There is growing interest in applying phase field methods as quantitative tools in materials discovery and development.However,large driving forces,common in many materials systems,lead to unstable phase field profile...There is growing interest in applying phase field methods as quantitative tools in materials discovery and development.However,large driving forces,common in many materials systems,lead to unstable phase field profiles,thus requiring fine spatial and temporal resolution.This demands more computational resources,limits the ability to simulate systems with a suitable size,and deteriorates the capability of quantitative prediction.Here,we develop a strategy to map the driving force to a constant perpendicular to the interface.Together with the third-order interpolation function,we find a stable phase field profile that is independent of the magnitude of the driving force.The power of this approach is illustrated using three models.We demonstrate that by using the driving force extension method,it is possible to employ a grid size orders of magnitude larger than traditional methods.This approach is general and should apply to many other phase field models.展开更多
We use a generalized scaling invariance of the dispersion-managed nonlinear Schrodinger equation to derive an approximate function for strongly dispersionmanaged solitons.We then analyze the regime in which the approx...We use a generalized scaling invariance of the dispersion-managed nonlinear Schrodinger equation to derive an approximate function for strongly dispersionmanaged solitons.We then analyze the regime in which the approximation is valid.Finally,we present a method for extracting the underlying soliton part from a noisy pulse,using the resulting approximate formula.展开更多
基金This work is sponsored by the Office of Naval Research(ONR)under grant N00014-20-1-2327.Additional support is provided in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost,the Office for Research,and Northwestern University Information Technology.
文摘There is growing interest in applying phase field methods as quantitative tools in materials discovery and development.However,large driving forces,common in many materials systems,lead to unstable phase field profiles,thus requiring fine spatial and temporal resolution.This demands more computational resources,limits the ability to simulate systems with a suitable size,and deteriorates the capability of quantitative prediction.Here,we develop a strategy to map the driving force to a constant perpendicular to the interface.Together with the third-order interpolation function,we find a stable phase field profile that is independent of the magnitude of the driving force.The power of this approach is illustrated using three models.We demonstrate that by using the driving force extension method,it is possible to employ a grid size orders of magnitude larger than traditional methods.This approach is general and should apply to many other phase field models.
文摘We use a generalized scaling invariance of the dispersion-managed nonlinear Schrodinger equation to derive an approximate function for strongly dispersionmanaged solitons.We then analyze the regime in which the approximation is valid.Finally,we present a method for extracting the underlying soliton part from a noisy pulse,using the resulting approximate formula.
