1983 — 1985 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences: Singularities of the Periodic Boussinesq's Equation 
0.964 
1985 — 1989 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences: Perturbations of Integrable Nonlinearpartial Differential Equations @ University of CaliforniaSanta Barbara 
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1986 — 1988 
Birnir, Bjorn Millett, Kenneth [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences Research Equipment @ University of CaliforniaSanta Barbara 
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1989 — 1990 
Birnir, Bjorn Millett, Kenneth (coPI) [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences Research Equipment 1989 @ University of CaliforniaSanta Barbara
This is a grant under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences of the National Science Foundation. This program supports the purchase of special purpose computing equipment dedicated to the conduct of research in the mathematical sciences. This equipment is required for several research projects and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers and with substantial costsharing from the institutions submitting the proposal. This program is an example of academic, corporate, and government cooperation in the support of basic research in the mathematical sciences. This equipment will be used to support five research projects in the Department of Mathematics at the University of California, Santa Barbara: Numerical Investigations of Nonlinear Partial Differential Equations, directed by Bjorn Birnir; Combinatorial Classification of Classical Knots and Links, directed by Kenneth Millett; Numerical Experiments and the Theory of Viscosity Solutions of Fully Nonlinear Equations, directed by Michael Crandall; Singularities in Nonlinear Hyperbolic Systems, directed by Thomas Sideris; and Character Varieties for Hyperbolic Manifolds, directed by Daryl Cooper.

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1989 — 1991 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences: Invariant Manifolds and Attracting Sets of Nonlinear Partial Differential Equations @ University of CaliforniaSanta Barbara
The central theme of this mathematical research project is the analysis of nonlinear partial differential equations. Particular emphasis will be placed on extending methods which describe invariant manifolds and attracting sets of perturbations of integrable nonlinear equations to the case of higher dimensional semilinear differential equations. Work will also be done in developing methods for determining global coordinates that best describe the finite dimensional attracting sets. Application of these investigations to problems of physical importance include studies of the damped and driven sineGordon equation describing the Josephson junction and the analysis of a system of EulerRaleighPlesset equations describing a cloud of gas bubbles in liquid. Additional work includes studies of perturbations that change the spatial structure of the perturbed equations; in particular the question of existence of breather solutions to these equations will be taken up. The bearing these answers have on the symplectic geometry of the phase space containing the solutions will also be considered. Long term objectives of this research include the application of bifurcation techniques developed in the study of perturbed integrable differential equations to improved understanding of general fluid equations.***

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1991 — 1994 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Mathematical Sciences: Attractors, WeakTurbulence and Nonexistence of Breathers @ University of CaliforniaSanta Barbara
This project will develop three topics concerning long time behavior of solutions to partial differential equations. First a descriptive theory of low dimensional attractors of dissipative forced nonlinear PDEs will be attempted in order to investigate weak turbulence. This theory exists for the damped and driven sineGordon equation in one dimension; the PI will extend it to the KleinGordon equations in higher dimensions and the Ginzburg Landau equation. The second topic is the nonexistence of breather solutions to nonlinear conservative hyperbolic PDEs. The third topic is the stability of solitary waves for equations describing a bubble cloud and longwave regularized Boussinesq equations. These problems will be studied numerically and analytically. Their solutions will accrue to our understanding of basic mathematical and physical issues. Atmospheric sciences and hydrodynamics, among others, will be impacted by the results of this project.

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1997 — 2001 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Applications of Qualitative Analysis of Nonlinear Pde's @ University of CaliforniaSanta Barbara
9704874 Birnir The dynamics of surge, stall, and flutter in jet engines will be investigated using the qualitative theory of nonlinear partial differential equations ( PDE's). The MooreGreitzer equations modelling the flow through a compressor will be used to analyze surge and stall. First it will be determined whether the dynamics are high or lowdimensional, then the bifurcation that causes stagnation stall identified and methods developed to control stall and surge. The results will be applied to the study of laboratory compressors and the analysis of laboratory data. A simple model for flutter in rotor (and stator) rings of blades is developed and used to study the possible flutter modes, then control strategies for these modes will be developed. This will first be done numerically and then analytically. Finally these methods will be used to study a realistic model of rotor rings and the real flutter modes and their bifurcations analyzed and methods developed to control them. The qualitative analysis of nonlinear PDE's will be extended to dimensions two and greater, numerically and analytically, first by studying damped and driven wave equations, and applications of the higher dimensional theory will be implemented. The purpose of the research is to help design jet engines that are lighter and can be operated more efficiently and safely than contemporary jet engines. These engines will be used in the airplanes of the 20th century and will make air travel faster, cheaper, and safer.

