- Jeffrey N Brooks -- ANL
- Daryl C Chrzan -- UC Berkeley
- Stephen Foiles -- Sandia Livermore
- Arthur J Freeman -- Northwestern U
- Bruce N Harmon -- Ames Laboratory
- Anthony C Hess -- PNL
- Richard G Hoagland -- Washington SU
- William Klein -- Boston U
- Kenneth Larner -- Colorado S of Mines
- Ki Ha Lee -- LBNL
- Larry R Myer -- LBNL
- John J Rehr -- U Washington
- William A Shelton -- ORNL
- Roger E Stoller -- ORNL
- Priya Vashishta -- Louisana SU
- Art Voter -- LANL
- John W Wilkins -- Ohio SU
- Dieter Wolf -- ANL
- David Yuen -- U Minnesota

It is well known that numerical investigation of materials properties, whether in Geosciences or Materials Science must deal with phenomena on many time and length scales. The non-linear nature of the systems, coupled with the need to understand extremely long time scales, combine to make numerical techniques of limited use in many problems of practical importance. However, numerical investigation is at present the only method we have that will allow us to probe dynamical mechanisms on microscopic length scales, information that is essential to the understanding of processes such as aging, fracture and degradation. To get some idea of the magnitude of the problem consider the question of molecular dynamics simulation of simple models such as Lennard-Jones that form glasses. Glasses of technological interest are expected to retain their properties on time scales of the order of decades. ($\sim 10^{9}$ seconds) Molecular dynamics simulations for $10^{5}$ particles can model these simple systems for roughly $10^{-5}$ - $10^{-4}$ seconds. Hardware advances alone will not bridge this gap of 13-14 orders of magnitude in the near future as long as the mismatch between the clock of the silicon device and the rate of molecular vibration remains. The maximum clock speed available, which is limited by the physics of the hardware is approximately $10^{8}$ Hz. If we assume a time step of $10^{-15}$ seconds to treat the fastest molecular vibrations faithfully, 100 operations per interacting pair of particles and 100 particles per processor we arrive at a crude estimate of $10^{11}$ seconds of CPU time for one second of real time. (In fact, real codes have a difficult time operating at this efficiency.) Even if the estimate is off by several orders of magnitude, the point is clear: $10^{8}-10^{10}$ seconds in real(physical) time translates to approximately $10^{11}-10^{13}$ years of computer time with present technology, and is not reachable in the foreseeable future by either advances in hardware or by conventional algorithms. It is essential then to develop algorithms that will exploit the understanding of the underlying physical mechanisms to accelerate t he dynamics. Such algorithms have been developed to look at equilibrium properties of simple systems but no one has been able to adapt this approach to treat the more complicated model s needed to understand materials or to treat even simple models far from equilibrium. The problems that need to be overcome are 1) Adapting the algorithms to continuum systems with a high degree of spatial heterogeneity 2) Dealing with the ``frustration'' found in systems where the repulsive part of the interaction potential dominates the physics and 3) Making the algorithm {\sl dynamically faithful,} that is, modifying the dynamics to obtain acceleration without destroying the ability to obtain information about the long-time evolution of the system under its natural dynamics. The time line for developing these algorithms is hard to predict since it requires understanding the fundamental relation between ``natural'' dynamical evolution and the way this evolution might be modeled on a computer. However the possible benefits are substantial. The algorithms would be useful for understanding materials in Geological systems as well as materials of use in civilian as well as military technologies. The would also be useful in other large scale computational problems such as the temporal evolution of networks of earthquake faults. The cost of such development would be small as is the risk.

Subsurface Imaging with Reflection Seismology Imaging the Earth's subsurface by means of reflection seismology, whether for environmental applications in the near-surface or for hydrocarbon exploration at larger depths, poses computational challenges on a grand scale. Tens of terabytes of data are recorded in modern 3D offshore seismic surveys, and the processing needed to mitigate shortcomings in data acquired in the uncontrolled laboratory that is the Earth and to image the Earth's structure, lithology, etc., requires yet 3-4 orders of magnitude more in computation. For a typical such survey, full 3D prestack depth migration, the key step in mapping the recorded seismic wave field into an image of the subsurface, can take 6-12 months of CPU time on a 32-node SGI. Moreover, the nonlinear inversion processes for estimating the seismic wave speed necessary to do accurate depth migration typically require many iterations of the costly depth migration process --- and ideally one would like to do the estimation of wave speed interactively. Over the years, research has been aimed at developing algorithmic approaches that minimize compromises in the quality of processing and imaging while introducing dramatic shortcuts in the required computation. Large as are these inversion and depth-migration problems, however, they currently are founded on simplistic models for the seismic wave propagation. They generally assume that the Earth is a fluid, thus ignoring the presence of shear waves; they do not seriously model attenuation of signal during propagation; and until recently, they have had no ability to take into account the fact that the Earth's strata are anisotropic. Moreover, attempts to characterize fluid-bearing reservoirs falter because so relatively little is known about wave propagation in fluid-filled porous media. Likewise, no adequate experimental results or effective-medium theory presently exists for understanding wave propagation in media that are strongly heterogeneous at all scales and thus likely to entail strong multiple scattering of waves. Moreover, even for today's relatively simplistic theories, computational tools are not capable of handling the problem of relating macro observations to microscopic complexity. These issues are of first order in attempting to understand the extremely heterogeneous near-surface of the Earth, which is the target in environmental investigations and through which waves must travel en route to deep exploration targets. Coupled processes such as seismo-electric phenomena and 4D multi-phase fluid flow in reservoirs are also poorly understood. Likewise, in a related method used in applied geophysics, only the surface has been scratched in the large problem of forward 3D vector electromagnetic wave propagation, let alone inversion, in heterogeneous media. Advances in these areas would measurably aid the finding and recovery of dwindling and ever-harder-to-find energy resources. The benefits to the DOE's mission and to society generally are thus large. The next 6-8 years should see measurable progress in the development of the mathematical tools for describing wave propagation in fractured and highly heterogeneous media. To make progress in understanding of the physics and necessary mathematics, however, will require more time as well as teams of physicists, mathematicians, and computation experts. Developments in inversion of seismic data to take transverse isotropy into account are happening at present, as are extensions to orthorhombic media. These will likely produce valuable spin-offs over the next few years, along the way toward more comprehensive solutions. Most of these problems will require higher-speed networks as well as codes that operate on distributed parallel, likely heterogeneous, computer systems.

