##### KMap

#### VOSviewer

##### 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

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