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Summary of research in applied mathematics, numerical analysis, and computer sciences
The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.
Psychophysica: Mathematica notebooks for psychophysical experiments (cinematica--psychometrica--quest)
Psychophysica is a set of software tools for psychophysical research. Functions are provided for calibrated visual displays, for fitting and plotting of psychometric functions, and for the QUEST adaptive staircase procedure. The functions are written in the Mathematica programming language.
Addressing Epistemic Uncertainty using Probability Theory and Beyond
Abstract Not Provided
Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.
Parallel multiscale simulations of a brain aneurysm
Cardiovascular pathologies, such as a brain aneurysm, are affected by the global blood circulation as well as by the local microrheology. Hence, developing computational models for such cases requires the coupling of disparate spatial and temporal scales often governed by diverse mathematical descriptions, e.g., by partial differential equations (continuum) and ordinary differential equations for discrete particles (atomistic). However, interfacing atomistic-based with continuum-based domain discretizations is a challenging problem that requires both mathematical and computational advances. We present here a hybrid methodology that enabled us to perform the first multiscale simulations of platelet depositions on the wall of a brain aneurysm. The large scale flow features in the intracranial network are accurately resolved by using the high-order spectral element Navier–Stokes solver NεκTαr. The blood rheology inside the aneurysm is modeled using a coarse-grained stochastic molecular dynamics approach (the dissipative particle dynamics method) implemented in the parallel code LAMMPS. The continuum and atomistic domains overlap with interface conditions provided by effective forces computed adaptively to ensure continuity of states across the interface boundary. A two-way interaction is allowed with the time-evolving boundary of the (deposited) platelet clusters tracked by an immersed boundary method. The corresponding heterogeneous solvers (NεκTαr and LAMMPS) are linked together by a computational multilevel message passing interface that facilitates modularity and high parallel efficiency. Results of multiscale simulations of clot formation inside the aneurysm in a patient-specific arterial tree are presented. We also discuss the computational challenges involved and present scalability results of our coupled solver on up to 300 K computer processors. Validation of such coupled atomistic-continuum models is a main open issue that has to be addressed in future work.
Box-Constrained L1/L2 Minimization in Single-View Tomographic Reconstruction
This manuscript will be submitted to one of two journals (SIAM Imaging, or Applied Mathematics and Computation)
Combustion of hydrogen injected into a supersonic airstream (the SHIP computer program)
The mathematical and physical basis of the SHIP computer program which embodies a finite-difference, implicit numerical procedure for the computation of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction is described. The physical hypotheses built into the program include: a two-equation turbulence model, and a chemical equilibrium model for the hydrogen-oxygen reaction. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. The computer time required for a given case is approximately 1 minute on a CDC 7600 machine. A discussion of the assumption of parabolic flow in the injection region is given which suggests that improvement in calculation in this region could be obtained by use of the partially parabolic procedure of Pratap and Spalding. It is concluded that the technique described herein provides the basis for an efficient and reliable means for predicting the effects of hydrogen injection into supersonic airstreams and of its subsequent combustion.
Quantum Computing for Enhancing Grid Security
This article introduces quantum computing as a necessary and viable tool in addressing the needs of a modernized power grid. The application of quantum computing in enhancing physical security of the grid – an increasingly difficult problem to solve– is investigated. A comparative study based on mathematically proven computing performance measures shows the merits of the proposed method and further unveils the potential benefits of quantum computing in improving grid performance.
High-Order Numerical Methods for the Simulation of Linear and Nonlinear Waves: High-Frequency Radiation and Dynamic Stability (Final Report)
Over the past four years the Principal Investigator (PI) David Nicholls has worked on several projects in connection with award DE-SC0001549. Of the greatest import has been the continued supervision of five Ph.D. students (Robyn Canning, Travis McBride, Andrew Sward, Zheng Fang, and Venu Tammali). Canning and McBride defended their theses and graduated in May 2012, while Sward defended his thesis and graduated in May 2013. Both Fang and Tammali plan to defend their theses within the year and graduate in May 2015. Fang is now a very experienced graduate researcher with one paper accepted for publication and another in preparation. Tammali is nearly to the point of writing a paper and will work this summer as an intern at Argonne National Laboratory in the Mathematics and Computer Science Division under the supervision of Paul Fischer.
Multiscale Modeling Meets Machine Learning: What Can We Learn?
Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learn- ing to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.
The Weak Form Is Stronger Than You Think
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .
Laboratory Directed Research and Development Annual Report, Fiscal Year 2011
This report documents progress made on all LDRD-funded projects during fiscal year 2011. The following topics are discussed: (1) Advanced sensors and instrumentation; (2) Biological Sciences; (3) Chemistry; (4) Earth and space sciences; (5) Energy supply and use; (6) Engineering and manufacturing processes; (7) Materials science and technology; (8) Mathematics and computing sciences; (9) Nuclear science and engineering; and (10) Physics.
A mathematical model of an active control landing gear for load control during impact and roll-out
A mathematical model of an active control landing gear (ACOLAG) was developed and programmed for operation on a digital computer. The mathematical model includes theoretical subsonic aerodynamics; first-mode wing bending and torsional characteristics; oleo-pneumatic shock strut with fit and binding friction; closed-loop, series-hydraulic control; empirical tire force-deflection characteristics; antiskid braking; and sinusoidal or random runway roughness. The mathematical model was used to compute the loads and motions for a simulated vertical drop test and a simulated landing impact of a conventional (passive) main landing gear designed for a 2268-kg (5000-lbm) class airplane. Computations were also made for a simply modified version of the passive gear including a series-hydraulic active control system. Comparison of computed results for the passive gear with experimental data shows that the active control landing gear analysis is valid for predicting the loads and motions of an airplane during a symmetrical landing. Computed results for the series-hydraulic active control in conjunction with the simply modified passive gear show that 20- to 30-percent reductions in wing force, relative to those occurring with the modified passive gear, can be obtained during the impact phase of the landing. These reductions in wing force could result in substantial increases in fatigue life of the structure.
Brochure on the 2024 ASCR Workshop on Energy-Efficient Computing for Science
Large-scale computing has enabled numerous scientific discoveries, including ground-breaking achievements facilitated by the US Department of Energy (DOE) supercomputers and advances in applied mathematics and computer science. While important advances were made in energy efficiency to enable exascale computing, continued efforts are needed to dramatically improve the energy efficiency of the next generation of high-performance computing (HPC) systems and, more broadly, AI data centers. Without substantial improvements in energy efficiency, the energy consumption associated with computing could become a limiting factor for future scientific discovery, national security, and technological advancement.