Numerical modeling of elastic waves across imperfect contacts

A numerical method is described for studying how elastic waves interact with imperfect contacts such as fractures or glue layers existing between elastic solids. These contacts have been classicaly modeled by interfaces, using a simple rheological model consisting of a combination of normal and tangential linear springs and masses. The jump conditions satisfied by the elastic fields along the interfaces are called the "spring-mass conditions". By tuning the stiffness and mass values, it is possible to model various degrees of contact, from perfect bonding to stress-free surfaces. The conservation laws satisfied outside the interfaces are integrated using classical finite-difference schemes. The key problem arising here is how to discretize the spring-mass conditions, and how to insert them into a finite-difference scheme: this was the aim of the present paper. For this purpose, we adapted an interface method previously developed for use with perfect contacts [J. Comput. Phys. 195 (2004) 90-116]. This numerical method also describes closely the geometry of arbitrarily-shaped interfaces on a uniform Cartesian grid, at negligible extra computational cost. Comparisons with original analytical solutions show the efficiency of this approach.Comment: to be published in SIAM Journal of Scientific Computing (2006

Sticky Actuator: Free-Form Planar Actuators for Animated Objects

We propose soft planar actuators enhanced by free-form fabrication that are suitable for making everyday objects move. The actuator consists of one or more inflatable pouches with an adhesive back. We have developed a machine for the fabrication of free-from pouches; squares, circles and ribbons are all possible. The deformation of the pouches can provide linear, rotational, and more complicated motion corresponding to the pouch's geometry. We also provide a both manual and programmable control system. In a user study, we organized a hands-on workshop of actuated origami for children. The results show that the combination of the actuator and classic materials can enhance rapid prototyping of animated objects.National Science Foundation (U.S.) (Grant 1240383)National Science Foundation (U.S.) (Grant 1138967

Ambiguity resolution for triple-frequency geometry-free and ionosphere-free combination tested with real data

The recent GPS Block IIF satellites SVN62 and SVN63 and the Galileo satellites GIOVE-A, GIOVE-B, PFM and FM2 already send signals on more than two frequencies, and more GNSS satellites will provide tracking data on at least three frequencies in the near future. In this paper, a simplified general method for ambiguity resolution minimizing the noise level for the triple-frequency geometry-free (GF) and ionosphere-free (IF) linear combinations is presented, where differently scaled code noise on the three frequencies was introduced. For the third of three required linear combinations, the most demanding one in triple-frequency ambiguity resolution, we developed a general method using the ambiguity-corrected phase observations without any constraints to search for the optimal GF and IF linear combination. We analytically demonstrate that the noise level of this third linear combination only depends on the three frequencies. The investigation concerning this frequency-dependent noise factor was performed for GPS, Galileo and Compass frequency triplets. We verified the theoretical derivations with real triple-frequency GPS and Galileo data from the Multi-GNSS Experiment (M-GEX) of the International GNSS Service (IGS). The data of about 30 M-GEX stations around the world over 11 days from 29 April 2012 to 9 May 2012 were used for the test. For the third linear combinaton using Galileo E1, E5b and E5a, which is expected to have the worst performance among all the GNSS frequency triplets in our investigation, the formal errors of the estimated ambiguities are in most cases below 0.2cycles after 400 observation epochs. If more GPS satellites sending signals on three frequencies or more stations tracking Galileo E6 signal are available in the future, an improvement by a factor of two to three can be expecte

Divergent streamlines and free vortices in Newtonian fluid flows in microfluidic flow focusing devices

The appearance of divergent streamlines and subsequent formation of free vortices in Newtonian fluid flows through microfluidic flow-focusing geometries is discussed in this work. The micro-geometries are shaped like a cross-slot but comprise three entrances and one exit. The divergent flow and subsequent symmetric vortical structures arising near the centreline of the main inlet channel are promoted even under creeping flow conditions, and are observed experimentally and predicted numerically above a critical value of the ratio of inlet velocities (VR). As VR is further increased these free vortices continue to grow until a maximum size is reached due to geometrical constraints. The numerical calculations are in good agreement with the experimental observations and we probe numerically the effects of the geometric parameters and of inertia on the flow patterns. In particular, we observe that the appearance of the central recirculations depends non-monotonically on the relative width of the entrance branches and we show that inertia enhances the appearance of the free vortices. On the contrary, the presence of the walls in three-dimensional geometries has a stabilizing effect for low Reynolds numbers, delaying the onset of these secondary flows to higher VR. The linearity of the governing equations for creeping flow of Newtonian fluids was invoked to determine the flow field for any VR as a linear combination of the results of three other independent solutions in the same geometry