News 1998 Army Science and Technology Master Plan



2. Mathematical Sciences

Table E–24 summarizes international research capabilities for the major subareas of mathematical science.

Basic research in applied analysis and physical mathematics directly contributes to the modeling, analysis, and control of complex phenomena and systems active within the Army. Applied mathematicians define practical boundaries, set the framework of analysis, and act as collaborators for scientists and engineers on many development projects. It is often the case that seemingly unrelated research will have effects on the development of critical technologies (e.g., the influence of advances in control theory on the development of nonskid brakes).

Many nations show significant capability in a number of areas identified as having potential impact on future Army technologies. This is consistent with the fact that many advanced applied mathematics research efforts involve only a small number of researchers and have minimal hardware requirements. Thus even nations without an extremely powerful industrial or research base can have a few specific points of excellence in mathematics.

Germany, France, and the United Kingdom are all considered to be on a par with the United States in a number of these areas of mathematics research. All of these countries are noted for developing partnerships between academic and industrial groups working on mathematical problems directly related to modeling and manufacturing issues. In general, Canada and Japan are also considered to be working at or near this high level. Both China and India exhibit strong potential research efforts, which are constantly improving and conceivably, will soon be world leading. The countries of the FSU show a declining capability, largely due to a lack of resources. For example, though many important numerical methods for modeling physical phenomena were developed in the Soviet Union in the 1950s and 1960s, current research is no longer considered world leading. Additionally, Ukraine is noted for a traditional weakness in more basic research and tends to be stronger in development areas. Many

Table E–24.  International Research Capabilities—Mathematical Sciences

Technology

United Kingdom

France

Germany

Japan

Asia/Pacific Rim

FSU

Other Countries

Applied Analysis & Physical Mathematics 1s.gif (931 bytes) Fluid dynamics 2s.gif (968 bytes) Bolzman’s equations; dynamic systems; computer vision 2s.gif (968 bytes) 5s.gif (958 bytes) China

4s.gif (949 bytes)

Russia

3s.gif (977 bytes) Numerical methods; mechanics

Hungary

4s.gif (949 bytes) Real variables

Canada

5s.gif (958 bytes) Analytic geometry; fluid dynamics

Israel

5s.gif (958 bytes) Symplectic geometry; fluid dynamics

Computational Mathematics 4s.gif (949 bytes) Linear algebra 2s.gif (968 bytes) Finite elements; nonsmooth optimization 1s.gif (931 bytes) Finite elements; interactive methods 4s.gif (949 bytes) India

1s.gif (931 bytes)

China

4s.gif (949 bytes)

Russia

6s.gif (990 bytes)

Israel

2s.gif (968 bytes) Computational physics

Discrete Mathematics 4s.gif (949 bytes) 4s.gif (949 bytes) Computer algebra 4s.gif (949 bytes) 4s.gif (949 bytes) China

4s.gif (949 bytes)

Russia

3s.gif (977 bytes)

Canada

4s.gif (949 bytes)

Hungary

5s.gif (958 bytes)

Czech Republic

5s.gif (958 bytes) Computational geometry

Systems & Control 4s.gif (949 bytes) 1s.gif (931 bytes) Control theory 4s.gif (949 bytes) 4s.gif (949 bytes) China

4s.gif (949 bytes)

Russia

6s.gif (990 bytes)

Canada

4s.gif (949 bytes)

Probability & Statistics 1s.gif (931 bytes) 1s.gif (931 bytes) Levy processes 4s.gif (949 bytes) 1s.gif (931 bytes) Fuzzy logic India

1s.gif (931 bytes)

China

4s.gif (949 bytes)

Russia

6s.gif (990 bytes)

Canada

4s.gif (949 bytes)

Austria

5s.gif (958 bytes) Fuzzy logic

Note: See Annex E, Section A.6 for explanation of key numerals.

other small countries have very strong mathematical talent—Holland, Denmark, Hungary, Israel, Poland, Romania, Greece, Sweden, and Norway—and all could be considered for potential cooperative efforts in specific areas. In addition, there are also significant efforts under way in Asia and the Pacific Rim (especially Singapore and Malaysia) to develop mathematical research enterprises, but these are not yet of world–class stature.

a. Applied Analysis and Physical Mathematics

Research in applied analysis and physical mathematics contributes to the modeling of physical processes critical to the development of new technologies in a variety of fields including smart materials, flow control, electromechanics, and optics. For example, CFD studies in the U.K., Canada, and Israel can contribute significantly to missile, rotor, and explosive design.

