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# Topic: Marginal stability

###### In the News (Mon 19 Aug 19)

 Sveriges Riksbank/Riksbanken - Glossary The central bank undertakes to ensure that the value of the currency is stable in relation to some other currency or currencies. The marginal rate was determined by the level in the interest rate stairs that the Riksbank applied on a daily basis. Thus, it was a marginal rate of interest at which banks borrowed or deposited funds at the Riksbank. www.riksbank.com /templates/Page.aspx?id=9108   (1301 words)

 Marginal stability - Wikipedia, the free encyclopedia In the theory of dynamical systems, and control theory, a continuous linear time-invariant system is marginally stable if and only if the real part of every eigenvalue (or pole) in the system's transfer-function is non-positive, and all eigenvalues with zero real value are simple roots (i.e. A discrete linear time-invariant system is marginally stable if and only if the transfer function's spectral radius is 1. A marginally stable system is one that, if given an impulse of finite magnitude as input, will not "blow up" and give an unbounded output. en.wikipedia.org /wiki/Marginal_stability   (262 words)

 MSM - Vol IV - Chapter 6.C Issue a stability letter to the owner of the vessel, send a copy to the OCMI to be referenced on the COI, and direct the load line assigning authority to indicate the date and issuing office on the face of the Load Line Certificate. Issue a stability letter to the owner to be placed on the vessel and send a copy to the assigning authority, directing its attachment to the Load Line Certificate and indication of the date and issuing office on the face of the certificate. Temporary stability letters should contain restrictions (e.g., a conservative curve of required metacentric height, a reduction in deck cargo, a reduction in the number of passengers or a reduced draft) to ensure that the vessel meets the applicable stability criteria and that owners have an incentive to obtain permanent stability letters as soon as possible. www.uscg.mil /hq/g-m/nmc/pubs/msm/v4/c6-sect_c.htm   (1350 words)

 [No title] Continuous-time systems: A system is marginally stable iff all eigenvalues of A have zero or negative real parts and those with zero real parts are simple roots of the minimal polynomial of A. Examples: (5.4 text p. BIBO stability does not in general imply asymptotic stability. Discrete-time systems: A system is marginally stable iff all eigenvalues of A have magnitudes less than or equal to 1 and those with unity magnitude are simple roots of the minimal polynomial of A. A system is asymptotically stable iff all (s of A have magnitudes less than 1. www.csus.edu /indiv/n/ngw/EEE-241/Stability.doc   (1164 words)

 CAMP/Nonlinear PDE's Seminar The background field method is interpreted as a rigorous implementation of heuristic marginal stability concepts producing rigorous upper limits on the time-averaged convective heat transport (the Nusselt number Nu) as a function of the Rayleigh number (Ra). The background field method is interpreted as a rigorous implementation of heuristic marginal stability concepts producing rigorous limits on the time-averaged convective heat transport, i.e., the Nusselt number Nu, as a function of the Rayleigh number Ra. Rigid body rotation of an inviscid, incompressible fluid in an axially symmetric container is stable, but, if the container departs even slightly from axial symmetry then the corresponding steady flow is known to be linearly unstable for certain values of the parameters (aspect ratios of the ellipsoid). people.cs.uchicago.edu /~schenkel/camp/camp.html   (2721 words)

 Evolutionary Bioinformatics Online 2006:2   (Site not responding. Last check: ) Others have suggested that stability and functionality are contradictory qualities, and that selection for both criteria results in marginally stable proteins, optimised to satisfy the competing design pressures. In the model, marginal stability is not required for ligand-binding functionality and we observe no competing design pressures. The resulting proteins are marginally stable, again demonstrating that neutral evolution is sufficient for explaining marginal stability in observed proteins. www.la-press.com /EBO-2-Williams.htm   (234 words)

