Fractional order models and discretized problems are
nonlocal. They provide better descriptions of and, ultimately, deeper insights into underlying complex phenomena in sciences and technologies.
The main approaches used to describe the small-scale effect in the analysis of nanostructures include
nonlocal continuum mechanics and the atomic theory of lattice dynamics [1].
The application of
nonlocal continuum mechanics allowing for the small scale effects to the vibrational analysis of nanomaterials has been recommended by many research workers.
Each provided detailed budget information for 2015, including labor, payments to local and
nonlocal artists, operations, administration, programming, facilities and capital expenditures/asset acquisition.
Local and
nonlocal sources of soot have different influences on radiative forcing--changing the Earth's energy balance--in its destination region.
In the EPR paper (Einstein, Podolsky and Rosen, 1935), the completeness of quantum theory implies
nonlocal interactions.
We consider
nonlocal singularly perturbed boundary value problem
The papers in this special issue cover the following topics: (i) static analysis, buckling, and vibration of micro-, meso-, and nanostructures; (ii) nanobeams, nanoshells, and nanoplates; (iii) micro-, meso-, and nanostructural effects; (iv) size effects; (v) microelectromechanical systems (MEMS); (vi) nanoelectromechanical systems (NEMS); (vii)
nonlocal theory applied to micro-, meso-, and nanoscales; (viii) nanocomposite materials; (ix) carbon nanotubes; (x) micro- and mesomechanics of concrete; (xi) functionally graded materials; (xii) piezo and magnetic elastic materials; (xiii) homogenization techniques.
These PSNRs indicate that the method proposed in this paper is superior to bilateral filtering, the adaptive wavelet threshold algorithm,
nonlocal means [20] algorithm, and BM3D [21] method.
The
nonlocal BC is an exact boundary that does not require the additional computational space in the form of absorbing layers.