James Scott
Auburn University, AL·Mathematics & Statistics
Many systems are shaped by interactions that reach across long distances, not just between immediate neighbors. A crack spreading through a solid, processes inside living cells, and the spread of influence through a social network all work this way.
- Fields
Mathematics & Statistics
Engineering
- Topics
nonlocal models
variational analysis
functional analysis
- Grants
- 1 known grant, through Aug 2029
What they work on
- Establish qualitative properties and convergence results for dynamics on graphons, the limit objects that describe very large networks, using variational and functional analysis.
- Address open problems in nonlocal continuum mechanics, where material points interact across distances, combining variational analysis with asymptotic methods to justify how the models capture fine-scale behavior.
- Develop rigorous variational analysis of nonlocal models of brittle fracture, so the models can accurately describe crack formation and other discontinuous material responses.
- Develop new analytical tools in function space theory and operator theory that emerge from the study of these nonlocal models.
More about the research
Mathematicians describe such systems with nonlocal models, equations in which what happens at one point depends on conditions far away. These models can capture sudden jumps, long-range effects and fine-scale structure that classical partial differential equations handle poorly. Their mathematical foundations are still incomplete. A central difficulty is that these systems contain quantities operating at very different scales, and each of them still affects the whole system.
Why it matters
Engineers and scientists already use nonlocal models to predict material damage and fracture and to analyze large networks. Firmer mathematical foundations could make those predictions more trustworthy. The results are expected to inform how such models are implemented in solid mechanics, damage prediction and large-scale network science.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Pablo Raúl Stinga
Iowa State University, IA·Mathematics & Statistics
Establish the analytical theory of surfaces of minimum mean curvature variation, smoothly bending surfaces used in data interpolation, image repair and hull design, including well-posedness and regularity of their equations.
Burak Aksoylu
Texas A&M University-San Antonio, TX·Mathematics & Statistics
Use machine learning to improve iterative local-to-nonlocal coupling, so that peridynamics models only the region where fracture occurs and cheaper local models handle the rest.
Artem Zvavitch
Kent State University at Kent, OH·Mathematics & Statistics
Prove Brunn–Minkowski and isoperimetric-type inequalities for principal eigenvalues of real Monge–Ampère operators on convex bodies, using convex geometry and symmetrization.
The school
Auburn University: 11 labs on PI Pages, $394M a year on research, 327 research doctorates a year.
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