Joint analysis of electromagnetic(EM), seismic and hydrological data Quantitative analysis of geophysical data has been an essential tool in understanding various subsurface phenomena such as changes in crustal dynamics over a long period of time, behavior of reservoir properties in producing petroleum and geothermal fields, and the near surface hydrology critically important for understanding environmental problems. Imaging techniques used to analyze realistic geophysical data require a great deal of computational resources. The number of unknowns involved in a typical imaging problem is on the order of 100 million. Fluids play important roles in determining the physical properties of rocks and soil. For most crustal rocks the electrical resistivity depends on ionic conduction in the pore fluids, hence resistivity is a strong function of porosity and interconnectedness (fluid permeability). These are the very parameters that are important in the fault mechanism, changes in reservoir property, and near surface fluid flow that transports toxic chemicals. It has been observed that seismic velocity and amplitude are also strongly affected by these parameters. Velocity distributions determined from 3-D seismic surveys have been used to estimate formation porosity between wells. If seismic and EM data are available at a common site it is possible to jointly analyze the combined data set to obtain better estimates of flow parameters; saturation, porosity and fluid type. As each geophysical parameter is individually related to a combination of flow parameters, only the simultaneous analysis of a combined data set would result in the optimum estimation of flow parameters. A critical component for this approach to be successful is, however, the knowledge that quantitatively relates geophysical parameters such as electrical conductivity and seismic velocity to the flow parameters. One can obtain this information through laboratory experiments on rock samples and well tests. The relationships are very site specific and scale dependent. Joint analysis involves the combination of four interrelated disciplines; EM, seismic, geohydrology, and rock physics. The first three require data acquisition and individual imaging capability on a common scale. The hydrologic inverse problem is notoriously ill-posed. However, when used in conjunction with other information, it may provide valuable information on well-field-scale permeability variations, which is often the key parameter needed to design an effective environmental remediation scheme. The rock physics part will focus on laboratory experiments under simulated conditions. Resulting data can be statistically analyzed to provide empirical relationships between geophysical and hydrological parameters. The approach to the joint analysis consists of minimizing the combined misfits in EM, seismic, and geohydrological data. Empirical relationships are used as constraints that ultimately connect the parameters. Due to the nonlinear coupling of the different parameters involved, the anticipated scale of the joint analysis problem is at least 10 times of those individual ones. Initial estimation suggests that one needs to have access to a computing facility that can handle one billion parameters at any given time. The computing environment may not have to be massively parallel, and a multi-tasking mode of operation can be equally effective. A software that allows users to access these computing facilities without having to modify their scalar algorithms will be greatly useful. A 4-year effort may be required for the completion of the proof of concept stage. Three tasks are involved in the joint analysis; task 1) data acquisition, task 2) joint inversion, and task 3) laboratory experiments on rock samples with additional well testing. Annual cost estimation is $200K for task 1, $400K for task 2), and $300K for task 3. Total cost over the 5-year period is $3.6M. This estimation does not include cost for the computer time.

Questions: What are the relationships between microscopic properties and characteristics of earth materials and their macroscopic properties, where microscopic refers to the scales of engineering interest, and properties refers to mechanical, hydrologic and geophysical properties. How can discontinuities be accounted for in these relationships? Benefits: Simulation and prediction of the behavior of earth materials for engineering applications impacts every aspect of society. Energy and resource extraction encompass mining of minerals, oil and gas recovery and geothermal resource exploitation. Simulation and modeling is involved in exploration for blue resources as well as in extraction. Management and utilization of water resources imports society in many ways and is closely tied to energy extraction and utilization. Simulation and prediction of flow and transport are integral to water management, design, construction and maintenance of infrastructure such as roads, tunnels, dams, and buildings require prediction of the mechanical behavior of earth materials. Evaluation of the environmental impact of societies activities as well as remediation and mitigation of previous activities requires simulation of earth materials incorporating complex chemical and biological processes. The impact of significantly improved understanding of macroscopic earth material properties will be large. Engineers have, in general, learned to compensate for uncertainty through conservative design and applications of empirical rules derived on a trial and error basis. Major difficulties, expense, and mistakes occur when unprecedented conditions as requirements arise. A recent example of this is the nuclear waste program. Improved understanding of material properties will lead to more cost effective design of civil structure, discovery of new mineral, oil and gas resources, and more efficient and complete extraction of these resources. Problem Definition: The major difficulty in deriving microscopic properties from microscopic ones is in identifying a representative volume of material whose properties can be sealed to a larger volume. This difficulty arises in large part due to the extreme heterogeneity of earth materials and, in particular, the presence of discontinuities at all scales. Microscopic discontinuities constitute grain boundaries and inter- and intra-granular cracks. Fractures and joints are ubiquitous at the macroscopic scale and tectonic faults and plate boundaries are examples of meso scale discontinuities. Though there is some evidence (hope) that properties such as length, stiffness, and conductance of discontinuities may be fractal, the question of how the properties of discontinuities scale is largely unanswered and how to account for these effects in extrapolating measurements from microscopic to macroscopic scales is unresolved. Direct measurement of properties at different scales is required. However, these are extremely difficult and expensive experiments. The hope is that computational experiments will replace some significant proportion of the required physical experiment. At present such experiments cannot be performed; if the complex mechanical, thermal, hydrologic and chemical processes are adequately modeled, then the size and geometric structure must be over simplified, and conversely. Specific research areas: 1) Deformation and fracture of discontinuous earth materials. Codes are needed which can analyze deformation and fracture in assemblages of blocks under arbitrary external and pore level loads. The blocks could be grains at the microscopic scale or blocks defined by fractures at the macroscopic scale. The physics is pretty well defined. Significant advances in computational efficiency are required for particle problems. Domain decomposition and parallel computing methods need to be applied. 2) Simulation of flow and transport. Pore level computations have been carried out but not for sufficiently large models to draw conclusions about scale. Nor have the simulations been efficient enough to be of practical engineering use. The physics and chemistry of many multiphase multicomponent processes needs to be better understood and incorporated into models. Efficient ways of converting the complex topography of the pore space into a numerical grid are needed. 3) Simulation of wave propagation in discontinuous media. Effects of discontinuities on wave propagation are only partially understood. For some combinations of frequency discontinuity stiffness and spacing it is appropriate to define effective media properties. However, for other combinations discontinuities need to be explicitly included in models even at macroscopic engineering scales. Simulations have been limited for the latter conditions due to computational efficiency. 3-D simulations have not been performed. Domain decomposition and parallel computing techniques need to be applied. 4) Visualization. As model complexity increases, so does the difficulty of interpreting results. Development of visualization capabilities coupled to the simulators are essential. Huge benefit would be gained, for example, from being able to visualize or "observe" the movement of a particle in a 3-D pore space while at the same time modifying input parameters to the model. In solid mechanics it would be beneficial to be able to visualize changes in propagation of fractures as loading conditions change. 5) Computational efficiency. More efficient equation solvers and adaptive gridding techniques need further development and application into earth materials. New approaches to numerical simulation may be required. For example, efficiency may be gained by integrating equation solving and mesh generation with knowledge of the structure of the material. In both mechanical and flow problems, the heterogeneity of the material results in localized regions which contribute more or less to the process being modeled. New methods for evaluating where these regions are and how they are connected are needed. It may thus be possible to use heterogeneity as an advantage in modeling.

Geodynamical modeling: a computational challenge for the 21st century The surface manifestations of geodynamical processes are revealed over a wide range spatial and temporal scales, from days to millions years and from inches to thousands of miles. Because of the inherent nonlinearity of the properties of rocks, numerical modeling plays an important role in our understanding of the dynamical processes in the shallow and deep parts of our planet, which is coupled by virtue of crustal-mantle flow process. Numerical modeling of geodynamical processes, such as fault movements and volcanic eruptions, demand greater and greater computer power, as we obtain more observational data and experimental constraints from mineral physics. The computational challenges facing geophysical modelers are no less demanding than those confronting nuclear engineers or astrophysicists. Geoscientists also have many problems requiring at least 10^9 grid points. Although the fundamental physical laws may be different, the nonlinearities in the governing equations are no less daunting in the earth science realm. In geodynamics one faces nonlinear problems with an intrinsic multiple scale nature in both space and time because of the many feedback processes. Indeed the problem has multiple physics and chemical processes. Earth scientists have to face problems spanning from the atomic to the geological scale. For instance, rheology depends on many state variables one of them is grain-size, which is coupled to the local chemical kinetics and temperature. Yes, this is a problem which geoscientists have tackled and tougher ones will arise yet. In the propagation of faults, we have to consider thermal-mechanical coupling in the same manner as ma terial scientists working on steel alloys. There are indeed many opportunities for geoscientists to learn and benefit from an integrated multidisciplinary effort. For instance, recently wavelet transforms were applied in geophysics, not for data compression, but for solving non-linear partial differential equations with sharply varying physical properties, using fewer grid points. Finally, we will emphasize the dire need for developing cost-effective solutions for visualization of extremely large (terabyte) data-sets, while at the same time for maintaining a vigorous effort on developing better and more robust numerical algorithms to get "more bang for the buck" on our investments in large-scale computational facilities.

