Bruno Welfert - US grants

The objective of the project is to develop a PC and Web based interactive "Systems and Controls" E-Book to address multidisciplinary curricular needs in Electrical, Mechanical, and Aerospace Engineering, and Mathematics. This E-book supports undergraduate controls curriculum classes such as differential equations, microprocessors, linear algebra, and senior design. It enables multidisciplinary curricular integration via case studies, and bridges theory and practice by using realistic design problems and capstone projects. It also enhances student learning through interactive modeling/simulation in MATLAB with 3D animation, interactive problems containing real-time solutions, case studies, and interactive multimedia topical lectures. It provides an enriched interactive learning experience which facilitates conveying fundamental/advanced concepts, asynchronous learning, and different teaching and learning styles. Multiple test sites, university and industrial partners, publishers, and an assessment specialist contribute to the development of this E-book.

The investigators develop tools and techniques to facilitate the accurate
reconstruction of spectral data from compressed images. Such reconstruction
typically aims at recreating gray-scale functions from their Fourier or
spectral coefficients, and necessarily requires both precise information
of the location of the jump discontinuities of the images, as well
as an appropriate conversion, usually via projection, so that the image
can be viewed in the regions of smoothness. Current techniques for edge
detection and projection reconstruction are somewhat successful in avoiding
Gibbs oscillations without compromising the integrity of the the images
around the edges (i.e. smearing). They also can retrieve information of small
scale features which arise in many scientific applications. However, the
success is seemingly function dependent, and it is difficult to choose
parameters that are robust to be effective in all cases, especially
when noise is present in the given data fields. Furthermore, they are
difficult to extend to higher dimensions. The investigators study new
ways to improve both edge detection and projection methods and ultimately
create an automated robust, user-friendly, computationally efficient, and
inherently multi-dimensional image reconstruction method. The study tests
the resulting procedures against current image reconstruction methods on a
range of applications.

Image reconstruction is of critical importance in many scientific fields.
The development of high order reconstruction techniques requires both
mathematical rigor to prove theoretical results and computational
robustness to ensure practical usage. The proposed activities address
how to obtain images efficiently and with high accuracy when small scale
features are of extreme interest in an increasingly image--oriented society.
These methods can, for example, enhance the diagnostic ability in medical
imaging applications. They can also be used to better identify the small
scale features in solar activity such as those in connection with Lockheed
Martin's Solar Imaging Suite. This research is also useful for weather
forecasting models, earthquake and tsunami prediction, and any other
fields in which visualization is critical. Finally, this study stands to
significantly enhance the ability to compress data, as it it will be
possible to optimize the reconstruction parameters when particular
compression requirements are proposed.

To study noise in the Navier-Stokes equations directly is a
formidable task, and so lower-dimensional reduced models are often
sought. The investigators introduce a new computational framework
for the study of high-dimensional nonlinear stochastic partial
differential equations, and apply this to hydrodynamic problems
for which there are well-controlled precision experiments with
which to compare. The main characteristics of the approach are:
(1) the noise is introduced in a physically motivated manner; (2)
the stochastic problem is reduced to a problem for the mean flow
and another for its variance; and (3) an efficient implementation
is developed involving state-of-the-art spectral discretization
and stochastic integration numerical techniques.

The equations governing hydrodynamics, the Navier-Stokes
equations, have been known for well over a century and have been
successful in describing many observed physical flows.
Nevertheless, the transition to complex flow and turbulence
remains an outstanding challenge; it is not clear what role noise
plays here. The investigators develop a novel framework for
studying the effect of noise on the properties, particularly the
stability and transition to turbulence, of dynamical systems
modeling fluid flows. The combined use of mathematical modeling
of stochastic processes, design of numerical algorithms, computer
simulations of physical problems and direct comparison with
experimental observations provides an enriching experience for the
students directly involved in the project. The ideas are also
incorporated into existing and new courses.

Kostelich
0703587

The goal of this CSUMS project is to build a diverse group
of undergraduate students in the computational mathematical
sciences program at Arizona State University, each of whom
participates in cutting-edge research projects during the last
two years of their undergraduate programs. At any given time,
two cohorts of 11 students each participate: they begin the
program at the start of their junior year and complete it at the
end of their senior year (i.e., after 4 semesters). Incoming
students, whose expected preparation includes multivariable
calculus, linear algebra, and ordinary differential equations,
participate in a 1-credit seminar course for two semesters to
prepare them for the upcoming summer's projects. Summer projects
consist of 8 to 10 weeks of full-time work on a research project
under the supervision of an experienced faculty mentor. Students
who have completed their projects give practice talks in the
seminar and are expected to present their work at appropriate
professional conferences as well as to write an honors thesis or
research paper.

