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Courses
- BHSBanach and Hilbert Spaces
- AODEAnalysis of Ordinary Differential Equations
- IODEIntroduction to Ordinary Differential Equations
- PMAMPrinciples and Methods of Applied Mathematics
- GDGGlobal Differential Geometry
- TFAMITheoretical Foundations of Applied Mathematics I
- PMProbability Math
- PAPrinciples of Analysis
- ILAInroduction to Linear Algebra
- CIICalculus II
- TAMTopics in Applied Mathematics
- IMPIntroduction to Mathematical Physics
- TFAMIITheoretical Foundations of Applied Mathematics II
- RAReal Analysis
Grants
- NSF-BSF: Nonlinearity, Randomness, and Dynamics: Vistas into the Extreme Mechanics of Non-Euclidean sheets
Principal Investigator (PI)
2021
$240.0K
Active - Exotic Continua: Geometry, Topology and Mechanics in Soft Matter
Principal Investigator (PI)
2020
$300.0K
Active - Collaborative Research: GCR: Collective Behavior and Patterning of Topological Defects: from String Theory to Crystal Plasticity
Principal Investigator (PI)
2020
$194.5K
Active - The Role of Weak forces in the self-similar buckling of non-Euclidean elastic sheets
Co-Investigator (COI)
2019
$4.0K
- Exotic Continua: Geometry, Topology, Dynamics and Growth in Soft Matter
Principal Investigator (PI)
2018
$73.4K
- Rough Solutions in Geometry, Physics and Mechanics
Principal Investigator (PI)
2017
$32.8K
- Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)
Co-Investigator (COI)
2011
$650.5K
- Collaborative Research: Lagrangian Data Blending for Hurricane Tracking and Source Estimation
Principal Investigator (PI)
2011
$196.7K
- Experimental and Theoretical Study of Actively Deforming Sheets
Principal Investigator (PI)
2009
$38.4K
- Developing Robust Techniques for the Analysis of Multiple-Scale Behaviors
Principal Investigator (PI)
2008
$259.9K
News
- UA Faculty Part of Major Study of Gulf Oil Spill
2011
Publications (65)
Recent
- The universal behavior of modulated stripe patterns
2023
- An SBV relaxation of the Cross-Newell energy for modeling stripe patterns and their defects
2022
- Corrigendum: Target patterns in a 2D array of oscillators with nonlocal coupling (2018 Nonlinearity 31 4162)
2022
- Computing with non-orientable defects: Nematics, smectics and natural patterns
2021
- Pattern dark matter and galaxy scaling relations
2021
- Remarks on the range and multiple range of a random walk up to the time of exit
2021
- Distributed Branch Points and the Shape of Elastic Surfaces with Constant Negative Curvature
2021
- Disk galaxies and their dark halos as self-organized patterns
2021
- Nature’s forms are frilly, flexible, and functional
2021
- A Modified Split Bregman Algorithm for Computing Microstructures Through Young Measures
2021
- Mechanics of moving defects in growing sheets: 3-d, small deformation theory
2020
- Pattern universes
2019
- On the Growth of a Superlinear Preferential Attachment Scheme
2019
- Buckling sheets open a door to understanding self-organization in soft matter
2019
- On the unusual swimming gaits of sea-slugs.
2019
- Modelling the mass exchange dynamics of oceanic surface and subsurface oil
2018
- Target patterns in a 2D array of oscillators with nonlocal coupling
2018
- Target Patterns in a 2-D Array of Oscillators with Nonlocal Coupling
2018
- Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport
2018
- Elastic Sheets, Phase Surfaces, and Pattern Universes
2017
- Elastic sheets, phase surfaces and pattern universes
2016
- Stochastic Longshore Current Dynamics
2016
- A scaling limit for the degree distribution in sublinear preferential attachment schemes
2016
- Dimension reduction for systems with slow relaxation
2016
- Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets
2016
- Displacement Data Assimilation
2016
- An Oil Fate Model for Shallow-Waters
2015
- Research Overview of the Consortium for Advanced Research on Transport of Hydrocarbon in the Environment (CARTHE)
2014
- How can you tell whether Earth is warming Up
2014
- Optical beam shaping and diffraction free waves: A variational approach
2014
- Nearshore sticky waters
2014
- Sharp interfaces in two-dimensional free boundary problems: Interface calculation via matched conformal maps
2014
- Defining a trend for time series using the intrinsic time-scale decomposition
2014
- Shape transitions in hyperbolic non-Euclidean plates
2013
- Asymptotic analysis of weakly nonlinear Bessel–Gauß beams
2013
- Propagation of Gaussian-apodized paraxial beams through first-order optical systems via complex coordinate transforms and ray transfer matrices.
2012
- Defects and boundary layers in non-Euclidean plates
2012
- Asymptotic analysis of weakly nonlinear Bessel-Gauss beams
2011
- Experimental study of shape transitions and energy scaling in thin non-euclidean plates
2011
- The 2D Selective Withdrawal Transition: Analogies with MEM Systems
2011
- Shape Selection in Non-Euclidean Plates
2010
- A Variational Theory for Point Defects in Patterns
2009
- Lower bounds for the energy in a crumpled elastic sheet—a minimal ridge
2004
- Discrete charges on a two dimensional conductor
2004
- Trapping of vibrational energy in crumpled sheets
2002
- Singularities, structures, and scaling in deformed m-dimensional elastic manifolds.
2002
- Pattern selection in extended periodically forced systems: A continuum coupled map approach
2001
- Front propagation of spatiotemporal chaos
2001
- Continuum Coupled Maps: a Model for Patterns in Vibrated Sand
2001
- Limitations on the smooth confinement of an unstretchable manifold
2000
- Diffusion, attraction and collapse
1999
- Noise stabilization of self-organized memories.
1999
- Cones, creases and crumpled sheets
1998
- Anomalous diffusion in bounded temporally irregular flows
1998
- Spatiotemporal Bifurcation Phenomena with Temporal Period Doubling: Patterns in Vibrated Sand
1998
- Self-organized short-term memories
1997
- Lévy Flights in Fluid Flows with no Kolmogorov-Arnold-Moser Surfaces
1997
- On-off intermittency: Power spectrum and fractal properties of time series
1996
- Riddling bifurcation in chaotic dynamical systems
1996
- Transitions to bubbling of chaotic systems
1996
- Bubbling transition
1996
- Riddling Bifurcation in Chaotic Dynamical Systems.
1996
- Blowout bifurcations: Symmetry breaking of spatially symmetric chaotic states
1995
- Characterization of on-off intermittent time series
1995
- Topology of event horizons and topological censorship
1995