Hierarchical Stability Research Articles

Bardic Nationalism: The Romantic Novel and the British Empire (review)

REVIEWS 239 have its excellent moments and fine insights, is crippling, a serious undermining of whatever authority Brown's readers will feel he has been able to muster. Which is not much. Jerry C. Beasley University of Delaware Katie Trumpener. Bardic Nationalism: The Romantic Novel and the British Empire. Princeton: Princeton University Press, 1997. xviii + 426pp. US$55.00 (cloth); US$19.95 (paper). ISBN 0-691-04481-3. Katie Trumpener's vastly ambitious book attempts "to redraw our picture of the origins of cultural nationalism, the lineages of the novel, and the early literary history of the English-speaking world. In the process, it argues implicitly for the disciplinary transformation of English literature, so called, and for a new way of conceiving the disciplinary mandate ofcomparative literature" (p. xi). Whether or not the reader grants the full success ofall these ambitions, this is ground-breaking work, one that will be a "citation classic" for some time to come. Consciously setting out to complement, specify, and correct Benedict Anderson's influential Imagined Communities, Trumpener opens the study of the Romantic novel in English to the methods, assumptions, and intents developed in the study of postcolonial literature. This aperture makes authors such as Walter Scott, John Gait, and Sydney Owenson current concerns in ways that they have not been for many years. (I assume I am not alone in the surprising experience of having graduate students working on contemporary Caribbean fiction knock at my door to discuss Guy Mannering.) Trumpener begins her study with the antiquarian revivalist figure of the bard and documents the opposed ways in which the figure was adopted and adapted by differing, contestatory groups in the as yet unimagined community of Great Britain. She distinguishes first the bard as figured in the writings of nationalists from Scotland, Wales, and Ireland from the bard of English writers: "Scottish, Welsh, and Irish nationalists conceive of a new national literary history under the sign of the bard, a figure who represents the resistance ofvernacular oral traditions to the historical pressures of English imperialism and whose performance brings the voices of the past into the sites of the present" (p. 33). In England, on the other hand, the bard becomes a figure for the sundered "organic character of literary life under feudal patronage" (p. 7) and, by inversion, for anxieties about the commodification of literary arts and the concomitant social marginalization of poets. The second crucial distinction is among the bardic nationalisms in cultural circulation in the early years ofthe nineteenth century: an old nationalism predicated on mourning what is more or less inevitably and irretrievably lost; a reactionary nationalism that refuses to accept loss and establishes a corollary longing 240 EIGHTEENTH-CENTURY FICTION 11:2 for a restored hierarchical stability under a national élite; a radical nationalism that merges nationalist consciousness with "Jacobin" political and economic critique . Trumpener's deployment of these three models especially as they manifest themselves in the multiple and coexisting discourses of the novel gives her analyses of individual texts an admirable suppleness and a keen insight into internal contradiction. Having established its ground, Trumpener's study proceeds to cases. Arthur Young's Tour in Ireland and Samuel Johnson's Journey to the Western Islands of Scotland serve as occasions for considering the clash between the imperial centre and its protonationalistperipheries. Each discussion moves from discussing its key imperial text to surveying responses from Irish or Scottish writers. Hence Young yields to Edgeworth, Owenson, and Maturin; Johnson enters protesting against Macpherson's Ossian, then withdraws grudgingly to make way for Mackenzie, Elizabeth Ryves, and Scott. Scott is at the centre ofTrumpener's third chapter and, after the Introduction, the most important one. This is very much a contextually defined Scott, no longer seen as creating the historical novel out of scraps of gothic romance, popular history, national fictions, and antiquarian researches. Trumpener's historical novel emerges very specifically in the context of the national tale. It is here that Trumpener strives to employ formal notions of genre to bridge what she earlier frames as the disciplinary fissures deepened "during the 1980s, when Marxist literary history did battle with rhetorically oriented deconstruction" (p. xv). She argues that...

