The Army has established a vigorous research program covering a wide range of disciplines to capture and exploit the new opportunities presented by research advances and discoveries. This program is executed primarily by university contractors and in–house laboratory and RDEC personnel, and maximizes the use of the initiatives noted in Section V–B above.

Within a wide spectrum of research, several primary areas emerge that are of particular importance to tomorrow’s Army. These efforts in the following research areas are described in the sections that follow:

1. Mathematical sciences

2. Computer and informational sciences

3. Physics

4. Chemistry

5. Materials science

6. Electronics research

7. Mechanical sciences

8. Atmospheric sciences

9. Terrestrial sciences

10. Medical sciences

11. Biological sciences

12. Behavioral, cognitive, and neural sciences.

a. Strategy

Mathematics plays an essential role in modeling, analysis, and control of complex phenomena and systems of critical interest to the Army. Mathematical modeling is increasingly being identified as critical for progress in many areas of Army interest. The mathematical and scientific tasks in these areas of interest are frequently of significant complexity. As a result, researchers from two or more areas of mathematics must often collaborate together and with experts from other areas of science and engineering to achieve Army goals. Some examples of cross–cutting areas of research include the breakup of liquid droplets in high–speed air flow (for determination of the dispersion of chemical or biological agents spilled from intercepted theater–range missiles), computational methods for penetration mechanics, and automatic target recognition. For example, promising approaches to computer vision for automatic target recognition require research in a wide range of areas including constructive geometry, numerical methods, stochastic analysis, Bayesian statistics, probabilistic algorithms, and distributed parallel computing. To achieve Army goals, research in several areas is important:

• Applied analysis

• Computational mathematics

• Probability and statistics

• Systems and control

• Discrete mathematics.

An investment strategy meeting with participants from ARO, ARL, RDECs, Corps of Engineer Waterways Experiment Station (WES), Concepts Analysis Agency (CAA), Deputy Under Secretary of the Army (Operations Research) (DUSA(OR)), and academia identified several exciting research areas that will have significant impact on future Army technologies. Based on these recommendations, research priorities inside these areas are listed below.

b. Major Research Areas

Applied Analysis

Physical modeling and mathematical analysis for nonlinear ordinary and partial differential, difference, and integral equations for:

• Advanced materials, including smart materials and
structure and advanced composites.

• Fluid flow, including flow around rotors,
missiles, and parachutes, combustion, detonation and explosion, two–phase flow, and
granular flow.

• Nonlinear dynamics for optics, dielectrics,
electromechanics, and other nonlinear systems, and physics–based mathematical models
of human dynamics.

Computational Mathematics

• Rigorous numerical methods for fluid dynamics, solid mechanics, material behavior, and simulation of large mechanical systems (see Figure V–7).

Figure V-7. Modeling the Fluid Flow Within the Muzzle Break of a Gun

• Optimization: large–scale integer programming, mixed–integer programming, and nonlinear optimization.

Probability and Statistics

• Stochastic analysis and applied probability:
stochastic differential equations and processes, interacting particle systems,
probabilistic algorithms, stochastic control, large deviations, simulation methodology,
and image analysis.

• Statistics: analysis for very large data sets
or very small amounts of data from nonstandard distributions, point processes, Bayesian
methods, integration of statistical procedures with scientific and engineering
information, Markov random fields, and cluster analysis.

Systems and Control

• Mathematical system theory and control theory:
control in the presence of uncertainties, robust and adaptive control for multivariable
and nonlinear systems, system identification and its relation to adaptive control, hybrid
control, hybrid–infinity control, and nonholonomic control.

• Foundations of intelligent control systems:
discrete event dynamical systems, hybrid systems, learning and adaptation, distributed
communication and control, and intelligent control systems.

Discrete Mathematics

• Computational geometry, logic, network flows, graph
theory, and combinatorics.