Student research projects involve timely problems in
atmospheric sciences, including weather and climate forecasting;
supply-chain modeling; mathematical techniques for improved
medical imaging (e.g., magnetic resonance imaging); and
mathematical biology (e.g., models for human cellular processes).
The students, who must be U.S. citizens or permanent residents,
have an opportunity to work on massively parallel (2000+
processor) machines through ASU's Fulton High Performance
Computing Initiative and to do high-performance graphics at ASU's
Decision Theater. These experiences prepare students for
advanced work in climate dynamics, drug discovery, aerospace
design, and similar topics at top graduate schools across the
United States. Special efforts are made to recruit students who
are first-generation college students, women, and members of
other underrepresented groups in the mathematical sciences. The
project is supported by the MPS Division of Mathematical
Sciences, the MPS Office of Multidisciplinary Activities, and the
EHR Division of Undergraduate Education.

Assumptions of extremes of wetted state of unsaturated soils during infrastructure lifetime (saturated or dry properties) have significant implications for design, construction, functionality, safety, and structural longevity. Assessment of the degree of saturation that occurs in the subsurface requires understanding and quantifying actual surface flux, a complex function of soil surface conditions, including in particular soil suction, degree of cracking, and slope geometry. There are two major related research issues yet to be adequately addressed in geotechnical applications: (1) the effect of surface cracking in volume-change-sensitive clays on unsaturated flow property functions, and (2) the effect of drainage conditions (well-sloped surface versus poorly drained) on surface flux of cracked and intact clays. Seasonal cracking of soil results in poor estimates of runoff and infiltration due to the changing soil storage conditions (Arnold et al, 2005). Prediction of soil suction profiles requires substantial improvements in current capabilities, both from a soil property and numerical modeling perspective. Several conditions present numerical solution challenges: (i) strong nonlinearities in soil properties, (ii) abrupt changes of moisture conditions at the surface boundary and wetting front, and (iii) the presence of surface runoff conditions (Scanlon et. al., 2002). The behavior of unsaturated cracked soil is quite different from that of intact soil, further complicating evaluation of surface flux conditions for clays.

This study addresses key remaining questions rarely, or only superficially, discussed in the geotechnical literature, and is geared toward transformation of surface flux modeling capabilities for cracked and intact clays. The geotechnical research team will work with a co-investigator in Applied Math towards addressing these needs through development of: (1) data and models for unsaturated soil properties of cracked clays including volume change of both the cracks and matrix; (2) data and models for run-off for well-inclined (sloped) and level-grade cracked and intact (3) improved solution methods for surface flux, including run-off, and (4) evaluation of field damage related to drainage and cracking for consistency with modeling and data. A key element of this research is the collaboration and sharing of physical resources among partners (ASU?s advanced unsaturated soils testing equipment and SDSU?s unique tilt table).

A wide range of problems arise from unsaturated soils. Damage to infrastructure from expansive clays alone is estimated to be as much as 15 billion/yr (Nuhfer et al., 1993; Wray and Meyer 2004). Krohn and Slossom (1980) estimated that 20% of surface soils of the U.S. are subject to shrink-swell (and cracking). Concerns over movement of contaminants to great depth have heightened interest in understanding unsaturated flow and the complex interactions between climate, human surface activities and unsaturated soil subsurface conditions and processes. Researchers have demonstrated the role of unsaturated soil behavior in rainfall-induced slope failure (Toll, 1999; Yin, 1998). Surface flux and surface runoff are critical to the performance of slopes, and little is known about the influence of cracks on the flux or on slope stability itself. In California in 1982, over 18,000 slides swept down slopes with little warning, damaging homes and killing 14 residents (Ellen and Wieczorek, 1988). U.S. costs for landslide repairs exceed $2 billion/yr and landslides, nearly all rainfall-induced, result in 25-50 deaths/yr (Spike and Gori, 2003). This research will have impact on solutions to all of these problems through enhancing our understanding and modeling of surface flux and unsaturated flow.

Students will be trained and will be engaged in dissemination, including conferences and publications. Findings will be presented in CE classrooms at ASU and SDSU, and integrated into ASU?s Math program where students will perform numerical simulations and compare with existing codes and data. On-going ASU recruiting programs focused on teachers and underrepresented students will be used to bring aspects of this study into junior and high school classrooms. A set of lectures will be developed on the research process and presented at a San Diego high school having an 82% female and non-white male student body. Students will also tour labs. Working with pre-engineering teachers, Co-Is will develop a means of attracting students to engineering and research.

An evaluation of the materials that have been prepared for an e-book for use in teaching control system engineering is being conducted. The evaluation will examine student learning outcomes and attitudes toward an electronic textbook. Additionally, representatives from industry are reviewing the materials and providing an assessment from the industry viewpoint. Faculty at other institutions who have used portions of the electronic book in their classes are also engaged in the evaluation efforts.