Two theorems by Helmholtz

Swimming microrobot actuated by two pairs of Helmholtz coils system

0957-4158/$ see front matter 2010 Elsevier Ltd. A doi:10.1016/j.mechatronics.2010.09.001 ⇑ Corresponding author. ⇑⇑ Corresponding author. E-mail addresses: [email protected] (J. Park), spark@jn Various electromagnetic based actuation (EMA) methods have been proposed for the actuation of microrobots. The advantage of EMA is that it can generate a wireless driving force for the microrobot, and this i...

Two-dimensional sonic crystals with Helmholtz resonators.

We present a type of sonic crystal composed with an array of two-dimensional Helmholtz resonators, which in the long-wave regime have both a high relative acoustic refractive index n and at the same time, a small acoustic impedance Z mismatch with air for airborne sound. We analyze the n and Z of such sonic crystals by finite-difference time-domain simulations, and by mapping our results to a c...

Families of Two-Colour Helmholtz Spatial Solitons

Multi-colour spatial solitons comprise localized optical components at distinct temporal frequencies [1]. The components (which may be bright-like and dark-like) tend to overlap in space, thereby allowing the interplay between linear spreading (diffraction) and nonlinear effects (selfand mutual-focusing) to result in an electromagnetic structure with a stationary intensity pattern. Two-colour s...

Two Pebbling Theorems

Two conductance theorems, two canonical path theorems, and two walks on directed Cayley graphs

We show two Conductance-like theorems for mixing time of non-reversible non-lazy walks. These bounds involve a measure of expansion which expresses how well ergodic flow is distributed among vertices, which while conceptually similar to Blocking Conductance apply to non-lazy non-reversible Markov chains as well. As an application we derive two canonical path theorems for mixing time of non-reve...