12,916 research outputs found
Kernel Analog Forecasting: Multiscale Test Problems
Data-driven prediction is becoming increasingly widespread as the volume of
data available grows and as algorithmic development matches this growth. The
nature of the predictions made, and the manner in which they should be
interpreted, depends crucially on the extent to which the variables chosen for
prediction are Markovian, or approximately Markovian. Multiscale systems
provide a framework in which this issue can be analyzed. In this work kernel
analog forecasting methods are studied from the perspective of data generated
by multiscale dynamical systems. The problems chosen exhibit a variety of
different Markovian closures, using both averaging and homogenization;
furthermore, settings where scale-separation is not present and the predicted
variables are non-Markovian, are also considered. The studies provide guidance
for the interpretation of data-driven prediction methods when used in practice.Comment: 30 pages, 14 figures; clarified several ambiguous parts, added
references, and a comparison with Lorenz' original method (Sec. 4.5
Chaos in a double driven dissipative nonlinear oscillator
We propose an anharmonic oscillator driven by two periodic forces of
different frequencies as a new time-dependent model for investigating quantum
dissipative chaos. Our analysis is done in the frame of statistical ensemble of
quantum trajectories in quantum state diffusion approach. Quantum dynamical
manifestation of chaotic behavior, including the emergence of chaos, properties
of strange attractors, and quantum entanglement are studied by numerical
simulation of ensemble averaged Wigner function and von Neumann entropy.Comment: 9 pages, 18 figure
Deterministic inhomogeneous inertia ratchets
We study the deterministic dynamics of a periodically driven particle in the
underdamped case in a spatially symmetric periodic potential. The system is
subjected to a space-dependent friction coefficient, which is similarly
periodic as the potential but with a phase difference. We observe that
frictional inhomogeneity in a symmetric periodic potential mimics most of the
qualitative features of deterministic dynamics in a homogeneous system with an
asymmetric periodic potential. We point out the need of averaging over the
initial phase of the external drive at small frictional inhomogeneity parameter
values or analogously low potential asymmetry regimes in obtaining ratchet
current. We also show that at low amplitudes of the drive, where ratchet
current is not possible in the deterministic case, noise plays a significant
role in realizing ratchet current.Comment: 15 pages, 15 figure
Scarring and the statistics of tunnelling
We show that the statistics of tunnelling can be dramatically affected by
scarring and derive distributions quantifying this effect. Strong deviations
from the prediction of random matrix theory can be explained quantitatively by
modifying the Gaussian distribution which describes wavefunction statistics.
The modified distribution depends on classical parameters which are determined
completely by linearised dynamics around a periodic orbit. This distribution
generalises the scarring theory of Kaplan [Phys. Rev. Lett. {\bf 80}, 2582
(1998)] to describe the statistics of the components of the wavefunction in a
complete basis, rather than overlaps with single Gaussian wavepackets. In
particular it is shown that correlations in the components of the wavefunction
are present, which can strongly influence tunnelling-rate statistics. The
resulting distribution for tunnelling rates is tested successfully on a
two-dimensional double-well potential.Comment: 20 pages, 4 figures, submitted to Ann. Phy
Semiclassical Field Theory Approach to Quantum Chaos
We construct a field theory to describe energy averaged quantum statistical
properties of systems which are chaotic in their classical limit. An expression
for the generating function of general statistical correlators is presented in
the form of a functional supermatrix nonlinear -model where the
effective action involves the evolution operator of the classical dynamics.
Low-lying degrees of freedom of the field theory are shown to reflect the
irreversible classical dynamics describing relaxation of phase space
distributions. The validity of this approach is investigated over a wide range
of energy scales. As well as recovering the universal long-time behavior
characteristic of random matrix ensembles, this approach accounts correctly for
the short-time limit yielding results which agree with the diagonal
approximation of periodic orbit theory.Comment: uuencoded file, 21 pages, latex, one eps figur
Nonlinear Analysis and Control of Interleaved Boost Converter Using Real-Time Cycle to Cycle Variable Slope Compensation
Switched-mode power converters are inherently nonlinear and piecewise smooth systems that may exhibit a series of undesirable operations that can greatly reduce the converter's efficiency and lifetime. This paper presents a nonlinear analysis technique to investigate the influence of system parameters on the stability of interleaved boost converters. In this approach, Monodromy matrix that contains all the comprehensive information of converter parameters and control loop can be employed to fully reveal and understand the inherent nonlinear dynamics of interleaved boost converters, including the interaction effect of switching operation. Thereby not only the boundary conditions but also the relationship between stability margin and the parameters given can be intuitively studied by the eigenvalues of this matrix. Furthermore, by employing the knowledge gained from this analysis, a real-Time cycle to cycle variable slope compensation method is proposed to guarantee a satisfactory performance of the converter with an extended range of stable operation. Outcomes show that systems can regain stability by applying the proposed method within a few time periods of switching cycles. The numerical and analytical results validate the theoretical analysis, and experimental results verify the effectiveness of the proposed approach
Quasilinear theory of collisionless Fermi acceleration in a multicusp magnetic confinement geometry
Particle motion in a cylindrical multiple-cusp magnetic field configuration
is shown to be highly (though not completely) chaotic, as expected by analogy
with the Sinai billiard. This provides a collisionless, linear mechanism for
phase randomization during monochromatic wave heating. A general quasilinear
theory of collisionless energy diffusion is developed for particles with a
Hamiltonian of the form , motion in the \emph{unperturbed} Hamiltonian
being assumed chaotic, while the perturbation can be coherent (i.e.
not stochastic). For the multicusp geometry, two heating mechanisms are
identified --- cyclotron resonance heating of particles temporarily
mirror-trapped in the cusps, and nonresonant heating of nonadiabatically
reflected particles (the majority). An analytically solvable model leads to an
expression for a transit-time correction factor, exponentially decreasing with
increasing frequency. The theory is illustrated using the geometry of a typical
laboratory experiment.Comment: 13 pages (.tex file, using REVTeX), 11 figures (.eps files). Sep. 30:
Word "collisionless" added to title, abstract and text slightly revised in
response to referee's comments (to be published in Phys. Rev. E
- …