1989 — 1991 |
Bernoff, Andrew |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Mathematical Sciences: Postdoctoral Research Fellowship
The Mathematical Sciences Postdoctoral Research Fellowships are awards to recent recipients of doctoral degrees. The fellowship is designed to provide 24 months of support divided into 18 academic months and 3 periods of two summer months. The recipient has the option of a Research Instructorship which allows the 18 months of academic support to be taken as 9 months of full-time support and 18 months of half-time support. Mathematical Sciences Postdoctoral Research Fellowship awards allow fellows to choose research environments that will have maximal impact on their future scientific development. Andrew Bernoff received his doctoral degree from the University of Cambridge, and will pursue research in the area of applied mathematics, specifically, the existence and motion of topological defects in nonlinear evolution equations, under the guidance of John Neu at the University of California, Berkeley.
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0.912 |
1992 — 1996 |
Lichter, Seth [⬀] Bernoff, Andrew |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Evolution and Viscous Decay of Dipolar Vortex Couples in Two Dimensional Fluid Mechanics @ Northwestern University
A joint analytical and experimental investigation is to be conducted of the viscous decay, evolution and interaction of vortex couples at large Reynolds number. Analytically, boundary layer ideas are used to derive their behavior from known inviscid solutions. The interaction of vortex couples with weak background vorticity or shear is studied using singular perturbation theory. By studying mixing in the large Peclet number limit, estimates on the efficiency of vortex couples in transport are derived. The experiments employ a novel use of stratification to create two-dimensional flows. Mixing is studied quantitatively by the optical tracking of tracer particles and dye. Data processing determines the velocity and vorticity fields as they evolve. Vortex couples, localised dipolar regions of vorticity, possess nearly closed streamlines, are self-propagating, and persist for long times. Consequently, they efficiently transport vorticity, momentum, heat and contaminants. Vortex couples arise in the shear layers and plumes observed in atmospheric chemistry, ocean mixing, convective cooling, and turbulent transport and mixing.
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0.942 |
1993 — 1996 |
Bernoff, Andrew |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Intrinsic Equations of Motion For Interfaces in Models of Solidification @ Northwestern University
A methodology is proposed for deriving equations of motion for interfaces in transition between two phases, such as the solidification of a liquid into a solid, in the asymptotic limit of small diffusion. The investigator will show that the velocity of the interface is a function of its local geometry, described by so-called intrinsic quantities such as the curvature. This model allows the computation of the radius at which a growing spherical particle becomes unstable and may allow a deeper understanding of the complex dendritic structures seen in solidification. The problem of the solidification of a liquid has many industrial applications, such as the growing of a quartz crystal from a melt for use in semiconductor devices like computer chips. For these applications it is desirable to grow smooth, regular crystals. Unfortunately, many substances tend to grow into irregular snowflake-like dendrites. In this study the investigator proposes a methodology for reducing the complex equations governing solidification to a relatively simple geometric description. This reduction should allow the prediction of the transition from regular to dendritic solidification. It may also give some insight into the process by which irregular dendritic structures form and grow.
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0.942 |
1993 — 1995 |
Bernoff, Andrew Kath, William [⬀] Riecke, Hermann (co-PI) [⬀] |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Mathematical Sciences Computing Research Environments @ Northwestern University
The Department of Engineering Sciences and Applied Mathematics of Northwestern University will purchase workstations which will be dedicated to support research in the mathematical sciences. The equipment will be used for several research projects concerning the dynamics of nonlinear partial differential equations and applications, including in particular: . Advection by a dipolar vortex couple in the presence of small diffusion. . The numerical computation of pulse propagation in nonlinear optical fibers. . The influence of noise and quenched disorder on the growth of spatial structures.
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0.942 |