| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | December 4, 2012 |
| Latest Amendment Date: | December 4, 2012 |
| Award Number: | 1217273 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Leland Jameson
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | December 15, 2012 |
| End Date: | November 30, 2015 (Estimated) |
| Total Intended Award Amount: | $99,997.00 |
| Total Awarded Amount to Date: | $99,997.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
160 ALDRICH HALL IRVINE CA US 92697-0001 (949)824-7295 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Rowland Hall 540H Irvine CA US 92697-3875 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The investigators and their colleagues study novel instabilities in fluids driven by material complexity occurring only at interfaces. For instance, when two reacting micellar liquids are brought into contact, the reaction may produce a growing gel-like phase at the interface, which significantly stiffens the boundary between the fluids. Another example arises from the presence of nanoscale colloidal particles which accumulate at interfaces. Intercolloid forces also endow the interface with stiffness, and may even jam the interface at sufficiently high volume fraction. The goal of this proposal is to develop comprehensive, physically appropriate models and simulations for these very difficult problems. The highly nonlinear nature of these problems makes fast, accurate and robust numerical methods essential to their study. The research team plans to investigate the nonlinear dynamics of interfaces endowed with complex physical properties and to develop strategies to control their pattern forming abilities by (1) developing and applying state-of-the-art adaptive numerical methods to large-scale computation; (2) performing analytical, numerical and modeling studies of important constituent processes; and (3) performing experiments to calibrate and validate the mathematical models, to test the model predictions, and to help elucidate the underlying physical processes.
Interfacial instabilities occur when driving forces compete with resistive forces with a consequence being the formation of complex patterns. Examples occur in diverse systems such as including filamentary microorganisms, growing biofilms, smoldering flame fronts, and lava flows. The goal of this project is to develop comprehensive, physically appropriate models and efficient numerical methods for solving such problems. Experiments will be performed to validate the models and test the model predictions, and to help elucidate the underlying physical processes. The research will focus on flows with complex interfacial physics such as reactions and nanoscale particles at interfaces. The research activities will provide new integrated theoretical, numerical and experimental results that can be used to (1) further explore these pattern forming systems that are driven out of equilibrium; (2)develop guidelines for controlling the evolving morphologies. While specific and novel applications are investigated here, the new mathematical and adaptive numerical techniques are expected have application beyond the present context. In addition, this project will provide valuable interdisciplinary training opportunities for young researchers, and outreach programs are planned for middle school and undergraduate students (Penn State), high school students (UC Irvine) and undergraduate students (Ill. Inst. Techn.).
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Growth and form in nature are the puzzles that the study of pattern formation aims to illuminate. From a mathematical point of view, studies of the pattern formation can be formulated as moving boundary problems with interfaces separating different physical domains. In the last few decades, theories, experiments, and nonlinear simulations have contributed to gain a better understanding of the mechanisms ruling the pattern selection, in which interfacial instability is the central question. Interfacial instabilities occur when driving forces compete with resistive forces and typically result in the formation of complex patterns. Driving forces include injection flux and mass proliferation. Resistive forces include surface tension, viscous dissipation, bending elasticity, and viscoelasticity. A significant challenge in all these systems is that patterns result from a complex interaction of reaction, diffusion and mechanical effects coupled to the specific properties such as the fluid rheology or the solid elasticity of the material produced. Indeed, controlling the interface morphology has proven to be a major challenge, and its dynamics remains poorly understood. Intellectual Merit: We have been developing comprehensive, physically appropriate models and numerical methods for these very difficult problems, focusing on growing interfaces in the classic setting of viscous fingering the flow between two narrowly spaced plates known as a HeleShaw cell. In this prototypical patternforming system, our group investigates the interaction of driving and resistive forces, and the dependence on material parameters. Our work is helping to provide an enhanced understanding of growth and form arising from complex interfacial physics. Our study has also provided insight into the dynamics of crystallization and melting at the nanoscale. Crystallization and melting are crucial in diverse contexts, ranging from crystal growth in manufacturing of semiconductor devices to the freezing process in ice cream making. Our theory is capable of predicting the consequences of the microscopic interactions in the system and capturing the nanoscale details such as the lattice structure of the solid. We have also advanced the state-of-the-art in simulating nonlocal hydrodynamic systems. Results have been published in peer-reviewed journals and codes are available upon request. Broader impacts included outreach programs for high school students through the California State Summer School for Mathematics and Science (COSMOS) and the Clubes de Ciencia Mexico, in addition to research training. The research program provided interdisciplinary training to four graduate students (one is an underrepresented minority and two are women) and three postdoctoral researchers in interdisciplinary and computational mathematics.
Last Modified: 03/03/2016
Modified by: John S Lowengrub
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