Criteria of Dynamical Isolation of Binaries and Multiples

In order to obtain an objective criterion for dynamical isolation of binaries within systems of large multiplicity we study numerically the dynamical behavior and average parameters of stable hierarchical triple systems containing a close binary. Using the new criterion for hierarchical stability of triple systems with different mass ratios of components (Kiseleva, Eggleton, Anosova 1994; Kiseleva, Eggleton, Orlov 1994) the perturbing force from the outer body on the close inner binary is estimated. On this basis, the critical separations are obtained when both inner and outer orbits are practically not perturbed. Because the dispersion of masses has a very strong influence on dynamical processes in N-body systems, mass ratios of subsystems, and sometimes within subsystems, should always be taken into account.

Effective potential, Hill-type stability and Sundman's inequality

The velocity decomposition of Saari ( Celest. Mech. 33, 299, 1984) is shown to capture the best possible effective potential of the general N-body problem. This improves the effective potential inherent to Sundman's inequality. Saari's approach is simplified by virtue of the inertia tensor and inertia ellipsoid. The inequality stronger than Sundman's obtained for the flat problem by Saari ( Celest. Mech. 40, 197, 1987) is not only extended to the general N-body problem but is also shown to be valid under more relaxed conditions. For the spatial three-body problem, we also obtain a more explicit expression of the inequality which was used to plot the Hill-type surfaces by Ge and Leng ( Celest. Mech. 53, 233, 1992). It is proved that Hill-type stability guarantees one of the hierarchical stability conditions, and prevents cross-over of orbits.

Drosophila segmentation: Supercomputer simulation of prepattern hierarchy

Spontaneous prepattern formation in a two level hierarchy of reaction-diffusion systems is simulated in three space co-ordinates and time, mimicking gap gene and primary pair-rule gene expression. The model rests on the idea of Turing systems of the second kind, in which one prepattern generates position dependent rate constants for a subsequent reaction-diffusion system. Maternal genes are assumed responsible for setting up gradients from the anterior and posterior ends, one of which is needed to stabilize a double period prepattern suggested to underly the read out of the gap genes. The resulting double period pattern in turn stabilizes the next prepattern in the hierarchy, which has a short wavelength with many characteristics of the stripes seen in actual primary pair-rule gene expression. Without such hierarchical stabilization, reaction-diffusion mechanisms yield highly patchy short wave length patterns, and thus unreliable stripes. The model yields seven stable stripes located in the middle of the embryo, with the potential for additional expression near the poles, as observed experimentally. The model does not rely on specific chemical reaction kinetics, rather the effect is general to many such kinetic schemes. This makes it robust to parameter changes, and it has good potential for adapting to size and shape changes as well. The study thus suggests that the crucial organizing principle in early Drosophila embryogenesis is based on global field mechanisms, not on particular local interactions.

Author's comment to “on decentralized hierarchic stabilization of a large-scale system with constraints”

Author's comment to “on decentralized hierarchic stabilization of a large-scale system with constraints”

The effects of eccentricity on the hierarchical stability of low-mass binaries in three-body systems

On discute de la stabilite de systemes binaires a faible masse, se deplacant sur des orbites elliptiques, en presence d'un troisieme corps de grande masse, en termes de surfaces de vitesse zero a trois corps

On decentralized hierarchic stabilization of a large-scale system with constraints

A new stabilization method of a large-scale dynamic system, consisting of a set of interconnected subsystems, is presented in this paper. The topology of the interconnected subsystems is given as a network containing nodes with only one ingoing link, and none, one, or more outgoing links. Here, when the notion “node” is used a subsystem is assumed, and the links stand for the subsystem interconnections. The stabilization method is made only by the use of local linear state feedback around each subsystem, in order to satisfy constraints given in the problem. The interconnections among the subsystems are assumed to be nonlinear, time-varying. According to the topology of the large-scale system, the method of stabilization is hierarchic, one proceeds from node to node, and is applicable from a computer standpoint. A design algorithm follows directly, and can be made using the Generate and Test method for each subsystem independently, thus enabling designers to use a computer which has a video terminal as a peripheral unit and providing a possibility for interactive applications.

