Related papers: Theory of the tune shift due to linear coupling
Analytic expressions for the amplitude-dependent tune shift driven by the quadrupole magnet fringe field have been obtained. The magnitude of the effect is compared with other sources of non-linearity such as chromatic sextupoles, octupole…
The motion of a particle in 6-dimensional phase space in the presence of linear coupling can be written as the sum of 3 normal modes. A cubic equation is found for the tune of the normal modes, which allows the normal mode tunes to be…
Fringe field becomes important when one requires more accurate modeling of a ring lattice to study the long-term beam dynamics in storage rings and deal with large aperture magnets in high-intensity proton synchrotrons or accumulator rings.…
Most music theory books are like medieval medical textbooks: they contain unjustified superstition, non-reasoning, and funny symbols glorified by Latin phrases. How does music, in particular harmony, actually work, presented as a real,…
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and…
Tune identification - i.e. attribution of the spectral peak to a particular normal mode of oscillations - can present a significant difficulty in the presence of strong transverse coupling when the normal mode with a lower damping rate…
Landau damping of head-tail modes in bunches due to spreads in the tune shift can be a deciding factor for beam stability. We demonstrate that the coherent tune shifts due to reactive impedances can enhance the space-charge induced damping…
In the production of modern music, the musical characteristics of the guitar or keyboard amplifier play an integral role in the creative process. This article explores the physics of music with an emphasis on the role of distortion in the…
It is shown that electron backscattering can enhance high-harmonic generation in periodic systems with broken translational symmetry. Paradigmatically, we derive for a finite chain of atoms the harmonic cutoff due to electrons backscattered…
The human sense of hearing perceives a combination of sounds 'in tune' if the corresponding harmonic spectra are correlated, meaning that the neuronal excitation pattern in the inner ear exhibits some kind of order. Based on this…
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions…
Musical chords, harmonies or melodies in Just Intonation have note frequencies which are described by a base frequency multiplied by rational numbers. For any local section, these notes can be converted to some base frequency multiplied by…
The principle underlying this paper is the basic observation that the problem of simultaneously solving a large class of composite monotone inclusions and their duals can be reduced to that of finding a zero of the sum of a maximally…
This paper develops a formal theory of musical scales and their harmonic coverings and introduces orbit covers: coverings obtained by translating a fixed subset across a scale via a group action. Orbit covers generalize familiar…
Shaped laser pulses are a powerful tool to induce population transfer between electronic molecular states, and time-dependent perturbation theory is suitable for a description of such a transfer in weak external fields. The application of…
Relativistic secular perturbation theory has ignited significant interest in uncovering intricate cross-term effects, especially the interplay between 1PN and quadrupole terms. While most existing studies rely on the Lagrangian planetary…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
We develop the perturbation theory of double field theory around arbitrary solutions of its field equations. The exact gauge transformations are written in a manifestly background covariant way and contain at most quadratic terms in the…
We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities:…
The head-tail modes are described for the space charge tune shift significantly exceeding the synchrotron tune. A general equation for the modes is derived. The spatial shapes of the modes, their frequencies, and coherent growth rates are…