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Research Areas
- Analysis and modeling of complex phenomena.
- Multiscale analysis for partial differential equations and integral equations.
- Homogenization methods and optimal design of composite materials.
- Computational mechanics of heterogeneous media, nonlocal theories, and fracture and fragmentation in composite materials.
- Mathematics of climate, and fracture and melting processes of sea-ice.
- Computer vision, and image processing and analysis.
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Publications
- Effective Conductivities of Thin-Interphase Composites,
Journal of the Mechanics and Physics of Solids,
doi:10.1016/j.jmps.2013.08.022, 2013. (With G. W. Milton).
- Transition in the fractal geometry of Arctic melt ponds,
The Cryosphere, 6, 1157-1162,
doi:10.5194/tc-6-1157-2012, 2012.
(With C. Hohenegger, K. Steffen, D. K. Perovich, and K. M. Golden).
- New bounds on local strain fields inside random heterogeneous materials,
Mechanics of Materials, 53, 111-122,
doi:10.1016/j.mechmat.2012.05.007, 2012.
(With R. Lipton).
- Multiscale dynamics of heterogeneous media in the peridynamic formulation,
Journal of Elasticity, 106(1), 71-103,
doi:10.1007/s10659-010-9291-4, 2012.
(With R. Lipton).
- Optimal lower bounds on local stress inside random media,
SIAM Journal on Applied Mathematics, 70(4), 1260-1282,
doi:10.1137/080744967, 2009.
(With R. Lipton).
- Multiscale analysis of fiber-reinforced composites in the peridynamic formulation. IMA Preprint Series 2241, Institute for Mathematics and its Applications,
University of Minnesota, February 2009. (With R. Lipton).
(link)
- Spectral upscaling for multiscale sea ice structures in the climate system.
(With N. B. Murphy, C. S. Sampson, C. Hohenegger, E. Cherkaev, D. K. Perovich, H. Eicken, and K. M. Golden).
(preprint).
- A general formulation for nonlocal calculus with applications.
(With M. Gunzburger).
(preprint).
- Nonlocal interface conditions for nonlocal continuum mechanics.
(With M. Gunzburger).
(preprint).
- Coordinate transformations of two-scale convergent sequences.
(preprint).
- Multiscale peridynamics: Macroscopic discontinuous forces.
(With R. Lipton and T. Mengesha).
(preprint).
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Recent Conferences and Workshops
- [2013] Joint Mathematics Meetings,
San Diego, California.
- [2012] 2012 Ocean Sciences Meeting, Salt Lake City, Utah.
- [2012] Large Scale Multimedia Search, Institute for Pure and Applied Mathematics (IPAM), Los Angeles.
- [2011] Mathematics and Climate Research Network Annual Meeting, Chapil Hill, North Carolina.
- [2011] New Kind of Science Summer School, Boston.
- [2011] Joint Mathematics Meetings, American Mathematical Society (AMS), New Orleans.
- [2010] Modeling and Mathematics of Sea Ice, Institute for Pure and Applied Mathematics (IPAM), University of California, Los Angeles.
- [2009] 10TH US National Congress On Computational Mechanics (USNCCM10), Columbus, Ohio.
- [2009] Stochastic Multiscale Methods: Mathematical Analysis and Algorithms, University of Southern California, Los Angeles.
- [2008] SIAM Conference on Mathematical Aspects of Materials Science (MS08), Philadelphia.
- [2007] SIAM Conference on Analysis of Partial Differential Equations (PD07), Mesa, Arizona.
- [2007] Workshop on Modeling, Analysis and Simulation of Multiscale Nonlinear Systems, Oregon State University, Corvallis, Oregon.
- [2007] DOE Summer School in Multiscale Mathematics and High Performance Computing, Oregon State University, Corvallis, Oregon.
- [2007] Workshop on Computational and Mathematical Aspects of Materials and Fluids (CAM2007), Ames, Iowa.
- [2006] Recent Advances in Nonlinear PDEs and Applications: A workshop in honor of Peter D. Lax and Louis Nirenberg, Toldeo (LN2006), Spain.
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