We introduce a new nonlocal calculus framework which parallels (and includes as a limiting case) the differential setting. The integral operators introduced have convolution structures and converge as the horizo
Keywords: acceleration gradient; atomic simulation; modified couple-stress theory; static and dynamic length scales. 1 Introduction Phonons, which describe vibrational motions in con- densed matter, are collective excitations in the periodic elastic arrangement of atoms [1]. Phonon propagation in ...
In this paper, we develop high order interpolants, from any basis that constitutes a partition of unity, which satisfy these integral relations exactly. The resulting gradient, curl and divergence conforming spaces have the...doi:10.1007/978-3-319-01601-6_23René Hiemstra...
These are used to construct tensor product solution spaces which satisfy the generalized Stokes theorem, as well as the annihilation of the gradient operator by the curl and the curl by the divergence. This allows for the exact conservation of first order moments (mass, vorticity), as well as...
The resulting gradient, curl and divergence conforming spaces have the property that the conservation laws become completely independent of the basis functions. Hence, they are exactly satisfied at the coarsest level of discretization and on arbitrarily curved meshes. As an illustration we apply our ...
The aim of this study was to quantify the distribution pattern of soil biological properties along a small (up to 100 m) topographic gradient and to identify how these biological properties are related to the chemical, physical, and topographic properties of soil in a fragment of the Atlantic ...