A multi-scale modeling approach is proposed in this paper that assists the user in constructing musculoskeletal system models from sub-models describing various mechanisms on different levels on the length scale. In addition, dynamic time-scale analysis has been performed on the developed multi-scale models of various parts of a human limb: on wrist, elbow and shoulder characterized by differen...

The paper deals with the mathematical models for the electrical activity of the heart at the microand macroscopic level. By using the tools of the Γ–convergence theory, a rigorous mathematical derivation of the macroscopic model called “bidomain” directly from the microscopic properties of the tissue is presented.

Article history: Received 1 July 2015 Received in revised form 22 March 2016 Accepted 17 April 2016 Available online 19 April 2016

Article history: Received 8 January 2017 Accepted 27 March 2017 Available online xxxx

An alternative example of the method of multiple scales is presented. This example arises in the study of the classical heat equation with a slowly varying flux imposed at one end. The module presents introductory ideas about dimensionless variables, multiple-scale expansions, and scaling of the dependent variable. The necessarily obfuscating algebraic computation is less than that for more fam...

Recent work of the authors and colleagues on the turbulent mixing of compressible fluids is developed and extended with an emphasis on the multiscale aspects of this work. Specifically, we study an interplay between micro and macro aspects of mixing. 2008 Elsevier B.V. All rights reserved.

We perform a systematic multiscale analysis for the 2-D incompressible Euler equation with rapidly oscillating initial data using a Lagrangian approach. The Lagrangian formulation enables us to capture the propagation of the multiscale solution in a natural way. By making an appropriate multiscale expansion in the vorticity-stream function formulation, we derive a well-posed homogenized equatio...

U O Q U A N T Fraction of surface atoms in contact, A /A f i c  Friction proportional to Ac and Ac proportional to load L for rough surfaces  Flat surfaces in complete contact at any load Molecular Simulations Differ on Applicability of Macroscopic Results at Atomic Scales friction and adhesion in macroscopic models  Results for flat surfaces can be mapped directly to other geometries usi...