Jerry Bona - US grants

This project is an equipment grant under the activity Grants For Scientific Computing Research Equipment For The Mathematical Sciences program. The project involves the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required jointly by several research projects and would be difficult to justify on one project alone. This research equipment support from the National Science Foundation is coupled with discounts and contributions of equipment from manufacturers and significant cost-sharing from the submitting institution. This project provides a good example of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. The equipment in this project will be used to conduct research in number theory and combinatorics, statistical mechanics, partial differential equations, control and optimization, wave absorption and reflection at coated boundaries, modelling of thunderclouds and lightning, nonlinear wave motion, free-boundary problems, viscous flows, and the collection and processing of experimental data.

This research program will involve theoretical, computational, and experimental studies of various problems in fluid mechanics. The problems have as a common theme consideration of viscous flows with free boundaries. Numerical predictions of free surface shapes will be compared with experimental measurements. Stability of free surface flows, and possible time-dependent flow states, will be examined. This work should lead to an improved understanding of travelling waves, the propogation of bores, the development of edge waves, and the movement of sand bars under the action of water waves.

This project will support the Conference on Nonlinear Phenomena in Fluid Mechanics to be held April 13-15, 1989 at Pennsylvania State University. The conference will be under the direction of Professor Jerry Bona of Penn State. It will focus on modern developments in the field of fluid mechanics with the goal of presenting a balanced view of current mathematical, theoretical, and experimental trends in this subject. Lectures will be presented by A. Acrivos, D. Benney, J. Hammack, J.-L. Lions, M. Longuet-Higgins, J.B. McLeod, J.W. Miles, T. Mullin, P. Saffman, J.T. Stuart, R. Temam, and J.F. Toland. The proceedings of this conference will be published and support for participants will be available.

This project is a CBMS Regional Conference in the Mathematical Sciences entitled "Non-linear Dispersive Wave Systems". This conference will be held at the University of Central Florida in December, 1990. This field has recently been spurred by developments of practical necessity in many areas of science and engineering, and new ideas have surfaced, giving it yet further impetus. These include fruitful use of algebraic techniques, the extension of Benjamin's stability theory, more reliance on Hamiltonian formulations, the use of computational techniques as an investigative tool, and the new perturbation theories for integrable systems. Professor Benjamin will present a unified mathematical treatment of the classical aspects of the field, as well as new results on hydrodynamic stability and instability.

This award will support U.S.-Greece cooperative research between a group headed by Prof. Jerry Bona of Penn State University and a similar group headed by Prof. Vassilios A. Dougalis of the University of Crete, Greece. The collaborators intend to conduct computational and theoretical research on numerical methods for solving two important nonlinear partial differential equations: the nonlinear Schroedinger equation and the Korteweg-de Vries equation. Over the past few years the collaborators have produced several important papers on the numerical solution of the mentioned partial differential equations. These equations are valued because they help to model certain nonlinear wave phenomena that occur in areas of applications such as water waves, plasma physics and nonlinear optics. By supporting the interaction of these experienced and productive collaborators, this award will help to advance our understanding of nonlinear phenomena.

The Seventh International Conference on Domain Decomposition Methods in Scientific and Engineering Computing will be held at Penn State University from October 27 to 30, 1993. Domain decomposition refers to a class of methods for the simulating large-scale scientific and engineering systems on computers. Using a divide-and conquer strategy to obtain the solution to a massive problem by combining the solutions to numerous smaller ones, domain decomposition offers the possibility of simulating systems that are too large and complex even for today's powerful supercomputers using conventional solution methods. Such problems include long term climate prediction and the study of global change and the design of space vehicles and structures. Among computational scientist, engineers, and mathematicians, domain decomposition techniques are of particularly intense interest now because they are well adapted to emerging high performance computer architectures. This conference will convene academic and industrial researchers in domain decomposition and allied areas in order to disseminate recent advances and stimulate further development in areas ranging from basic theoretical research on the analysis and validation of domain decomposition algorithms to specific industrial applications. The conference will enhance the technology transfer between academia and industry, and provide opportunities for students and young scientists and engineers to become involved in this important new class of computational methods. Graduate students, young researchers, women, minorities and people with disabilities are being especially encouraged to attend the conference and to contribute papers. The proceedings of this conference will be published by the American Mathematical Society and are expected to become an important resource for researcher and users of domain decomposition.

