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Mathematical Sciences
Joyce McLaughlin
Department of Mathematical Sciences Faculty:

Kristin Bennett
Mohamed Boudjelkha
Margaret Cheney
Donald Drew
Joseph Ecker
Joseph E. Flaherty
Isom Herron
Mark Holmes
David Isaacson
Ashwani Kapila
Maya Kiehl
Gregor Kovacic
Peter Kramer
Gina Kucinski
Rongjie Lai
Fengyan Li
Chjan Lim
Yuri Lvov
Harry McLaughlin
Joyce McLaughlin
John Mitchell
Clifford Nolan
Bruce Piper
Victor Roytburd
David Schmidt
Donald Schwendeman
William Siegmann
Michael Zuker

Mathematical Sciences Faculty
Joyce McLaughlin

Ford Foundation Professor of Mathematical Sciences; Member, Faculty of Information Technology; Director, IPRPI


Ph.D. University of California, Riverside

Recent Career Highlights:

ICM Invited Lecture 1994
SIAM Board of Trustees Chair, 1996-1998
CBMS Lecturer, 2001
Kovalevsky Prize and Lecture, 2004
Inaugural Fellow of the Society for Industrial and Applied Mathematics, 2009
Inaugural Fellow of the American Mathematical Society, 2012

Research Areas:

Professor McLaughlin's main research area is in nonlinear analysis as applied to parameter identification in inverse problems. Her research includes inverse spectral theory, biomechanical imaging of tissue, and identification of seabottom characteristics and biomasses in the sea.

In inverse problems the data is very indirectly related to the physical or biological property that is to be determined and usually is imaged. So it is essential to utilize the mathematical model of the physical process that creates the data in order to create an image. These problems are ill-posed; that is, small changes in the data can produce large changes in the image so careful mathematical analysis is needed in order to create an accurate image.

McLaughlin was first known for her work in inverse spectral theory, in which natural frequencies and/or subsets of mode shapes, such as nodal sets, of a vibrating system are used to identify physical properties.

A long standing research focus for McLaughlin has been the imaging of seabottom characteristics and biomasses in the sea, particularly when the sea is modeled by a wave guide.

More recently McLaughlin has become known for her work in biomechanical imaging of tissue. The physical process that produces the data is the dynamic movement of tissue with a low amplitude of displacement (on the order of microns) and the mathematical model for that process is used to create images of biomechanical tissue properties. These images are being utilized, together with ultrasound or MRI images, as a new medical diagnostic tool.

Selected Publications:

N. Honda, J.R. McLaughlin, and G. Nakamura, “Conditional stability for a single interior measurement,” Inverse Problems, 30, 2014, 19 pages.

P. Zheglova, J.R. McLaughlin, S.W. Roecker, J.R. Yoon, D. Renzi, “Imaging quasi vertical geologic faults with earthquake data,” Geophys. J. Int, 189(3), 2012, pp. 1584-1596. (text of paper)

J.R. McLaughlin, A. Oberai and J-R. Yoon, “Formulas for detecting a spherical stiff inclusion from interior data: A sensitivity analysis for the Helmholtz equation,” Inverse Problems, Special Issue on Coupled Physics, 28, 2012, 21 pages. (text of paper)

Klein, J., McLaughlin, J. and Renzi, D. “Improving Arrival Time Identification in Transient Elastography”, Physics in Medicine and Biology. 57(8), 21 Apr 2012, Pages 2151-2168.

J. Mclaughlin, J-R Yoon. "Arrival times for the wave equation”, Communications on Pure and Applied Mathematics (CPAM), Vol. (64) no. 3, March 2011, pp. 313-327.

Lin, K., Mclaughlin, J., Thomas, A., Parker, K., Castaneda, B., and Rubens, D. "Two-dimensional shear wave speed and crawling wave speed recoveries from in vitro prostate data". Journal of Acoustical Society of America130(1):585-98., July 2011 (text of paper)

Mclaughlin, J., Thomas, A., and Yoon, J.R."Basic Theory for Generalized Linear Solid Viscoelastic Models". AMS Contemporary Mathematics Volume: Tomography and Inverse Transport Theory, editors: G. Bal, D. Finch, P. Kuchment, J. Schotland, P. Stefanov, and G. Uhlmann. 2011, pp. 101-134. (text of paper)

S. Ahmed, S. Bak, J. McLaughlin, and D. Renzi.  “A Third Order Accurate Fast Marching Method for the Eikonal Equation in Two Dimensions,” SIAM J. Scientific Computing 33(5): 2402-2420 (2011). (text of paper)

S. Bak, J. McLaughlin, and D. Renzi. "Some Improvements for the Fast Sweeping Method," SIAM Journal on Scientific Computation (SISC) (32), 2010, pp. 2853-2874.(text of paper)

