A Stochastic Phase-Field Model Determined from Molecular Dynamics

• Phase-field
• molecular dynamics
• coarse graining
• Smoluchowski dynamics
• stochastic differential equation

A stochastic collocation method for elliptic partial differential equations with random input data

• Stochastic collocation methods
• partial differential equations with random inputs
• Finite elements
• Uncertainty Quantification
• convergence rates
• multivariate polynomial approx- imation
• Smolyak approximation
• anisotropic sparse approximation

Adaptive weak approximation of reflected and stopped diffusions

• Adaptive weak approximation of reflected and stopped diffusions

Taylor expansion and discretization errors in Gaussian beam superposition

• Wave propagation
• High frequency
• Asymptotic approximation
• Gaussian beam superposition
• Accuracy
• error estimates