Related papers: Approximate Entropy Analysis for Nonlinear Beam Dy…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
The interaction of a charged particle beam with radio-frequency (RF) systems in most linear or circular accelerators is an non-linear process. The large longitudinal electric fields for acceleration and longitudinal beam manipulations can…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
Ensemble of initial conditions for nonlinear maps can be described in terms of entropy. This ensemble entropy shows an asymptotic linear growth with rate K. The rate K matches the logarithm of the corresponding asymptotic sensitivity to…
We extend the notion of estimation entropy of autonomous dynamical systems proposed by Liberzon and Mitra [1] to nonlinear dynamical systems with uncertain inputs with bounded variation. We call this new notion the {$\epsilon$}-estimation…
In this work a two-particle irreducible (2PI) closed-time-path (CTP) effective action is used to describe the nonequilibrium dynamics of a Bose Einstein condensate (BEC) selectively loaded into every third site of a one-dimensional optical…
A non-relativistic, charged-particle beam is placed into a crossed magnetic field. For such a system, the nonlinear electrostatic oscillations generation in the different degrees of the beam freedom may be triggered by the energy/momentum…
It is well known that, for chaotic systems, the production of relevant entropy (Boltzmann-Gibbs) is always linear and the system has strong (exponential) sensitivity to initial conditions. In recent years, various numerical results indicate…
We study the notion of approximate entropy within the framework of network theory. Approximate entropy is an uncertainty measure originally proposed in the context of dynamical systems and time series. We firstly define a purely structural…
Evidence theory is that the extension of probability can better deal with unknowns and inaccurate information. Uncertainty measurement plays a vital role in both evidence theory and probability theory. Approximate Entropy (ApEn) is proposed…
We present a method to construct high-order polynomial approximate invariants (AI) for non-integrable Hamiltonian dynamical systems, and apply it to modern ring-based particle accelerators. Taking advantage of a special property of one-turn…
Dynamic aperture is an important concept for the study of non-linear beam dynamics in circular accelerators. It describes the extent of the phase-space region where a particle's motion remains bounded over a given number of turns.…
We present the Complex Envelope Variable Approximation (CEVA) as the very useful and compact method for the analysis of the essentially nonlinear dynamical systems. It allows us to study both the stationary and non-stationary dynamics even…
We present the first part of an efficient framework for nonlinear beam dynamics, termed Approximate Invariant Analysis (AIA). The framework is based on the construction of approximate invariants~[Y.~Li, D.~Xu, and Y.~Hao, Phys.\ Rev.\…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
Many advanced techniques have been developed, tested and implemented in the last decades in almost all circular accelerators across the world to measure the linear optics. However, the greater availability and accuracy of beam diagnostics…
Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied.…
We use tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the…
Single particle dynamics in electron microscopes, ion or electron lithographic instruments, particle accelerators, and particle spectrographs is described by weakly nonlinear ordinary differential equations. Therefore, the linear part of…