Morphology transitions in three-dimensional domain growth with Gaussian random fields

Three-dimensional numerical simulation of temperature and flow fields in a Czochralski growth of germanium

For a Czochralski growth of Ge crystal, thermal fields have been analysed numerically using the three-dimensional finite volume method (FLUENT package). The arrangement used in a real Czochralski crystal growth lab included a graphite crucible, heat shield, heating device, thermal insulation and chamber including two gas outlets. We have considered two cases for calculations, which are configur...

Skew-Gaussian Random Fields

Skewness is often present in a wide range of spatial prediction problems, and modeling it in the spatial context remains a challenging problem. In this study a skew-Gaussian random field is considered. The skew-Gaussian random field is constructed by using the multivariate closed skew-normal distribution, which is a generalization of the traditional normal distribution. We present an Metropolis...

Singularities in Gaussian Random Fields

Gaussian Process Random Fields

Gaussian processes have been successful in both supervised and unsupervised machine learning tasks, but their computational complexity has constrained practical applications. We introduce a new approximation for large-scale Gaussian processes, the Gaussian Process Random Field (GPRF), in which local GPs are coupled via pairwise potentials. The GPRF likelihood is a simple, tractable, and paralle...

Credit Risk Modeling with Gaussian Random Fields

The literature on credit risk consists of different approaches in modeling the behavior of defaultable bonds. The structural approach is based on the evolution of the firm value to determine default and recovery. In contrast, the more recently developed intensity-based models specify the default time exogenously. In this approach the defaultable yield curve results from the risk-free yield curv...