

The kinetic theory for inhomogeneous MCF system involves 3-degrees of freedom in the translational space and 2 or 3 degrees of freedom in the molecular configurational or phase space. When coupled to the transport equation for the macroscopic momentum, mass, and energy for the isothermal processes, a formidable partial differential equation system emerges. A projection method is normally used to deal with the incompressible nature of the material system, an operator splitting strategy is better off used to discretize the kinetic equation leading to a large system suitable to be implemented in scalable HPC environment. High order numerical treatment like spectral method can be implemented in geometries to improve the computational efficiency.

Multiscal Modeling of Bifunctional Catalysts for the Water-Gas-Shift Reaction (Dr. Andreas Heyden, Chemical Engineering)

A deeper understanding of the metal – support interaction, the role of catalyst supports, and the function of promoter metals in supported bimetallic catalysts at the molecular level has the potential for significant future breakthroughs in catalyst science, which will guide future design of catalysts to better use world’s limited resources.  It is the objective of this proposed research to significantly enhance this molecular understanding by studying the water-gas-shift (WGS) reaction on TiO2 and CeO2 supported clusters of Au, Pt, Au-Pt, and Pt-Re, which serves as a crucial step in maximizing hydrogen yield and providing clean hydrogen for a future hydrogen economy.

The main challenges in the study of the system are (i) that a relatively large unit cell of 50 to 100 atoms is required for the calculations, (ii) that we are required to use computational methods that are significantly more accurate than that currently offered by the density function theory (DFT) for estimating reaction barriers and interactions with/in oxides, and (iii) that we are required to use methods that are significantly more accurate than standard hybrid DFT methods for calculating the interaction with metal clusters. We propose here a new, potentially transformative, approach to circumvent some of the inherent problems in current state-of-the-art strategies for simulating chemical reactions at the three-phase boundary of supported metals.  We first perform state-of-the-art periodic slab calculations to build and validate a periodic electrostatic embedded cluster model.  Unlike periodic slab models, the periodic cluster model permits the use of novel double hybrid exchange-correlation functional with significantly improved accuracy for modeling chemical kinetics and noble metal clusters [28-33]. Then, we will perform a thorough investigation of various reaction pathways (including reaction barriers) to develop a micro-kinetic model based on data obtained only from first principles and absolute rate theory.  Using this micro-kinetic model, we will be able to identify key reaction intermediates and rate-limiting steps at specific gas phase environments as well as the nature and role of the oxide support, the role and state of the supported metal, and the function of promoter metals in the supported bimetallic catalyst.  This computational study depends heavily on the availability of a high performance computing facility. A typical calculation requires at least 32 processors for multiple days while hundreds of calculations have to be performed for this project, current resources are insufficient and significantly more computational resources are necessary.

New Approaches to DNA Sequencing and Detection (Dr. Yuriy Pershin, Physics and Astronomy )

Developing a low-cost and rapid method to sequence DNA would dramatically change the medical field and help study biological functions and evolution. Recently, several radical new techniques have been proposed, all of them having a common trait: they use nanoscale probes to examine electronic or structural features of individual DNA bases. The present project will involve theoretical investigations of molecular dynamics and electronic transport in two different DNA probing configurations: in nanopore-based sequencing devices and in biological sensors based on DNA self-assembled monolayers. In this part of the project, the physics of ssDNA interaction with functionalized nanopore will be studied using large scale molecular-dynamics simulations coupled to quantum-mechanical current calculations.   In order to study the system dynamics on a longer time scale (we are interested in the dynamics of a system of ~105 atoms at times up to 1 milisecond), an access to a high performance computational facility, such as those at ORNL, is required.

The second part of the project is to develop a computational model in relation to recent experimental results on biosensors obtained by Crawford’s group. It was found that when ssDNA probes attached to 30nm gold film pairs with complementary ssDNA from solution, the resistivity of the gold film changes by several percents. This result appears to be extremely useful for future chemical and biological sensors, which will perform measurements rapidly, accurately, and at increasingly lower cost. Our studies will focus on understanding dynamical, hybridization and transport processes in this system.

