Examples of Motivating Scientific Problems in NCC

New Challenges in Computation (NCC) will provide the computational capability to solve many complex scientific problems involving (1) multiple scales and structures in space or time and (2) the dynamic interplay between computations and data, often in real time. Selected, illustrative (not comprehensive) examples are provided below for the various directorates at the National Science Foundation. Since NCC is inherently cross-disciplinary, many examples listed under a given directorate may actually be appropriate for other directorates as well. For example, many of the examples for the Directorate for Geosciences would interest mathematicians and computer scientists. It is therefore advisable to look at all the examples to fully capture the flavor of what types of research are possible under NCC.

Directorate for Mathematical and Physical Sciences

Application of non-perturbative techniques to strongly correlated systems in the study of condensed matter physics, including challenges to basic concepts raised by the discovery of high temperature superconductors and heavy fermion materials.

Utilization of lattices and matrix inversions in calculations for the simulation of quantum chromodynamics and nuclear structure.

Discovery of a solution to the coupled PDE's of Einstein, involving complex geometries and both elliptic and hyperbolic equations, for predicting waveforms observed in experiments related to gravitational physics.

Development and implementation of new methods to study quantum dynamical processes in condensed phases, including an accurate theoretical description of solvent effects in activated rate processes (most chemical reactions) and other condensed phase dynamical phenomena.

Improvement of the real time processing of large amounts of data to (1) allow the flagging of rare events, such as gamma ray bursts in time, thus enabling other instruments to be directed to the study of the transient phenomena; (2) extract patterns from relativistic heavy ion collision data, with particle multiplicities in the thousands, which exhibit signals of the formation of a quark-gluon plasma; (3) correlate information from several independent databases in order to provide a complete picture of an "event" and maximize the extraction of information (such as subdetector components and calibration data, or data from several particle astrophysics detectors); and (4) efficiently extract single "events" from databases which may exceed 10^S events, often by collaborators from geographically divergent locations.

Understanding the non-linear effects in circular accelerators of charged particle beams that limit long-term stability.

Calculating detailed nuclear structure properties with ab initio few-body methods, to make connections to nucleon substructure and other short-distance behavior, and to understand the quantitative basis for the nuclear shell model.

Extending the nuclear shell model to heavier nuclei and very large basis sets, in order to enable reliable predictions of structure and reaction properties, with applications to star formation and supernovae.

Extending the quantitative successes of comprehensive, semi-analytic many-body procedures such as correlated-basis, coupled-cluster, and self-consistent Green's function theories to predict structure, quantum coherence phenomena, excitations, dynamics, and phase transitions in nuclear, atomic, electronic, and spin systems in complex geometries and under extreme conditions of temperature and pressure.

Extending the quantitative successes of comprehensive, semi-analytic many-body procedures such as correlated-basis and self-consistent Green's function theories to study structure, pairing properties, excitations, and dynamics in exotic nuclear systems present in neutron stars and created by radioactive beams and heavy-ion colliders.

Application of recent advances in artificial intelligence, statistical inference, and pattern recognition to databases in nuclear, molecular, and condensed-matter physics, with the promise of discovering new regularities and developing reliable predictive models.

Solving the coupled, time dependent, non-linear partial differential equations which arise from theoretical studies of Bose-Einstein condensates at finite temperatures.

Calculation of total and differential cross sections for the scattering of electrons from atoms at energies above the ionization threshold.

Application of non-perturbative methods to calculate the stripping of electrons from atoms in the presence of ultra-intense laser fields.

Use of enzyme modeling to explain how the atomic level structure of an enzyme leads to its functional, enzyme catalysis.

Theoretical description of highly complex enzymatic processes including investigations of unusually large active sites, many of which contain a transition metal, often occur on several low-lying potential energy surfaces, and undergo conformational changes as part of reaction catalysis.

Simulation of large protein molecules which consist of tens of thousands of atoms in solution over a micro-second time interval_a major challenge in molecular dynamics.

Uniting combinatorial chemistry with structural biology to deduce the rules of molecular recognition, which may ultimately allow us to build accurate models of multiprotein complexes from the structures of their components.

Prediction of the macroscopic behavior of polymeric materials (macromolecules) based on the molecular composition of the included polymers, even when their structures are unknown; and to allow for the design and engineering of new materials from first principles.

Simulation of equilibrium and non-equilibrium macromolecule (polymers and proteins) conformation and properties, that drive many chemical processes (such as separations, coatings, adhesion), for understanding how they interact with each other, with solid and fluid interfaces, and their rheological properties.

Simulation of large molecular ensembles for better chemical process design_for example, molecular clustering at high pressures, supercritical phenomena, nucleation kinetics, and molecular behavior at extreme conditions_and to adapt them for large systems.

Complete description of key molecular processes involved in combustion and atmospheric chemistry, from a detailed description of the interaction energies of the constituent species to the impact on atmospheric modeling, engineering, ecology, pollution, and energy conservation.

