Publications Home Page


Peer-Reviewed Publications

[J1]
“An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems.” SIAM Journal on Applied Mathematics, 55 (1995): 662-676 (with Donald S. Cohen).
 
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[J2]
“Constant Front Speed in Weakly Diffusive Non-Fickian Systems.” SIAM Journal on Applied Mathematics, 55 (1995): 1039-1058.

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[J3]
“The Effect of a Changing Diffusion Coefficient in Super-Case II Polymer- Penetrant Systems.” IMA Journal of Applied Mathematics, 55 (1995): 49-66 (with Donald S. Cohen).

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[J4]
“A Mathematical Model for a Dissolving Polymer.” AIChE Journal, 41 (1995): 2345-2355 (with Donald S. Cohen).

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[J5]
“Non-Fickian Diffusion in Thin Polymer Films.” Journal of Polymer Science, Part B: Polymer Physics Edition, 34 (1996): 981-997.
 
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[J6]
“Perturbation Analysis of Thomas’ and Windle’s Model of Case II Transport.” AIChE Journal, 42 (1996): 2025-2035 (with Christopher J. Durning and Donald S. Cohen).
 
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[J7]
“Viscous Boundary-Layer Effects in Nearly Inviscid Cylindrical Flows.” Nonlinearity, 10 (1997): 277-290.
 
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[J8]
“Trace Element Disequilibria and Magnesium Isotope Heterogeneity in 3655A: Evidence for a Complex Multi-Stage Evolution of a Typical Allende Type B1 CAI.” Geochimica et Cosmochimica Acta, 61 (1997): 1541-1561 (with Allen K. Kennedy et al.).
 
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[J9]
“A Mathematical Model for Trapping Skinning in Polymers.” Studies in Applied Mathematics, 99 (1997): 49-80.
 
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[J10]
“Trapping Skinning in Polymers: Theoretical Predictions.” Chemical Engineering Communications, 166 (1998): 201-216.
 
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[J11]
“Asymptotic and Computational Analysis of Large Shear Deformations of a Thermoplastic Material.” SIAM Journal on Applied Mathematics, 59 (1998): 700-24 (with Donald A. French).
 
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[J12]
“An Asymptotic Analysis of Polymer Desorption and Skinning.” Macromolecular Theory and Simulations, 8 (1999): 10-14.
 
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[J13]
“Skinning During Desorption of Polymers: An Asymptotic Analysis.” SIAM Journal on Applied Mathematics, 59 (1999): 1134-55.
 
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[J14]
“Estimating Rate Constants in a Convection-Diffusion System with a Boundary Reaction.” IMA Journal of Applied Mathematics, 63 (1999): 89-112.

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[J15]
“Transport Effects on Surface-Volume Biological Reactions.” Journal of Mathematical Biology, 39 (1999): 533-61 (with Byron Goldstein and Donald S. Cohen).
 
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[J16]
“Biochemical Reactions on Helical Structures.” SIAM Journal on Applied Mathematics, 60 (2000): 1425-46.
 
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[J17]
“An Alternative Example of the Method of Multiple Scales.” SIAM Journal on Applied Mathematics, 42 (2000): 317-32.
 
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[J18]
“Surface Reaction Near a Stagnation Point.” Studies in Applied Mathematics, 105 (2000): 1-29.
 
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[J19]
“The Effect of a Receptor Layer on the Measurement of Rate Constants.” Bulletin of Mathematical Biology, 63 (2001): 301-327.
 
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[J20]
“A Spatially Nonlocal Model for Polymer-Penetrant Diffusion.” ZAMP, 52 (2001): 254-288.
 
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[J21]
“A Differential Equation Model of North American Cinematic Box-Office Dynamics.” IMA Journal of Management Mathematics, 12 (2001): 41-74 (with Ron A. Buckmire).
 
