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In this chapter we give an introduction to the transverse dynamics of the particles in a synchrotron or storage ring. The emphasis is more on qualitative understanding rather than on mathematical correctness, and a number of simulations are…
The effective numerical method is developed performing the test of the hyperbolicity of chaotic dynamics. The method employs ideas of algorithms for covariant Lyapunov vectors but avoids their explicit computation. The outcome is a…
Shannon entropy, as a chaos indicator, is used for online Poincar\'e map regularization and dynamic aperture optimization in the National Synchrotron Light Source-II (NSLS-II) ring. Although various chaos indicators are widely used in…
Chaotic behavior in dynamical systems poses a significant challenge in trajectory control, traditionally relying on computationally intensive physical models. We present a machine learning-based algorithm to compute the minimum control…
Eccentric mixing is a typical chaotic mixing method, and the study of its mixing characteristics is beneficial to the optimization of the mixing process. In this study, the effects of eccentricity (E/R) and rotational speed (N) on the…
The optimization problems with simple bounds are an important class of problems. To facilitate the computation of such problems, an unconstrained-like dynamic method, motivated by the Lyapunov control principle, is proposed. This method…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability,…
In this work, we tackle the Dynamic Optimization Problem (DOP) of IA in a real-world application using a Dynamic Optimization Algorithm (DOA) called Fractal Decomposition Algorithm (FDA), introduced by recently. We used FDA to perform IA on…
In a recent work, [1] the equilibrium of a cluster of charged dust particles mutually interacting with screened Coulomb force and radially confined by an externally applied electric field in a 2-D configuration was studied. It was shown…
Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…
Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…
In this paper, synchronization of fractional order Coullet system with precise and also unknown parameters are studied. The proposed method which is based on the adaptive backstepping, has been developed to synchronize two chaotic systems…
Most recent works in optical flow extraction focus on the accuracy and neglect the time complexity. However, in real-life visual applications, such as tracking, activity detection and recognition, the time complexity is critical. We propose…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time -- the most clear example being the Solar System -- but the situation for their quantum counterparts is less well understood. As a…
We investigate the ability to discover data assimilation (DA) schemes meant for chaotic dynamics with deep learning. The focus is on learning the analysis step of sequential DA, from state trajectories and their observations, using a simple…
The presence of chaos in classical Hamiltonian systems is witnessed by its maximal Lyapunov exponent, that quantifies the instability of motion through the exponential growth of indicators such as the trace of the stability matrix or the…
Reactive trajectory optimization for robotics presents formidable challenges, demanding the rapid generation of purposeful robot motion in complex and swiftly changing dynamic environments. While much existing research predominantly…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
A new approach is developed to integrate numerically the equations of motion for systems of interacting rigid polyatomic molecules. With the aid of a leapfrog framework, we directly involve principal angular velocities into the integration,…