Abstract: Using Fourier transform and based on the Mindlin's 2nd gradient model that involves two length scale parameters, the Green's function, the Eshelby tensor, and the Eshelby-like tensor for a spherical inclusion are derived. It is proved that the Eshelby tensor consists of two parts; the classical Eshelby tensor and a gradient part including the length scale parameters which enable the interpretation of the size effect. When the strain gradient is not taken into account, the obtained Green's function and Eshelby tensor reduce to its analogue based on the classical elasticity. The Eshelby tensor in and outside the inclusion, the volume average of the gradient part and the Eshelby-like tensor are explicitly obtained. Unlike the classical Eshelby tensor, the results show that the components of the new Eshelby tensor vary with the position and the inclusion dimensions. It is demonstrated that the contribution of the gradient part should not be neglected.
Abstract: A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.
Abstract: In this paper electrical characteristics of various kinds
of multiple-gate silicon nanowire transistors (SNWT) with the
channel length equal to 7 nm are compared. A fully ballistic quantum
mechanical transport approach based on NEGF was employed to
analyses electrical characteristics of rectangular and cylindrical
silicon nanowire transistors as well as a Double gate MOS FET. A
double gate, triple gate, and gate all around nano wires were studied
to investigate the impact of increasing the number of gates on the
control of the short channel effect which is important in nanoscale
devices. Also in the case of triple gate rectangular SNWT inserting
extra gates on the bottom of device can improve the application of
device. The results indicate that by using gate all around structures
short channel effects such as DIBL, subthreshold swing and delay
reduces.