This paper builds on recent developments of a unified asymptotic approach to meteorological modeling [ZAMM, 80:765–777, 2000, SIAM Proc. App. Math. 116, 227–289, 2004], which was used successfully in the development of Systematic multiscale models for the tropics in Majda and Klein [J. Atmosph. Sci. 60: 393–408, 2003] and Majda and Biello [PNAS, 101: 4736–4741, 2004]. Biello and Majda [J. Atmos...

Multiscale image registration techniques are presented for the registration of medical images using deformable registration models. The techniques are particularly effective for registration problems in which one or both of the images to be registered contains significant levels of noise. A brief overview of existing deformable registration techniques is presented, and experiments using B-splin...

Developing an effective turbulence model is important for engineering applications as well as for fundamental understanding of the flow physics. We present a mathematical derivation of a closure relating the Reynolds stress to the mean strain rate for incompressible flows. A systematic multiscale analysis expresses the Reynolds stress in terms of the solutions of local periodic cell problems. W...

This paper provides a comprehensive review of the literature, mostly of the last 10–15 years, that is enhancing our understanding of the mechanics of the rapidly growing field of micromachining. The paper focuses on the mechanics of the process, discussing both experimental and modeling studies, and includes some work that, while not directly focused on micromachining, provides important insigh...

A consensus has recently emerged that further progress in understanding human physiopathology will demand integrative views of biological systems. In this context, complex systems and related interdisciplinary approaches of biology are expected to help. The aim of this collective paper is basically to provide a starting point for further discussions and interactions within the community of comp...

In this paper, we propose the first numerical study of nanotube-based torsional oscillators via developing a new multiscale model. The edge-to-edge technique was employed in this multiscale method to couple the molecular model, i.e., nanotubes, and the continuum model, i.e., the metal paddle. Without losing accuracy, the metal paddle was treated as the rigid body in the continuum model. Torsion...

Current metropolises largely depend on a functioning transport infrastructure and the increasing demand can only be satisfied by a well organized mass transit. One example for a crucial mass transit system is New York City’s Staten Island Ferry, connecting the two boroughs of Staten Island and Manhattan with a regular passenger service. Today’s demand already exceeds 2500 passengers for a singl...

Vertically Aligned Carbon Nanotube (VACNT) – based electrochemical double layer capacitors, called “supercapacitors” are intermediate systems that can potentially bridge the power/energy gap between traditional dielectric capacitors (high power) and batteries (high power density). However, their future is uncertain because of technical stumbling block in their fabrication related to the post-gr...

This paper considers the numerical solution of elliptic boundary value problems with a complicated (nonperiodic) diffusion matrix which is smooth but highly oscillating on very different scales. We study the influence of the scales and amplitudes of these oscillations to the regularity of the solution. We introduce weighted Sobolev norms of integer order, where the (p + 1)st seminorm is weighte...