Large Scale Electronic Structure and Properties of Pure and Defective Materials: Modeling Linking Spatial and Energy Scales. As distinct from pure (ideal) crystals, for which there is a well developed theory, the term "real crystal" is used to emphasize the crucial importance of considering specific defects including: (i) impurity or vacancy defects; (ii) dislocations (including misfit dislocations of interfaces) or other faults, (iii) grain boundaries (GB) and (iv) domain walls (for magnetic materials). The structure of these defects, their interactions and energetics are characteristics which govern the macroscopic properties of real materials on a fundamental level. Extended defects such as dislocations and GB most directly manifest themselves in mechanical properties, including ductility and fracture properties of various structural materials. Interactions of extended and point defects determine fundamental mechanisms of solid-solution hardening. The structure and energetics of domain walls and their interactions with lattice defects are fundamental characteristics which determine remagnetization processes. There are also a number of "secondary" effects determined by these defects which for some problems or materials may become "primary". Such phenomena as leakage current in metal/insulator interfaces, effects of density of dislocations in semiconductor devices or the well-known electromigration problem are determined on a fundamental level by specific defect properties. Modeling fundamental properties of such defects will play an increasing role since the progress of experimental techniques are much slower than the development of hardware and software. The greatest challenge for modeling of real crystals properties is determined by the multiscale nature of the problem when formulated on a very general level. On the one hand, these defects are too "big" to belong on the microscale but they are too "small" to be considered as macro-objects. On the other hand, the recent experience with atomistic simulations clearly demonstrates that details of the complex non-central , non-pairwise interactions in metals and intermetallics which can not be described with simple models of interatomic interactions (such as pair potentials or embedded atom) may have a strong effect on characteristics of such defects. Thus, the problem can not be reduced in a universal way to multi-scale modeling (micro-electronic structure calculations to fit potentials) and further mesoscale /atomistic simulations (with millions atoms using parallel computers) but require the development of method for modeling based on a natural linking of different length scale descriptions. Thus, the development of a strategy which comprises data bases, improved computational methods and models which start from electronic structure and proceed one step up in essential length scales should be a focus of the CSI. One has to emphasize that it is a very timely and reliable investment of efforts: reliable since it focuses on the next step after the micro-scale to build a solid basis for further macroscale modeling: reliable since it is based on microscale methods that were developed in recent years, including ab-initio techniques and expected improvements for large-scale simulations. Obviously, however, the most rewarding strategy in this direction could be the use of hybrid approaches. The general idea of such approaches can be illustrated using the Peierls-Nabarro model for dislocations. Despite a number of assumptions and its simplicity, this model gives an unprecedent example of naturally linked atomistic and continuum descriptions. The idea is exceptionally rich and goes far beyond this particular case and its Peierls implementation. This strategy should be explored for various problems including magnetic defects such as domain walls. Different approaches for hybrid simulation techniques may include: 1. Continuum/quasi-continuum mesoscopic models parametrized using ab-initio methods. Models in spirit of Peierls model suited for natural, feasible parametrization using ab-initio methods. (The simplest , almost trivial (but successful) examples of such models are Rice-Wang for interfacial embritlement and Rice-Tomson for brittle-ductile behavior) Further analysis of these parametrized models using both numerical and analytic techniques, with the possibility of solving inverse problems, needs to be emphasized as potentially very useful for computer aided design of materials. 2. Atomistic simulations with adjustable interatomic interaction potentials. This will require the development of new concepts of constructing interatomic potentials suitable for adjustment at each step of the system in evolution, in keeping with results of electronic structure calculations for the local environment. In contrast with the standard EAM, this should include not only total charge density but components coming from particular chemical bonds that vary in direction. 3. Hybrid of ab-initio (full-potential) description in the critical region (area near the crack tip, interface-impurity) with continuum elasticity employed for the rest of the simulation sample. The benefits are clear: a) A consistent, reliable description of defect properties starting from electronic structure. b) A solid basis for microstructure/macroscale simulations. c) A powerful universal methodology of hybrid computational methods. d) A basis for understanding particular defect properties and how to relate results to chemical bonding or other information that may prove insightful for designers of materials. As another example to improve the mechanical properties of high temperature structural intermetallic alloys of great importance for the aerospace industry, we will investigate microscopic mechanisms governing the deformation and fracture properties of these materials using first-principles electronic structure methods. These results will be used in the design of new advanced materials with improved mechanical properties. We will develop effective ab-initio real-space techniques and algorithms, to overcome the drawbacks of both band-structure and semiempirical methods for electronic structure calculations. These techniques will allow multi-scale simulations of "real" materials, whose properties are essentially determined by their defective structure, and to bridge the gap between a microscopic quantum-mechanical description of the electronic structure and chemical bonding and mesoscopic phenomena which govern the mechanical response of intermetallics. Examples include dislocations and impurity-dislocation interactions. These real-space approaches will permit large-scale investigations of the role of deformations and defects on mechanical, magnetic, transport and optical properties of a wide class of materials, including magnetic materials (giant magneto-resistance materials, hard magnets, magneto-optical materials ect.), semiconductors, HTSC. Future theoretical developments of ab-initio real-space methods will include corrections to the local density approximation, such as LDA+U and beyond, effects of many-body interactions, full potential corrections. Taking advantage of the order-N scalabilty of real-space techniques, highly-effective and optimized parallel codes will be developed and used for large-scale simulations. As an example of status, we have calculated the electronic structure of an edge dislocation, modeled with a core of 100-200 non-equivalent atoms in a cluster of ~10,000 atoms; the time on an ORIGIN 2000 single processor is ~45 min. for one iteration with 50-100 interations needed. The scalabilty with respect to number of non-equivalent atoms is linear, and almost linear with respect to the number of processors.

Materials, Methods, Microstructure and Magnetism The impact on societies and economies of the development of new materials with unique or improved properties has a history extending back thousands of years. The material of choice may exhibit a desired property only a few percent better than the next candidate material, yet this may be enough to dominate a market and to generate sufficient income to justify sizable research expenditures. Often, in the process of incrementally improving an existing material a new material will be discovered that causes a revolution in technology. The availability of computers operating in the teraflop range owes much to the dramatic long term improvements in materials and processing techniques. Besides manufacturing and market forces, there are fundamental science issues demanding explanations of how large aggregates of atoms behave collectively, particularly when the behavior depends critically on temperature and on microstructure. The strength of materials, the quality permanent magnets, and even the function of biological molecules all depend on microscopic interactions over distances larger than the scale of individual atoms and bonds. Magnetism is an area where microstructure is vital but poorly understood. Consider this quote from a Reviews of Modern Physics article: "The technical magnetic characteristics... are extrinsic inasmuch as they depend crucially on the microstructure of the material. The microstructure involves the size, shape, and orientation of crystallites of the compound and also the nature and distribution of secondary phases, which usually control domain-wall formation and motion and hence determine the magnetization and demagnetization behavior." The market for magnetic materials is $10 billion/year and $100 billion for all items containing magnets in the United States alone. The long term goal for this topic is the understanding of the microscopic, quantum mechanical, interactions governing magnetic properties of technically important materials. This entails accurate and detailed determination of the relevant microstructures: dislocations, grain boundaries, interfaces, impurities, surfaces. For this work a hierarchy of techniques are needed to span the length scales involved. Already very accurate first principles calculations (100's of atoms) are used to create data bases to fit parameters for environmental tight binding molecular dynamics methods capable of accurate 10,000 atom simulations. The development of such accurate empirical methods is still an art. Extending calculations to larger numbers of atoms and to larger length scales is necessary for many problems, but testing of algorithms for speed and accuracy is progressing now. The calculations for the magnetic calculations need to proceed along a similar hierarchy. First principles methods have been developed to allow non-collinear magnetic structures, and extended to parallel machines for 1024 atom simulations. Running such codes with a stochastic thermal bath will require teraflop level computing. For Heisenberg models with exchange parameters determined from first principles, stochastic equations of motion can be run for 1000's of atoms on modern parallel machines. Accurate calculations of temperature dependent magnetic interactions near defects (of various sizes) will require first principle results feeding into more empirical methods. Within a few years the atomistic approach will overlap the programs of the micro-magnetics community and they will no longer have to rely on continuum models with empirically determined parameters.