Simulation of how molecules and colloids assemble, not in isolation, but in a realistic environment, to assist in the design of self-assembling nanostructures for advanced materials applications.

Elucidation of aspects of computational materials science, including non-equilibrium dynamical processes such as materials deposition and growth, sintering, pattern formation, micro and nanostructural evolution; the growth and control of artificially structured materials; and materials failure.

Prediction of the final properties of a manufactured material, determined by its crystal orientation and arrangement, as the manufacturing environment of temperature and pressure is imposed.

Directorate for Engineering

Elucidation of the two-phase, turbulent, chemically reacting, three-dimensional unsteady fluid flow in a gas turbine across large spatial scales_for example, while the combustor itself may be about a meter long, the reaction zone where chemical reactions occur is of size 10-100 micrometers, the turbulent flow-field is of the order of 100 micrometers to a centimeter, and injection of fluids through atomization leads to drops of size 10-100 micrometers.

More realistic and more accurate models of the heart by simultaneous inclusion of details such as realistic heart geometries, inhomogeneous material properties, anisotropic muscle fiber orientation, and accurate membrane kinetics_to solve, for example, fluid dynamics problems in the three spatial dimensions and time, such as simulations of the embryonic and fetal heart at different stages of development to clarify the role of fluid forces in shaping the developing heart.

Comprehensive modeling and physical simulation tools for human joints based on medical imaging data in order to provide non- invasive diagnostic tools; custom prosthesis design and placement; systematic pre-operative planning; quantitative models of strain injuries; and simulation of wear in articulating mechanical components, such as the prosthetic hip, starting from seconds and extending to years for obtaining long-term wear predictions.

Directorate for Biological Sciences

Modeling of physiological systems to explain how molecular detail produces cellular and organismal physiology is the problem of understanding how a cell, as a system, exhibits stability, flexibility, and robustness in its biochemical and dynamical responses to genetic and environmental changes applications 1nclude modeling biochemical networks (including genetic and regulatory networks here), models of cellular processes such as the cell cycle or neuronal response to transmitters and effectors, and the rational design of new strains for productive purposes.

Description and prediction of the relationships between structure and function, not just at the molecular level (vice supra), but at the levels of cells, tissues, organs, and organisms for example, what are the mechanisms of pattern formation during development and how are they coordinated and synchronized; what functional patterns emerge when neurons are connected differently or are constrained to interact in different ways, and how do these in turn effect behaviors and selection for behaviors; how much plasticity is there in biological structures (e.g., genomes, mitotic apparatus, and livers), and can they be made more efficient; and what mechanical, electrical, or dynamical properties are important in achieving functions?

Understanding how behavior emerges from properties of neurons and networks of neurons through advances in experimental methodologies that provide detailed information on ionic channels, their distribution over the dendritic and axonal membranes of cells, their regulation by modulatory agents, and the kinetics of synaptic interactions; and through the development of fast computing, sophisticated simulation tools, and improved numerical algorithms for detailed biophysically-based computational models that reproduce the complex dynamic firing properties of neurons and networks.

Prediction of short- (such as reflexes) and long-term behaviors (such as migratory behavior triggered by the perceived time of sunrise) on the basis of patterns of 1mpulses that encode sensory stimuli that, in turn, are based on the transitions between open and closed states of sodium channels.

Understanding how the orderly behavior of groups arises from individual behavior, especially when the individual behavior seems less predictable_for such phenomena as the swarming of honey bees, foraging of honey bees or ants, nest- construction of ants or termites, and the movement of fish schools or bird flocks.

Prediction of specific paths, and their attendant adaptations, of a set of species as they move through evolutionary space-time_applications include understanding how species and populations change in response to environmental changes, and managing those; the impact of new selective pressures on species; and the relationships among species, populations, and landscapes over time.

Elucidation of the connections between the physical and biological parts of the global biosphere, and the multiple scales of space, time, and organizational complexity on which critical processes are played out_for example, how are individual plants influenced by changes in atmospheric patterns and, more difficult, how do those effects on individual plants feed back to influence regional and global patterns of climate and biological diversity?

Directorate for Geosciences and Office of Polar Programs

Integration of our understanding of the various components of Earth (atmosphere, oceans, solid earth, biosphere) to better understand their dynamic interactions and ultimately to develop a predictive capability for the Earth System and its response to perturbations, both natural and human-induced_a scaling problem, since we begin with empirical observations (at scales from atomic to regional and from nanosecond to decades or millennia) and build models that extrapolate to the outer reaches of the ionosphere and to geologic time; and then we then wish to "scale down," and use the models to predict behavior and phenomena at regional or local spatial scales and hours to decades in time.

Developing and testing advanced methods of data assimilation on ocean circulation models of increasing complexity that can take advantage of new computer technology, both in hardware and software. The goal is to reduce (1) the lack of skill in the underlying model, due to both poor initial data and dynamical deficiencies, (2) the poor knowledge of the statistics of the forcing and parameterization errors, and (3) the lack of sufficient resolution due to the insufficient computing power in order to produce an accurate representation of the state of the ocean and predict its future state.