Mathematical modeling and large-scale computation in energy research (Dr. Hong Wang, Mathematics)

It is vital in the energy industry to understand complex biological, chemical and physical processes occurring in geological formation in order to optimize the recovery of hydrocarbon and natural gas.   Mathematical models for subsurface multiphase/multicomponent flows and their transport processes lead to strongly coupled nonlinear partial differential equations and nonlinear constraining equations with multiple spatial and temporal scales.  Traditional finite difference and finite element methods for solving these PDE systems constantly run into bottlenecks at data storage and communication. In addition, uncertainty in geological environment and data collection is fairly common. The combination of significant spatial heterogeneity and large degree of uncertainty about the geological formation often leads to great challenges in modeling and computation. One thus resorts to a large number of Monte Carlo iterations to handle the problems. The development of biofilms in subsurface can significantly change the porosity and permeability of the porous media adding another level of complication.

We propose to attack these difficult problems through the following approaches: (i) Develop novel mathematical and numerical solution techniques to accurately resolve the complex systems of nonlinear partial differential equations coupled to the nonlinear constraining equations in an accurate and efficient manner. (ii) Develop more efficient simulation techniques to treat uncertainties in the problems. (iii) Develop and implement fully parallel, large-scale simulations in the state of the art HPC environment.
These computational efforts will require the access to the state-of-the-art HPC facilities available at ORNL.

Parallel Simulations of Ice and Sea Modeling (Dr. Lili Ju, Mathematics)

Modeling and simulation of the entire ice sheet is computationally challenging because of the spatial and temporal scales. In recent years, great efforts have been taken by the climate modeling community to make efficient use of emerging distributed and shared parallel computing resources involving flexible domain decomposition strategies and large-scale preconditioned sparse linear solvers. These substantial improvements were accomplished to obtain the robust and scalable simulations by taking advantage of the cutting edge parallel computing power and data grid available at the time.

The primary emphasis of our ongoing research is toward the large-scale parallel finite element /volume simulation of the coupled ocean and ice modeling deciphering the complex interactions between fluid and geophysical processes. We are currently developing a fully coupled 3-D model based on the Stokes and energy equations and its numerical simulations using tens of millions of unstructured 3-D grids, which are often required for credible predictions of ice sheet evolution and sea level rise. The overarching purpose of this work is to determine how to resolve the critical aspects of ocean and ice systems while striving to improve computational efficiency of designed computing schemes.

Given the current simulation strategy and scales, we need to solve over thirty million orders sparse linear system at each linear iteration step, this application requires at least 200 CPUs and 200GB memory space at each run-time. This is a communication intensive, memory intensive and also I/O intensive computational job, requiring a significant amount of storage space and parallel processing of computation and visualization capability. Therefore, a fully developed cyber-infrastructure, consisted of computing power, data grid archive and parallel visualization tools, is strongly suggested to perform the calculations over the course of this research.

Computational study of spin coupling in transition metal containing clusters (Vitaly Rassolov, Chemistry and Biochemistry)

The traditional ab initio methods of electronic structure theory have been very successful in their application to energetics and geometries of molecules and molecular clusters.  The same framework is much less successful in the description of electronic spins. The primary reason for this is the imbalance between the description of high and low spin states in the commonly used wave-functional forms. Currently, there are no methods that can compute spin coupling in transition metal ™ containing clusters, such as copper oxides. Recently we have developed a model that can describe spin coupling in the balanced way in polynomial scaling based on the geminal form of the wave function. In the geminal form, its computational cost is slightly higher compared to that of the Hartree-Fock, which implies that the calculation of a system with tens to low hundreds atoms in a cluster can only be performed on high performance supercomputer. 

We propose to study the chemical dependence of spin coupling in TM containing clusters aiming at developing chemical control of the magnetic properties of TM compounds. Our model will be applied and, if necessary, modified, to study structures, energetics, and spin polarizations in TM containing clusters. The methods will be verified on the small (two to five transition metal atoms) clusters, for which there is significant amount of computational, spectroscopic, and magnetic data. The early stages of the proposed work can be done on the model systems, with large effective core potentials. Such calculations may lack predictive powers, but they can be performed in reasonable time on the planned University computer. The production calculations will have to be performed on supercomputing facilities at national labs.

Semiclassical molecular dynamical simulation of complex molecular system (Dr. Sophya Garashchuk, Chemistry and Biochemistry)

Quantum-mechanical (QM) effects in molecular dynamics are essential for accurate description and understanding of many chemical processes, such as surface reactions, photochemistry, interactions of molecules with electric field, 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. A true QM calculation is basically prohibitive so far while the molecular dynamic simulation based on classical trajectories, routinely applied to high-dimensional systems of hundreds of atoms, is fundamentally limited.

