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Stability Limit (stability + limit)
Selected AbstractsStability limits for the quasi-satellite orbitMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2006S. Mikkola ABSTRACT An asteroid moving around the Sun having approximately the same mean motion and mean longitude as a planet, but a different eccentricity, circles the planet like a retrograde satellite even when the distance is large enough so that it is not a bound satellite. If the orbits are coplanar, then the motion is stable in the secular approximation. When the orbits are inclined enough, an asteroid can be trapped into such a quasi-satellite (QS) motion for a finite period of time. The conditions under which this can occur are discussed, improved criteria for the recognition of this type of motion are developed, and numerical examples from real QS objects are provided. [source] Methane steam reforming at microscales: Operation strategies for variable power output at millisecond contact timesAICHE JOURNAL, Issue 1 2009Georgios D. Stefanidis Abstract The potential of methane steam reforming at microscale is theoretically explored. To this end, a multifunctional catalytic plate microreactor, comprising of a propane combustion channel and a methane steam reforming channel, separated by a solid wall, is simulated with a pseudo 2-D (two-dimensional) reactor model. Newly developed lumped kinetic rate expressions for both processes, obtained from a posteriori reduction of detailed microkinetic models, are used. It is shown that the steam reforming at millisecond contact times is feasible at microscale, and in agreement with a recent experimental report. Furthermore, the attainable operating regions delimited from the materials stability limit, the breakthrough limit, and the maximum power output limit are mapped out. A simple operation strategy is presented for obtaining variable power output along the breakthrough line (a nearly iso-flow rate ratio line), while ensuring good overlap of reaction zones, and provide guidelines for reactor sizing. Finally, it is shown that the choice of the wall material depends on the targeted operating regime. Low-conductivity materials increase the methane conversion and power output at the expense of higher wall temperatures and steeper temperature gradients along the wall. For operation close to the breakthrough limit, intermediate conductivity materials, such as stainless steel, offer a good compromise between methane conversion and wall temperature. Even without recuperative heat exchange, the thermal efficiency of the multifunctional device and the reformer approaches ,65% and ,85%, respectively. © 2008 American Institute of Chemical Engineers AIChE J, 2009 [source] Precessing warped accretion discs in X-ray binariesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2001G. I. Ogilvie We study the radiation-driven warping of accretion discs in the context of X-ray binaries. The latest evolutionary equations are adopted, which extend the classical alpha theory to time-dependent thin discs with non-linear warps. We also develop accurate, analytical expressions for the tidal torque and the radiation torque, including self-shadowing. We investigate the possible non-linear dynamics of the system within the framework of bifurcation theory. First, we re-examine the stability of an initially flat disc to the Pringle instability. Then we compute directly the branches of non-linear solutions representing steadily precessing discs. Finally, we determine the stability of the non-linear solutions. Each problem involves only ordinary differential equations, allowing a rapid, accurate and well-resolved solution. We find that radiation-driven warping is probably not a common occurrence in low-mass X-ray binaries. We also find that stable, steadily precessing discs exist for a narrow range of parameters close to the stability limit. This could explain why so few systems show clear, repeatable ,superorbital' variations. The best examples of such systems, Her X-1, SS 433 and LMC X-4, all lie close to the stability limit for a reasonable choice of parameters. Systems far from the stability limit, including Cyg X-2, Cen X-3 and SMC X-1, probably experience quasi-periodic or chaotic variability as first noticed recently by Wijers and Pringle. We show that radiation-driven warping provides a coherent and persuasive framework but that it does not provide a generic explanation for the long-term variabilities in all X-ray binaries. [source] A fast method for computing time-dependent normal pressure distributions with cellular automatonPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009Matthias Graf When two bodies slide against each other, one part of the dissipated energy causes a topography change. Tribological research on brake bads shows a rich dynamic of the boundary layer: plateau-like structures of a typical length scale grow with time due to agglomerating wear particles and collapse spontaneously at a stability limit [4], [1]. This time-dependent behaviour can be modeled with cellular automata, which consider local resolution of temperature, wear particle density and frictional power [4]. Beside this the instationary normal pressure distribution and the distinction between areas with and without contact is expected to have a significant influence [3]. This paper derives a fast scheme to estimate the time-variant pressure distribution of a deterministic and dynamic topography by a cellular automaton. The approach is discussed in the light of computational performance and the solution's characteristics. