The reorganization of secondary school mathematics

Thesis (M.A.)--Boston Universit

Affordances of spreadsheets in mathematical investigation: Potentialities for learning

This article, is concerned with the ways learning is shaped when mathematics problems are investigated in spreadsheet environments. It considers how the opportunities and constraints the digital media affords influenced the decisions the students made, and the direction of their enquiry pathway. How might the leraning trajectory unfold, and the learning process and mathematical understanding emerge? Will the spreadsheet, as the pedagogical medium, evoke learning in a distinctive manner? The article reports on an aspect of an ongoing study involving students as they engage mathematical investigative tasks through digital media, the spreadsheet in particular. In considers the affordances of this learning environment for primary-aged students

Active nematic gels as active relaxing solids

I put forward a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as an external remodeling force that competes with the passive relaxation dynamics and drags the system out of equilibrium. In a simple one-dimensional channel geometry, we show that the interaction between non-uniform nematic order and activity results in either a spontaneous flow of particles or a self-organization into sub-channels flowing in opposite directions

Two-level system with a thermally fluctuating transfer matrix element: Application to the problem of DNA charge transfer

Charge transfer along the base-pair stack in DNA is modeled in terms of thermally-assisted tunneling between adjacent base pairs. Central to our approach is the notion that tunneling between fluctuating pairs is rate-limited by the requirement of their optimal alignment. We focus on this aspect of the process by modeling two adjacent base pairs in terms of a classical damped oscillator subject to thermal fluctuations as described by a Fokker-Planck equation. We find that the process is characterized by two time scales, a result that is in accord with experimental findings.Comment: original file is revtex4, 10 pages, three eps figure