The hierarchical stability of satellite systems

On a utilise le critere de stabilite C 2 H pour determiner la stabilite hierarchisee des systemes planetaires dont les masses et les elements orbitaux sont bien connus. On a trouve qu'ils satisfont tous a ce systeme. On discute d'une approximation valable quand la primaire est beaucoup plus massive que les satellites

Resonant structure of the outer Solar System

Hierarchical stability of the outer Solar System is monitored through its 3-body subsystems by using numerically computed ephemerides for 5×106 yr. It is found that the stability parameters of Sun-Jupiter-Saturn and Sun-Uranus-Neptune oscillate in anti-phase in ∼1.1×106 yr. The mechanism responsible for this locking is a secular resonance between Uranus' perihelion and Jupiter's aphelion: the difference between the two librates within ∼±70° with the same period of ∼1.1×106 yr.

On the stability of hierarchical four-body systems

Generalized Jacobian coordinates can be used to decompose anN-body dynamical system intoN-1 2-body systems coupled by perturbations. Hierarchical stability is defined as the property of preserving the hierarchical arrangement of these 2-body subsystems in such a way that orbit crossing is avoided. ForN=3 hierarchical stability can be ensured for an arbitrary span of time depending on the integralz=c 2 h (angular momentum squared times energy): if it is smaller than a critical value, defined by theL 2 collinear equilibrium configuration, then the three possible hierarchical arrangements correspond to three disconnected subsets of the invariant manifold in the phase space (and in the configuration space as well; see Milani and Nobili, 1983a). The same definitions can be extended, with the Jacobian formalism, to an arbitrary hierarchical arrangement ofN≥4 bodies, and the main confinement condition, the Easton inequality, can also be extended but it no longer provides separate regions of trapped motion, whatever is the value ofz for the wholeN-body system,N≥4. However, thez criterion of hierarchical stability applies to every 3-body subsystem, whosez ‘integral’ will of course vary in time because of the perturbations from the other bodies. In theN=4 case we decompose the system into two 3-body subsystems whosec 2 h ‘integrals’,z 23 andz 34, att=0 are assumed to be smaller than the corresponding critical values $$\tilde z_{23} $$ and $$\tilde z_{34} $$ , so that both the subsystems are initially hierarchically stable. Then the hierarchical arrangement of the 4 bodies cannot be broken until eitherz 23 orz 34 is changed by an amount $$\tilde z_{ij} - z_{ij} \left( 0 \right)$$ ; that is the whole system is hierarchically stable for a time spain not shorter than the minimum between $$\Delta t_{23} = {{\left( {\tilde z_{23} - z_{23} \left( 0 \right)} \right)} \mathord{\left/ {\vphantom {{\left( {\tilde z_{23} - z_{23} \left( 0 \right)} \right)} {\dot z_{23} }}} \right. \kern-\nulldelimiterspace} {\dot z_{23} }}$$ and $$\Delta t_{34} = {{\left( {\tilde z_{34} - z_{34} \left( 0 \right)} \right)} \mathord{\left/ {\vphantom {{\left( {\tilde z_{34} - z_{34} \left( 0 \right)} \right)} {\dot z_{34} }}} \right. \kern-\nulldelimiterspace} {\dot z_{34} }}$$ . To estimate how long is this stability time, two main steps are required. First the perturbing potentials have to be developed in series; the relevant small parameters are some combinations of mass ratios and length ratios, theɛ ij of Roy and Walker. When an appropriate perturbation theory is based on theɛ ij , the asymptotic expansions are much more rapidly decreasing than the usual expansions in powers of the mass ratios (as in the classical Lagrange perturbation theory) and can be extended also to cases such as lunar theory or double binaries. The second step is the computation of the time derivatives $$\dot z_{ij} $$ (we limit ourselves to the planar case). To assess the long term behaviour of the system, we can neglect the short-periodic perturbations and discuss only the long-periodic and the secular perturbations. By using a Poisson bracket formalism, a generalization of Lagrange theorem for semimajor axes and a generalization of the classical first order theories for eccentricities and pericenters, we prove that thez ij do not undergo any secular perturbation, because of the interaction with the other subsystem, at the first order in theɛ ik . After the long-periodic perturbations have been accounted for, and apart from the small divisors problems that could arise both from ordinary and secular resonances, only the second order terms have to be considered in the computation of Δt 23, Δt 34. A full second order perturbative theory is beyond the scope of this paper; however an order-of-magnitude lower estimate of the Δt ij can be obtained with the very pessimistic assumption that essentially all the second order terms affect in a secular way thez ij . The same method could be applied also toN≥5 body systems. Since almost everyN-body system existing in nature is strongly hierarchical, the product of twoɛ ij is very small for almost all the real astronomical problems. As an example, the hierarchical stability of the 4-body system Sun, Mercury, Venus, and Jupiter is investigated; this system turns out to be stable for at least 110 million years. Although this hierarchical stability time is ∼10 times less than the real age of the Solar System, taking into account that many pessimistic assumptions have been done we can conclude that the stability of the Solar System is no more a forbidden problem for Celestial Mechanics.

