We will discuss, theoretically and experimentally, the existence of a limit to possibility arbitrarily increasing electromagnetic confinement in polaritonic systems, where strongly sub-wavelength fields can excite continuum high-momenta propagative magnetoplasmons. This leads peculiar nonlocal effects, as certain features disappear system enters regime discrete-to-continuum strong coupling. wel...

In this paper we review recent developments in blending methods for atomistic-to-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased inter...

Nonlocal continua have been proposed to offer a more realistic model for the electrostatic response of solutions such as the electrolyte solvents prominent in biology and electrochemistry. In this work, we review three nonlocal models based on the Landau–Ginzburg framework which have been proposed but not directly compared previously, due to different expressions of the nonlocal constitutive re...

*Correspondence: [email protected] School of Mathematics and Statistics, Shandong University, Weihai, Shandong 264209, P.R. China Abstract This paper studies the spectral problem of a class of fractional differential equations from nonlocal continuummechanics. By applying the spectral theory of compact self-adjoint operators in Hilbert spaces, we show that the spectrum of this problem consists of ...

An algorithm is developed for performing calculations for the nonlocal electrostatic solvation theory of an ion in a cavity, accounting for electrostatic boundary conditions. The latter implies an induced charge distribution on the cavity surface as well as an induced volume charge distribution in the medium. This approach is validated by a variational derivation which also provides a general e...

The accuracy of the quasicontinuum method is analyzed using a series of models with increasing complexity. It is demonstrated that the existence of the ghost force may lead to large errors. It is also shown that the ghost force removal strategy proposed by E, Lu and Yang leads to a version of the quasicontinuum method with uniform accuracy.