9403915 Bona This project comprises a broadly-based investigation of some fundamental aspects of mechanics, including the development of some of the relevant mathematical techniques and tools. Included within its auspices are theoretical and experimental studies of various fluid flows, studies of water waves and formation of sand structures in the near- shore zone of large bodies of water, and theoretical and experimental studies of liquid crystals. One of the larger investigations will be concerned with the modelling of water waves with an eye toward a better understanding of the interaction of waves travelling in opposite directions. Another interesting study is concerned with flows in which there is a balance between dissipative effects and surface tension. Still another sub-project will reconsider some classical flows such as flow past a sphere in a pipe, Taylor-Couette flow and the related issues of stability and vortex breakdown. The complex mathematical modelling needed to describe exotic materials like liquid crystals will also be high on the agenda. Allied to all of these investigations will be the development of specific theoretical results in partial differential equations and in numerical analysis. Especially important in the latter area will be work on highly efficient methods for the solution of large linear systems arising in the algorithms for the solution of complicated nonlinear differential equations. The resulting computer codes will be used in conjunction with experimental work on all the forementioned topics and the outcomes interpreted within the relevant theoretical framework. This work is exciting for several reasons. First, many of the issues being addressed are not only of fundamental theoretical importance, but they also have potential to provide new insights into engineering and technological design and processing. Secondly, because of the presence of the fluid mechanics laboratory sited within the mathematics department at Pe nn State, the group has the ability to combine theoretical, numerical and experimental work in a rarely realized close collaboration. In addition, some of the work on development of optimal numerical techniques will have impact in a much broader arena of science and engineering activity than just the confines of the present study.

This award supports cooperative research between three U.S. researchers, Jerry Bona at the Pennsylvania State University, Ohannes Karakashian at the University of Tennessee, and William McKinney at North Carolina State University, and two Greek researchers, George Akrivis at the University of Crete and Vassilios Dougalis at the National Technical University in Athens. The collaboration will occur at the Institute of Applied and Computational Mathematics (FORTH) in Heraklion, Greece. The objective of the research concerns the numerical solution of three types of partial differential equations that model various aspects of wave propagation phenomena in nonlinear dispersive systems. The research is concerned with the design and analysis of numerical schemes for the integration of interesting and useful classes of nonlinear, dispersive wave equations. Such numerical methods are crucially important for use in conjunction with laboratory experiments and for the study of the detailed structure of solutions including singularity formation. The project also includes implemen tation of the schemes as computer codes and the use of these codes int he investigation of theoretical and applied issues connected with this class of partial differential equations.

The Principal Investigators will study several related
asymptotic limits of nonlinear partial differential
equations arising in fluid mechanics. Interest is focused
on how solutions behave in limits where certain terms in
the equations become increasingly negligible. For the
situations in view here, these terms correspond to the
physical effects of dissipation and dispersion. It is
planned to work at two levels of complexity. The first,
and easier level is that of model equations for wave
propagation where nonlinear, dispersive and dissipative
effects are all present. Both qualitative and quantitative
information will be sought. The information obtained
will yield information helpful to modelling near-shore
zone processes. At a more complex level, it is planned
to investigate various limits of the Navier-Stokes
equations including the inviscid limit for the
Navier-Stokes equations in bounded domains with fixed
boundaries, and for statistical solutions with periodic
boundary conditions (or in all of space). It is also
intended to investigate how well the Navier-Stokes
equations posed in a channel are modelled by dissipative
nonlinear wave equations.

The present award will support research on several interesting
and important asymptotic limits for mathematical models. The
kind of limits under consideration here arise in various
areas of physics, mechanics, oceanography, materials science,
biology, and elsewhere when partial differential equations
are used as models. The problems considered here derive
principally from fluid mechanics, but in so far as we are
successful in our program, there is a broader implied scope.
The zero-limits under study are those associated with
dissipation and dispersion in fluid motion. In various
modeling situations, one or the other of these effects may
be ignored. The question then arises whether or not such
approximations are justified and, if so, under what flow conditions
and over what time scales. These questions are of
theoretical and practical importance since the approximating
equations are often easier to use. This award will support work that
aims to address issues including fundamental points and aspects
that arise in the use of these equations as descriptions of
real phenomena.