Real-Space Many-body Methods for Optical Response I. Proposal: Development of robust real space codes for excited state electronic structure calculations that go beyond the independent-electron approximation, in particular GW, TDLDA, etc. Applications are intended primarily for excited states probed by the interaction between photons and condensed matter, e.g. by synchrotron radiation experiment. We propose a systematic development of real space many-body methods applicable to general condensed systems and their implementation in portable codes. 1) GW and Dielectric Response: The GW approximation provides a natural "quasi-particle" description of excited states that is directly applicable to optical response. The GW approach is analogous to density functional theory, but with an energy dependent self-energy rather than a local exchange approximation. GW calculations require the dielectric response function of a material, which can be evaluated using density functional theory (DFT) calculations. This additional calculational overhead increases the complexity of the calculations compared to DFT by an order of magnitude or more. 2) Dynamic Response - The GW approximation is a good approximation at high excitation energies. However, low energy optical excitations can also be treated with the TDLDA (time dependent local density approximation). Also calculations of optical response near an absorption edge can depend on the relaxation of a system to the creation of core hole and photoelectron, i.e., the transient response of a system. A treatment of this problem requires algorithms for treating time-dependent response and the cross-over from the sudden to adiabatic limits. Generalizations of GW and the TDLDA will be developed for such dynamic screening problems. Benefits: This effort addresses the fundamental, computationally challenging problems of optical and dielectric response, which are of great importance in many scientific fields. Presently there is a great need for such an effort to complement the experimental effort at several major synchrotron radiation photon sources for probing properties of complex materials. This initiative is a timely and natural sequel to current ground state density functional approaches, addressing a range of problems that go beyond the one electron approximation. The effort would yield a quantitative many-body treatment of synchrotron photon spectroscopies: e.g., theories of x-ray absorption and emission, thus improving the utility of the major synchrotron facilities. For example x-ray absorption spectra is used to determine the geometrical structure of complex materials, and edge spectra contain electronic and magnetic information. These spectroscopies also provide quantitative tests of theoretical developments. Finally our approach would be based on the development of robust, automated modular codes that could be used reliably by other scientists, in a way similar to that with our group's real space x-ray absorption spectroscopy codes (the FEFF codes). Computational tools needed: algorithms for calculating dielectric response based, for example, on full potential real space multiple scattering algorithms. The real space approach is well suited for parallelized algorithms. Parallelized large matrix utilities are also needed. Effects of local vibrations and disorder could be added using results from other CSI developments, e.g., algorithms for MD simulations. Advances/barriers: Efficient algorithms for real space calculations of dielectric response and efficient full potential, all electron real space electronic structure algorithms are needed. Though formal theories exist, efficient algorithms for transient response calculations are not well developed. Projected time scale: 10 years The algorithms can be developed hierarchically, starting e.g., from local, electron gas approximation, and successively adding refinements. Time line: 2001-3 full potential generalization of our real-space multiple scattering codes with local GW; adaptation of our codes to TDLDA calculations; 2002-5 successive improvements in both G and W; 2005-7 development of dynamic response functions based on generalizations of GW and TDLDA; 2007-2010 implementation in general optical response codes. Cross-cutting: This work parallels interests Workshop area 3: large quantum mechanical systems and chemistry. Presently our local real space multiple scattering muffin-tin based codes already require complex non-sparse matrices of dimensions of order 16Nx16N, where N is the number of atoms in a cluster (typically 100-500) and requires storage typically of about 100 MB for an adequate treatment. Present calculations can be done on modern workstations in cpu hours. Extensions to full potential, full GW will increase the complexity by several orders of magnitude.

