Related papers: Mathematical and Numerical Methods for Non-linear …

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…

Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to…

Nonlinear programming targets nonlinear optimization with constraints, which is a generic yet complex methodology involving humans for problem modeling and algorithms for problem solving. We address the particularly hard challenge of…

The Fourier spectral techniques that are common in Astronomy for analyzing periodic or multi-periodic light-curves lose their usefulness when they are applied to unsteady light-curves. We review some of the novel techniques that have been…

Particle acceleration at plasma shocks appears to be ubiquitous in the universe, spanning systems in the heliosphere, supernova remnants, and relativistic jets in distant active galaxies and gamma-ray bursts. This review addresses some of…

Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…

We present here a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream. This solution, besides allowing us to determine the spectrum of particles…

In recent years, intense efforts have been devoted to studying how nonlinear effects can be used to shape the transverse beam distribution by means of an adiabatic crossing of nonlinear resonances. By this approach, it is possible to split…

A nonlinear partial differential equation is a nonlinear relationship between an unknown function and how it changes due to two or more input variables. A numerical method reduces such an equation to arithmetic for quick visualization, but…

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…

The analysis of nonlinear wave equations has experienced a dramatic growth in the last ten years or so. The key factor in this has been the transition from linear analysis, first to the study of bilinear and multilinear wave interactions,…

Numerical simulations have become an important tool to understand and predict non-perturbative phenomena in particle physics. In this article we attempt to present a general overview over the field. First, the basic concepts of lattice…

Nonlinear string vibration, in particular the case of nonplanar motion, has been an area of intense study for many years. Numerical simulation methods, essential for the comparison between measured data and theory, have received somewhat…

Diffusive acceleration at collisionless shock waves remains one of the most promising acceleration mechanisms for the description of the origin of cosmic rays at all energies. A crucial ingredient to be taken into account is the reaction of…

We survey recent results on controlled particle systems. The control aspect introduces new challenges in the discussion of properties and suitable mean field limits. Some of the aspects are highlighted in a detailed discussion of a…

An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The…

The field of particle therapy is quickly growing and yet it's more widespread adoption is limited by size, cost and adaptation to the more conformal treatment techniques. In order to realize the benefits of this modality the equipment used…

Accelerator and beam physics (ABP) is the science of the motion, generation, acceleration, manipulation, prediction, observation and use of charged particle beams. It focuses on fundamental long-term accelerator and beam physics research…

This paper gives a very brief summary of longitudinal beam dynamics for both linear and circular accelerators. After discussing synchronism conditions in linacs, it focuses on particle motion in synchrotrons. It summarizes the equations of…

We describe the advantages and disadvantages of numerical methods when Bohmian trajectory-grids are used for numerical simulations of quantum dynamics. We focus on the crucial non crossing property of Bohmian trajectories, which numerically…