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MODELING OF COMPLEX SYSTEMS The Modeling of Complex Systems Program is a program of fundamental
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MODELING OF COMPLEX SYSTEMS
The Modeling of Complex Systems Program is a program of fundamental
mathematics-oriented research the objectives of which are to
Develop quantitative models of complex phenomena of interest to the Army, especially
those for which current models are not based on first/basic principles
Develop new metrics, preferably those based on first/basic principles, for these models.
The complex phenomena of interest to the Modeling of Complex Systems
Program include 1) physical phenomena, 2) abstract phenomena in information theory
and networks and 3) behavioral phenomena. Complete and consistent mathematical
frameworks for the modeling effort are the preferred context for the research, but
research that does not take place in such frameworks can be considered if the
phenomena are so complex that the frameworks are not feasible. Metrics are part of
the mathematical framework and are of great interest. Traditional metrics, when they
exist, often do not measure the characteristics in which observers in general and the
Army in particular are interested. For many complex phenomena, new metrics need to
be developed at the same time as new models. Just as is the case for the modeling
effort, these metrics should preferably be in a complete mathematical framework.
The research in modeling of and metrics for complex phenomena of interest to
the Modeling of Complex Systems Program may include numerical/computational work
as
a
subordinate
component.
However,
research
that
focuses
mainly
on
numerical/computational issues should be directed to the ARO Computational
Mathematics Program in the ARO Mathematics Division.
The investment in the Modeling of Complex Systems Program is in the following
areas
AA-1: Advanced Complex Materials for Structures, Armor and Sensors
AA-2: Inverse Scattering in Complex Media
AA-3: Modeling of Multiscale Objects and Functions
AA-4: Nonlinear Dynamics for Communication
AA-5: Data Fusion in Complex Networks
AA-6: Dynamics of Distributed Networks of Embedded Sensors and Actuators
AA-7: Additional Areas of Opportunity
The Modeling of Complex Systems Program seeks to have a balance between
research for hard (physics-based) areas and soft (information and behavioral-based)
areas.
Thrust AA-1: Advanced Complex Materials for Structures, Armor and Sensors 2
The
analysis,
design
and
manufacture
of
advanced
materials
is
an
interdisciplinary area in which the basic principles are often known.
However, the
current models for meso and macro behavior of materials are often not based on these
principles because implementation of the basic principles in the models results in
inordinate complexity and because principles on intermediate levels are not well known.
The Modeling of Complex Systems Program supports research oriented toward
optimizing properties or performance characteristics of highly nonlinear materials,
including advanced composites for structures and armor and smart materials for
sensors.
Light-weight,
high-strength
structural
components,
including
advanced
composites, contribute to attaining mobility and protection requirements for U.S. forces
(as well as to the fuel efficiency and safety of the U.S. automobile fleet). Advanced
composites are challenging to analyze and design because of the presence of many
interacting length scales.
Smart materials, the functional ingredients of actuators,
sensors and transducers, that have a load- or field-dependent (crystal or other)
structure. Such materials may undergo a phase transformation when some mechanical,
thermal, electrical or magnetic factor changes and vice versa. Advanced composites
and smart materials are typically highly nonlinear.
In seeking to understand the
relationship between the microscopic and macroscopic length scales of these materials,
fundamental issues in nonlinear modeling arise. The program invests in research on
these fundamental issues, including development of basic equations and constitutive
laws.
Thrust AA-2: Inverse Scattering in Complex Media
Inverse scattering is of interest to the Army for detection and identification of
landmines and unexploded ordnance with low false alarm rates.
This is an area
involving the interaction between the propagation of various types of waves in cluttered
soils and the inverse problem of detecting location, shape and material properties of
solid objects having various waveform signatures. Currently available techniques often
have high false alarm rates, which impedes mine clearance. Additional Army interests
include electromagnetic sensing through cluttered battlefield atmospheres, including
smoke, fog, flames, etc.
Application of inverse scattering techniques for stand-off
detection of chemical and biological agents is of interest.
One of the directions of research supported by the Program is that of creating
models for currently unused sources of information, validating these models and
integrating them into larger models or systems.
Traditionally, imaging by ground-
penetrating radar and by x-rays has utilized information only from singly scattered
waves, that is, waves that are scattered by a collision with only one object and then
return to the detectors. For such imaging, multiply scattered waves that arrive at the
detectors create error, because they are erroneously presumed to have resulted from a
single scattering event. However, multiply scattered waves contain information, not just
error. Creating models that are able to access the information in multiply scattered
waves is of considerable interest to the Program.
Integrating these models into 3
models/systems that also use the information in singly scattered waves is of interest.
The interests of the Program in research on multiple scattering in complex media
include research on models for utilizing other sources of information that are ignored by
current models.
Thrust AA-3: Modeling of Multiscale Objects and Functions
Representation of complex, multiscale/mulitresolution geometric objects and of
complicated, often high-dimensional abstract phenomena and functions is fundamental
for Army, DoD and civilian needs in modeling of terrain, geophysical features, biological
objects (including humans and their clothing), computational learning and many other
objects and functions. Real-time visualization of huge terrain databases with glitch-free
zoom-in/out cannot be achieved with current techniques. Progress in automatic target
recognition, robotic vision, representation/compression of data in general and many
other areas depends on advances in approximation theory. A key to achieving these
goals is data compression at ratios and with accuracy that exceed what is currently
known.
A multitude of variants of piecewise planar surfaces (including those on
triangulated irregular networks or TINs), splines , multiquadrics, kriging, wavelets,
neural nets and many other techniques developed in the past perform well on many
types of data. However, none of these procedures are able to provide, without human
intervention, representation of geometry and data with the accuracy and compression
that is needed. To achieve such representation, new types of approximation theory
appropriate for complicated multiscale/multiresolution surfaces and phenomena need to
be developed.
In these cases, the objects/functions being approximated are not
consistent with the assumptions of classical approximation theory.
Approximation
theory research that results in highly compressed, loss-free or minimally lossy
representation is of particular interest. Approximation theory for information flow and
other abstract items in large communication and computer networks is an area of
interest.
The approximation theory developed under support of this program is expected
to provide building blocks for computational geometry, pattern recognition, automatic
target recognition and visualization systems.
However, research that is focused on
these areas rather than on approximation theory is beyond the scope of the Modeling of
Complex Systems Program and fits best with the Image Fusion, Processing and Circuits
Program of the ARO Computing and Information Sciences Division and with the
Discrete Mathematics and Computer Science Program of the ARO Mathematics
Division.
Thrust AA-4: Nonlinear Dynamics for Communication
Enhanced capability in digital communication is recognized as a pivotal element
in a mod