2015 — 2018 |
Ristroph, Leif Zhang, Jun (co-PI) [⬀] Shelley, Michael [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Collaborative Research: Frg: Understanding and Controlling Active Fluids Through Modeling, Simulation, and Experiment
Soft active materials are collections of particles, cells, or molecules that are capable of converting chemical energy from their environment into motion and mechanical stresses. Examples include swimming microorganisms, cellular extracts, biological polymers, and molecular motors, as well as a wealth of synthetic particles designed to mimic biological systems. These active systems, which have generated considerable excitement over the last decade in many disciplines from engineering to physics to applied mathematics, evince behaviors that are fundamentally different from traditional passive materials, and their understanding is just beginning to illuminate long-standing problems in biology and to suggest new engineering devices. This research project aims to use experiments, modeling, and simulations, to further enhance understanding of a variety of active materials. The project will also involve training through research involvement of postdoctoral researchers, graduate students, and undergraduates.
The aim of this project is to use a combination of modeling, mathematical analysis, numerical simulations, and experiments to explore the dynamics of archetypal active fluids as their microstructural components interact with obstacles, walls, and each other. Computational and coarse-grained models will explore the interaction of microswimmers, individually and collectively, with boundaries and obstacles. Microfluidic environments will be fabricated to explore how active particle transport is affected and controlled by boundaries and obstacles, and tools of shape optimization will be used to guide the design. Specialized particles will be fabricated to elucidate different aspects of active matter. New types of active matter will be explored, both by considering modifications in particle-scale activity and system-scale confinement. These investigations will include detailed and coarse-grained computational models of recently synthesized active fluids in which immersed microtubules interact through motor-protein cross-linking and pulling, as well as a new active matter system in which particle activity couples to interfacial forces to drive large-scale flows.
|
1 |
2017 — 2022 |
Peskin, Charles (co-PI) [⬀] Tabak, Esteban (co-PI) [⬀] Donev, Aleksandar [⬀] Ristroph, Leif Holmes-Cerfon, Miranda (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Rtg: Research Training Group in Mathematical Modeling and Simulation
This Research Training Group (RTG) project is devoted to training through research of undergraduates, graduate students, and postdoctoral fellows in several salient aspects of modern applied mathematics. The activities that this project is based upon recognize the fundamental importance of the interplay between modeling and simulation for most real-life applications. Modeling involves identifying the fundamental components of a problem and posing them in mathematical terms. Simulation solves the mathematical problems thus posed using computers to make quantitative predictions. Both modeling and simulation will be used to investigate a wide variety of phenomena in physics, chemistry, engineering, and biology, such as how microorganisms swim, how blood flows in the heart, the unusual properties of suspensions of bacteria or active particles, and how to efficiently design new materials. A unique element of the project is an experimental laboratory (Applied Mathematics Laboratory at the Courant Institute) that will provide raw data and motivation for mathematical models and simulations as well as measurements for quantitative validation. The Courant Institute is particularly well-positioned for this enterprise. Since early on, the Institute had a strong emphasis in applied mathematics, with modeling and simulation at its core. This research and training project will increase the number of U.S. citizens, nationals, and permanent residents who are well prepared to undertake careers that require a thorough understanding of applied and computational mathematics, not only in academics, as is the case with many educational mathematics programs, but also in business, industry, and government.
This RTG program will emphasize the connections among modeling, simulation and experimental observation. The project, coordinated by five Co-PIs, will provide academic-year and summer funding for a growing number of Ph.D. students, starting from three and increasing to six by the end of the project, two postdoctoral scholars per year, as well as a number of undergraduate summer internships, for a duration of five years. The project will support the formation of a vertically-integrated activity which integrates a new research course, a seminar on oral and written presentation, a collaborative research seminar, visitor seminars and undergraduate summer research activities. A unifying theme of the study of passive and active particle suspensions will be used to build collaborations among computational scientists at Courant, the Applied Mathematics Laboratory, and the Soft Condensed Matter physics group at NYU's Physics Department. This research theme and the associated collaborations will serve as a framework for investigating other themes. For all themes, the research activities in this project will train students and postdocs to work in a multidisciplinary environment in which they have access to world leading experts in several disciplines. Furthermore, this research is expected to have substantial scientific impacts and to lead to new discoveries and potential applications. The five-year project will create new activities that will become a permanent part of mathematics teaching, research and training efforts at the Courant Institute, and will provide valuable experience that can be exported to other institutions.
|
1 |
2022 — 2025 |
Ristroph, Leif |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Shape Dynamics of Melting Ice: Experiments, Simulations, Modeling and Analysis
The Earth's ice reserves are melting with increasing rate. Interpreting what these changes mean for the health of our planet requires models that account for complex processes that act interdependently over immense ranges of length and time scales. The accuracy of global-scale climate models depends on the physics at the most fundamental scales, such as how the melting of ice depends on the shape of its interface with liquid water and the local temperature, salinity, and flow conditions. Applied and computational mathematics and mathematical modeling provide many methods that are well suited to addressing these problems. Applying such techniques and developing new ones specifically for ice melting can provide critical information needed to improve climate models. Better understanding the underlying physics and mathematics can also help to explain the diverse shapes and patterning of natural ice, which could allow local environmental conditions to be inferred from observations of ice. Investigating these important issues also provides opportunities to educate students and train researchers, thereby contributing to a workforce that is well prepared to tackle these and related problems.<br/><br/>These projects investigate the melting dynamics of ice through laboratory experiments, numerical simulations, mathematical modeling, and analysis. The general progression of the research program is from idealized settings such as melting of fixed bodies with simple initial forms in fresh water at fixed far-field temperature to increasingly elaborate situations involving changes in geometry, temperature, and salinity. Further extensions address additional couplings such as melting-induced motions of free ice. Experiments will focus on accurate measurement of ice-water interface forms and motions in laboratory settings where the initial geometry, far-field temperature, and salinity profiles can be controlled and systematically varied. Direct numerical computations will employ phase-field methods to simulate the evolution of the temperature, flow, and salt concentration fields that give rise to the interfacial dynamics. Modeling will invoke idealizations based, for example, on boundary layer theory to derive moving-boundary descriptions and stability analyses that relate to pattern formation. All methods will be combined interactively towards targeting significant gaps in the current understanding of how the evolving shape of ice feeds back on the melting process and how the morphology of ice can be used to infer ambient conditions.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
|
1 |