Nanobeams with Internal Discontinuities: A Local/Nonlocal Approach

The aim of the present work is to extend the two-phase local/nonlocal stress-driven integral model (SDM) to the case of nanobeams with internal discontinuities: as a matter of fact, the original formulation avoids the presence of any discontinuities. Consequently, here, for the first time, the problem of an internal discontinuity is addressed by using a convex combination of both local and nonlocal phases of the model by introducing a mixture parameter. The novel formulation here proposed was validated by considering six case studies involving different uncracked nanobeams by varying the constrains and the loading configurations, and the effect of nonlocality on the displacement field is discussed. Moreover, a centrally-cracked nanobeam, subjected to concentrated forces at the crack half-length, was studied. The size-dependent Mode I fracture behaviour of the cracked nanobeam was analysed in terms of crack opening displacement, energy release rate, and stress intensity factor, showing the strong dependency of the above fracture properties on both dimensionless characteristic length and mixture parameter values.

Poincaré and Log–Sobolev Inequalities for Mixtures

This work studies mixtures of probability measures on R n and gives bounds on the Poincaré and the log–Sobolev constants of two-component mixtures provided that each component satisfies the functional inequality, and both components are close in the χ 2 -distance. The estimation of those constants for a mixture can be far more subtle than it is for its parts. Even mixing Gaussian measures may produce a measure with a Hamiltonian potential possessing multiple wells leading to metastability and large constants in Sobolev type inequalities. In particular, the Poincaré constant stays bounded in the mixture parameter, whereas the log–Sobolev may blow up as the mixture ratio goes to 0 or 1. This observation generalizes the one by Chafaï and Malrieu to the multidimensional case. The behavior is shown for a class of examples to be not only a mere artifact of the method.

Genetic grey wolf optimization and C-mixture for collaborative data publishing

Data publishing is an area of interest in present day technology that has gained huge attention of researchers and experts. The concept of data publishing faces a lot of security issues, indicating that when any trusted organization provides data to a third party, personal information need not be disclosed. Therefore, to maintain the privacy of the data, this paper proposes an algorithm for privacy preserved collaborative data publishing using the Genetic Grey Wolf Optimizer (Genetic GWO) algorithm for which a C-mixture parameter is used. The C-mixture parameter enhances the privacy of the data if the data does not satisfy the privacy constraints, such as the [Formula: see text]-anonymity, [Formula: see text]-diversity and the [Formula: see text]-privacy. A minimum fitness value is maintained that depends on the minimum value of the generalized information loss and the minimum value of the average equivalence class size. The minimum value of the fitness ensures the maximum utility and the maximum privacy. Experimentation was carried out using the adult dataset, and the proposed Genetic GWO outperformed the existing methods in terms of the generalized information loss and the average equivalence class metric and achieved minimum values at a rate of 0.402 and 0.9, respectively.

Rainfall-Rate Estimation Using Gaussian Mixture Parameter Estimator: Training and Validation

This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.