We construct self-similar functions and linear operators to deduce a self-similar variant of the Laplacian operator and of the D'Alembertian wave operator. The exigence of self-similarity as a symmetry property requires the introduction of nonlocal particle-particle interactions. We derive a self-similar linear wave operator describing the dynamics of a quasicontinuous linear chain of infinite ...

Aquaporins are integral membrane proteins from a larger family of major intrinsic proteins that formpores in the membrane of biological cells. Aquaporins form tetramers in the cell membrane with eachmonomer acting as a water channel.In this research, the AQP4 tetramer was modeled from its PDBstructure file, then, we have performed the intraction of aquaporin4 in different temperatures (298k,300...

in this research, the surface stress effect on the nonlocal vibration of piezoelectric square plate reinforced by single walled carbon nanotubes (swcnts) based on classical plate theory (cpt) and first order shear deformation theory (fsdt) is presented. the elastic properties of piezoelectric nanocomposite plate are estimated by eshelby-mori-tanaka and the extended mixture rule approaches. the ...

At what characteristic length scale does classical continuum elasticity cease to accurately describe small deformation mechanical behavior? The two dominant physical mechanisms that lead to size dependency of elastic behavior at the nanoscale are surface energy effects and nonlocal interactions. The latter arises due to the discrete structure of matter and the fluctuations in the interatomic fo...

The respective roles of local and nonlocal interactions in the thermodynamic cooperativity of proteins are investigated using continuum (off-lattice) native-centric Gō-like models with a coarse-grained Ca chain representation. We study a series of models in which the (local) bondand torsion-angle terms have different strengths relative to the (nonlocal) pairwise contact energy terms. Conformati...

Biological aggregations such as insect swarms and bird flocks may arise from a combination of social interactions and environmental cues. We focus on nonlocal continuum equations, which are often used to model aggregations, and yet which pose significant analytical and computational challenges. Beginning with a particular nonlocal aggregation model [Topaz et al., Bull. Math. Bio., 2006], we der...