We study the weight dynamics of the floating-gate pFET synapse and the effects of the pFET’s gate and drain voltages on these dynamics. We show that we can derive a weight update rule such that the equilibrium weight value is proportional to the correlation between the gate and drain voltages. In particular, we want a rule of the form _ = + [ ], where is a voltage signal on the gate terminal an...

The purpose of this article is to present a multiscale finite element method that captures nanoscale surface stress effects on the dynamic mechanical behavior of nanomaterials. The method is based upon arguments from crystal elasticity, i.e. the Cauchy–Born rule, but significantly extends the capability of the standard Cauchy–Born rule by accounting for critical nanoscale surface stress effects...

The Cauchy-Born rule postulates that when a monatomic crystal is subjected to a small linear displacement of its boundary, then all atoms will follow this displacement. In the absence of previous mathematical results, we study the validity of this rule in the model case of a 2D cubic lattice interacting via harmonic springs between nearest and diagonal neighbours. Our main result is that for fa...

The Cauchy-Born rule provides a crucial link between continuum theories of elasticity and the atomistic nature of matter. In its strongest form it says that application of affine displacement boundary conditions to a monatomic crystal will lead to an affine deformation of the whole crystal lattice. We give a general condition in arbitrary dimensions which ensures the validity of the Cauchy-Born...

ABSTRACT. We extend a recent result on third and fourth-order Cauchy-Euler equations by establishing the Hyers-Ulam stability of higher-order linear non-homogeneous Cauchy-Euler dynamic equations on time scales. That is, if an approximate solution of a higher-order Cauchy-Euler equation exists, then there exists an exact solution to that dynamic equation that is close to the approximate one. We...