Related papers: Stability of non-linear integrable accelerator
We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…
Integrable systems appeared in physics long ago at the onset of classical dynamics with examples being Kepler's and other famous problems. Unfortunately, the majority of nonlinear problems turned out to be nonintegrable. In accelerator…
We report an optical fiber experiment in which we study nonlinear stage of modulational instability of a plane wave in the presence of a localized perturbation. Using a recirculating fiber loop as experimental platform, we show that the…
A treatment is given of the orbit dynamics for linear unstable motion that allows for the zeros in the beta function and makes no assumptions about the realness of the betatron and phase functions. The phase shift per turn is shown to be…
Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…
Some limit theorems are proven for the linear oscillator with random coefficients. The asymptotic behaviour of the moments is studied in detail. The technique presented in this paper can be applied to general linear systems with noise and…
In this work we solve the position-aided 3D navigation problem using a nonlinear estimation scheme. More precisely, we propose a nonlinear observer to estimate the full state of the vehicle (position, velocity, orientation and gyro bias)…
We analyzed the stability of the uniform flow solution in the optimal velocity model for traffic and granular flow under the open boundary condition. It was demonstrated that, even within the linearly unstable region, there is a parameter…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a…
Robust stereo visual-inertial odometry (VIO) remains challenging in low-texture scenes and under abrupt illumination changes, where point features become sparse and unstable, leading to ambiguous association and under-constrained…
The Laser Interferometer Space Antenna (LISA) and its metrology chain have to fulfill stringent performance requirements to enable the space-based detection of gravitational waves. This implies the necessity of performance verification…
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…
Plasma acceleration promises to deliver high-energy particle beams by combining, or staging, several low- or medium-energy accelerator stages. However, chromatic aberrations from the combination of high divergence and energy spread make it…
We present approximate analytical method of analysis of stationary states of nonlinear quantum systems with the noise. As an example we consider quantum nonlinear oscillator excited by fluctuating force and found parameter regions with more…
The optical truss interferometer (OTI) is a contingent subsystem proposed for the LISA telescopes to aid in the verification of a $1 \frac{\mathrm{pm}}{\sqrt{\mathrm{Hz}}}$ optical path length stability. Each telescope would be equipped…
In this study, a distinct reconfigurable fault-tolerant flight control strategy is addressed for mitigating one of the persistent safety-critical issue, i.e. loss of control triggered by actuator faults. The attainable acceleration set…
The stability of autonomous vehicle platoons with limits on acceleration and deceleration is determined. If the leading-vehicle acceleration remains within the limits, all vehicles in the platoon remain within the limits when the…
This study comprehensively investigates the mechanical stability of intraocular lenses (IOLs) - critical components in cataract surgery - by analyzing their haptic designs. Three commercial models (ALSEE, GF3, and UD613) and five geometric…
The adaptive Iterative Soft-Thresholding Algorithm (ISTA) has been a popular algorithm for finding a desirable solution to the LASSO problem without explicitly tuning the regularization parameter $\lambda$. Despite that the adaptive ISTA is…