Over the last six years we have been developing a semiclassical molecular dynamics methodologies with compatible quantum trajectories to study dynamics of complex molecular systems. The main target application areas are (i) proton transfer processes in enzymes and other biomolecular environments and (ii) incoherent electron transport in open quantum systems, such as molecular electronic devices. Right now our dynamics method has been successfully applied to a number of small gas phase reactions and to model high-dimensional systems (up to 40 dimensions) and it is ready to be applied to new large molecular systems of experimental interest.  However, the cost of generating the quantum trajectories is very high. To obtain useful information in a single study, we need thousands of trajectories. The need for a large-scale computational facility is obvious. A high-performance computer cluster with professional system administration and software support here at USC, will enable us to develop, test and run smaller pilot applications.  More interesting and challenging studies of larger molecular systems will certainly require supercomputers such as those available at ORNL

High resolution Imaging processing (Peter Binev, Department of Mathematics)

Recent advances in hardware-based aberration correction have significantly expanded the nanoscale direct imaging capabilities of scanning transmission electron microscopes (STEM). These instrumental advances are beginning to radically transform the imaging of nanoscale matter and to provide huge opportunities for the investigation of biological structures. However, severe bottlenecks of these techniques are the manual operation and labor intensive search procedures, the damage due to the electron beam and the extreme environmental sensitivity of these instruments.

Our research efforts are focused at formulating and exploring a new mathematical model to treat a collection of electron microscopy low-resolution/low-energy scans of the same sample. While the standard methods consider them as a collection of images, our model will explore the fact that the 'pixels' in these 'images' are actually showing the state of the sample in different times. In this way a 'pixel' means not just a 'picture element' but has in addition a time stamp, which will help to connect the results of the scanning with the ongoing time dependent processes. The treatment of the scans as time series will allow superior modeling of the environmental noise and better understanding of the processes occurring during the scans.  Although our goal is to develop algorithms, which can run on a standard workstation, the development of the model for such algorithms and understanding the nature of the undergoing processes will require an amount of computations on much higher scale. To understand the scale of the computations, we note that a signal scan typically has about 100 frames with 1024x1024 pixels each, which must be geometrically registered in 3D. That makes a total of more than 100,000,000 pixels for a single time series. For the necessary low-energy scans, the noise typically washes out fine detail, which must be extracted using mathematical learning theory and data redundancy. Thus, we would need weeks of computing time on a small cluster just to examine the results of each small change of the model. A HPC environment will certainly allow us to develop the imaging technology on shorter turnaround cycles.

Stabilization of biologicals by trehalose and LEA proteins in the dry state: A molecular dynamic investigation (Xiaoming He, Mechanical Engineering and Biomedical Engineering Program)

With recent advances in tissue engineering, regenerative medicine, cell/organ transplantation, stem cell therapy, and assisted reproduction, living cells are becoming more and more important in clinical medical care1,2. Due to the limited availability of cell sources, effective long-term stabilization of living cells (i.e., biopreservation) is critical to the success of these emerging cell based medicines1-4. Biopreservation can be achieved by either cooling/freezing the cells to preserve at a cryogenic temperature (i.e., cryopreservation) or drying the cells to preserve at an ambient temperature (i.e., dry or lyopreservation)4,5.    Recent studies of living systems have discovered that a disaccharide of glucose (i.e., trehalose) and/or late embryogenesis abundant (LEA) proteins is critical for the survival in the dry state8-14. As a result, efforts have been made to utilize both molecules to stabilize mammalian cells in the dry state at ambient temperatures. However, the mechanisms by which trehalose and/or LEA proteins stabilize biologicals in the dry state are still not well understood.

We propose to obtain a mechanistic understanding of the biostabilization properties of trehalose and LEA proteins at the molecular level by molecular dynamic modeling. The stability of trehalose, LEA proteins, and their mixture at different ratios in the presence of various amount of water will be investigated by understanding the intra and intermolecular interactions such as hydrogen bonding and their life time, electrostatic interactions, van der waals forces, and cohesive energy density or solubility factor under the various conditions in both the aqueous or glassy states as well as interactions between cellular proteins/lipids and the two stabilizing molecules will be further investigated. In addition, the diffusion of water in the glassy matrix of trehalose will also be studied to understand the kinetics and thermodynamics of stability of the glassy trehalose matrix for long-term stabilization of biologicals.