Billion-atom molecular dynamics simulations of processing, mechanical behavior, and fracture of nanostructured ceramics and ceramic matrix composites Proposed research: Atomic MD-FE Continuum Simulation of Dynamic Fracture: Understanding of mechanical failure in ceramic and ceramic-matrix composites requires microscopic examination of plasticity due to dislocation emission and the interaction of cracks with defects such as grain boundaries. In this connection, it is also important to have a knowledge of stress inhomogeneities in the system. The hybrid approach will link atomistic molecular dynamics (MD) simulations with continuum thermodynamic approaches. This is the single most challenging problem in the entire field of simulations. The Atomistic- Continuum hybrid simulation techniques will cover time scales from a fraction of fempto seconds to micro seconds and length scales from angstroms to microns. It will have profound impact on simulations of high temperature ceramics, ceramic matrix composites, and MEMS. Effect of Environment - Aging due to Oxidation: Oxidation is one of the major causes of damage, especially at high temperatures and under stress. For example, oxidation embrittlement of ceramic matrix composites involves ingress of oxygen through matrix cracks in the composite, and it drastically changes the structural performance. Design and lifetime prediction of materials depend crucially on understanding the effects of oxidation. Most metals and alloys are not stable against oxidation. Processing of Nanostructured Ceramics and Ceramic/Matrix Composites: Morphology, micro and macro structure of the material as a function of cooling rates, chemical additives, and environmental gases will be investigated. Simulation of evolution of microstructure from cooling of ceramic melts is possible by using hybrid atomistic MD-continuum method on teraflop parallel computers. Micro-Electro-Mechanical Systems (MEMS): Currently there is a great deal of interest in the fabrication of MEMS. Efforts are underway in many different laboratories to design complex systems, including micro robots, by integrating sensors, processing circuitry, and actuators on the same chip. Using hybrid electronic-atomistic-continuum approach it will be possible to simulate electro-mechanical behavior of the system under a variety of extreme conditions and hostile environments. Relation to DOE mission and benefits: Lifetime extension of structural components requires simulation-based prediction of aging problems before the nondestructive or other evaluation program will detect them. Relevant materials include various ceramic materials and ceramic-matrix composites with complex microstructures. Reliable methods to include the effects of aging and microstructures in the assessment of subcritical growth of flaws are essential. The proposed program will implement an integrated, scalable MD and FE software capable of incorporating these effects, which will be valuable to other scientists at DOE laboratories. Time scale for proposed tasks: 2001: Billion-atom MD simulation of mechanical behavior and fracture in silicon nitride in extreme environments. 2003: Billion-atom MD plus FE continuum approach to dynamic fracture in nanostructured ceramics and ceramic/matrix composites. Materials will include silicon nitride, silicon carbide, and alumina. 2005: Evolution of nanostructures to microstructures using atomistic/continuum hybrid simulations. 2007: Effects of oxidation and corrosion on mechanical behavior and fracture incorporating immersive, interactive visualization and real-time remote collaboration using CAVE. 2010: Simulation of MEMS on emerging Petaflop architectures -- friction, wear, and lubrication in submicron-size moving components. High-performance computing resources for billion-atom MD: Teraflop Computers: A teraflop machine consists of 4,000 to 8,000 processors, each with a performance of 125 to 250 Mflops, connected via a high speed-high bandwidth interconnect. Whereas theoretical maximum performance of teraflops on a parallel supercomputers has been claimed, sustained teraflop performance on a variety of applications will be attained in the time period 1999-2000. There are large scale computation problems (simulations of real materials processing, high temperature ceramics, ceramic matrix composites, and MEMS) which could benefit from sustained teraflop computing. Petaflop Computers: Present thinking in the high performance computing community is that it is feasible to build a petaflop machine with components which will be available in years 2,007-2,010, assuming the current growth rate in the performance of the memory and processors. This would imply a processor clock speed of 1.25 GHz, eight eight-way parallel complex CPUUs per processor chip giving 80 Gigaflops performance per node. The machine will have 8,000 processing nodes giving a theoretical maximum performance of 0.64 petaflops. A superconducting design with 200 GHz superconducting CPU with conventional memory subsystem is also feasible. A more promising architecture is processor-in-memory (PIM) model. Parallel simulation algorithms and their implementations will have to take into consideration these emerging developments if the goal of simulation based virtual materials design is to be achieved in the early part of the 21st century. Need for scalable parallel-computing and visualization tools: Space-Time Multiresolution Algorithms: Molecular dynamics (MD) is a powerful tool for the atomistic understanding of long-range stress-mediated phenomena, phonon properties, and mechanical failure of nanostructures. For realistic modeling of these systems, however, the scope of simulations must be extended to large system sizes and long simulated times. New space-time algorithms and physical models encompassing multiple levels of abstraction are being developed. Fast Multipole Methods: The most prohibitive computational problem in simulations is associated with the calculation of long range part of the interatomic potentials. To overcome this problem, space-time multiresolution algorithms have been designed. These include the computation of the Coulomb interaction with the Fast Multipole Method (FMM) which reduces the computation from O(N**2) to O(N) for an N-atom system. A multiple time-scale (MTS) approach is used to exploit disparate time scales associated with slowly and rapidly varying parts of interatomic interactions. These multiresolution algorithms have been implemented on various parallel computers using spatial decomposition. Dynamic Load Balancing: Realistic simulations of fracture and materials processing are characterized by irregular atomic distributions. One practical problem in simulating such irregular systems on parallel computers is that of load imbalance which degrades computing efficiency. This necessitates a dynamic load-balancing scheme in which workloads are repartitioned adaptively during the simulation. High Performance Programming Environments and Message-Passing Interfaces: Past efforts in developing large scale, massively parallel applications have been hampered by the lack of a stable, high-performance programming environment. MPI provides an effective mechanism for developing grand challenge materials simulations by supporting code modularity. Tera Scale Data Management: Disk space and I/O speed present a major bottleneck in large-scale materials simulations, which require storing positions and velocities of billions of atoms. This problem can be addressed using data compression. However, common compression schemes perform poorly for this specific kind of data. Scalable compression algorithms are needed to optimize the storage of molecular-dynamics simulation data. Interactive and Immersive Visualization: A critical aspect of large-scale simulations is the ability to represent information contained in massive amounts of data in a form and via media that enhance both understanding and visual appreciation of the scientific content. Towards this objective, use of a CAVE-- a fully immersive and interactive, multi-viewer environment that links human perception (audio, visual, and tactile) to the simulated world on parallel machines is highly desirable. The CAVE will address the primary visualization paradigms for materials-simulation effort by providing adequate visual bandwidth for real-time interaction and immersion in very large atomistic simulations. High-performance network connections will enable collaborative exploration of large-scale datasets resulting from simulation work.

Extending Simulation Time Scales Recently there has been broadening interest in developing simulation approaches to link the disparate length scales that control material behavior. Assuming that this problem is well addressed by other authors on this panel, I focus on a related but sometimes overlooked issue, that of time scales. The use of molecular dynamics (MD) simulations in materials science has increased rapidly in the last decade, due to both the improved quality of available interatomic potentials and the increasing speed of computers. In addition, massively parallel computers (available to a subset of researchers) now allow simulations of very large systems (10^7-10^9 atoms) that seemed inaccessible just a few years ago. In contrast, the accessible time scales have increased only in proportion to the speed of a single processor, and hence have remained anchored in the nanosecond range (picoseconds for first-principles descriptions or for very large systems). These times are too short to study many of the interesting and critical processes involved in plastic deformation, transport, or annealing. Recent developments offer hope of overturning this paradigm. For systems whose dynamical evolution can be characterized by infrequent transition events, two new methods have been presented that can extend the time scale significantly, reaching microseconds, and perhaps milliseconds. The first approach, termed hyperdynamics, accelerates the transition rate (e.g., for diffusive events) using a biased potential surface in which basins are made less deep. An especially appealing feature is that, in some cases, the the accessible simulation time increases superlinearly with computer speed. With the development of more general bias potentials, this approach should become especially powerful over the next 10 years. The second approach, also for infrequent-event systems, harnesses (for the first time) the power of parallel computers to achieve longer time scales instead of length scales. Again, this should become dramatically useful within the next few years as the typical desktop workstation evolves into a platform with tens or hundreds of parallel processors. Finally, I note that these two methods can be used in conjunction to achieve a multiplicative gain in simulation speed. A research investment to investigate and develop these approaches, and related methods for finding transition states efficiently, should have a profound impact on our ability to connect to time scales that have previously seemed hopelessly distant. This in turn assists in the connection of length scales. For example, in the annealing of a radiation-damaged region, no adequate approach exists for characterizing the complicated defect dynamics during the first few microseconds, yet such an understanding is critical as input to kinetic Monte Carlo and continuum models that can then predict macroscopic properties over human time scales. Other processes where extending and motion of dislocation kinks in a bcc crystal, dynamics of a crack tip at low strain rate, and growth of thin films. These studies will clearly impact energy-related problems, especially in the design of improved materials for fission and fusion environments. It is interesting to note the synergistic relationship between the advance of computer speeds (and increasing parallelism) and the simulation approaches that best take advantage of them. For example, neither of the two methods discussed above would have been very useful if invented ten years ago, but with present computer speeds they begin to offer a significant gain. A similar effect can be seen in the development of the new, powerful first-principles approaches that scale as the number of atoms (N). Until recently, no computer could have run a case large enough to reach the breakeven point where N-scaling was more efficient than a traditional algorithm. Taking advantage of this natural time evolution of the most efficient approach requires an ongoing investment in method development, and the nature of the payoff is not necessarily predictable.