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[J22]
“Testing the Validity of the Effective Rate Constant Approximation for Surface Reaction with Transport.” Applied Mathematics Letters, 15 (2002): 547-552 (with Seth A. Jackson).
 
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[J23]
“Desorption Overshoot in Polymer-Penetrant Systems: Asymptotic and Computational Results.” SIAM Journal on Applied Mathematics, 63 (2002): 98-115 (with Richard A. Cairncross).
 
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[J24]
“Traveling Waves for Anomalous Diffusion in Polymers.” Applied Mathematics Letters, 17 (2004): 7-12 (with Sumanth Swaminathan).
 
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[J25]
“Refining the Measurement of Rate Constants in the BIAcore.” Journal of Mathematical Biology, 49  (2004): 272-292.

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[J26]
“The Effect of Receptor Site Nonuniformity on the Measurement of Rate Constants.” Applied Mathematics Letters, 18 (2005): 1101-1107 (with S. Swaminathan).

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[J27]
“A Spatially Nonlocal Model for Polymer Desorption.” Journal of Engineering Mathematics, 53 (2005): 221-238.

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[J28]
“Convection Effects in the BIAcore Dextran Layer: Surface Reaction Model.” Bulletin of Mathematical Biology68 (2006): 627-654.
 
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[J29]
“Convection Effects in Thin Reaction Zones: Applications to BIAcore.” SIAM Journal on Applied Mathematics, 66 (2006): 1978-1997.
 
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[J30]
“Steric Hindrance Effects on Surface Reactions: Applications to BIAcore.” Journal of Mathematical Biology, 55 (2007): 517-539.
 
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[J31]
“Perturbation Approximation of Solutions of a Nonlinear Inverse Problem Arising in Olfaction Experimentation.” Journal of Mathematical Biology, 55 (2007): 745-765 (with Donald A. French).
 
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[J32]
“Steric Hindrance Effects in Thin Reaction Zones: Applications to BIAcore.” IMA Journal of Applied Mathematics, 72 (2007): 865-893.
 
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[J33]
“Identification of Cl(Ca) Channel Distributions in Olfactory Cilia.” Mathematical Methods in the Applied Sciences, 31 (2008): 1860-1873 (with Donald A. French, Dorjsuren Badamdorj, and Steven Kleene).
 
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[J34]
“The Optimal Prepayment Strategy for Fixed Rate Mortgages.” In Proceedings of the World Congress on Engineering and Computer Science 2008. (2008): 898–903 (with D. Xie and G. Schleiniger)
 
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[J35]
“An Asymptotic Method to a Financial Optimization Problem.” In Advances in Machine Learning and Data Analysis, vol. 72. S. Ao, et al., eds.; New York: Springer (2009): 79-94 (with D. Xie and G. Schleiniger).
 
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[J36]
“Characterizing Molecular Diffusion in the Lens Capsule.” Matrix Biology, 29 (2010): 228-236 (with Brian Danysh, et al.).
 
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[J37]
“Transport Effects on Surface Reaction Arrays: Biosensor Applications.” Mathematical Biosciences, 230 (2011): 12-22.
 
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[J38]
“Characterization of the American Put Option Using Convexity.” Applied Mathematical Finance, 18 (2011): 353-365 (with D. Xie, Gilberto Schleiniger, and Qinghua Zhu).
 
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[J39]
“Sharp Fickian Behavior of Electrogenerated Chemiluminescence Waves in Conjugated Polymer Films.” Journal of Physical Chemistry, Part C, 117 (2013): 6747-6751.
 
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[J40]
“Wavefunction Delocalization in Quantum Dot Arrays: An Asymptotic Analysis.” Journal of Engineering Mathematics, 81 (2013): 191-211 (with William M. Reid and Matt Doty).
 
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[J41]
“An Application of Matrix Theory to the Evolution of Coupled Modes.” SIAM Review, 55 (2013): 764-787 (with Joseph Fehribach, Richard Moore, and Colin McKinstrie).
 
