We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in one spatial dimension. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming partial differential equations.… (More)
Transitional Pipe Flow " Although in most ways the exact manner in which water moves is difficult to perceive and still more difficult to define, as are also the forces attending such motion, certain general features both of the forces and motions stand prominently forth, as if to invite or to defy theoretical treatment. " O. Reynolds  Praise be to the… (More)
Microfluidic technology has revolutionized the control of flows at small scales giving rise to new possibilities for assembling complex structures on the microscale. We analyze different possible algorithms for assembling arbitrary structures, and demonstrate that a sequential assembly algorithm can manufacture arbitrary 3D structures from identical… (More)
Sequencing by Hybridization (SBH) reconstructs an n-long target DNA sequence from its biochemically determined l-long subsequences. In the standard approach, the length of a uniformly random sequence that can be unambiguously reconstructed is limited to n = O(2(l)) due to repetitive subsequences causing reconstruction degeneracies. We present a modified… (More)
(1994). The use of splints in the treatment of joint stiffness: biologic rationale and an algorithm for making splints. (2004). Therapy interventions for improving joint range of motions: a systematic review.
When a fluid-immersed array of supported plates or pillars is dried, evaporation leads to the formation of menisci on the tips of the plates or pillars that bring them together to form complex patterns. Building on prior experimental observations, we use a combination of theory and computation to understand the nature of this instability and its evolution… (More)