Model potential suite for multi-scale modeling. Proposal: systematic development of suite of model potentials for simulation of long-time molecular dynamics of large-scale defected materials, including semiconductor and metallic alloys, composites, polymers, and proteins. Types of potentials: range of applicability. (presented in increasing order of difficulty of application and potential accuracy in mimicking first-principles calculations) (1) classical potentials -- pair potentials plus three-body interactions: equilibrium structure especially for molecular-dynamics time-evolved defected material; "prediction" of phase diagrams; starting structures for next two potential types. (2) effective-medium/embedded-atom potentials -- simplest treatment of electronic degrees of freedom: defect energies in bulk and on surfaces; molecular dynamics of processes such as diffusion of defects in bulk and clusters on surfaces (3) tight-binding potentials -- treats orbital character of electronic wavefunctions: bonding in insulators, semiconductors and metals; defect energies and energetics. Benefits: (a) Validation of potential suite for individual atoms or atom pairs allows systematic calculation of increasingly larger systems by using computationally less-intensive potentials. (b) Study of materials in non-equilibrium situations such as high temperature, strain, and time-dependent forces. (c) Study of large-scale composites, multi-phase materials, strongly defected material. (d) Molecular dynamics studies on macroscopic time scales (microsecond to millisecond). Computation tools needed: automatic first-principle and model-potential code running for many structures to build up data base that allows parameter optimization. Advances/barriers: understanding of what features of different structures dominate parameter selection and model form. Projected time scale: Example of silicon -- most studied single structure -- helps indicate time scale. Classical potential, after initial Stillinger-Weber breakthrough, is still evolving to handle increasing range of problems: dimers on surface, molten state, defected material. EM/EA potential is in more primitive state due to lack of interest or rather greater attention on classical and tight-binding potentials. Much work needs to be done on tight-binding potentials to cover wide range of situations. Biggest challenge is energetics of different bonding geometries; for example, to explain relevant geometries of bulk, graphitic, and fullerene structures. 2001: agreement on criteria for judging potential form and parameters 2003: tight-binding potentials for single element structures 2004: tight-binding potentials for a few alloys 2005: pair-potentials for same elemental structures and same alloys 2007: effective-medium/embedded atoms potentials for above 2010: steady progress on all three schemes to build up potential suite Computational infrastructure advances: Assume that scalable computing will steadily advance: specifically, compilers and preprocessors/optimizers that are effective across different platforms; shared memory architecture. Cross-cutting computational science needs: Most urgent need is for effective tools for debugging and monitoring parallel code development and use; visual tools are essential. Sparseness of tight-binding potentials called for advances in handling parallel sparse matrix-matrix operations. Matrix operations involving only subsets of the indices of the objects require advances in optimizer schemes to produce efficient parallel code. For example, some of the indices could involve fast-Fourier transforms, and the optimizers must be able to handle them together with the sparse operations.

The Relation between Microstructure and Mechanical Properties: Challenges to Multiscale Modeling Modeling is making important contributions to understanding the origins of mechanical properties of crystalline solids in critical areas where experimental techniques are unable (currently and for the foreseeable future) to extract key pieces of information about the unit processes that influence strength, toughness, and ductility over a range of environments and temperatures. I will cite three areas: 1. Defect interactions - atomic scale problems involving elastically nonlinear interactions between defects. 2. Hardening mesoscale phenomena involving the interaction between very large groups of dislocations. 3. Composites continuum level problems involving the deformation and fracture of inhomogeneous and multiphase materials. Some relevant caveats and observations: There are many problems that remain to be explored even though they may require relatively modest computational horsepower. Such problems are often overlooked in a rush to find an application for new hardware and/or where there exists a disconnect between programmers and materials scientist and engineers. For example, some of the most fundamental issues concerning defect-defect interaction have yet to be explored, even though qualitative descriptions of many of these interactions have been around for decades. Good, empirical interatomic potentials such as embedded atom method, are OK for probing generic features of atomic scale problems. In general, exploration of specific materials requires better (faster) ab initio methods and probably enormous improvements in hardware. Two-dimensional problems are generally computationally convenient at all scales. 3D problems typically engulf and expand beyond the bounds of capability of commonly available hardware using typical computational algorithms. A short (and very incomplete) list of examples of areas where modeling is currently making contributions (and could become a critical factor in material development): 1. superplasticity and creep suggest favorable grain boundary structures to augment sliding kinetics 2. ultra-high strength materials suggest critical length scales and interfacial properties in nanophase and layered structures. 3. fracture suggest methods for changing crack tip processes 4. high temperature composites suggest types of microstructural arrangements that improve both low and high temperature properties. Areas where collaborative improvements would benefit include: 1. fluid mechanics behavior of fluids in small interstices. 2. hybrid calculations mixed EAM, ab initio, continuum. 3. parallelization of code.

Primary Damage Formation and Microstructural Evolution in Irradiated Materials When materials are exposed to high-energy neutrons, the energy of the incident particle is dissipated in a series of billiard-ball-like elastic collisions among the atoms in the material. This series of collisions is called a displacement cascade. In the case of crystalline materials, the cascade leads to the formation of two types of point defects: empty lattice sites called vacancies and atoms left in the interstices of the lattice which are called interstitials. Small clusters that contain several vacancies or interstitials can also be formed. Although the time and spatial scale characteristic of displacement cascades is only about 10-11 s and 10-8 m, respectively; the time scale required for radiation-induced mechanical property changes can range from weeks to years and the size of the affected components can be as large as several meters in height and diameter. For example, radiation-induced void swelling can lead to density changes greater than 50% in some grades of austenitic stainless steels and changes in the ductile-to-brittle transition temperature greater than 200°C have been observed in the low-alloy steels used in the fabrication of reactor pressure vessels. These phenomena, along with irradiation creep and radiation-induced solute segregation have been extensively investigated by both theoretical modeling and irradiation experiments for a number of years. The differences in the time and spatial scales of the phenomena involved in radiation-induced microstructural evolution has lead to the use of several different methods of computer simulation to model different components of the problem. For example, recent improvements in computer technology and the interatomic potentials used to describe atomic systems have broadly advanced the state of the art in displacement cascade simulation using the method of molecular dynamics (MD). Molecular dynamics simulations involving more than 1,000,000 atoms have been carried out in order to study high-energy displacement cascades. The results of these simulations are quite detailed, but are limited to simulation times of only about 100 ps. Monte Carlo (MC) methods have been used to extend the effective time scale of the atomistic simulations long enough (~10s of seconds) to investigate point defect and solute atom diffusion, and some aspects of solute segregation. Finally, kinetic models such as those based on reaction rate theory have been used to investigate long-range diffusion and microstructural evolution on the time scale of years and the spatial scale of tens of micrometers. In order to relate the predicted microstructural changes to mechanical property changes, simple dislocation barrier hardening models are typically used. Although current models are fairly robust, there are significant limitations in each area. The most detailed atomistic modeling (MD and MC) has employed embedded-atom type potentials and has been limited to pure metals. Simulations with higher-order interatomic potentials (such as tight-binding potentials) are needed to verify the details of defect energies and the behavior of point defect clusters, particularly in transition metals such as iron. Interatomic potentials for metallic alloys and ceramics are needed to investigate the behavior of materials that are relevant to engineering structures. Both of these improvements will increase the need for higher-speed computers and/or the development of improved parallel computing algorithms to compensate for the higher level of numerical complexity. The effective-medium kinetic models are generally limited by a lack of detailed thermodynamic information. They are able to simulate some of the effects of long irradiation exposures by averaging out the details of primary damage formation and the spatial dependence that would arise from local composition variations. As such, they can not properly account for radiation-induced phase decomposition and precipitation. Improved models relating mechanical properties to microstructural are also required to account for the superposition of incremental changes in complex, radiation- induced microstructures and to explain effects such as radiation-induced flow localization. Although the use of more detailed models in either of these latter two areas would increase computational requirements, the greater need is for model development. In each area, the need for visualization tools increases as data sets become larger and more complex. The specific needs of radiation damage modeling are directly related to fundamental issues in other areas of materials science, e.g. questions of defect properties (point defects, solutes, dislocations, ...) and defect- defect interactions generally control material behavior.