Bona
9974116
The overall technical objective of the project is to develop
three-dimensional topographical models that describe seabed
dynamics in wave-dominated near-shore zones and shelf regions
where single and multiple sand bars or sand ridges form a central
morphological feature. The investigator models and analyses the
effects of waves and currents on coastal dynamics. This is
challenging because of the presence of two free surfaces, the
water surface and the movable bottom, both of which change over
time, and which interact with each other through complex,
nonlinear processes. The model features nonlinear, dispersive,
dissipative partial differential equations to describe the
evolution of waves coming in to the shore from deep water. These
equations, which are of Boussinesq type, are coupled to a model
for run-up and reflection at the shoreline. Once the evolution of
the water surface is approximately known, the velocity field in
the bulk of the fluid may then be determined via potential
theory. This velocity field is then viewed as driving a viscous,
sediment-laden boundary layer in which the sediment transport is
taking place. The velocity distribution in this layer is
determined using ideas similar to those pioneered by
Longuet-Higgins. By applying conservation of sediment mass in an
infinitesimal form, a differential equation is thereby inferred
that serves to determine the bottom deformation. Thus the entire
model is somewhat complicated, consisting of a nonlinear
initial-boundary-value problem for the wave motion coupled in a
nonlocal way to a conservation law for the bottom movement. This
model is developed in detail, analysed and implemented as a
computer code. Model predictions are compared with field data.
It is also proposed to link the computer code with input from a
Geographical Information System, to allow easier deployment of
the model in real situations.
The underlying motivation for the project is two-fold.
First, there is a desire to understand both qualitatively and
quantitatively some of the fundamental processes that lead to the
formation and maintenance of bottom structure in coastal zones
and on continental shelves. This involves a thorough knowledge
of both the wave environment and the dynamics of the bed as it is
influenced by waves and by currents. Second, and not less
important, the project responds to the need for new and more
sophisticated tools to aid in the development of strategies to
deal with real coastal engineering problems. The project has the
potential to contribute to the study of a number of important
scientific and environmental issues. The ocean margins in North
America are vast and in many places, troubled. Indeed, erosion
of unconsolidated coastlines is a world-wide phenomenon that is
not well understood. Global warming will aggravate these
problems by increasing sea levels, thus causing shore retreat and
providing a better base for the scour and erosion associated with
wave activity. Fragile Arctic coasts and low-altitude regions
are already displaying unmistakable signs of deterioration caused
by these global changes. Severe erosion may well spread to other
coast regions within the next half century, and thus there will
be an increased interest in effective prevention methods. In
addition to "hard" protection schemes such as the construction of
seawalls and the like, there will be an increased demand for
"soft" protection strategies that take advantage of natural
processes.

Proposed here is a study featuring models for the interaction of surface and internal oceanic waves with sediment-laden bottom topography. The project includes derivation and mathematical analysis of models, development of algorithms for the approximation of solutions, implementation of the algorithms as computer codes, comparisons of the output of numerical simulations with field data, the use of the models for prediction and their development as a tool for effective coastal engineering. The basic issue under consideration is challenging in that it involves the temporal evolution of two free surfaces whose dynamics are connected in a complex and nonlinear way. The wave motion involves the deformation of the water's surface, or in the case of internal waves, the pycnoclines. Even over a fixed bottom, these issues are difficult in their exact formulation, and consequently model equations are typically used. In the present conception, the bottom is not fixed, and this added complexity is what makes the issues proposed here for study scientifically very interesting. In view are three-dimensional models that are initiated by incoming wave fields from deep water. These models will allow for long-shore variation and take account of reflection. It is planned to develop such models and to test them extensively against both laboratory experiments and field observation. Comparisons are in view at several sites around the world, including the Field Research Facility of the US Army Corps of Engineers at Duck, NC, a site of the Polish Academy of Sciences on the Baltic Sea, the North Coast of the Magdelan Islands in the Gulf of St. Lawrence, the Gold Coast of Australia, the Island of Djerba off the Tunisian coast and two regions in Morocco (Alger in the Gibraltar Strait and Agadir on the Atlantic coast).

