312 research outputs found
On the boundedness of some nonlinear differential equation of second order
In this paper we study the boundedness of the solutions of some nonlinear dofferential equation using as a key tool the Second Lyapunov method, i.e. find sufficient conditions under which the solutions of this equation are bounded. Variuos particular cases and methodological remarks are included at the end of paper.Fil: Guzmán, Paulo Matias. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientÃficas y Técnicas; ArgentinaFil: Napoles Valdes, Juan Eduardo. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; ArgentinaFil: Lugo, Luciano Miguel. Universidad Nacional del Nordeste. Facultad de Ciencias Exactas y Naturales y Agrimensura. Departamento de Matemática; Argentin
Quasi-isotropic cycles and non-singular bounces in a Mixmaster cosmology
A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous
solution of Einstein's equations and it can represent the space-averaged
Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe
with non-singular bounces which are quasi-isotropic. A fluid with a non-linear
equation of state allows non-singular bounces. Using negative anisotropic
stresses successfully isotropises this Universe and mitigates the well known
Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster,
going through an infinite series of different cycles separated by bounces, with
a sizable fraction of cycles isotropic enough to be well approximated by a
standard Friedmann-Lema\^itre-Robertson-Walker model from the radiation era
onward.Comment: 5 pages, 4 figure
The historical development of classical stability concepts: Lagrange, Poisson and Lyapunov stability
A brief historical overview is given which discusses the development of classical stability concepts, starting in the seventeenth century and finally leading to the concept of Lyapunov stability at the beginning of the twentieth century. The aim of the paper is to find out how various scientists thought about stability and to which extent their work is related to the stability concepts bearing their names, i.e. Lagrange, Poisson and Lyapunov stability. To this end, excerpts of original texts are discussed in detail. Furthermore, the relationship between the various works is addresse
A Curvature Principle for the interaction between universes
We propose a Curvature Principle to describe the dynamics of interacting
universes in a multi-universe scenario and show, in the context of a simplified
model, how interaction drives the cosmological constant of one of the universes
toward a vanishingly small value. We also conjecture on how the proposed
Curvature Principle suggests a solution for the entropy paradox of a universe
where the cosmological constant vanishes.Comment: Essay selected for an honorable mention by the Gravity Research
Foundation, 2007. Plain latex, 8 page
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From Andronow to Zypkin: an outline of the history of non-linear dynamics in the USSR
By employing the conventional German, rather than English or international transliterations – particularly of the name written ‘Tsypkin’ in English –I artfully suggest that this talk is an ‘A to Z’ of Russian non-linear dynamics. However, the period under consideration is not delineated by these two names. Rather, I begin with the Poincaré-Lyapunov heritage – but then concentrate on the way that this thinking was transformed through Russian mathematicians, scientists and engineers such as Mandelshtam, Andronov, Lure and others, over a large part of the twentieth century. (Tsypkin, in fact, receives only a minor mention, as his major achievements were in other areas.) As a historian of automatic control, I draw primarily on applications of non-linear theory in feedback systems
Estabilidad de Sistemas No Lineales Basada en la TeorÃa de Liapunov
ResumenEl comportamiento dinámico de los sistemas no lineales es mucho más rico que el de los lineales y su análisis mucho más complicado. Para el análisis de estabilidad, las técnicas basadas en la teorÃa de Liapunov tienen un lugar destacado. En este articulo se revisa parte de esta teorÃa incluyendo las técnicas de estimación de la cuenca de atracción. También se repasan los resultados que han aparecido en los últimos años sobre la aplicación a este campo de los métodos numéricos de optimización de suma de cuadrados
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