Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Surface modeling with oriented particle systems
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Image Sharpening by Flows Based on Triple Well Potentials
Journal of Mathematical Imaging and Vision
Partial and approximate symmetry detection for 3D geometry
ACM SIGGRAPH 2006 Papers
ACM SIGGRAPH 2007 papers
A context-sensitive active contour for 2D corpus callosum segmentation
Journal of Biomedical Imaging
Computational Approaches for Automatic Structural Analysis of Large Biomolecular Complexes
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Automatic ultrastructure segmentation of reconstructed CryoEM maps of icosahedral viruses
IEEE Transactions on Image Processing
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Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose a differential geometry-based multiscale paradigm to model complex biomolecule systems. In our approach, the differential geometry theory of surfaces and geometric measure theory are employed as a natural means to couple the macroscopic continuum domain of the fluid mechanical description of the aquatic environment from the microscopic discrete domain of the atomistic description of the biomolecule. A multiscale action functional is constructed as a unified framework to derive the governing equations for the dynamics of different scales. We show that the classical Navier-Stokes equation for the fluid dynamics and Newton's equation for the molecular dynamics can be derived from the least action principle. These equations are coupled through the continuum-discrete interface whose dynamics is governed by potential driven geometric flows.