The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium, and we propose an unambiguous and physically sound definition.
Abstract
The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains [...]
Data loss is a common problem in intelligent transportation systems. And the tensor-based interpolation algorithm has obvious superiority in multidimensional data interpolation. In this paper, a Bayesian robust tensor decomposition method (MBRTF) based on MCMC (Markov chain Monte Carlo) algorithm is proposed. The underlying low CANDECOMP/PARAFAC (CP) rank tensor captures the global information and the sparse tensor captures local information (also regarded as anomalous data), which achieves a reliable prediction of missing terms. The low CP rank tensor is modeled by linear interrelationships among multiple latent factors, and the sparsity of the columns on the latent factors is achieved through a hierarchical prior approach, while the sparse tensor is modeled by a hierarchical view of the Student-t distribution. It is a challenge for traditional tensor-based interpolation methods to maintain a stable performance under different missing rates and non-random missing scenarios. The MBRTF algorithm is an effective multiple interpolation algorithm that not only derives unbiased point estimates, but also provides a robust method for the uncertainty measures of these missing values.
Abstract
Data loss is a common problem in intelligent transportation systems. And the tensor-based interpolation algorithm has obvious superiority in multidimensional data interpolation. In this paper, a Bayesian robust tensor decomposition [...]