Related papers: A first taste of nonlinear beam dynamics
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
By numerical simulation of exact equations of motion (in terms of conformal variables) for planar non-stationary potential flows of an ideal fluid with a free surface over a strongly non-uniform bottom profile, the effect of nonlinear…
Investigating the possibility of applying techniques from linear systems theory to the setting of nonlinear systems has been the focus of many papers. The pseudo linear form representation of nonlinear dynamical systems has led to the…
In this paper we show how nonlinear internal models can be effectively used in the design of output regulators for nonlinear systems. This result provides a significant enhancement of the non-equilibrium theory for output regulation, which…
Existing smart composite piezoelectric beam models in the literature mostly ignore the electro-magnetic interactions and adopt the linear elasticity theory. However, these interactions substantially change the controllability and…
This paper presents the work devoted to the study of the operation of a miniaturized membrane Stirling engine. Indeed, such an engine relies on the dynamic coupling of the motion of two membranes to achieve a prime mover Stirling…
Beam instabilities and resonances affect the transverse dynamics in particle accelerators and, when encountered, can trigger emittance growth and beam loss. Resonance lines originate from non linear elements and effects in the lattice,…
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…
These lectures aim to describe instruments and methods used for measuring beam parameters in particle accelerators. Emphasis will be given to new detection and analysis techniques in each field of accelerator instrumentation. A clear…
This article addresses the following problems: 1) First, a nonlinearity analysis is made looking for the presence of nonlinearities in an early phase of the identification process. The level and the nature of the nonlinearities should be…
Coupled-bunch instabilities excited by the interaction of the particle beam with its surroundings can seriously limit the performance of circular particle accelerators. These instabilities can be cured by the use of active feedback systems…
A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. Symmetry assumptions are shown to lead to the planar 1D pendulum and to the…
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…
The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
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…
We investigate the effects of a localized constant wake and a localized linear wake on the longitudinal beam distribution in equilibrium. We also examine the effects of the composite wake on the particle distribution when the constant wake…
Under certain conditions, the dynamics of a nonlinear mechanical system can be represented by a single nonlinear modal oscillator. The properties of the modal oscillator can be determined by computational or experimental nonlinear modal…
Laser-generated plasma gratings are dynamic optical elements for the manipulation of coherent light at high intensities, beyond the damage threshold of solid-stated based materials. Their formation, evolution and final collapse require a…
We consider a curved chain of nonlinear oscillators and show that the interplay of curvature and nonlinearity leads to a number of qualitative effects. In particular, the energy of nonlinear localized excitations centered on the bending…