Stability analysis and limit cycles of high order sigma-delta modulators

In this chapter we present an unified approach for study the stability and validation of potential limit cycles of one bit high order Sigma-Delta modulators. The approach is general because it uses the general form of a Sigma-Delta modulator. It is based on a parallel decomposition of the modulator and a direct nonlinear systems analysis. In this representation, the general N-th order modulator is transformed into a decomposition of low order, generally complex modulators, which interact only through the quantizer function. The developed conditions for stability and for validation of potential limit cycles are very easy for implementation and this procedure is very fast

Perturbative momentum transport in MAST L-mode plasmas

Non-axisymmetric magnetic fields are used to perturbatively probe momentum transport physics in MAST L-mode plasmas. The low beta L-mode target was chosen to complement previous experiments conducted in high beta NSTX H-mode plasmas (β N = 3.5-4.6) where an inward momentum pinch was measured. In those cases quasi-linear gyrokinetic simulations of unstable ballooning micro-instabilities predict weak or outward momentum convection, in contrast to the measurements. The weak pinch was predicted to be due to both electromagnetic effects at high beta and low aspect ratio minimizing the symmetry-breaking of the instabilities responsible for momentum transport. In an attempt to lessen these electromagnetic effects at low aspect ratio, perturbative experiments were run in MAST L-mode discharges at lower beta (β N = 2). The perturbative transport analysis used the time-dependent response following the termination of applied 3D fields that briefly brake the plasma rotation (similar to the NSTX H-mode experiments). Assuming time-invariant diffusive (χ ℓ) and convective (V ℓ) transport coefficients, an inward pinch is inferred with magnitudes, (RV ℓ/χ ℓ) = (-1)-(-9), similar to those found in NSTX H-modes and in conventional tokamaks. However, if experimental uncertainties due to non-stationary conditions during and after the applied 3D field are considered, a weak pinch or even outward convection is inferred, (RV ℓ/χ ℓ) = (-1)-(+5). Linear gyrokinetic simulations indicate that for these lower beta L-modes, the predicted momentum pinch is predicted to be relatively small, (RV ℓ/χ ℓ) sim ≈ -1. While this falls within the experimentally inferred range, the uncertainties are practically too large to quantitatively validate the predictions. Challenges and implications for this particular experimental technique are discussed, as well as additional possible physical mechanisms that may be important in understanding momentum transport in these low aspect ratio plasmas. </p

The effect of intracellular Ca2+ on GABA-activated currents in cerebellar granule cells in culture

The patch clamp technique was used to study the effects of intracellular free calcium ([Ca2+]i) on GABAA-evoked whole-cell and single channel currents of cultured cerebellar granule cells. Changes in [Ca2+]i were obtained by adding to the extracellular solution the calcium ionophore A23187 (2 \u3bcm). The relationship between [Ca2+]i and [Ca2+]O in the presence or absence of A23187 was assessed using fluorimetric measurements from Fura-2 loaded cells. In 2 m m [Ca2+]o and A23187, [Ca2+]i was about 1.5 \u3bcm, whereas in the absence of A23187 it was about 250 n m. In whole-cell experiments (symmetrical chloride concentrations) at -50 mV, GABA (0.5 \u3bcm) evoked inward currents that did not desensitize. Bath application of A23187 significantly reduced the steady-state amplitude of GABA currents by 37 \ub1 6%. Single channel currents activated by GABA (0.5 \u3bcm) were also recorded in the outside-out configuration of the patch clamp technique. Kinetic analysis of single channel events revealed that A23187 significantly increased the long closed time constant (\u3c4c3) without affecting the open time constants (\u3c4o1 and \u3c4o2) or the short and medium closed time constants (\u3c4c1 and \u3c4c2). Moreover, application of A23187 induced a significant reduction of burst duration (\u3c4b). We conclude that a rise in [Ca2+]i by A23187 may decrease the binding affinity of GABA for the GABAA receptor. We thank Prof. D. Colquhoun for critical reading of the manuscript and Drs. F. Vittur and M. Fragonas for allowing us the use of the spectrofluorimeter. \ua9 1994 Springer-Verlag New York Inc

Invariantization of numerical schemes using moving frames

This paper deals with a geometric technique to construct numerical schemes for differential equations that inherit Lie symmetries. The moving frame method enables one to adjust existing numerical schemes in a geometric manner and systematically construct proper invariant versions of them. Invariantization works as an adaptive transformation on numerical solutions, improving their accuracy greatly. Error reduction in the Runge-Kutta method by invariantization is studied through several applications including a harmonic oscillator and a Hamiltonian system.close111

Laxative treatment with polyethylene glycol does not affect lipid absorption in rats

Item does not contain fulltextOBJECTIVES: Polyethylene glycol (PEG) is a frequently used laxative agent. It is unknown, however, whether PEG affects the absorptive capacity of the intestine. Reduced lipid (dietary fat and cholesterol) absorption induced by long-term PEG treatment could negatively affect growth in children. We tested whether PEG accelerates gastrointestinal transit and alters lipid absorption and plasma lipid levels. METHODS: Wistar rats were administered drinking water with or without PEG (7%) for 2 weeks. We studied whole gut transit time by recording the first appearance of red feces after intragastric carmine red administration. We measured plasma concentrations of cholesterol and triglycerides, dietary fat absorption by 48-hour fat balance and by plasma appearance of intragastrically administered stable-isotope labeled fats, and cholesterol absorption with a dual stable isotope technique. RESULTS: PEG decreased whole gut transit time by 20% (P=0.028) without causing diarrhea. PEG treatment did neither affects overall dietary fat balance nor fat uptake kinetics, cholesterol absorption, or plasma lipid concentrations. CONCLUSIONS: PEG does not affect lipid absorption nor steady-state plasma lipid levels in rats, although it accelerates the gastrointestinal transit