12,180 research outputs found
Solvable model for spatiotemporal chaos
We show that the dynamical behavior of a coupled map lattice where the individual maps are Bernoulli shift maps can be solved analytically for integer couplings. We calculate the invariant density of the system and show that it displays a nontrivial spatial behavior. We also introduce and calculate a generalized spatiotemporal correlation function
Memory difference control of unknown unstable fixed points: Drifting parameter conditions and delayed measurement
Difference control schemes for controlling unstable fixed points become
important if the exact position of the fixed point is unavailable or moving due
to drifting parameters. We propose a memory difference control method for
stabilization of a priori unknown unstable fixed points by introducing a memory
term. If the amplitude of the control applied in the previous time step is
added to the present control signal, fixed points with arbitrary Lyapunov
numbers can be controlled. This method is also extended to compensate arbitrary
time steps of measurement delay. We show that our method stabilizes orbits of
the Chua circuit where ordinary difference control fails.Comment: 5 pages, 8 figures. See also chao-dyn/9810029 (Phys. Rev. E 70,
056225) and nlin.CD/0204031 (Phys. Rev. E 70, 046205
Robustness of predator-prey models for confinement regime transitions in fusion plasmas
Energy transport and confinement in tokamak fusion plasmas is usually determined by the coupled nonlinear interactions of small-scale drift turbulence and larger scale coherent nonlinear structures, such as zonal flows, together with free energy sources such as temperature gradients. Zero-dimensional models, designed to embody plausible physical narratives for these interactions, can help to identify the origin of enhanced energy confinement and of transitions between confinement regimes. A prime zero-dimensional paradigm is predator-prey or Lotka-Volterra. Here, we extend a successful three-variable (temperature gradient; microturbulence level; one class of coherent structure) model in this genre [M. A. Malkov and P. H. Diamond, Phys. Plasmas 16, 012504 (2009)], by adding a fourth variable representing a second class of coherent structure. This requires a fourth coupled nonlinear ordinary differential equation. We investigate the degree of invariance of the phenomenology generated by the model of Malkov and Diamond, given this additional physics. We study and compare the long-time behaviour of the three-equation and four-equation systems, their evolution towards the final state, and their attractive fixed points and limit cycles. We explore the sensitivity of paths to attractors. It is found that, for example, an attractive fixed point of the three-equation system can become a limit cycle of the four-equation system. Addressing these questions which we together refer to as “robustness” for convenience is particularly important for models which, as here, generate sharp transitions in the values of system variables which may replicate some key features of confinement transitions. Our results help to establish the robustness of the zero-dimensional model approach to capturing observed confinement phenomenology in tokamak fusion plasmas
Comment on "White-Noise-Induced Transport in Periodic Structures"
In the paper by J.\L uczka {\em et al.} ({\em Europhys. Lett.}, {\bf 31}
(1995) 431), the authors reported by rigorous calculation that an additive
Poissonian white shot noise can induce a macroscopic current of a dissipative
particle in a periodic potential -- even {\em in the absence} of spatial
asymmetry of the potential. We argue that their main result is an obvious one
caused by the spatially broken symmetry of a probability distribution of the
additive noise, unlike the similar result caused by chaotic noise which has a
symmetric probability distribution ({\em J.Phys.Soc.Jpn.}, {\bf 63} (1994)
2014).Comment: 2 pages (Latex); submitted to Europhys.Let
Pinning control of spatiotemporal chaos
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a coupled map lattice as an example. The optimal arrangement of the control sites is shown to depend on the symmetry properties of the system, while their minimal density depends on the strength of noise in the system. The method is shown to work in any region of parameter space and requires a significantly smaller number of controllers compared to the method proposed earlier by Hu and Qu [Phys. Rev. Lett. 72, 68 (1994)]. A nonlinear generalization of the method for a 1D lattice is also presented
One-dimensional Hubbard model at quarter filling on periodic potentials
Using the Hubbard chain at quarter filling as a model system, we study the
ground state properties of highly doped antiferromagnets. In particular, the
Hubbard chain at quarter filling is unstable against 2k_F- and 4k_F-periodic
potentials, leading to a large variety of charge and spin ordered ground
states. Employing the density matrix renormalization group method, we compare
the energy gain of the ground state induced by different periodic potentials.
For interacting systems the lowest energy is found for a 2k_F-periodic magnetic
field, resulting in a band insulator with spin gap. For strong interaction, the
4k_F-periodic potential leads to a half-filled Heisenberg chain and thus to a
Mott insulating state without spin gap. This ground state is more stable than
the band insulating state caused by any non-magnetic 2k_F-periodic potential.
Adding more electrons, a cluster-like ordering is preferred.Comment: 8 pages, 5 figures, accepted by Phys. Rev.
Plasmon Evolution and Charge-Density Wave Suppression in Potassium Intercalated Tantalum Diselenide
We have investigated the influence of potassium intercalation on the
formation of the charge-density wave (CDW) instability in 2H-tantalum
diselenide by means of Electron Energy-Loss Spectroscopy and density functional
theory. Our observations are consistent with a filling of the conduction band
as indicated by a substantial decrease of the plasma frequency in experiment
and theory. In addition, elastic scattering clearly points to a destruction of
the CDW upon intercalation as can be seen by a vanishing of the corresponding
superstructures. This is accompanied by a new superstructure, which can be
attributed to the intercalated potassium. Based on the behavior of the c-axis
upon intercalation we argue in favor of interlayer-sites for the alkali-metal
and that the lattice remains in the 2H-modification
Parallels between the dynamics at the noise-perturbed onset of chaos in logistic maps and the dynamics of glass formation
We develop the characterization of the dynamics at the noise-perturbed edge
of chaos in logistic maps in terms of the quantities normally used to describe
glassy properties in structural glass formers. Following the recognition [Phys.
Lett. \textbf{A 328}, 467 (2004)] that the dynamics at this critical attractor
exhibits analogies with that observed in thermal systems close to
vitrification, we determine the modifications that take place with decreasing
noise amplitude in ensemble and time averaged correlations and in diffusivity.
We corroborate explicitly the occurrence of two-step relaxation, aging with its
characteristic scaling property, and subdiffusion and arrest for this system.
We also discuss features that appear to be specific of the map.Comment: Revised version with substantial improvements. Revtex, 8 pages, 11
figure
Bifurcations and Chaos in Time Delayed Piecewise Linear Dynamical Systems
We reinvestigate the dynamical behavior of a first order scalar nonlinear
delay differential equation with piecewise linearity and identify several
interesting features in the nature of bifurcations and chaos associated with it
as a function of the delay time and external forcing parameters. In particular,
we point out that the fixed point solution exhibits a stability island in the
two parameter space of time delay and strength of nonlinearity. Significant
role played by transients in attaining steady state solutions is pointed out.
Various routes to chaos and existence of hyperchaos even for low values of time
delay which is evidenced by multiple positive Lyapunov exponents are brought
out. The study is extended to the case of two coupled systems, one with delay
and the other one without delay.Comment: 34 Pages, 14 Figure
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