Continuum modeling of many physical systems typically assumes that the spatial extent of an atom is small compared to the quantities of interest and can therefore be neglected. We show that this is valid only asymptotically. For many applications of practical interest, the spatial extent of a discrete atom cannot be neglected. We have developed a model for the description of epitaxial growth ba...

A new class of matching conditions between the atomistic and continuum regions is presented for the multiscale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and at the same time minimize the reflection of phonons at the interface. These matching conditions can be made adaptive if we choose appropriate weight functio...

In this research, the influence of structure on the tensile properties of single- walled carbon nanotubes (CNTs) is evaluated using molecular mechanics technique and finite element method. The effects of diameter, length and chiral angle on elastic modulus and Poisson’s ratio of armchair, zigzag and chiral structures are investigated. To simulate the CNTs, a 3D FEM code is developed using the A...

We consider nanometer-sized fluid annuli (rings) deposited on a solid substrate and ask whether these rings break up into droplets due to the instability of Rayleigh-Plateau-type modified by the presence of the substrate, or collapse to a central drop due to the presence of azimuthal curvature. The analysis is carried out by a combination of atomistic molecular dynamics simulations and a contin...

Beam on a Nonlinear Winkler Foundation (BNWF) approach is widely used in practice since the simulation process is rather simple and requires less computational efforts compared to three-dimensional continuum modeling approaches. In the recent decades, this approach has been extended by proposing advanced onedimensional models in order to better simulate the soil-pile interaction. In this paper,...

Agent-based models (ABMs) provide a number of advantages relative to traditional continuum modeling approaches, permitting incorporation of great detail and realism into simulations, allowing in silico tracking of single-cell behaviors and correlation of these with emergent effects at the macroscopic level. In this study we present BSim 2.0, a radically new version of BSim, a computational ABM ...

Let 8 denote the real line. If TQ& and r £ 8 , we set {t+r: / £ J H } = r [ r ] . In [ l ] we have proved these two theorems: (BK) Let S C S , T C 8 , S be at most enumerable and T be of first category. Then 8 contains a residual subset R such that SC\T\r\ is empty for every rÇzR. (BM) Let S C S , 2"C8, S be at most enumerable and T be of measure zero. Then 8 contains a subset R such that 8— Ri...