4,342 research outputs found
Controlling Quantum Chaos: Optimal Coherent Targeting
One of the principal goals of controlling classical chaotic dynamical systems is known as targeting, which is the very weakly perturbative process of using the system's extreme sensitivity to initial conditions in order to arrive at a predetermined target state. It is shown that a generalization to chaotic quantum systems is possible in the semiclassical regime, but requires tailored perturbations whose effects must undo the dynamical spreading of the evolving quantum state. The procedure described here is applied to initially minimum uncertainty wave packets in the quantum kicked rotor, a preeminent quantum chaotic paradigm, to illustrate the method, and investigate its accuracy. The method's error can be made to vanish as ℏ→0
Amplitude Death: The emergence of stationarity in coupled nonlinear systems
When nonlinear dynamical systems are coupled, depending on the intrinsic
dynamics and the manner in which the coupling is organized, a host of novel
phenomena can arise. In this context, an important emergent phenomenon is the
complete suppression of oscillations, formally termed amplitude death (AD).
Oscillations of the entire system cease as a consequence of the interaction,
leading to stationary behavior. The fixed points that the coupling stabilizes
can be the otherwise unstable fixed points of the uncoupled system or can
correspond to novel stationary points. Such behaviour is of relevance in areas
ranging from laser physics to the dynamics of biological systems. In this
review we discuss the characteristics of the different coupling strategies and
scenarios that lead to AD in a variety of different situations, and draw
attention to several open issues and challenging problems for further study.Comment: Physics Reports (2012
Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos
We present a novel technique, which we term bailout embedding, that can be
used to target orbits having particular properties out of all orbits in a flow
or map. We explicitly construct a bailout embedding for Hamiltonian systems so
as to target KAM orbits. We show how the bailout dynamics is able to lock onto
extremely small KAM islands in an ergodic sea.Comment: 3 figures, 9 subpanel
Kinematics of Clustering
The dynamical system for inertial particles in fluid flow has both attracting
and repelling regions, the interplay of which can localize particles. In
laminar flow experiments we find that particles, initially moving throughout
the fluid domain, can undergo an instability and cluster into subdomains of the
fluid when the flow Reynolds number exceeds a critical value that depends on
particle and fluid inertia. We derive an expression for the instability
boundary and for a universal curve that describes the clustering rate for all
particles.Comment: 13 pages, 6 figure
The Control of Dynamical Systems - Recovering Order from Chaos -
Following a brief historical introduction of the notions of chaos in
dynamical systems, we will present recent developments that attempt to profit
from the rich structure and complexity of the chaotic dynamics. In particular,
we will demonstrate the ability to control chaos in realistic complex
environments. Several applications will serve to illustrate the theory and to
highlight its advantages and weaknesses. The presentation will end with a
survey of possible generalizations and extensions of the basic formalism as
well as a discussion of applications outside the field of the physical
sciences. Future research avenues in this rapidly growing field will also be
addressed.Comment: 18 pages, 9 figures. Invited Talk at the XXIth International
Conference on the Physics of Electronic and Atomic Collisions (ICPEAC), July
22-27, 1999 (Sendai, Japan
Drift and its mediation in terrestrial orbits
The slow deformation of terrestrial orbits in the medium range, subject to
lunisolar resonances, is well approximated by a family of Hamiltonian flow with
degree-of-freedom. The action variables of the system may experience
chaotic variations and large drift that we may quantify. Using variational
chaos indicators, we compute high-resolution portraits of the action space.
Such refined meshes allow to reveal the existence of tori and structures
filling chaotic regions. Our elaborate computations allow us to isolate precise
initial conditions near specific zones of interest and study their asymptotic
behaviour in time. Borrowing classical techniques of phase- space
visualisation, we highlight how the drift is mediated by the complement of the
numerically detected KAM tori.Comment: 22 pages, 11 figures, 1 table, 52 references. Comments and feedbacks
greatly appreciated. This article is part of the Research Topic `The
Earth-Moon System as a Dynamical Laboratory', confer
https://www.frontiersin.org/research-topics/5819/the-earth-moon-system-as-a-dynamical-laborator
- …