K. Lin, J. McLaughlin, D. Renzi.  Thomas, A. “Shear wave speed recovery in sonoelastography using crawling wave data,” Journal of the Acoustical Society, July 2010, 128(1):88-97. (text of paper)

J. McLaughlin, N. Zhang, and A. Manducca. "Calculating shear modulus and pressure by 2D log-elastographic methods", Inverse Problems, Vol. 26, no.8, August 2010, pp. 25. (text of paper)

S. Roecker, J. McLaughlin, B. Baker. "A Finite-Difference Algorithm for Full Waveform Teleseismic Tomography". International Journal of Geophysics, 2010, 181, 1017–1040. (text of paper)

J. McLaughlin and K. Lin. "An error estimate on the direct inversion model in shear stiffness imaging", Inverse Problems, Vol 25(7), July, 2009. (text of paper)

J. McLaughlin, K. Lin, N. Zhang."Log-elastographic and non-marching full inversion schemes for shear modulus recovery from single frequency elastographic data", Inverse Problems, Vol 25(7), July, 2009.  (text of paper)

J. McLaughlin, D. Renzi, K. Parker, C. Wu. "Shear Wave Speed recovery using moving interference patterns obtained in sonoelastography experiments", JASA, Vol. 121 (4), 2007, pp.2438-4226.

J. McLaughlin, Daniel Renzi, Jeong-Rock Yoon. "Anisotropy reconstruction from wave fronts in transversely isotropic acoustic media" SIAM J. Appl. Math Vol. 68, Issue 1, 2007, pp. 24-42.

J. McLaughlin (with Daniel Renzi, Jeong-Rock Yoon, R. L. Ehman, A. Manducca), "Variance Controlled Shear Stiffness Images for MRE Data", IEEE International Symposium on Biomedical Imaging: Macro to Nano, 2006, pp. 960-963. (text of paper)

Joyce McLaughlin (with S. Dediu), "Recovering inhomogeneities in a waveguide using eigensystem decomposition", Inverse Problems, vol.22, June, 2006, pp.1227-1246. (text of paper)

J. McLaughlin (with D.Renzi) "Shear Wave Speed Recovery in Transient Elastography and Supersonic Imaging Using Propagating Fronts", Inverse Problems, 22 , pp. 681-706, (2006). (text of paper of paper with figures).

J. McLaughlin (with D.Renzi) "Using Level Set Based Inversion of Arrival Times To Recover Shear Wavespeed In Transient Elastography And Supersonic Imaging " Inverse Problems, 22 , pp. 707-725, (2006) (text of paper with figures).

J. McLaughlin and J.-R. Yoon, "Unique Identifiability of Elastic Parameters from Time Dependent Interior Displacement Measurement," Inverse Problems, 20, (1) 25-45, (2004). (text of paper with figures)

L. Ji and J. McLaughlin, "Recovery of the Lamé Parameter µ in Biological Tissues," Inverse Problems, 20, (1), 1-24, (2004). (text of paper with figures)

L. Ji and J. McLaughlin, "Using a Hankel Function Expansion to Identify Stiffness for the Boundary Impulse Input Experiment," AMS Contemporary Mathematics (CONM) Book Series: Proceedings of the Conference on Inverse Problems and Applications, eds. G. Allessandrini and G. Uhlman, Pisa, Italy; (2003). (text of paper with figures)

L. Ji, J. McLaughlin, D. Renzi, and J.-R. Yoon, "Interior Elastodynamics Inverse Problems: Shear Wave Speed Reconstruction in Transient Elastography," Inverse Problems, Special Issue on Imaging, 19, (6), S1-S29, (2003). (text of paper with figures)

B. Geist and J. McLaughlin, "Asymptotic Formulas for the Eigenvalues of the Timoshenko Beam," Journal of Mathematical Analysis and Applications, 253, 341-380, (2001). (text of paper)

J. McLaughlin, "Solving Inverse Problems with Spectral Data," Surveys on Solution Methods for Inverse Problems, eds. D. Colton, H. Engl, A. Louis, J. McLaughlin, and W. Rundell, Springer, New York, 169-194, (2000). (text of paper with figures)

O.H. Hald and J. McLaughlin, "Inverse Problems: Recovery of BV Coefficients from Nodes," Inverse Problems, 14, (2), 245-273, (1998). (text of paper without figures)

S. Wang and J. McLaughlin, "Recovery of a Vertically Stratified Seabed in Shallow Water," in Mathematical and Numerical Aspects of Wave Propagation, ed. J.A. DeSanto, SIAM, Philadelphia, 232-236, (1998). (text of paper with figures)

O.H. Hald and J. McLaughlin, Inverse Nodal Problems: Finding the Potential from Nodal Lines, American Mathematical Society (AMS) Memoir, 119, (572), (1996). (introduction)

(Additional publications on link below.)

Contact Information:

Joyce McLaughlin
(518) 276-6349

More Info:


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