b. Computational Mathematics and Discrete Mathematics

There are many examples of specific areas of computational mathematics and discrete mathematics that hold promise for military applications. Research in numerical methods and optimization is the basis for many advances in fluid dynamics, material behavior, and simulation of large mechanical and computational systems. Advanced work in finite element analysis in France and Germany can be applied to the problems of the design and function of complex mechanical structures. Also of interest are international research efforts in linear algebra (France) and computational geometry (Czechoslovakia) that are applicable to the development of new computer network hardware and software platforms.

c. Systems and Control

Systems and control theory work has also been used as the basis for the development of computer systems as well as applications in robotics. Research areas include work in control in the presence of uncertainties, robust and adaptive control for multivariable and nonlinear systems, and distributed communication and control. France is considered a world leader in control theory research. The United Kingdom, Germany, Japan, Canada, China, and Russia have significant capabilities in this area as well.

d. Probability and Statistics

Research in probability and statistics, especially stochastic analysis and statistical methods, is integral in the development of simulation methodologies, data analysis systems, and complex image analysis technology, including new approaches to computer vision for ATR. Fuzzy logic research in Japan is an example of international research that can significantly contribute to Army goals in these areas.

The following highlight a few selected examples of specific research facilities engaged in work in the mathematical sciences:

United Kingdom—The Basic Research Institute in the Mathematical Sciences (BRIMS), Bristol.  BRIMS was set up by Hewlett–Packard in 1994 as part of an initiative to widen the corporate research base. BRIMS is an experiment in fostering basic research in an industrial setting. All scientific work undertaken at BRIMS is in the public domain. Main areas of research are dynamical systems, solitons, quantum chaology, quantum computation, probability, and information theory. Research into topological phase effects explores the nature of quantum eigenstates and geometric phase, and applications in a wide range of disciplines throughout physics, including atomic and molecular physics, condensed matter physics, optics, and classical dynamics. BRIMS shares a close relationship with the Isaac Newton Institute in Cambridge, England.

Germany—The Weierstrass Institute for Applied Analysis (WIAS). WIAS performs mathematical research projects in various fields of the applied sciences. These research projects include modeling in cooperation with researchers from the applied sciences, mathematical analysis of properties of these models, development of numerical algorithms and of software, and numerical simulation of processes in economy, and S&T. One program in control theory is concerned with the behavior of nonlinear dynamic systems. General approaches are developed for analysis and control of the longtime behavior of dynamical systems. These methods are applied to simulations and control of processes in chemical engineering, optoelectronics/nonlinear optics (NLOs), and problems in geophysics.

France—French National Institute for Research in Computer Science and Control (INRIA). INRIA is made up of five research units spread in various French regions and one service unit. The main activities of this government institute consist of basic research and realization of experimental systems in computer science, mathematics, and automatic control. INRIA has adopted five major strategic directions in its research activities. They are the control of distributed computer information, programming of parallel machines, development and maintenance of safe and reliable software, construction of systems integrating images and new forms of data, analysis, simulation, and control and optimization of systems.

Austria—Department of Medical Computer Science, University of Vienna. Research here focuses on the applications of fuzzy logic in the field of expert systems for internal medicine. Work has centered on the CADIAG project, which has already produced a number of advanced systems assisting the differential process of diagnostics through indicating all possible diseases, that might be the cause of a patient’s pathological finding (with special emphasis on rare diseases), by offering further useful examination to confirm or to exclude gained diagnostic hypothesis, and by indicating patients’ pathological findings not yet accounted for by expert system’s proposed diagnoses. The system has a database of profiles and rules for diseases that can be easily integrated with an expert’s definition and judgmental knowledge from experience to assist in medical care.

Russia—St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences (SPIIRAS). SPIIRAS conducts basic and applied research in the fields of computer science, computer systems, and automation of scientific research and manufacturing. One research thrust studies the automation and quality testing of models, algorithms, and programs. Problem of models qualimetry are formulated, and some results for solving a problem of adequacy of mathematical models, applied to problems of forecasting and optimization are developed. Technology, methods and tools for automation of complex systems modeling based on their representation visualization using language of algorithmic networks and cognitive graphics are developed. Algorithms for numerical solution of ordinary differential equations in a network structure are used to increase modeling accuracy. This work can be applied to the analysis and evaluation of complex systems, including computer networks, information processing systems, and telecommunication systems.

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