The motivation for carrying out the study outlined above is several-fold. First is the pure science of the subject. The project involves interesting and substantial issues from hydrodynamics, partial differential equations, and sediment transport theory. Secondly, it is an ideal venue in which to acquaint students with interdisciplinary research. There is a strong practical reason for this study as well. The erosion and retreat of coastlines is a worldwide phenomenon. Global warming will increase the activity of storms, raise the sea level, and further degrade the present, sometimes catastrophic state of many beaches. Fragile Arctic coasts, beaches on the Great lakes and on many coastal regions already display the unmistakable signs of deterioration caused by these global changes and aggravated by social developmental pressure. Severe erosion is likely to spread to many coastal areas within half a century and thus increase the demand for effective prevention methods. The present project aims at deepening our understanding of fundamental wave-bottom interaction processes, especially as regards sediment dispersal. Going beyond the science, the project also grapples with the intelligent use of this kind of knowledge in designing coastal protection strategies. With experience already in hand, it is clear that there are a variety of protection options and that it is not always smart to simply build some permanent, often-ugly structure. So-called 'soft' protection methods are a useful addition to the reperatoire of the coastal engineer. These are much less expensive when they can be made to work. The assessment of the practicality of a protection plan, be it 'hard' or 'soft' relies upon the kind of knowledge investigated under the auspices of this project.

This award supports participants in The Third IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, held at the University of Georgia on 7-10 April 2003. The interdisciplinary meeting, sponsored by the International Association for Mathematics and Computers in Simulation, focuses on computational and theoretical aspects of nonlinear waves and optical solitons, and brings together researchers in applied mathematics, computational mathematics, and applied physics. Topics of interest include theoretical aspects of solitons and integrability, nonlinear waves in fluids, symbolic and numeric computations for integrable evolution equations, numerical methods for nonlinear waves (symplectic, IST and Fast Fourier methods, adaptive methods of lines, parallel algorithms), nonlinear waves in optics, dispersion managed solitons in optical fibers, and advances in modeling optical fiber transmission systems. The interdisciplinary meeting will provide excellent opportunities for communication and collaboration between senior and junior researchers.

The proposal is to provide support for speakers and attendees at the semiannual Midwest Partial Differential Equations seminars to be held between Fall 2007 and Spring 2010. Each semester this seminar is hosted by a different department in the Midwest.

This series of seminars has a considerable history and has contributed significantly to the advancement of research in partial differential equations. These funds will support the expenses of some invited speakers, post-docs and graduate students who do not have current research support to attend the conference. The funds will be administered by the University of Illinois at Chicago in cooperation with the departments hosting the meetings.

The Fourth IMACS International Conference on Nonlinear Evolution
Equations and Wave Phenomena: Computation and Theory
April 11-14, 2005
University of Georgia
Athens, GA 30602, USA

ABSTRACT

Partial Support is requested for `The Fourth IMACS International Conference
on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory'
to be held at the University of Georgia (April 11- 14, 2005) and sponsored by
IMACS (International Association for Mathematics and Computers in Simulation).
Presentations will be both invited (about 4) and submitted (about 120), and
attendance is estimated to be 150 or so. The requested support is for the
expenses of the four invited speakers, students, recent doctoral recipients,
and some of the direct costs of operating the conference.

The proposed conference will focus on computational and theoretical
aspects of nonlinear waves and optical fiber communication systems.
Nonlinear wave equations describe a wide class of physical phenomena in
plasma physics, anharmonic crystals, bubble-liquid mixtures, fiber optics, etc.
It is to be noted that fiber optics communications has experienced tremendous
growth in the last twenty years. In the last decade alone, data rates have
increased by orders of magnitude. At the same time, the recent rise of the
Internet and the World-Wide Web has quickly contributed to make this area one
of the key technological sectors in the national and global economy, and has
generated an unprecedented demand for even higher transmission capacities.
At the conference, researchers will present recent research in the broad area
that include theory and computations of solitons.
In addition, research will be presented that uses high performance computers
for solving computationally intensive problems.
This conference will build on the success of the previous year's conference.
In 2003, at the third conference in this series, more than 135 research papers
were presented. This includes contributed papers and papers presented in
organized sessions. In addition, a tutorial on `Introduction to Optical Fiber
Communication Systems' was given. Six invited speakers, ten students and
1 post-doc were fully or partially supported by the grant. Three `best paper'
awards were give to graduate students. More than 13 students and post-docs as
well as 11 women have participated in the conference. A good number of
scientists from the Naval research laboratories as well as the Los Alamos
National laboratories were present. We expect an even greater representation
of women at the fourth conference, and we are working hard to increase the
representation of minorities and persons with disabilities.
This conference is expected to have a substantial impact on the quality of the
research and teaching in the major areas of discourse which is due to its
interdisciplinary nature as well as to the high quality of the invited
speakers and participants. Participants from Mathematics, Physics, Chemistry,
Computer Science, Engineering and Industry were present at the previous
conferences.

