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In this paper, we investigate the impact of the electromagnetic scattering caused by other objects in nonfree space on the time-averaged force exerted upon a Rayleigh particle, which is conventionally referred to as the backaction effect. We show that backaction modifies the gradient force, radiation pressure, and spin curl force exerted upon Rayleigh particles, and gives rise to an additional force term which stems from the gradient of the backaction field in nonfree space. As a numerical example, we look into the trapping of a dielectric nanoparticle at the center of curvature of a spherical mirror, and study how it is affected by the backaction effect. We show that backaction can enhance... 

Peridynamics is a nonlocal theory of solid mechanics which is suitable for modeling discontinuities and fractures without requiring external theories. In the original peridynamic equation of motion, the internal forces are integrated over the entire domain of the body. Although this equation complies perfectly with physical principles, its heavy calculations make it practically impossible to use. To avoid this difficulty, we can benefit from a special case of the peridynamic equation of motion in which the integration domain of the internal forces is limited to the family of particles. A limitation of this special equation, which is the most common equation in the peridynamic literature, is...