Asymptotic Approach to Mirror Conditions as a Trapping Mechanism in N-Body Hierarchical Dynamical Systems

AbstractThe consequences for hierarchical stability of almost circular almost coplanar, low perturbation orbits in an n-body hierarchical dynamical system is discussed. It is shown that frequent close approaches to mirror conditions with subsequent reversing of perturbations is ensured by such properties. The part played by near commensurabilities in mean motion is also discussed, the Sun-Jupiter-Saturn case being taken as an example.

Hierarchical stability and alert state steering control of interconnected power systems

A state-space model of an interconnected power system having both generator and load nodes is proposed. The resulting system of equations is interpreted as the degenerate limit of a singularly perturbed system. The model is used to derive a condition for the (local) asymptotic stability of an equilibrium. This condition decomposes in an intuitive way for subsystems interconnected via a backbone network. The model is used to formulate the problem of steering the power system from a postdisturbance alert state to a secure state, and a solution to the steering problem is also proposed.

Some types of stability in the study of students' work values

It is suggested the concept of “stability” in the study of work values has at least three facets: (1) hierarchical stability, (2) response pattern stability, and (3) factor stability. These three facets are investigated using a sample of 165 Australian students, assessed using a work values list initially in Grade 12 and then 2 1 2 years later during which time all had engaged in full-time tertiary study. Of the 13 work values assessed only independence and intellectual stimulation increased in importance and surroundings decreased. Canonical correlation analysis revealed four significant response patterns which indicated that the same work value may sometimes be stable or changeable in combination with other work values. It was also found using factor analysis that two rotated principal components appeared stable over time. They were identified as an Intellectual Concern factor and People Concern factor. An Extrinsic Concern factor for subjects as high school students was found to differentiate into a Status/Power Concern factor and a Co-workers Concern factor by the time of the second assessment. A Freedom Concern factor found in the Grade 12 assessment was not discovered until 2 1 2 years later. The results confirm the need for further theoretical and methodological refinement of the notion of stability in the study of work values.

Decentralization, Stabilization, and Estimation of Large-Scale Linear Systems

In this work, we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation.A r.1ethod is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systema and is performed on the subsystem level.A multi level control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems. Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations.The proposed out-put decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low order estimators, thus avoiding a design of a single estimator for the overall system.

Decentralization, stabilization, and estimation of large-scale linear systems

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems. Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.