Longitudinal Losses Due to Breathing Mode Excitation in Radiofrequency Linear Accelerators

Transverse breathing mode oscillations in a particle beam can couple energy into longitudinal oscillations in a bunch of finite length and cause significant losses. We develop a model that illustrates this effect and explore the dependence on mismatch size, space-charge tune depression, longitudinal focusing strength, bunch length, and RF bucket length

Nearest neighbor embedding with different time delays

A nearest neighbor based selection of time delays for phase space reconstruction is proposed and compared to the standard use of time delayed mutual information. The possibility of using different time delays for consecutive dimensions is considered. A case study of numerically generated solutions of the Lorenz system is used for illustration. The effect of contamination with various levels of additive Gaussian white noise is discussed.Comment: 4 pages, 5 figures, updated to final versio

Multivariate phase space reconstruction by nearest neighbor embedding with different time delays

A recently proposed nearest neighbor based selection of time delays for phase space reconstruction is extended to multivariate time series, with an iterative selection of variables and time delays. A case study of numerically generated solutions of the x- and z coordinates of the Lorenz system, and an application to heart rate and respiration data, are used for illustration.Comment: 4 pages, 3 figure

Total destruction of invariant tori for the generalized Frenkel-Kontorova model

We consider generalized Frenkel-Kontorova models on higher dimensional lattices. We show that the invariant tori which are parameterized by continuous hull functions can be destroyed by small perturbations in the $C^r$ topology with $r<1$

Chaotic versus stochastic behavior in active-dissipative nonlinear systems

We study the dynamical state of the one-dimensional noisy generalized Kuramoto-Sivashinsky (gKS) equation by making use of time-series techniques based on symbolic dynamics and complex networks. We focus on analyzing temporal signals of global measure in the spatiotemporal patterns as the dispersion parameter of the gKS equation and the strength of the noise are varied, observing that a rich variety of different regimes, from high-dimensional chaos to pure stochastic behavior, emerge. Permutation entropy, permutation spectrum, and network entropy allow us to fully classify the dynamical state exposed to additive noise

Graded infinite order jet manifolds

The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds in terms of the Grassmann-graded variational bicomplex.Comment: 30 page

Noether's second theorem for BRST symmetries

We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles over X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.Comment: 31 pages, to be published in J. Math. Phy