About this Abstract |
Meeting |
2022 TMS Annual Meeting & Exhibition
|
Symposium
|
Algorithm Development in Materials Science and Engineering
|
Presentation Title |
Combining Discrete and Continuous in Time Stochastic Simulations in a Solid-solid Phase Field Simulation |
Author(s) |
Nicholas H. Julian, Enrique Martinez Saez, Jaime Marian |
On-Site Speaker (Planned) |
Nicholas H. Julian |
Abstract Scope |
Models driven by stochastic processes capture fluctuations found in natural systems which are absent in the solution of ordinary and partial differential equations. However, due to disparities between the characteristics of discrete and continuous-in-time stochastic processes, models are often restricted to quantities which are exclusively either discrete or continuous in time, such as the Poisson processes of kinetic Monte Carlo or the Brownian motion of fluctuation hydrodynamics. In addition to having distinct probability distributions, discrete and continuous in time processes impose different restrictions on the numerical integration schemes applied to them, e.g. the Stratonovich numerical integration scheme typically applied to multiplicative Gaussian white noise does not preserve the chain rule of differentiation when applied to multiplicative Poisson noise. In this presentation we explore the difference in distributions of stochastic processes driven by both Gaussian and Poisson multiplicative noises through an application of Marcus canonical integral to a solid-solid phase transformation. |
Proceedings Inclusion? |
Planned: |
Keywords |
Computational Materials Science & Engineering, Phase Transformations, Modeling and Simulation |