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1999 — 2003 
Birnir, Bjorn Smith, Terence [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Towards a Qualitative Theory On NonLinear Geographic Systems: Regular and Stochastic Evolution in Fluvial Landforms @ University of CaliforniaSanta Barbara
Spatial patterns and processes characterizing geographical entities and phenomena, such as drainage basins, systems of cities, and flows of information, often show a remarkable mix of organization and complexity. These arise from a large number of interactions that are spatially distributed and characterized by nonlinear processes involving stochastic effects and instabilities. The dominant objective of this research is to refine and extend a family of physically based models for simulating key aspects of drainage basin evolution. The project will incorporate theoretical, computational, and fieldbased investigations to accomplish the following: (1) apply emerging methodologies for characterizing the qualitative behavior of infinitedimensional, nonlinear dynamical systems in explaining the emergence of spatial patterns in the evolution of drainage basins; (2) demonstrate that such methods must be used in conjunction with traditional methods in developing a full characterization of the evolution of fluvial land surfaces and an understanding of various scaling laws; (3) develop additional tools for such analyses and apply them to other examples of complex geographic phenomena; and (4) disseminate an understanding of these methods and their value. The mathematical and modeling results will provide a basis for qualitative and quantitative predictions that may be compared with observations on real landscapes, and ultimately, models of analogous geographic phenomena, such as population movements, diffusion of innovations, and information flows can be developed based on this understanding.

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2000 — 2003 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Analysis and Control of Flow and Flutter in Aeroengines @ University of CaliforniaSanta Barbara
0072191 Birnir
In a program of analytical and computational investigations, the investigator will develop control theory to make jet engines lighter, more efficient and safer. Surge and stall are instabilities in the flow of air through the engines; flutter is an oscillation of the blades compressing the air. These instabilities decrease the efficiency of the engine and can be dangerous. The control theory aims at controlling all of these instabilities.
If lighter, more fuel efficient and safer aircraft engines are to be made the current technology needs to be improved. This research tries to accomplishes this goal by first developing a mathematical model for the jet engine, then simulating this model of the engine on a computer and using the results to figure out how to design a much more efficient and safer jet engine. Then this design is implemented and checked in the laboratory. Similar technology is also used to compress rocket fuel before combustion and an optimization of the technology as a whole may lead to cheaper space travel.

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2001 — 2004 
Sideris, Thomas (coPI) [⬀] Liu, XuDong (coPI) [⬀] Ceniceros, Hector (coPI) [⬀] Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Scientific Computing Research Environments For the Mathematical Sciences (Screms) @ University of CaliforniaSanta Barbara
The Department of Mathematics at the University of California, Santa Barbara will purchase a Beowulf Cluster consisting of 16 dual processor node, one single processor controlling node, a network switch, backup tape drive, and a rack. This hardware will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular: Computations of scaling of fluvial landscapes, computations of effectively nonlinear quantum systems, dynamically adaptive and nonstiff boundary integral methods, numerical schemes for simulations of multiphase fluids and vorticity deformation in 2D ideal incompressible fluid flow.

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2002 — 2013 
Birnir, Bjorn Petzold, Linda [⬀] Homsy, George (coPI) [⬀] Meiburg, Eckart (coPI) [⬀] Maroudas, Dimitrios (coPI) [⬀] 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Igert: Graduate Education Program in Computational Science and Engineering With Emphasis On Multiscale Problems in Fluids and Materials @ University of CaliforniaSanta Barbara
This IGERT program is structured to provide a unique Ph.D. program in interdisciplinary research and education in Computational Science and Engineering (CSE). The vision is to educate students for whom working in interdisciplinary teams is the norm, and who have the ability to acquire knowledge, ways of thinking, and perspectives from other disciplines. The proposed IGERT PhD experience is different from one in a traditional discipline, and possibly unique among CSE programs in the USA. The IGERT PhD theses will be jointly supervised, and those students with a particular disciplinary orientation will share resources, knowledge, and approaches with IGERT students with other orientations. While a typical IGERT PhD thesis will still have a strong focus in a discipline, it will contain major elements of independent creative work in other disciplines relevant to the general problem area under study. IGERT students and faculty will work together in three Focus Groups: Microscale Engineering, Complex Fluids, and Computational Materials Science, to solve a wide range of important and timely problems that depend deeply on integration of information from the smaller scales to the larger scales. These multiscale problems require a strong foundation in both engineering and the mathematical and computational sciences. The curriculum ensures depth in one area and a significant exposure to high level courses in one or more ancillary areas. It includes new courses in atomicscale computer simulation, and computing for high performance, to specifically address the multiscale nature of the Focus Group problems and their computational requirements. An internship is required to broaden and reinforce the interdisciplinary research experience, and a required series of workshops and seminars will give IGERT students a significant exposure to important aspects of career development and ethics.
IGERT is an NSFwide program intended to meet the challenges of educating U.S. Ph.D. scientists and engineers with the multidisciplinary backgrounds and the technical, professional, and personal skills needed for the career demands of the future. The program is intended to catalyze a cultural change in graduate education by establishing innovative new models for graduate education and training in a fertile environment for collaborative research that transcends traditional disciplinary boundaries. In the fifth year of the program, awards are being made to twentyone institutions for programs that collectively span the areas of science and engineering supported by NSF.

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2004 — 2007 
Birnir, Bjorn 
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information 
Stochastic Theory of Turbulent Combustion @ University of CaliforniaSanta Barbara
This award supports exploratory work in the analysis and numerical simulation of stochastic partial differential equations with colored noise. The study is motivated by the modeling of turbulent combustion in jet engines.
This Small Grant for Exploratory Research (SGER) facilitates a program of analytical and computational studies to improve the safety and performance of jet engines. The focus is on the turbulent combustion in the engines and their afterburners, chambers where unburnt fuel combusts. The project aims to use recent advances in the theory of stochastic partial differential equations and complex systems to develop a model for turbulence that is applicable to jet engine combustion. The project is a step towards cheaper, safer, and more environmentally friendly air travel.

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