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[J42]
“A Mathematical Model of Cinematic Box-Office Dynamics with Geographic Effects.” IMA Journal of Management Mathematics, 25 (2014): 233-257 (with Ron A. Buckmire and Jacob Ortega-Gingrich).
 
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[J43]
“Multiple Surface Reactions in Arrays with Applications to Optical Biosensors.” Bulletin of Mathematical Biology, 76 (2014): 1783-1808 (with Matthew E. Zumbrum).
 
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[J44]
“Improving a Fuel Cell Assembly Process.” Mathematics-in-Industry Case Studies, 6 (2014): 22-47 (with Ibrahim Diakite, et al.).
 
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[J45]
“Sharp Fickian Fronts in Conjugated Polymer Films.” IMA Journal of Applied Mathematics, 80 (2015): 533-553.
 
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[J46]
“Conformal Mapping in Optical Biosensor Applications.” Journal of Mathematical Biology, 71 (2015): 533-550 (with Matthew E. Zumbrum).
 
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[J47]
“Asymptotic Results for a Barrier Potential Model.” European Journal of Applied Mathematics, 26 (2015): 863-886 (with Christopher S. Raymond).
 
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[J48]
“Modal Analysis of Spatial Pattern Formation in Fused Silica under Ultraviolet Irradiation.” Journal of the Optical Society of America B, 33 (2016): 1709-1715 (with Richard Moore).
 
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[J49]
“The Performance of the Hot End in a Plasticating 3D Printer.” Journal of Rheology 62 (2017): 229–236 (with Michael Mackay, et al.).
 
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[J50]
“Applications of Fractional Calculus in Solving Abel-Type Integral Equations: Surface-Volume Reaction Problem.” Computers & Mathematics With Applications, 73 (2017): 1346–1362 (with Ryan Evans, Udita Katugampola).
 
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[J51]
“Measuring Kinetic Rate Constants of Multiple-Component Reactions with Optical Biosensors.” Analytical Biochemistry, 533 (2017): 41-47 (with Ryan Evans, Wenbin Li).
 
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[J52]
“Transport Effects on Multiple-Component Reactions in Optical Biosensors.” Bulletin of Mathematical Biology, 79 (2017): 2215-41 (with Ryan Evans).
 
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[J53]
“Receptor Heterogeneity in Optical Biosensors.” Journal of Mathematical Biology, 76 (2018): 795-816 (with Ryan Evans).
 
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[J54]
“Simulation Solution to a Two-Dimensional Mortgage Refinancing Problem.” Computational Economics, 52 (2018): 479-92 (with Dejun Xie, Nan Zhang).
 
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[J55]
“An Optimal Mortgage Refinancing Strategy with Stochastic Interest Rate.” Computational Economics, 53 (2019): 1353-75 (with Xiaoxia Wu, Dejun Xie).
 
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[J56]
“Maximal 3-D Printing Extrusion Rates.” IMA Journal of Applied Mathematics, 84 (2019): 1022–43 (with Michael Mackay, et al.).
 
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[J57]
“Postextrusion Heating in Three-Dimensional Printing.” Journal of Heat Transfer, 142 (2020): 052101 (with Michael Mackay).
 
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[J58]
“Nonisothermal Welding in Fused Filament Fabrication.” Additive Manufacturing, 33 (2020): 101140 (with Keith Coasey, et al.).
 
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[J59]
“The Heat Balance Integral Method for Cylindrical Extruders.” Journal of Engineering Mathematics, 122 (2020): 1-16 (with Jacob Sitison).
 
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[J60]
“Mathematical Models for the Effect of Anti-Vascular Endothelial Growth Factor on Visual Acuity.” Journal of Mathematical Biology, 81 (2020): 1397-1428 (with Anna Kondic, et al.).
 