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] A New Delay-Dependent Stability Criterion For Neutral Delay-Differential SystemsASIAN JOURNAL OF CONTROL, Issue 3 2003Bin Yang ABSTRACT This paper investigates the problem of asymptotic stability for neutral delay-differential systems. Using the Lyapunov method, we derive a new delay-dependent sufficient condition for the stability of systems in terms of the linear matrix inequality (LMI). Numerical examples show that the results obtained in this paper significantly improve the estimate of stability limit over some existing results reported previously in the literature. [source] Instabilities of Boussinesq models in non-uniform depthINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2009F. Løvholt Abstract The von Neumann method for stability analysis of linear waves in a uniform medium is a widely applied procedure. However, the method does not apply to stability of linear waves in a variable medium. Herein we describe instabilities due to variable depth for different Boussinesq equations, including the standard model by Peregrine and the popular generalization by Nwogu. Eigenmodes are first found for bathymetric features on the grid scale. For certain combinations of Boussinesq formulations and bottom profiles stability limits are found in closed form, otherwise numerical techniques are used for the eigenvalue problems. Naturally, the unstable modes in such settings must be considered to be as much a result of the difference method as of the underlying differential (Boussinesq) equations. Hence, modes are also computed for smooth depth profiles that are well resolved. Generally, the instabilities do not vanish with refined resolution. In some cases convergence is observed and we thus have indications of unstable solutions of the differential equations themselves. The stability properties differ strongly. While the standard Boussinesq equations seem perfectly stable, all the other formulations do display unstable modes. In most cases the instabilities are linked to steep bottom gradients and small grid increments. However, while a certain formulation, based on velocity potentials, is very prone to instability, the Boussinesq equations of Nwogu become unstable only under quite demanding conditions. Still, for the formulation of Nwogu, instabilities are probably inherent in the differential equations and are not a result of the numerical model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Influence of the Weißenberg number on the stability of Oldroyd kind fluidsASIA-PACIFIC JOURNAL OF CHEMICAL ENGINEERING, Issue 4 2010N. Scurtu Abstract This paper is concerned with nonlinear rheological fluids of Oldroyd type. We present a (formal) stability analysis of the corresponding system of equations, showing stability limits on the Weißenberg number in certain cases. To this end, we proceed in several steps, thus separating the possible sources for instabilities. First, a spectral analysis of the linearized Oldroyd system is presented. Then, the influence of the ,a -term on the stability of the constitutive stress equation and of the full Oldroyd system is examined. Moreover, because this stability analysis is of formal and linear nature, we complement it by numerical simulations for the system showing that the upper limit of the Weißenberg number found by the stability analysis is fairly sharp. We thereby try to shed some light on the high Weißenberg number problem, that is, the problem why in certain cases there seem to exist no solutions to the Oldroyd problem for large Weißenberg numbers. Copyright © 2009 Curtin University of Technology and John Wiley & Sons, Ltd. [source] Inert Gas and Fuel Gas Influence on the Pressure Limits of Stability of AcetyleneCHEMICAL ENGINEERING & TECHNOLOGY (CET), Issue 11 2003K. Holtappels Chemically unstable gases obtained in many processes of, for example, the chemical and petrochemical industries, can decompose explosively also in the absence of oxidizing agents. In order to avoid hazards resulting from explosion reactions, safety measures need to be developed. Key to such methods is the knowledge of stability limits of unstable gases. In the present paper, an experimental method for determining the pressure limits of stability of unstable gases and gas mixtures is presented. It has proved useful when examining C2H2/inert gas and C2H2/fuel gas mixtures. [source] | |||||||||||||