• Symbolic methods: computational algebraic
geometry for polynomial systems, discrete methods for combinatorial optimization, symbolic
methods for differential equations, mixed symbolic–numerical methods, parallel
symbolic sparse matrix methods, and algorithmic methods in symbolic mathematics.

c. Potential Military Benefits

With the change from a predictable large threat to numerous and often unpredictable regional threats, the need for more flexibility in Army systems and more rapid development of these systems increases. As the cost of physical experimentation increases, the role of mathematical modeling becomes more important. Mathematical modeling is a major factor in ensuring that a system is well designed and that it will work once built. In all of the following areas, mathematics is a fundamental tool required by the Army of the present and the future:

• Design of advanced materials and novel
manufacturing processes.

• Behavior of materials under high loads,
failure mechanics.

• Structures, including flexible and adaptable
structures.

• Fluid flow, including reactive flow.

• Power and directed energy.

• Microelectronics and photonics.

• Sensors.

• Automatic target recognition.

• Soldier and aggregates of soldiers as systems:
behavioral modeling, performance, mobility, hear–stress reduction, camouflage
(visible, IR), chemical and ballistic protection.

2. Computer and Information Sciences

a. Strategy

The computer and information sciences address fundamental issues in understanding, formalizing, acquiring, representing, manipulating, and using information. The advanced systems, including the software engineering environments and new computational architectures facilitated by this research will often be interactive, adaptive, sometimes distributed and/or autonomous, and frequently characterized as intelligent. Computer–based systems that process information and transfer data and analysis among various Army commanders and units are essential for military success.

The computer science and software issues that arise in this context often require input from a number of subdisciplines of computer science, as well as from other disciplines. Multisensor fusion, multi–image fusion, image understanding, language processing, distributed interactive simulation, multivariable and multiresolution methods for terrain modeling, scalable parallel algorithms and algorithms for processing large–scale data are but a few of these areas. In these areas, computer and information sciences research is organized in a cross–cutting fashion to provide the expertise needed to accomplish the Army goal (rather than remain within traditional disciplinary boundaries). Based on the recommendations from an investment strategy meeting among senior scientists from ARO, ARL, RDECs, TRADOC, DUSA(OR), CAA, COE, and academia, research in the following areas was determined to be important to the Army:

• Theoretical computer science

• Formal methods for software engineering

• Software prototyping, development, and
evolution

• Knowledge base/database systems

• Natural language processing

• Intelligent systems.

b. Major Research Areas

Theoretical Computer Science

• Formal models underlying computing technology,
optimization of input/output (I/O) communication, new computing architectures,
multiprocessing, parallel systems, and advanced architectures.

• Graph theoretic methods applied to parallel
and distributed computation, models, and algorithms for the control of heterogeneous
concurrent computing.

Formal Methods for Software Engineering

• Software engineering architectures: environments,
tools, integrated tool sets.

• Graphical interfaces: multilevel displays for
requirements elicitation, simulation, logic visualization.

• Software generation: invocation of formal
methods, software reuse.

• Software evolution: change, merging,
documentation.

• Software reliability: validation,
verification.

Knowledge Base/Database Sciences

• Heterogeneous data structures: mediators, complex
reasoning.

• Machine learning: methodologies for
uncertainty, incompleteness, information recognition and content–based retrieval.

• Multimodal information: synthesis of knowledge
from multimodal resources.

• Query/interrogation languages:
domain–specific languages.

Natural Language Processing

• Text: content–based retrieval and
understanding.

• Speech: translation, understanding, and
generation with dialogue.

c. Potential Military Benefits

The contributions of the computer and information sciences to a well–equipped strategic force capable of decisive victory in conflicts in the Information Age are important in the following areas:

• Digitized battlefield

• Distributed C^{2}

• Information processing

• Distributed interactive simulation (DIS) (see
Figure V–8)

**Figure V-8. High-Performance Concurrent Simulations.**

High-performance concurrent simulation provides enabling technology and prototype
framework for seamless, portable, secure, scalable, and fault-tolerant concurrent
computing on heterogeneous networked computers for collaborative applications.

Click on the image to view enlarged version

• Design and validation of software and of large
software systems

• Adaptive, anticipative systems

• Intelligent systems

• Human/machine interface

• Intelligence augmentation of
human–centered systems

• Battlefield management.

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