 Nivedita Gupta's Home Page In addition, a secondary branch of marginal stability is obtained where highly deformed drops with lower surface tension are found to stabilize. The stability of the drops can be increased by increasing the thermal conductivity or the viscosity of the drop phase as compared to the bulk phase. The effect of thermocapillarity on the stability of drops in the secondary branch is currently being pursued. pubpages.unh.edu /~ngupta   (1361 words)

 Control System Stability The stability of a control system is often extremely important and is generally a safey issue in the engineering of a system. An example to illustrate the importance of stability is the control of a nuclear reactor. There is a need for stability analysis to determine how close the system is to instability and how much margin when disturbances are present and when the gain is adjusted.. www.roymech.co.uk /Related/Control/Stability.html   (601 words)

 Astron. Astrophys. 339, 887-896 (1998) Shown is the marginal stability length as a function of the number of expansion functions used (the number of terms in the Fourier series, or twice the number of gridpoints for the finite element code). The superb agreement between the numerically calculated marginal stability length and the WKB results is most clearly displayed in Figs. What actually happens is that at the lower values of m the marginal stability length begins to assume a different form of scaling, one that is typical for force-free and nearly force-free fields. aa.springer.de /papers/8339003/2300887/sc4.htm   (1358 words)

 Global Alfvén Eigenmodes Stability in ITER The stability of Alfvén eigenmodes (AE) is one of the key issues which needs to be addressed to build tokamak reactors [1], but cannot really be tested experimentally in the smaller, near to break-even plasmas achievable today. In DIII-D, the coupling to a drift-kinetic Alfvén wave in the plasma core has been shown to be responsible for the destabilization of AE by neutral beams [2, 3] and the wavelength modifications due to the magnetic shear in the plasma core/edge to change dramatically the damping rates measured in JET [4, 5]. The marginal stability of TAE modes is determined globally as a function of the critical volume averaged pressure www.nada.kth.se /~jaun/Research/pub/ITER97/iter.html   (1232 words)

 Marginal stability diagrams for infinite-n ballooning modes The perturbed equilibria are analysed for infinite-n ballooning stability and marginal stability diagrams are constructed that are analogous to the (s, α) diagrams constructed for axisymmetric configurations. Stability diagrams for the quasi-axially symmetric NCSX, a quasi-poloidally symmetric configuration and the quasi-helically symmetric HSX are compared. To explain the different regions of stability, the curvature and local shear of the quasi-poloidal configuration are analysed. stacks.iop.org /0741-3335/46/869   (420 words)

 Research projects of Ian A. Hiskens The stability of a limit cycle is determined by its characteristic multipliers. Stability theory for switched ODE systems is being adapted to switched DAE systems, which are more common in power system applications. This project is exploring algorithms for determining parameter values that result in marginal stability of a system. eceserv0.ece.wisc.edu /~hiskens/research.htm   (1170 words)

 Marginal Stability of Thick Continental Lithosphere   (Site not responding. Last check: ) The alteration of ancient lithosphere within plate interiors, independent of spatial proximity to continental margins, suggests that lithosphere may not be perfectly stable. We argue that subcontinental mantle lithosphere, not just on its margins, but also within its interior, has persisted in a thermal and mechanical state near the threshold of stability, such that the local Rayleigh number for the lithosphere is close to a critical value, $Ra_c$. Applied to continental lithosphere in a thermal and mechanical state near the instability threshold, this relationship implies that the lithospheric thickness \emph{must} decrease as the mean density of the lithospheric mantle increases, consistent with the geological record. www.ldeo.columbia.edu /~liz/MargStabAbs.html   (423 words)

 Hybrid simulations of the magnetosheath compression: Marginal stability path In this stable region the plasma behaves double-adiabatically and an important proton temperature anisotropy appears. When the plasma becomes unstable to AIC instability, the adiabatic behavior is broken and the AIC waves keep the system close to marginal stability, the theoretical growth rate being about constant, small and positive. This marginal stability behavior is slightly disrupted for high proton parallel beta, where the mirror mode becomes unstable. www.agu.org /pubs/crossref/2003/2003GL017855.shtml   (315 words)

 stability For an analysis of the longitudinal stability of the craft it is convenient to use the centre of gravity (CG) as the origin of the coordinate system and to transform all the relevant forces and moments to this point. The criterion for static height stability is that the centre in height is located upstream of the centre in pitch. A general rule to increase longitudinal stability of the wing is to unload the rear and load the front. www.se-technology.com /wig/html/main.php?open=stability&code=0   (2156 words)