Encouragement of new mathematical and computational formulations for general ocean circulation models than can be used in coupled earth system models to study climate change due to anthropogenic effects and natural variability over long time periods (century to millennium).

Development of fine-scale ocean-atmosphere-land regional models that can be coupled to or nested within global climate models to understand how climatic events such as E1 Nino and the North Atlantic Oscillation affect major weather events (storms, floods, droughts).

Development of methods by which sparse data, generally representing time- averaged climatologies, can be integrated into three-dimensional models. An example would be the interpretation of paleo-oceanographic records that represents past ocean conditions and cover a very wide range of time scales. Another example could be the incorporation of sparse biogeochemical data into models for estimates of global C02 budget.

Improvement in the linkages between physical and biological models of the ocean and embed regional models within basin and global scale circulation models. This will require different governing equations from those ordinarily used in physical oceanography as well as variable size grids.

Development of virtual reality as a tool to fundamentally change the current paradigms of how scientists use oceanographic information. Viewing, navigating through and interacting with multidimensional data fields (e.g., hydrographic data, circulation vectors, larval fish distributions) in the virtual environment provides a sense of presence which greatly improves our ability to understand inherently complex processes. Work would entail the construction and use of virtual environments based on environmental data.

Enabling distributed teams to work together to build global space weather models to provide predictive capability to forecast the state of the coupled sun-solar wind- magnetosphere-ionosphere- upper atmosphere system and to run, test and verify models against real time observations.

Building collaboratories to give distributed teams of scientists a virtual presence at multiple distributed remote instrument locations in order to optimize instrument operating modes to fit the particular geophysical conditions and to coordinate operations during measurement campaigns.

Establishing collaboratories to enable distributed teams of scientists to undertake joint data analysis and collaboration to develop models of the physical processes with couple energy between the solar wind, the Earth's magnetosphere, ionosphere, and upper atmosphere.

Simulation of molecular dynamics of silicate melts (at high temperatures and pressures) to model convection in the Earth's mantle, which in turn drives plate tectonics, causing earthquakes.

Modeling of data from laboratory experiments on crack propagation in minerals and brittle failure of rocks to understand mechanisms of fault rupture and propagation (hence earthquakes).

Modeling the magnetohydrodynamic aspects of the Earth's liquid core, which results in Earth's magnetic field (geodynamo), which influences the ionosphere and "space weather."

Prediction and development of control strategies for the infiltration and spread of contaminants in the soil subsurface, requiring simulations that integrate several orders of both the time and length scale to account for the influence of contamination that may be distributed over several miles and several years.

Directorate for Social, Behavioral, and Economic Sciences

Adoption of geographic information systems and multi-scale computer simulations for the analysis of complex phenomena_such as, for ecosystems and human- ecosystem processes; for the modeling of spatial labor markets (since this is one economic market where distance is relevant, but cannot be modeled with a simple or single metric, as it has different meanings and barriers in different social, occupational, and urban contexts); and for analyzing urban traffic processes in real time for routing improvements and understanding the interaction of land use, public regulation, auto traffic, and air pollution.

Understanding the behavior of a system that emerges from collective interactions of its relatively simpler components for such problems as determining fluid flows in reservoirs at the level of the reservoir field from a knowledge of flows at the level of pores in the ground, predicting macroscopic properties of materials from a knowledge of atomistic properties, understanding the regulation of interacting metabolic pathways, and studying the interplay of natural and anthropogenic factors in issues of environment and biodiversity.

Modeling behavior, using nonlinear dynamical systems, that takes place over time and which involves the observation of many variables at once_examples abound in human social interaction, and cognitive, social, and motor development.

Simulation of social systems in which individuals are modeled as intelligent actors, whether by neural networks, symbolic processors, or other computational models; building beyond the level of individuals and small groups, these computer simulation studies could explore social organization dynamics, organizational ecology, and evolution of complex social systems.

Utilization of computer-aided developments in the traditional social sciences for enhancing progress in computationally-based theories of complexity and self- organization in social and economic systems.

Expansion of the scale of laboratory experimentation on socio-economic exchange_in terms of the number of subjects, the number of locations, the amount of time, the complexity of problems, the complexity of communication, and the numbers and diversity of faculty and students who can participate in experimental research in such fields as economics, sociology, political science and social psychology.

Directorate for Computer and Information Science and Engineering

Discrete-event simulation to predict the behavior of large scale networks such as the internet and to investigate alternate designs or the implications of management policies for example, it is recognized that the internet has deleterious behavior that emerges only when the network is large enough and to anticipate and correct such situations depends on discrete-event simulations that require enormous amounts of computation.

Development of a "tuneable" simulator of computer architectures that allows one to look at the machine at any level of detail needed from studying timing and interrupts of a single processor or memory controller, to predicting the behavior of realistic application kernels on the whole machine.

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