Writhing instabilities of twisted rods: from infinite to finite length

We use three different approaches to describe the static spatial configurations of a twisted rod as well as its stability during rigid loading experiments. The first approach considers the rod as infinite in length and predicts an instability causing a jump to self-contact at a certain point of the experiment. Semi-finite corrections, taken into account as a second approach, reveal some possible experiments in which the configuration of a very long rod will be stable through out. Finally, in a third approach, we consider a rod of real finite length and we show that another type of instability may occur, leading to possible hysteresis behavior. As we go from infinite to finite length, we compare the different information given by the three approaches on the possible equilibrium configurations of the rod and their stability. These finite size effects studied here in a 1D elasticity problem could help us guess what are the stability features of other more complicated (2D elastic shells for example) problems for which only the infinite length approach is understood.     

A Radiation Imaging Detector Made by Postprocessing a Standard CMOS Chip

An unpackaged microchip is used as the sensing element in a miniaturized gaseous proportional chamber. This letter reports on the fabrication and performance of a complete radiation imaging detector based on this principle. Our fabrication schemes are based on wafer-scale and chip-scale postprocessing. Compared to hybrid-assembled gaseous detectors, our microsystem shows superior alignment precision and energy resolution, and offers the capability to unambiguously reconstruct 3D radiation tracks on the spot.     

Isotone relations revisited

We propose a new approach towards proving that the fixed point property for ordered sets is preserved by products. This approach uses a characterization of fixed points in products via isotone relations. First explorations of classes of isotone relations are presented. These first explorations give us hope that this approach could lead to advances on the Product Problem.     

Stark's conjecture over complex cubic number fields

Systematic computation of Stark units over nontotally real base fields is carried out for the first time. Since the information provided by Stark's conjecture is significantly less in this situation than the information provided over totally real base fields, new techniques are required. Precomputing Stark units in relative quadratic extensions (where the conjecture is already known to hold) and coupling this information with the Fincke-Pohst algorithm applied to certain quadratic forms leads to a significant reduction in search time for finding Stark units in larger extensions (where the conjecture is still unproven). Stark's conjecture is verified in each case for these Stark units in larger extensions and explicit generating polynomials for abelian extensions over complex cubic base fields, including Hilbert class fields, are obtained from the minimal polynomials of these new Stark units.

     

Solutions of the WDVV Equations and Integrable Hierarchies of KP Type

We show that reductions of KP hierarchies related to the loop algebra of SL_n with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten– Dijkgraaf–E. Verlinde–H. Verlinde equations.     

Noise modeling for RF CMOS circuit simulation

The RF noise in 0.18-/spl mu/m CMOS technology has been measured and modeled. In contrast to some other groups, we find only a moderate enhancement of the drain current noise for short-channel MOSFETs. The gate current noise on the other hand is more significantly enhanced, which is explained by the effects of the gate resistance. The experimental results are modeled with a nonquasi-static RF model, based on channel segmentation, which is capable of predicting both drain and gate current noise accurately. Experimental evidence is shown for two additional noise mechanisms: 1) avalanche noise associated with the avalanche current from drain to bulk and 2) shot noise in the direct-tunneling gate leakage current. Additionally, we show low-frequency noise measurements, which strongly point toward an explanation of the 1/f noise based on carrier trapping, not only in n-channel MOSFETs, but also in p-channel MOSFETs.