
Surface Fluctuating Hydrodynamics Methods for the DriftDiffusion Dynamics of Particles and Microstructures within Curved Fluid Interfaces
We introduce fluctuating hydrodynamics approaches on surfaces for captur...
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Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving LeastSquares (GMLS) Approach
We utilize generalized moving least squares (GMLS) to develop meshfree t...
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SurfNet: Generating 3D shape surfaces using deep residual networks
3D shape models are naturally parameterized using vertices and faces, , ...
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DriftDiffusion Dynamics and Phase Separation in Curved Cell Membranes and Dendritic Spines: Hybrid DiscreteContinuum Methods
We develop methods for investigating protein driftdiffusion dynamics in...
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Intrinsic Integration
If we wish to integrate a function hĪ©ā^nā along a single Tlevel surfac...
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Parametrizing FlatFoldable Surfaces with Incomplete Data
We propose a novel way of computing surface folding maps via solving a l...
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Antialiasing for fused filament deposition
Layered manufacturing inherently suffers from staircase defects along su...
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FirstPassage Time Statistics on Surfaces of General Shape: Surface PDE Solvers using Generalized Moving Least Squares (GMLS)
We develop numerical methods for computing statistics of stochastic processes on surfaces of general shape with driftdiffusion dynamics dX_t = a(X_t)dt + b(X_t)dW_t. We consider on a surface domain Ī© the statistics u(š±) = š¼^š±[ā«_0^Ļ g(X_t)dt ] + š¼^š±[f(X_Ļ)] with the exit stopping time Ļ = inf_t {t > 0  X_t āĪ©}. Using Dynkin's formula, we compute statistics by developing highorder Generalized Moving Least Squares (GMLS) solvers for the associated surface PDE boundaryvalue problems. We focus particularly on the mean First Passage Times (FPTs) given by the special case f = 0, g = 1 with u(š±) = š¼^š±[Ļ]. We perform studies for a variety of shapes showing our methods converge with highorder accuracy both in capturing the geometry and the surface PDE solutions. We then perform studies showing how FPTs are influenced by the surface geometry, drift dynamics, and spatially dependent diffusivities.
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