Smart-pixel architectures, which use the cells of field-programmable gate arrays to provide electronic functionality and intraplane communication, offer a general-purpose approach to exploiting new application areas that would benefit from this kind of structure. One such area, that of the encryption of digital data, is discussed here. Some of the characteristics exhibited by encryption algorithms and ways in which these are applicable to smart-pixel technology are described. The implementation of an algorithm in current use, the SAFER K-64, and its interfacing to an electronic host are then considered in detail. It is shown that this encryption algorithm maps well onto smart-pixel technology because it involves only parallel data transfers, simple regular operations, and interconnections plus a relatively low rate of transfer to the host.
Alfvén eigenmodes driven by energetic particles are routinely observed in tokamak plasmas. These modes consist of poloidal harmonics of shear Alfvén waves coupled by inhomogeneity in the magnetic field. Further coupling is introduced by 3D inhomogeneities in the ion density during the assimilation of injected pellets. This additional coupling modifies the Alfvén continuum and discrete eigenmode spectrum. The frequencies of Alfvén eigenmodes drop dramatically when a pellet is injected in JET. From these observations, information about the changes in the ion density caused by a pellet can be inferred. To use Alfvén eigenmodes for MHD spectroscopy of pellet injected plasmas, the 3D MHD codes Stellgap and AE3D were generalised to incorporate 3D density profiles. A model for the expansion of the ionised pellet plasmoid along a magnetic field line was derived from the fluid equations. Thereby, the time evolution of the Alfvén eigenfrequency is reproduced. By comparing the numerical frequency drop of a toroidal Alfvén eigenmode (TAE) to experimental observations, the initial ion density of a cigar-shaped ablation region of length 4cm is estimated to be n * = 6.8×10 22 m −3 at the TAE location (r/a ≈ 0.75). The frequency sweeping of an Alfvén eigenmode ends when the ion density homogenises poloidally. Modelling suggests that the time for poloidal homogenisation of the ion density at the TAE position is τ h = 18 ± 4 ms for inboard pellet injection, and τ h = 26 ± 2 ms for outboard pellet injection. By reproducing the frequency evolution of the elliptical Alfvén eigenmode (EAE), the initial ion density at the EAE location (r/a ≈ 0.9) can be estimated to be n * = 4.8 × 10 22 m −3. Poloidal homogenisation of the ion density takes 2.7 times longer at the EAE location than at the TAE location for both inboard and outboard pellet injection. MHD spectroscopy, Alfvén eigenmodes, pellet injection ‡ See the author list of "Overview of the JET preparation for Deuterium-Tritium Operation" by E.
In the teaching of elementary mathematics, one of the areas that seems to give the most trouble is that of the reduction of simple fractions. For example, let us consider a proper fraction of the form a/b. We can reduce a/b to lowest terms by finding the greatest common divisor of a and b, denoted by GCD (a, b), and factoring it out of both numerator and denominator. This method, of course, calls for an understanding of factoring. Factoring is not beyond the realm of understanding of the students, but the method is so time-consuming and laborious that most students, especially the slower ones, are disenchanted with it and do not use it. Students then resort to the old standby method of trial-and-error, accompanied by a few rules of divisibility, which is, of course, also very time-consuming and laborious on many fractions. Too many students become discouraged with the whole process and tend to give up, thereby retarding their learning of how to properly reduce fractions.
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