We’ve been busy in the trenches of our R&D department designing a working prototype of the “RoboRoach,” a remote control system to enable left and right turning in running cockroaches. This began as a University of Michigan Senior Engineering Project we sponsored in Winter 2010, and over the past year we’ve incrementally been working to improve it, especially after getting great feedback from our colleagues at the latest Society for Neuroscience conference (thanks Cindy ). By taking the small, lightweight control circuitry out of the toy “ HEXBug Inchworm ” and modifying it with low-power 555 timer chips to create biphasic pulses, we can deliver 55 Hz stimulation to the antennae nerves of large discoid and fuscia cockroaches. We gave a seminar recently on Feb. 25th to the undergraduate students at Grand Valley State University (thanks for the invite John and Merritt !), and we publicly unveiled a working prototype!
Adaptive frequency oscillators Our first attempt toward adaptive dynamical systems was to develop the concept of adaptive frequency oscillators, which are oscillators that can adapt their parameters to learn the frequency of any periodic input signal. It means that they change their parameters in order to have an intrinsic frequency that corresponds to the frequency of the input.
Chemical reactions are often modeled as continuous differential equations with reaction rates related to chemical concentrations ( law of mass action ). As many have pointed out (e.g., Gillespie, Lok, Salwinski and Eisenberg, or Keane, et.al.) reactions actually occur as discrete events involving molecules. The reaction has some probability of occuring, but either occurs, or does not. Thus we replace concentrations with counting individual molecules and differential equations with rolling the dice to see if a reaction occurs. For a bimolecular reaction involving two molecules A and B, with concentrations [A] and [B] and a rate constant K, the probability of the reaction occuring (from mass action) will be K[A][B] .
How are mathematics connected and applied to physics, engineering problem solving and computer technology ? Below are links to some of these problems and topics. Mathematics Applied to Physics and Engineering Applications and Use of the Inverse Functions . Examples on how to aplly and use inverse functions in real life situations and solve problems in mathematics.
Spring 1995 A number of descriptive and prescriptive design methodologies have been developed for general engineering design problems, i.e., product design [Pahl 1984, Pugh 1990, Ullman 1992, Ulrich 1994, Asimow 1962]. While these methodologies are applicable to different types of design (adaptive, variant, etc.), they tend to emphasize design problems that seek "original solutions." This emphasis provides a sound foundation for teaching engineering design; it also provides a foundation for establishing corporate design processes in industry. However, for the class of problems known as redesign (adaptive, variant, etc.), an emphasis on original design may be too general as a problem solving approach. Sferro, Bolling, and Crawford argue the legitimacy of this claim, based on an analysis of the current variant design processes in the automobile industry [Sferro 1993].