Georgia, April 16-19, 2007.

The conference is organized by the International Association for Mathematics and Computation in Simulation (IMACS). It is the fifth in a series of conferences held every other year. The last conference was held at the University of Georgia in June 2005. The program will consist of invited lectures and contributed talks. A tutorial will precede the conference. This year the topic of the conference is Nonlinear Evolution Equations and Wave Phenomena, with applications in optical fiber communication systems. A website for the conference Proposal: 0631857
Principal Investigator: Taha, Thiab R.
Institution: University of Georgia Research Foundation Inc
Proposal Title: The Fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Theory and Computation

ABSTRACT

This award will fund travel and local expenses of four invited speakers and 14 students and postdocs to attend the Fifth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena, to be held at the University of can be accessed from the IMACS web page, http://www.imacs-online.org.

This award provides support for the Sixth International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory, sponsored by the International Association for Mathematics and Computers in Simulation (IMACS), held at the University of Georgia on 23-26 March 2009. The interdisciplinary conference focuses on computational and theoretical aspects of nonlinear wave propagation and optical fiber communication systems, bringing together researchers in theoretical and computational mathematics, applied physics, and engineering.

In addition to invited lectures, the conference includes contributed papers and poster sessions. Awards are given for the best undergraduate and graduate papers presented. The conference encourages and supports participation by students, recent doctoral recipients, women, minorities, and other groups underrepresented in the mathematical sciences.

Conference web site:
http://www.cs.uga.edu/%7Ethiab/waves2009.html

This award supports travel for participants in the Seventh International Association for Mathematics and Computers in Simulation (IMACS) Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory," held 4-7 April 2011 at the University of Georgia. The workshop brings together researchers in theory, computation, and applications of models for nonlinear waves. The conference program, which includes tutorials suitable for students, is designed to be valuable for young researchers.

The workshop will enhance communication among junior and senior researchers in nonlinear evolution equations. Conference proceedings will be published. The conference encourages and supports participation by graduate students, junior researchers, and members of under-represented groups.

Conference web site: http://www.cs.uga.edu/~thiab/waves2011.html

This award provides funding for US participation in four installments of the conference series "Midwest Partial Differential Equations Seminar" that will be held at University of Wisconsin, Madison in Spring 2018, University of Indiana, Bloomington in Fall 2018, Purdue University, West Lafayette in Spring 2019, and another midwestern university, to be determined, in Fall 2019.

The conference focuses on recent developments in Analysis, especially in the field of partial differential equations. A number of distinguished mathematicians have agreed to attend and speak at this conference series. This award gives early career researchers, members of underrepresented groups, researchers not funded by NSF and the like an opportunity to attend and participate in this conference. The organizing committee will strive to make this funding opportunity known to target groups through a number of different activities. More information will be made available at: http://homepages.math.uic.edu/~jlewis/midwpde/

The Eighth IMACS International Conference on Nonlinear Evolution Equations and Wave Phenomena: Computation and Theory will be held at the
University of Georgia from March 25 to March 28, 2013. More information is available on the conference website: waves.uga.edu

The proposed conference will focus on the derivation, theory, numerical simulation and application of nonlinear wave equations. Despite several decades of intense activity, this general area shows no sign of abating nor of calcification. Indeed, two of the recent Fields medalists are cited for their work in this area, and major new forays into geophysical modeling and high-speed communication have made use of nonlinear wave equations. The conferences in this series are well known for bringing together researchers in theoretical and computational mathematics, the applied sciences and engineering.

The conference will feature several invited, one-hour presentations on some of the most topical aspects of the area and an estimated 180 shorter talks, most of which will be in a focused session format. Past experience suggests that well over 200 participants will attend. At the most recent conference in 2011, 229 research papers were presented. In addition to 161 participants from the USA, there were 68 international scientists and students from 36 countries. We had 41 graduate and undergraduate students, 3 junior faculty and 27 women who attended the conference. This conference we will have 20 organized sessions, 3 keynote speakers, and two tutorials for students and young faculty. The requested support is for the expenses of the invited speakers and to defray the costs of younger participants, with special attention paid to students, women, minorities, persons with disabilities, postdocs and junior faculty. As of mid-November, 2012, more than 50 applications were received from students, women, underrepresented groups, and young faculty requesting financial support to attend the conference.