 MT 5632 Hydrodynamic Stability Theory In this course we investigate the hydrodynamic stability of a variety of fluid ranging from thin layers heated from below, to the flow between rotating cylinders, and shear and boundary layer flows. The aim of this course is to look at various topics in hydrodynamic stability theory and introduce students to some of the classical as well as more modern ideas and techniques. By the end of this course students should be able to (i) derive linearised stability equations for a given basic state, (ii) perform a normal-mode analysis leading to an eigenvalue problems, (iii) use the ideas of weakly non-linear stability theory in simple flows, (iv) appreciate the different physical mechanisms leading to instability in fluid flows. www.ma.man.ac.uk /DeptWeb/MScCourses/APPMSC/newmtp/mt5632hy.htm   (304 words)

 Marginal Revolution: Current Affairs Archives Betsey Stevenson and I had an op-ed in yesterday’s New York Times noting a very simple fact: those married in the 1990s have proved less likely to divorce than those wed in the 1980s, which were less likely to divorce than those wed in the 1970s. The two women carried on about liquidity and profit margins, and recalled with pride attending the first shareholder meeting of KenGen this year, an event so huge that it had to be held in the city's largest soccer stadium. This is testament to the remarkable new-found stability of the Mexican peso. www.marginalrevolution.com /marginalrevolution/current_affairs   (11459 words)

 MHD accretion disks Treating the region within the radius of marginal stability as force-free, some authors have argued that the large-scale magnetic field near the fl hole is always weak due to the relatively weak fields at which the MRI saturates (Ghosh and Abramowicz 1997; Livio, Ogilvie and Pringle 1999). Such fields may be effective at extracting the rotational energy of the fl hole and/or creating a flow of energy and angular momentum from within the radius of marginal stability to outer parts of the accretion disk. Our preliminary investigation (Armitage, Reynolds and Chiang 2000) reveals that the field does indeed become strong within the radius of marginal stability, but there is very little transport of energy or angular momentum from this region to the outer accretion disk. www.astro.umd.edu /~chris/Research/mhd_prof/mhd_prof.html   (705 words)

 Nonlinear Theory for Fishbone Modes   (Site not responding. Last check: ) One is where the diamagnetic drift dominates the mode response and the hot particle response is dominantly are a perturbation, resonant at the precessional drift frequency, that destabilizes the wave. The second is where the diamagnetic drift is not dominant and the hot particles are essential in allowing the existence of a kink eigenmode that gives rise, at marginal stability, to an oscillating perturbation whose frequency is characterized by the hot particle precession drift. In all limits we can develop a nonlinear theory near marginal stability and determine whether modes can saturate at a low level characterized by the distance from marginal stability or explode to a higher level. flux.aps.org /meetings/BAPSDPP96/abs/S740041.html   (199 words)

 Axisymmetric stability   (Site not responding. Last check: ) We perform a local stability analysis, which is correct for axisymmetric disturbances that cannot propagate to the boundaries of our system, by restricting The stability diagram for clumping into axisymmetric rings by a self-gravitating, differentially rotating, gaseous disk. This coincidence between the conditions prevailing locally in the Galaxy and those required for marginal axisymmetric stability has prompted speculation concerning how such a state might have arisen naturally because of the action of past instabilities in the disk of stars, or because of some self-regulation by the interstellar gas. grus.berkeley.edu /~jrg/ay202/node155.html   (619 words)

