Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. [1], in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between ...

The present study investigates buckling characteristics of both nonlinear symmetric power and sigmoid functionally graded (FG) beams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by the sigmoid-law distribution (S-FGM), and the symmetric power function (SP-FGM). These functions have smooth variation of properties across the boundary rather tha...

In this article we derive the deflection equation of a simple beam using screw theory. The effects of tension, torsion and bending of the beam can be unified into a single equation. We begin by looking at the compliance matrix for small elements of the beam. This is loosely based on work by von Mises in the 1920s. We reproduce von Mises results for the compliance matrix of the entire beam by in...

Multibeam satellite networks can extend the service coverage as deploying its spot beam. It is important to allocate the appropriate resources to downlink multibeams to prevent the unnecessary waste of resources in the satellite system. This paper presents an optimum beam allocation scheme for multi-spot beam satellite system, as beam bandwidth to be allocated is controlled dynamically. We appl...

This study investigates that the sound wave propagation of multiferroic thermo elastic Nanofibers under the influence of surface effect and parametric excitation via Timoshenko form of beam equations. The equation of analytical model is obtained for Nanofiber through shear and rotation effect. The solution of the problem is reached through the coupled time harmonic equations in flexural directi...

A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outline...

To study the fast-ion transport in a well controlled background plasma, a 3-cm diameter rf ion gun launches a pulsed, ,300 eV ribbon shaped argon ion beam parallel to or at 15° to the magnetic field in the Large Plasma Device sLAPDd fW. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 s1991dg at UCLA. The parallel energy of the beam is measured by...

not only provides an elegant formula for evaluating ζ(2n), but it also tells us of the arithmetical nature of ζ(2n). In contrast, we know very little about ζ(2n + 1). One of the major achievements in number theory in the past half-century is R. Apéry’s proof that ζ(3) is irrational [2], but for n ≥ 2, the arithmetical nature of ζ(2n+ 1) remains open. Ramanujan made many beautiful and elegant di...