In this project, an effective technique for site-selective, multicomponent assembly on the nanoand microscale has been developed. Creation of practical nanosystems using this technique is underway. This approach offers great promise for assembling arbitrary (not necessarily periodic) systems of different types of nanoscale components, such as electronics (memory, logic, interconnects, displays)...

Modeling of flow and transport in environmental systems often involves formulation of conservation equations at spatial scales involving tens to hundreds of pore diameters in porous media or the depth of flow in a channel. Quantities such as density, temperature, internal energy, and velocity may not be uniform over these macroscopic length scales. The external gravitational potential causes gr...

Three formulations for the problem of an elastica adhering to a rigid surface are discussed and compared. These include stationary principles, the surface integral of Eshelby’s energy-momentum tensor, and the material (configurational) force balance. The configuration at static equilibrium is predicted in closed form for a pair of structures that arise in nanoand microscale applications. 2006 E...

Macroscale connectivity of the mammalian brain has been shown to display several characteristics of an efficient communication network architecture. In parallel, at the microscopic scale, histological studies have extensively revealed large interregional variation in cortical neural architectonics. However, how these two "scales" of cerebrum organization are linked remains an open question. Col...

When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by microscale properties and interactions of many variables, while the behavior of interest often occurs at the macroscale level and at large time scales, often ...

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity ...

A systematic study of the across scale coupling phenomenology in scattering problems is addressed using the theory of multiresolution decomposition and orthogonal wavelets. By projecting an integral equation formulation of the scattering problem onto a set of subspaces that constitutes a multiresolution decomposition of L 2 (R), one can derive two coupled formulations. The rst governs the macro...

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of thi...