Faculty Research Publications (Mathematics)
http://hdl.handle.net/1957/13818
20141021T20:35:10Z

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.
©2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
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

Twoscale convergence of a model for flow in a partially fissured medium
http://hdl.handle.net/1957/51230
Twoscale convergence of a model for flow in a partially fissured medium
Clark, G. W.; Showalter, R. E.
The distributedmicrostructure model for the flow of single phase
fluid in a partially fissured composite medium due to DouglasPeszyńskaShowalter [12] is extended to a quasilinear version. This model contains the
geometry of the local cells distributed throughout the medium, the flux exchange
across their intricate interface with the imbedded fissure system, and
the secondary flux resulting from diffusion paths within the matrix. Both the
exact but highly singular micromodel and the macromodel are shown to be
wellposed, and it is proved that the solution of the micromodel is twoscale
convergent to that of the macromodel as the spatial parameter goes to zero.
In the linear case, the effective coefficients are obtained by a partial decoupling
of the homogenized system.
This is the publisher’s final pdf. The published article is copyrighted by Texas State University and can be found at: http://www.emis.ams.org/journals/EJDE/index.html.
19990114T00:00:00Z