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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 the
Navier-stokes, fluid dynamics, and image and video inpainting
TLDR
A class of automated methods for digital inpainting using ideas from classical fluid dynamics to propagate isophote lines continuously from the exterior into the region to be inpainted is introduced.
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 the
Self-propelled particles with soft-core interactions: patterns, stability, and collapse.
TLDR
For the first time, a coherent theory is presented, based on fundamental statistical mechanics, for all possible phases of collective motion of driven particle systems, to predict stability and morphology of organization starting from the shape of the two-body interaction.
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.
Inpainting of Binary Images Using the Cahn–Hilliard Equation
TLDR
The use of a model for binary inpainting based on the Cahn-Hilliard equation is outlined, which allows for fast, efficient inPainting of degraded text, as well as super-resolution of high contrast images.
A STATISTICAL MODEL OF CRIMINAL BEHAVIOR
TLDR
This work focuses on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker.
A Nonlocal Continuum Model for Biological Aggregation
TLDR
A continuum model for biological aggregations in which individuals experience long-range social attraction and short-range dispersal is constructed, and energy arguments are used to understand the nonlinear selection of clump solutions, and to predict the internal density in the large population limit.
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 the
A Variational Approach for Sharpening High Dimensional Images
TLDR
A new variational method for sharpening high dimensional spectral images with the help of a high resolution gray-scale image while preserving the spectral characteristics used for classification and identification tasks is proposed.
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