1,631 research outputs found
Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling
In this work a robust exponential function based controller is designed to
synchronize effectively a given class of Chua's chaotic systems. The stability
of the drive-response systems framework is proved through the Lyapunov
stability theory. Computer simulations are given to illustrate and verify the
method.Comment: 12 pages, 18 figure
Dewetting dynamics of stressed viscoelastic thin polymer films
Ultrathin polymer films that are produced e.g. by spin-coating are believed
to be stressed since polymers are 'frozen in' into out-of-equilibrium
configurations during this process. In the framework of a viscoelastic thin
film model, we study the effects of lateral residual stresses on the dewetting
dynamics of the film. The temporal evolution of the height profiles and the
velocity profiles inside the film as well as the dissipation mechanisms are
investigated in detail. Both the shape of the profiles and the importance of
frictional dissipation vs. viscous dissipation inside the film are found to
change in the course of dewetting. The interplay of the non-stationary
profiles, the relaxing initial stress and changes in the dominance of the two
dissipation mechanisms caused by nonlinear friction with the substrate is
responsible for the rich behavior of the system. In particular, our analysis
sheds new light on the occurrence of the unexpected maximum in the rim width
obtained recently in experiments on PS-PDMS systems.Comment: 11 pages, 10 figure
Finite-time synchronization of tunnel diode based chaotic oscillators
This paper addresses the problem of finite-time synchronization of tunnel
diode based chaotic oscillators. After a brief investigation of its chaotic
dynamics, we propose an active adaptive feedback coupling which accomplishes
the synchronization of tunnel diode based chaotic systems with and without the
presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov
stability theories. This feedback coupling could be applied to many other
chaotic systems. A finite horizon can be arbitrarily established by ensuring
that chaos synchronization is achieved at a pre-established time. An advantage
of the proposed feedback coupling is that it is simple and easy to implement.
Both mathematical investigations and numerical simulatioComment: 11 pages, 43 figure
On a Lie Algebraic Characterization of Vector Bundles
We prove that a vector bundle is characterized by the Lie
algebra generated by all differential operators on which are eigenvectors
of the Lie derivative in the direction of the Euler vector field. Our result is
of Pursell-Shanks type but it is remarkable in the sense that it is the whole
fibration that is characterized here. The proof relies on a theorem of [Lecomte
P., J. Math. Pures Appl. (9) 60 (1981), 229-239] and inherits the same
hypotheses. In particular, our characterization holds only for vector bundles
of rank greater than 1
Modulation Theory and Systems
Contains research objectives and reports on three research projects
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