• Publications
  • Influence
Vorticity and Incompressible Flow: Index
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. Although theExpand
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Navier-stokes, fluid dynamics, and image and video inpainting
We introduce a class of automated methods for digital inpainting. Expand
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Vorticity and incompressible flow
Preface 1. An introduction to vortex dynamics for incompressible fluid flows 2. The vorticity-stream formulation of the Euler and the Navier-Stokes equations 3. Energy methods for the Euler and theExpand
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Self-propelled particles with soft-core interactions: patterns, stability, and collapse.
Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design ofExpand
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Inpainting of Binary Images Using the Cahn–Hilliard Equation
A model for binary image inpainting based on the Cahn-Hilliard equation, which allows for fast, efficient in painting of degraded text, text reparation, road interpolation, and super-resolution. Expand
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Motivated by empirical observations of spatio-temporal clusters of crime across a wide variety of urban settings, we present a model to study the emergence, dynamics, and steady-state properties ofExpand
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Global regularity for vortex patches
We present a proof of Chemin's [4] result which states that the boundary of a vortex patch remains smooth for all time if it is initially smooth.
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A Nonlocal Continuum Model for Biological Aggregation
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal. For the case of one spatial dimension, we study theExpand
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Linear stability and transient growth in driven contact lines
Fluid flowing down an inclined plane commonly exhibits a fingering instability in which the contact line corrugates. We show that below a critical inclination angle the base state before theExpand
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The lubrication approximation for thin viscous films: Regularity and long-time behavior of weak solutions
We consider the fourth-order degenerate diffusion equation, in one space dimension. This equation, derived from a lubrication approximation, models the surface-tension-dominated motion of thinExpand
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