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[J61]
“Quasisteady Models for Weld Temperatures in Fused Filament Fabrication.” IMA Journal of Applied Mathematics, 87 (2022): 291-313.
 
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[J62]
“Optimal Exercise Frontier of Bermudan Options by Simulation Methods.” International Journal of Financial Engineering, 9 (2022): 2250013 (20 pages) (with Dejun Xie, et al.).
 
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[J63]
“Dependence of Fused Filament Fabrication Weld Strength on Experimental Parameters: A Numerical Study.” Journal of Manufacturing Processes, 85 (2023): 1066-76.
 
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Other Publications

[O1]
“A Model for Venous Blood Flow in the Legs.” Mathematical Modeling: IMA Summer Program for Graduate Students. IMA
Preprint Series 1021
(1992): 31-54 (with Tara Athan [Mary Brewster], et al.).
 
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[O2]
“Risk Assessment for Propane Gas Leakage in Valleys.” Mathematical Modeling: IMA Summer Program for Graduate Students. IMA Preprint Series 1021 (1992): 109-34 (with Tara Athan [Mary Brewster], et al.).
 
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[O3]
“Fluid Flow in a Filtering Device.” Mathematical Modeling: IMA Summer Program for Graduate Students. IMA Preprint Series 1021 (1992): 191-221 (with Donald Drew, et al.).
 
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[O4]
“Flow Improvement in Hydrofractured Reservoirs.” Mathematical Modeling: IMA Summer Program for Graduate StudentsIMA Preprint Series 1021 (1992): 269-95 (with Pat Hagan, et al.).
 
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[O5]
A Model for Nonlinear Diffusion in Polymers. Ph.D. thesis, California Institute of Technology, 1994.
 
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[O8]
“Optimizing Membrane Separations of Two-Component Protein Solutions.” In Proceedings of the Twelfth Workshop on Mathematical Problems in Industry (1996): 61-84 (with Skand Saksena, et al.).
 
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[O9]
“Gas Concentration Measurements in Underground Waste Storage Tanks.” In Proceedings of the Thirteenth Workshop on Mathematical Problems in Industry (1997) (with Tara Athan [Mary Brewster], et al.).
 
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[O11]
“Thermomechanical Models of Air Gap Nucleation During Pure Metal
Solidification on Moving Molds with Periodic Surface Topographies.” In Proceedings of the Fourteenth Workshop on Mathematical Problems in Industry (1999): 11-47 (with Louis G. Hector, Jr. et al.).
 
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[O13]
“Options on Baskets.” In Proceedings of the Sixteenth Workshop on Mathematical Problems in Industry (2001) (with Pat Hagan et al.).
 
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[O14]
“Multi-Name Credit Derivatives.” In Proceedings of the Seventeenth Workshop on Mathematical Problems in Industry (2002) (with Pat Hagan et al.).
 
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[O15]
“Testing the Validity of the Averaged Approximation for the IAsys.” University of Delaware Technical Report 2002-3 (2002) (with S. A. Jackson).
 
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[O16]
“A Mathematical Model for Blood Clotting.” University of Delaware Technical Report 2004-04 (2004) (with S. Swaminathan).
 
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[O17]
“Multi-Phase Flow in a Thin Porous Material.” Proceedings of the Twentieth Workshop on Mathematical Problems in Industry (2005) (with Uwe Beuscher et al.).
 
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[O18]
“Advanced Leak Detection.” Proceedings of the Twenty-First Workshop on Mathematical Problems in Industry (2006) (with R. P. Hart and D. Reicher et al.).
 
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[O19]
“Development of a Quaternion-Based Algorithm to Process Data in Robotics Applications.” In Proceedings of the Twenty-Second Workshop on Mathematical Problems in Industry (2007) (with J. Ashmore, et al.).
 
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[O20]
“Characterizing Molecular Diffusion in the Lens Capsule.” In Proceedings of the Twenty-Third Workshop on Mathematical Problems in Industry (2008) (with M. Duncan, et al.).
 