 Asymptotic stability - Wikipedia, the free encyclopedia A discrete linear time-invariant system is asymptotically stable if and only if the poles (or eigenvalues) of its transfer function lie strictly within the unit circle centered on the origin of the complex plane. If oscillations do not die away, or the system does not return to its original output when an impulse is applied, the system is instead marginally stable. It will stay in the same position and will not, as would be the case if the system were only marginally stable or entirely unstable, continue to move away from the bottom of the ladle under this constant force equal to its weight. en.wikipedia.org /wiki/Asymptotic_stability   (491 words)

 Marginal stability of micropolar ferromagnetic fluid saturating a porous medium   (Site not responding. Last check: ) Marginal stability of micropolar ferromagnetic fluid saturating a porous medium This paper deals with the theoretical investigation of the marginal stability of a micropolar ferromagnetic fluid layer heated from below saturating a porous medium subjected to a transverse uniform magnetic field. The principle of exchange of stabilities is found to hold true for the micropolar ferromagnetic fluid saturating a porous medium heated from below in the absence of the micropolar viscous effect and microinertia. stacks.iop.org /1742-2140/3/i=4/a=005?rss=1.0   (376 words)

 [48.06] Marginal Gravitational Stability and Viscous Transport in Saturn's A Ring   (Site not responding. Last check: ) Recurrent local gravitational instabilities in the outer portions of Saturn's rings tend to form hundred-meter-scale wakes" that are believed to cause the observed azimuthal brightness asymmetry in the rings. A self-consistent theory of viscous transport in a marginally stable planetary ring has been derived from kinetic theory, which includes both the enhanced viscous stirring by gravitational instabilities and the inhibition of instabilities by viscous stirring. This theory extends the work of Ward and Cameron by predicting the steady-state velocity dispersion and the amplitude of the wakes" in a marginally stable planetary ring. www.aas.org /publications/baas/v32n3/dps2000/542.htm   (292 words)

 Course Descriptions In this course we investigate the hydrodynamic stability of a variety of flows ranging from thin layers heated from below, to the flow between rotating cylinders, shear and boundary layer flows. The aim of this course unit is to look at various topics in hydrodynamic stability theory and introduce students to some of the classical as well as more modern ideas and techniques. Basic concepts of stability theory, stability, instability, normal modes, marginal stability, neutral curves, temporal/spatial growth. www.ma.man.ac.uk /DeptWeb/UGCourses/Syllabus/Level4/MT4632.html   (253 words)

 Astron. Astrophys. 346, 303-312 (1999) on m, it is very obvious that the leading contribution of the marginal stability length, does follow the assumed linear scaling with m, as specified in Eq. So, to determine the WKB estimate of the marginal stability length in sheared force-free equilibria, we proceed as follows. term in the expansion of the marginal stability length, i.e. aa.springer.de /papers/9346001/2300303/sc2.htm   (3022 words)

 Learn more about the safety features of your vehicle with the car safety guide at CarsDirect.com Automotive Engineers have designed the body parts of a vehicle to crumple in predetermined patterns to absorb the energy from a crash's impact and maintain the integrity of the passenger compartment, keeping the driver and passengers safer. The individual systems are combined in an effort to reduce tire spinning, skidding, and tractionless cornering, keeping your tires in maximum contact with the road. Found mostly on luxury models, stability systems are slowly working their way into more vehicles. www.carsdirect.com /features/safetyfeatures   (1074 words)

 Urea-induced denaturation of apolipoprotein serum amyloid A reveals marginal stability of hexamer -- Wang and ... Urea-induced denaturation of apolipoprotein serum amyloid A reveals marginal stability of hexamer -- Wang and Colón 14 (7): 1811 -- Protein Science Urea-induced denaturation of apolipoprotein serum amyloid A reveals marginal stability of hexamer stability of hexameric SAA2.2 and the presence of residual structure www.proteinscience.org /cgi/content/abstract/14/7/1811   (281 words)

 Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis ... The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields. www.hindawi.com /GetArticle.aspx?doi=10.1155/S1023621X98000074   (238 words)

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