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- W4286292963 abstract "Stochastic modelling approaches are presented to capture random effects at multiple time and length scales. Random processes that occur at the microscale produce nondeterministic effects at the macroscale. Here we present three stochastic modeling approaches that describe random processes at microscopic length scales and map these processes to the macroscopic length scale. The first stochastic modeling approach is based upon a particle based numerical technique to solve a Stochastic Differential Equation (SDE) using an arbitrary diffusion process to capture random processes at the microstructural level. The second approach prescribes a Probability Density Function (PDF) for the drift and diffusion of the random variable derived using the forward and backward Kolmogorov equations. This method requires mean and drift evolution PDF transport equations. The third approach is the coupling of multiple random variables which are dependent on each other. The relationship of the PDFs and a coupling function, known as a copula, produces a Joint Probability Density Function (JPDF). These stochastic modeling approaches are implemented into a Multiple Component (MC) shock physics computational code and used to model statistical fracture and reactive flow applications." @default.
- W4286292963 created "2022-07-21" @default.
- W4286292963 creator A5063609870 @default.
- W4286292963 date "2022-06-01" @default.
- W4286292963 modified "2023-09-27" @default.
- W4286292963 title "Stochastic Modeling in a Multimaterial Continuum Mixture Shock Physics Code" @default.
- W4286292963 doi "https://doi.org/10.2172/1870769" @default.
- W4286292963 hasPublicationYear "2022" @default.
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