Dynamical Effects from Asteroid Belts for Planetary Systems

The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed points around the inner and outer edges of the belt. Our results show that for the planets, the probability to move stably around the inner edge is larger than the one to move around the outer edge. It is also interesting that there is a limit cycle of semi-attractor for a particular case. Applying our results to the Solar System, we find that our results could provide a natural mechanism to do the orbit rearrangement for the larger Kuiper Belt Objects and thus successfully explain the absence of these objects beyond 50 AU.Comment: accepted by International Journal of Bifurcation and Chaos in Aug. 2003, AAS Latex, 27 pages with 6 color figure

Effect of dialysate temperature on central hemodynamics and urea kinetics

Effect of dialysate temperature on central hemodynamics and urea kinetics. Use of cool dialysate is associated with increased intradialytic blood pressure, but the hemodynamic mechanism is unknown. Whether changes in dialysate temperature affect muscle blood flow, which may the alter the degree of urea compartmentalization, also is unknown. We measured hemodynamics and blood and dialysate-side urea kinetic indices in nine hemodialysis patients during two cool (35.0°C) versus two warm (37.5°C) dialysate treatments. The % change in mean arterial pressure was different when using the cool (+6.5 ± 9.7 mm Hg) versus the warm (-13.4 ± 3.6) dialysate (P < 0.01), despite comparable amounts of fluid removal. Percent changes in cardiac output were similar with the two dialysates, and thus the blood pressure effect was due primarily to changes in total peripheral resistance (%ΔTPR, cool +26 ± 13.6, warm +8.6 ± 14.5; P < 0.02). During cool dialysate use tympanic membrane temperature changed by -0.51 ± 0.23°C, whereas body temperature increased by 0.52 ± 0.14°C during use of warm dialysate. Measured urea recovery normalized to the predialysis urea nitrogen concentration was similar with the two treatments: cool 31.3 ± 0.039 liter-1; warm 29.7 ± 0.021; P = NS. In a second study, post-dialysis urea rebound values from 15 seconds to 30 minutes, expressed as the percent of the post-dialysis SUN, were similar after the two treatments: cool 11.79 ± 1.4; warm 12.21 ± 2.27, P = NS. The results suggest that increased blood pressure associated with use of cool dialysate is due to an increased TPR, and that this alteration in hemodynamics has no clinically important effects on either the amount of urea removal or the extent of post-dialysis urea rebound

Bifurcation for Dynamical Systems of Planet-Belt Interaction

The dynamical systems of planet-belt interaction are studied by the fixed-point analysis and the bifurcation of solutions on the parameter space is discussed. For most cases, our analytical and numerical results show that the locations of fixed points are determined by the parameters and these fixed points are either structurally stable or unstable. In addition to that, there are two special fixed points: the one on the inner edge of the belt is asymptotically stable and the one on the outer edge of the belt is unstable. This is consistent with the observational picture of Asteroid Belt between the Mars and Jupiter: the Mars is moving stablely close to the inner edge but the Jupiter is quite far from the outer edge.Comment: AAS Latex file, 31 pages, accepted for publication in International Journal of Bifurcation and Chao

Thoughts and Progress

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75183/1/j.1525-1594.1999.06248.x.pd

Biogas laminar burning velocity and flammability characteristics in spark ignited premix combustion

Spherically expanding flames propagating at constant pressure were employed to determine the laminar burning velocity and flammability characteristics of biogas-air mixtures in premixed combustion to uncover the fundamental flame propagation characteristics of a new alternative and renewable fuel. The results are compared with those from a methane-air flame. Biogas is a sustainable and renewable fuel that is produced in digestion facilities. The composition of biogas discussed in this paper consists of 66.4% methane, 30.6% carbon dioxide and 3% nitrogen. Burning velocity was measured at various equivalence ratios (φ) using a photographic technique in a high pressure fan-stirred bomb, the initial condition being at room temperature and atmospheric pressure. The flame for methane-air mixtures propagates from φ=0.6 till φ=1.3. The flame at φ ≥ 1.4 does not propagate because the combustion reaction is quenched by the larger mass of fuel. At φ≤0.5, it does not propagate as well since the heat of reaction is insufficient to burn the mixtures. The flame for biogas-air mixtures propagates in a narrower range, that is from φ=0.6 to φ=1.2. Different from the methane flame, the biogas flame does not propagate at φ≥1.3 because the heat absorbed by inhibitors strengthens the quenching effect by the larger mass of fuel. As in the methane flame, the biogas flame at φ≤0.5 does not propagate. This shows that the effect of inhibitors in extremely lean mixtures is small. Compared to a methane-air mixture, the flammability characteristic (flammable region) of biogas becomes narrower in the presence of inhibitors (carbon dioxide and nitrogen) and the presence of inhibitors causes a reduction in the laminar burning velocity. The inhibitor gases work more effectively at rich mixtures because the rich biogas-air mixtures have a higher fraction of carbon dioxide and nitrogen components compared to the lean biogas-air mixtures