Patterning: Three-Dimensional Fabrication at Small Size Scales Small 7/2010

Low dimensional attractors arise from forcing at small scales

Standard estimates of the dimension of the attractor of the 2D Navier–Stokes equations are given in terms of a dimensionless Grashof number that measures the total amount of energy injected into the flow. However, this result takes no account of whether the forcing is concentrated at large or small scales. By a simple modification of the usual argument, this paper provides a bound that is linea...

Turbulence Effects at Small Scales

It is most natural to assume that mysterious Small Ionized and Neutral Structures (SINS) in diffuse ISM arise from turbulence. There are two obvious problem with such an explanation, however. First of all, it is generally believed that at the small scales turbulence should be damped. Second, turbulence with Kolmogorov spectrum cannot be the responsible for the SINS. We consider, however, effect...

Plasticity Theory at Small Scales

Three-dimensional tissue fabrication.

In recent years, advances in fabrication technologies have brought a new dimension to the field of tissue engineering. Using manufacturing-based methods and hydrogel chemistries, researchers have been able to fabricate tissue engineering scaffolds with complex 3-D architectures and customized chemistries that mimic the in vivo tissue environment. These techniques may be useful in developing the...

Origin of sample size effect: Stochastic dislocation formation in crystalline metals at small scales

In crystalline metals at small scales, the dislocation density will be increased by stochastic events of dislocation network, leading to a universal power law for various material structures. In this work, we develop a model obeyed by a probability distribution of dislocation density to describe the dislocation formation in terms of a chain reaction. The leading order terms of steady-state of p...