Materials Durability and Lifetime Prediction: Connecting Atomic, Mesoscopic and Macroscopic Properties (1) Opportunity. A massive computational effort is needed to develop models that will allow the prediction of the degradation behavior and time to failure of polycrystalline materials, coatings and components from fundamental, atomic-level materials properties. This behavior is intimately tied to the evolution of polycrystalline microstructures (e.g., the grain sizes and grain shapes, interfacial cracks, porosity) under the influences of stress and temperature, giving rise to irreversible processes (such as grain growth and recrystallization, stress development, crack nucleation and growth, plastic deformation) that result in the degradation and, ultimately, the failure of the component. The main challenge is to establish two key links among the three different length scales involved. First, the physical behavior at the mesoscale, i.e., at the level of the interfaces, grain junctions and dislocations in the microstructure, has to be linked to the under lying atomic-level structure and composition of these key defects. Second, the overall materials response to thermal and mechanical driving forces has to be linked to the interplay between the underlying interfacial and dislocation processes (involving for example grain sliding, grain-boundary migration, cavitation, dislocation and crack nucleation and propagation). Information on these types of processes is inherently difficult or impossible to obtain from experiments (see Sec. 4). The conceptual advances needed to link the three length scales therefore have to come from a hierarchically structured modeling approach with theory. No such approach is currently available. - Atomistic modeling is limited by available computational resources to systems which are too small to be representative of an actual component. - Modeling at the mesoscopic level is limited by insufficient atomic-level understanding of the nature of the inhomogeneous regions of the material; i.e., of the underlying interfacial processes and atomic-level mechanisms that govern key aspects of microstructural evolution. - Phenomenological theories can only be applied to highly simplified microstructural models, with virtually no information on a variety of crucial effects known only from atomistic modeling. What is particularly missing at this stage of development is the ability to simulate properties at the mesoscale, using the results of large-scale atomistic simulations as input to predict macroscopic behavior for comparison with existing and the development of new phenomenological models. (2) Approach. In a small effort developed in recent years at ANL, molecular dynamics simulations are used for the synthesis of controlled, fully dense or porous, bulk or thin-film microstructures by growth from a melt into which small, more or less randomly oriented crystalline seeds are inserted. Being able to control the misorientations and initial positions of the seed grains provides the unique capability to manipulate the microstructure, for example, via tailoring the distributions in the grain size and grain shapes, the porosity, as well as the types of grain boundaries in the system. With presently available computational resources the grain size and the number of grains that can be considered are too small for any realistic comparison with key experiments. However, the significant increase in computer power expected from the Computational Sciences Initiative would enable key processes and mechanisms taking place in model microstructures to be identified at the atomic level. The insights and certain key parameters that could be extracted from such simulations could then be used as input for mesoscopic-level simulations. (3) Benefits. A dramatically improved fundamental understanding of how tailored polycrystalline microstructures evolve under the effects of temperature and stress will provide the guidance needed for a systematic approach to the development of microstructurally and interfacially engineered materials. Such guidance is likely to facilitate major breakthroughs, for example, in the design of fracture-resistant cast steels, toughened yet creep-resistant high-temperature structural ceramics, hard and corrosion-resistant coatings for cutting tools, thermal-barrier coatings for turbine-engine applications, etc. Industrial companies, such as Caterpillar and McDonnell-Doug lass, have expressed a strong interest in this type of a simulation approach which could provide a core tool linking up atomic-level type simulations with macroscopic industrial-design tools, such as the DOE sponsored Casting Process Simulator, CaPS. (4) Parallel Experimental Efforts. As mentioned above, experimental information on the interfacial processes and atomic-level mechanisms that control microstructural evolution is extremely difficult or impossible to obtain. Moreover, even simple parameters characterizing an evolving microstructure, such as the average grain size and information on the grain shapes and grain junctions, is very difficult to access. The modeling program outlined above should therefore be accompanied by an experimental program on the non-destructive characterization of evolving microstructures. In one such attempt presently in its infancy stage, high-energy x-ray scattering at the Advanced Photon Source combined with advanced robotics techniques would be used to image the grain boundaries and grain junctions in an evolving microstructure. This effort is presently being formed among teams from Carnegie-Mellon University , the University of Riso, the European Synchrotron Radiation Facility in Grenoble and ANL. (5) Computational Resources, New Developments. In order to bridge the length-scale gap to the mesoscale, the atomic-level simulations will require the massive computational and graphic visualization resources which the Computational Sciences Initiative would provide. Simultaneously, however, key conceptual theoretical advances are needed to identify exactly what type of atomic-level information is needed and the manner in which it is fed into the mesoscopic-level Monte-Carlo type simulations. Guidance for the development of such a conceptual framework will come from in-depth analysis of key atomic-level simulations on the evolution of designed model microstructures, which will provide insights into the critical aspects in the physical behavior of individual interfaces and grain junctions that control the evolution of the microstructure as a whole.

Connection between geoscience and materials; computational issues. The techniques used by both the material science community and the geophysics/geochemistry community are identical up to certain time and length scales (years, and meters). This includes atomic scale methods, such as solid state quantum mechanics, molecular dynamics, and Monte Carlo techniques, micro-scale models that describe microstructural evolution, and macroscopic strategies such as finite-element approaches and computational fluid dynamics. Understanding the response of a metal or alloy to external temperature and pressure conditions could, under the proper circumstances, be treated with the same methodologies regardless of the origin of the problem. Researchers in the earth sciences, however, regularly work on length an time scales that are vastly larger and longer than those that appear in typical material science applications. Natural systems are also thermodynamically open, unbelievably heterogeneous and contain biological systems. The strategies adopted by researchers working on these larger time and length scales or directly in the field have no direct parallel in the material sciences. A range of techniques including, atomic scale theories, computational fluid dynamics, finite element simulations, seismic imaging, transport models will require machines of the order of 1-10 sustained Teraflops in the near term with data requirements in 10=s of pedabytes. In addition to the computer hardware, a strong, sustained commitment to scientific software development including basic tools (message passing, global arrays, languages, math libraries, etc.) as well as end user application codes. Significant resources must also be allocated for software development and the cost of maintaining large groups of research teams in the host of application areas to do the scientific work. Interactive 3D visualization technology is also necessary to understand the results generated by many disciplines. Today=s computing engines can easily generate gigabytes of data; tomorrows methods and computing machines will generate pedabytes. High speed networks capable of moving this amount of data between researchers in reasonable amounts of wall time must also be established (transfer rates in excess of gigabytes/sec).

Compuational Issues A major focus of materials research in the future will be to establish the microscopic foundations for the relationship between technical magnetic properties and microstructure. The achievement of the above goals will require overcoming a number of major problems involving microstructure (independent of magnetism), magnetism (independent of microstructure), giant magneto-resistance, and thermal and transport properties. The quality of permanent magnets depends on understanding how large aggregates of atoms behave collectively, particularly when the behavior depends critically on temperature and microstructure (e.g. defects and interfaces). Accurate first principles and semi-empirical methods for evaluating the properties of large systems of atoms are needed. The success of future theoretical models will be predicated on exploiting the power of massively parallel supercomputers and developing a software environment for performing large scale quantum simulations on microstructural length and time scales. To achieve the above long term goals will require significant new code and algorithm developments that push the envelope of what is possible in terms of length and time scales, as well as complexity of phenomena that can be treated. This would require the development of finite temperature spin dynamics (non-collinear magnetic moments) within both the O(N) ab-initio methods and the tight-binding molecular dynamics (TBMD). The tight binding molecular dynamics method also needs to be extended to multi-component systems, transition metals and magnetic materials for performing simulations with a sufficient number of atoms to accurately treat long range magnetic correlations in alloys. This would ultimately require spin-orbit coupling, intrasite exchange, and single site anisotropy TBMD parameters. To development these new codes and algorithms will require the development of new models based on advanced computational methods. For example, the quasi-classical spin dynamics formalism can be cast as a stochastic differential equation and requires the development of advanced numerical methods for the solution of stochastic differential equations that include various types of random components, either additive or multiplicative. In addition, new large scale first principles methods can be developed using a wavelets basis which results in a large complex nonsymmetric sparse matrix formalism that that could be solved using preconditioned iterative methods or nonsymmetric complex sparse matrix methods. Developing robust non-linear optimization algorithms is necessary since the number SCF iterations necessary to achieve convergence rapidly grows with increasing system size. Equally important is the need for improved time stepping algorithms in order to perform the dynamical simulations over the appropriate length of time. Computational tools to aid the materials scientist with developing or adapting computer codes that are not necessarily their own codes are needed. A graphical user interface that would graphical represent the individual routines of an entire code would be useful, in adapting a large unknown code, to be able to plug in new algorithms within the entire code or to select and combine different routines. This environment would allow the materials scientist to evaluate various routines of differing complexity within the entire code. Finally, a seamless computing environment would allow the materials scientist to submit a job where they only have to include a time they would like the job to finish. This would relieve the materials scientist of the burdens associated with worrying about resource management issues including scheduling, task migration, load balancing and fault tolerance. This type of system would allow the scientist to concentrate more on the science rather than on the computer science.