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[O21]
“Development and Persistence of ‘Static’ or ‘Dead’ Zones in Flows.” In Proceedings of the Twenty-Fifth Workshop on Mathematical Problems in Industry (2009) (with J. Abbott, et al.).
 
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[O22]
“Medical Ultrasound Imaging.” In Proceedings of the Twenty-Sixth Workshop on Mathematical Problems in Industry (2010) (with B. Haider, et al.).
 
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[O23]
“Modeling Photon Generation.” In Proceedings of the Twenty-Seventh Workshop on Mathematical Problems in Industry (2011) (with C. McKinstrie, et al.).
 
Download this file. (253K).

[O24]
“Fuel Cell Assembly Process Flow for High Productivity.” In Proceedings of the Twenty-Eighth Workshop on Mathematical Problems in Industry (2012) (with R. Ramanan, et al.).
 
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[O25]
“Phase Field Formulation for Microstructure Evolution in Oxide Ceramics.” In Proceedings of the Twenty-Ninth Workshop on Mathematical Problems in Industry (2013) (with
L. Button, et al.).
 
Download this file. (2.1M).
 
[O26]
“Spatial Pattern Formation in Fused Silica Under UV Irradiation.” In Proceedings of the Thirtieth Workshop on Mathematical Problems in Industry (2014) (with L. Button, et al.).
 
Download this file. (1.2M).
 
[O27]
“Desulfurization of Natural Gas for Fuel Cells.” In Proceedings of the Thirty-First Workshop on Mathematical Problems in Industry (2015) (with E. Campbell, et al.).
 
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[O28]
“Hybrid Programmatic TV Markets.” In Proceedings of the Thirty-Second Workshop on Mathematical Problems in Industry (2016) (with M. Montes de Oca, et al.).
 
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[O29]
“On Characterizing and Simulating Porous Media.” In Proceedings of the Thirty-Third Workshop on Mathematical Problems in Industry (2017) (with Z. He, V. Venkateshwaran, et al.).
 
Download this file. (2.2M).
 
[O30]
“The Problem of Freezing of Copper Water Heat Pipes.” In Proceedings of the Thirty-Fourth Workshop on Mathematical Problems in Industry (2018) (with J. Cepeda-Rizo, et al.).
 
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[O31]
“Parametric Models for Clinical Measurements in Ophthalmology.” In Proceedings of the Thirty-Fifth Workshop on Mathematical Problems in Industry (2019) (with A. Kondic, et al.).
 
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[O32]
“Evaporation from Porous Media.” In Proceedings of the Thirty-Sixth Workshop on Mathematical Problems in Industry (2020) (with U. Beuscher, et al.).
 
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[O33]
“Differential Privacy in Travel Data.” In Proceedings of the Thirty-Seventh Workshop on Mathematical Problems in Industry (2021) (with J. Dumont, et al.).
 
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[O34]
“The Problem of Freezing of Copper Water Heat Pipes.” Mathematics in Industry Reports (2021) (with S. Acharya, et al.).
 
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[O35]
“Parametric Models for Clinical Measurements in Ophthalmology.” Mathematics in Industry Reports (2022) (with A. Kondic, et al.).
 
Download this file. (7.7M).
 
[O36]
“Development of a Quaternion-Based Algorithm to Process Data in Robotics Applications.” Mathematics in Industry Reports (2022) (with J. Ashmore, et al.).
 
Download this file. (770K).
 
[O37]
“Finding the Limits of Machine Learning in Optimization.” Mathematics in Industry Reports (2022) (with D. Kane, et al.).
 
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Poster Presentations

[P1]
“Improved Rate Constants Using the BIAcore.” BIAsymposium poster presentation, November 1999.

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[P2]
“Surface Reaction Near a Stagnation Point.” Nonlinear Analysis 2000–> poster presentation, May 2000.

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Return to my CV.