Stability of the solutions of the Gross-Pitaevskii equation

We examine the static and dynamic stability of the solutions of the Gross-Pitaevskii equation and demonstrate the intimate connection between them. All salient features related to dynamic stability are reflected systematically in static properties. We find, for example, the obvious result that static stability always implies dynamic stability and present a simple explanation of the fact that dynamic stability can exist even in the presence of static instability.Comment: 7 pages, 1 figur

Wealth inequality and dynamic stability

In this paper we explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. The stability of the steady state depends on the various parameters of the model and in particular on individual preferences. We show that when consumers have identical preferences and the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral. As there is not yet evidence on the concavity of absolute risk tolerance, our results unfortunately do not lead to a unique conclusion on the sign of the effect of wealth inequality on stability.Economic growth; Heterogeneity; Wealth and Income Inequality; Instability

Tropical Atmospheric Circulations: Dynamic Stability and Transitions

In this article, we present a mathematical theory of the Walker circulation of the large-scale atmosphere over the tropics. This study leads to a new metastable state oscillation theory for the El Nino Southern Oscillation (ENSO), a typical inter-annual climate low frequency oscillation. The mathematical analysis is based on 1) the dynamic transition theory, 2) the geometric theory of incompressible flows, and 3) the scaling law for proper effect of the turbulent friction terms, developed recently by the authors

Dynamic Stability and Reform of Political Institutions

This paper studies dynamic, endogenous institutional change. We introduce the class of dynamic political games (DPGs), dynamic games in which future political aggregation rules are decided under current ones, and the resulting institutional choices do not affect payoffs or technology directly. A companion paper (Lagunoff (2005b)) establishes existence of Markov Perfect equilibria of dynamic political games. The present paper examines issues of stability and reform when such equilibria exist. Which environments tend toward institutional stability? Which tend toward reform? We show that when political rules are dynamically consistent and private sector decisions areinessential,reform never occurs: all political rules are stable. Roughly,private sector decisions are inessential if any feasible ``social' continuation payoff can achieved by public sector decisions alone. More generally, we identify sufficient conditions for stability and reform in terms of recursive self selection and recursive self denial,incentive compatibility concepts that treat the rules themselves as ``players' who can strategically delegate future policy-making authority to different institutional types. These ideas are illustrated in an example of dynamic public goods provision.Recursive, dynamic political games, institutional reform, stability, dynamically consistent rules, inessential, recursive self selection.

A discussion of dynamic stability measurement techniques

Techniques for the measurement of the dynamic stability of linear systems are discussed. Particular attention is given to an analysis of the errors in the procedures, and to methods for calculating the system damping from the data. The techniques discussed include: transient decay, moving block analysis, spectral analysis, random decrement signatures, transfer function analysis, and parameter identification methods. The special problems of rotorcraft dynamic stability testing are discussed