Plasma/Surface Interaction Analysis for Fusion* Motivation: Understanding and control of the plasma surface interaction (PSI) is probably the most single critical issue for magnetic fusion power development. The key PSI issues are boundary material erosion by plasma particles, hydrogen and helium recycling, and plasma contamination. Integrated computer codes have been successfully developed to analyze limited aspects of PSI phenomena. Advanced computers and numerical techniques would permit us to substantially advance our PSI predictive capability and aid the choice and optimization of fusion surface materials and plasma regimes. A "virtual" tokamak where numerical experiments could be conducted, is a possibility with advanced computing. Problem: The phenomena to be analyzed are (1) net sputtering erosion of fusion surface materials by charged and neutral particles, (2) heat and particle removal at the surface, (3) surface evolution, melting, and vaporization due to plasma high-power transients, and (4) effect of plasma surface interactions on the edge and core plasmas. These require a wide range of integrated models/codes particularly for edge plasma parameters and magnetic field geometry, sheath physics, molecular dynamics and/or binary collision sputtering/reflection, material thermal and mechanical response, 3-D line radiation transport, and atomic and molecular processes of surface materials in the plasma. Analysis of the self-consistent full boundary problem-not to mention the non-linear problem (surface materials significantly changing the plasma)-requires substantially faster computers and numerical methods than presently available. Opportunity: A two to three order of magnitude increase in computer power, and associated advancements in numerical techniques would substantially improve the study of plasma surface interactions in fusion reactors. Since prototype fusion power reactors will cost ~5-10 billion dollars, and PSI issues are critical to their design and operation, there is a very high potential for cost savings from advanced computation.

Statistical Mechanics at the Microscale It is apparent that many outstanding problems in materials science require theories to span many orders of magnitude in both space- and time-scales. A survey of existing theories suggests that our understanding of the atomic and macroscopic scales is quite advanced. What we really lack is the ability to connect these two types of calculations. This is, and has always been, one of the greatest challenge faced by materials theorists. The following is motivated by a desire to develop a fundamental understanding of mechanical properties in a broad range of materials. The rapid increase in available computing power suggests new ways in which we might approach these types of problems. One way is to envision creating a general theory capable of modeling a wide variety of materials. These theories are likely to involve some type of hybrid technique in which atomic scale calculations are used to model small scale behavior, and finite-element techniques are used to couple the atomic scale behavior. (The work of Ortiz and Phillips represents one attempt to move in this direction.) Certainly, these approaches should be pursued. If developed successfully, they offer a powerful modeling tool destined to be applied in numerous fields. (The equivalent of a band-theory for mechanical properties?) An alternate approach is to couple the scales on a material by material basis. The proposed technique is best understood through example. Suppose we wish to understand the contribution of dislocation motion to deformation of a BCC material under high temperatures and stresses. Our first task is determine the nature of dislocations in BCC materials. These are most often observed to be long, straight screw segments. It is thought that the screw segments are not mobile because of the noncompact nature of the core. In order for the dislocation to move, the core must become compact - a thermally activated process. It is unlikely that the entire core will constrict, and this necessitates the development of double kink pairs: Segments of dislocations will reside in adjacent Peierls valleys, and they will be joined by near-edge oriented kinks. The motion of the dislocation, then, takes place through the lateral motion of these kinks. At this point, a statistical analysis is necessary to connect the scales. One envisions a model in which double-kink pairs are formed through a thermally activated process, and then move according to a set of appropriately defined rates. Their formation rates and mobilities are determined by the applied stress and the long-ranged interaction stresses. (These interaction stresses can be calculated using calculated elastic constants and elasticity theory.) The kink formation energies and rates may be obtained from atomic scale calculations of the sort suggested by others at this workshop. An important step, then, becomes the application of ideas borrowed from statistical mechanics to the analysis of the interactions of the micro scale particles - the dislocation segments. A suitable analysis may yield equations of motion for the dislocations that can then be used as input for larger scale calculations. In addition, these simulations allow one to determine which atomic-scale parameters are relevant to the larger scale dislocation dynamics, and will serve to focus the atomic-scale efforts. The above is just one example. One can envision similar statistical analyses being applied to superplasticity and reactive metal infiltration of ceramic preforms to create metal ceramic composites. Also, a statistical analysis of the many dislocation problem may be at hand. These calculations may now be possible: Computers have advanced to the point in which a single dislocation simulation will run on a single processor. Parallel processing machines allow one to obtain the necessary statistics. The tools necessary to accomplish this task are at hand. Monte Carlo techniques are advancing at a rapid pace, and they are easily "parallelized." In terms of other tools, what would be really nice is a "toolbox" which would allow for rapid prototyping of statistical models. (The "toolbox" might be something along the lines of MatLab's Simulink, but allow for more complicated models involving thousands of elements, and flexible couplings between them.) As with all modeling efforts, experiments must be designed and executed to verify/disprove the ideas arising from the analysis. In situ microscopy experiments seem the most natural means to check many of these ideas. The overlap between these ideas, and those necessary for some geophysical calculations is evident. (For example, one may view reactive metal infiltration as an invasion percolation model.)

Importance of Entropy in Materials Modeling One of the current goals of materials modeling is to bridge between length scales. One approach to this problem is to use atomic scale simulations to determine critical materials properties that are then input into continuum level descriptions. As examples, the energy of interphase interfaces is a crucial input to models of the nucleation and growth of second phase precipitates. Another is the importance of fault energies to the determination of the structure and mechanical properties of dislocations. In most cases, the quantity needed is not an internal energy, but rather a free energy. The general problem of the determination of the free energy of material defects in the relevant case of complex multi-component systems and finite temperature does not have a general computationally tractable and quantitatively accurate solution. There are various approaches to these issues that are currently available. Each of them has significant drawbacks, though. MD or MC approaches are typically performed based on approximate interatomic interactions. The accuracy of these interactions limits the accuracy of the simulations. Further, the free energy is not a simple ensemble average, so the determination of the free energy of the defects in general requires time consuming thermodynamic integrations. Current computational hardware and algorithms do not allow first-principles based MD or MC to be performed on complex systems with high statistical accuracy. Methods based on cluster expansions of the energy in terms of lattice variables are useful for coherent interfaces and faults where there is a common lattice. These models can use ab initio methods to determine the energy parameters. However, these methods cannot treat general structural defects and only treat the compositional entropy, not entropy due to nuclear motion. With regard to nuclear motion, it is now possible to compute the contribution of phonons to thermodynamic properties based on ab initio density functional techniques. Again, computational limitations restrict these applications to simple systems and this does not treat the compositional entropy. The development of computational techniques to accurately determine this class of problems would be a great value.

Your comments and suggestions are appreciated.

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Edited by: wilkins@mps.ohio-state.edu [January 1998]