Faculty Research Publications (Mathematics)
http://hdl.handle.net/1957/13818
20141031T09:56:56Z

Eliminating flutter for clamped von Karman plates immersed in subsonic flows
http://hdl.handle.net/1957/53233
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
Lasiecka, Irena; Webster, Justin
We address the longtime behavior of a nonrotational von Karman plate in an inviscid potential flow. The model arises in aeroelasticity and models the interaction between a thin, nonlinear panel and a flow of gas in which it is immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component of the dynamics (in the presence of a physical plate nonlinearity) converge to a global compact attracting set of finite dimension; these results were obtained in the absence of mechanical damping of any type. Here we show that, by incorporating mechanical damping the full flowplate system, full trajectoriesboth plate and flowconverge strongly to (the set of) stationary states. Weak convergence results require "minimal" interior damping, and strong convergence of the dynamics are shown with sufficiently large damping. We require the existence of a "good" energy balance equation, which is only available when the flows are subsonic. Our proof is based on first showing the convergence properties for regular solutions, which in turn requires propagation of initial regularity on the infinite horizon. Then, we utilize the exponential decay of the difference of two plate trajectories to show that full flowplate trajectories are uniformintime Hadamard continuous. This allows us to pass convergence properties of smooth initial data to finite energy type initial data. Physically, our results imply that flutter (a nonstatic end behavior) does not occur in subsonic dynamics. While such results were known for rotational (compact/regular) plate dynamics [14] (and references therein), the result presented herein is the first such result obtained for nonregularizedthe most physically relevantmodels.
This is the publisherâ€™s final pdf. The published article is copyrighted by the American Institute of Mathematical Sciences and can be found at: http://www.aimsciences.org/journals/home.jsp?journalID=3.
20140901T00:00:00Z

Optimal Placement of Marine Protected Areas: a Tradeoff Between Fisheries Goals and Conservation Efforts
http://hdl.handle.net/1957/52053
Optimal Placement of Marine Protected Areas: a Tradeoff Between Fisheries Goals and Conservation Efforts
De Leenheer, Patrick
Marine Protected Areas (MPAs) are regions in the ocean or along coastlines where fishing is controlled to avoid the reduction or elimination of fish populations. A central question is where exactly to establish an MPA. We cast this as an optimal problem along a onedimensional coastline, where fish are assumed to move diffusively, and are subject to recruitment, natural death and harvesting through fishing. The functional being maximized is a weighted sum of the average fish density and the average fishing yield. It is shown that optimal controls exist, and that the location of the MPA is determined by two key model parameters, namely the size of the coast, and the weight of the average fish density in the functional.
This is an author's peerreviewed final manuscript, as accepted by the publisher. The published article is copyrighted by IEEEInstitute of Electrical and Electronics Engineers and can be found at: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=9.
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20140601T00:00:00Z

A Note on the Transcendence of Zeros of a Certain Family of Weakly Holomorphic Forms
http://hdl.handle.net/1957/51982
A Note on the Transcendence of Zeros of a Certain Family of Weakly Holomorphic Forms
JenningsShaffer, Chris; Swisher, Holly
See article for Abstract.
This is an author's peerreviewed final manuscript, as accepted by the publisher. The published article is copyrighted by World Scientific Publishing Co. and can be found at: http://www.worldscientific.com/worldscinet/ijnt.
20140301T00:00:00Z

Skew Disperson and Continuity of Local Time
http://hdl.handle.net/1957/51760
Skew Disperson and Continuity of Local Time
Results are provided that highlight the effect of interfacial discontinuities in the
diffusion coefficient on the behavior of certain basic functionals of the diffusion, such
as local times and occupation times, extending previous results in [2, 3] on the behavior
of first passage times. The main goal is to obtain a characterization of large scale
parameters and behavior by an analysis at the fine scale of stochastic particle motions.
In particular, considering particle concentration modeled by a diffusion equation with
piecewise constant diffusion coefficient, it is shown that the continuity of a natural
modification of local time is the individual (stochastic) particle scale equivalent to continuity
of flux at the scale of the (macroscopic) particle concentrations. Consequences
of this involve the determination of a skewness transmission probability in the presence
of an interface, as well as corollaries concerning interfacial effects on occupation time
of the associated stochastic particles.
This is an author's peerreviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Springer and can be found at: http://link.springer.com/journal/10955.
20140701T00:00:00Z