Some of the problems associated with the monitoring of accelerator beams, particularly storage rings' beams, are reviewed along with their most common solutions. The various electrode structures used for the measurement of beam current, beam position and the detection of the bunches' transverse oscillations yield pulses with sub-nanosecond widths. The electronics for the processing of these sho...

It is shown that Hermite-Gaussian beams, Laguerre-Gaussian beams, and certain linear combinations thereof are the only finite-energy coherent beams that propagate, on free propagation, in a shape-invariant manner. All shape-invariant beams have Gouy phase of the universal c arctan(z/zR) form, with quantized values for the prefactor c. It is also shown that, as limiting cases, even two- and thre...

We investigate the propagation of one-dimensional and two-dimensional (1D, 2D) Gaussian beams in the fractional Schrödinger equation (FSE) without a potential, analytically and numerically. Without chirp, a 1D Gaussian beam splits into two nondiffracting Gaussian beams during propagation, while a 2D Gaussian beam undergoes conical diffraction. When a Gaussian beam carries linear chirp, the 1D b...

frps (fiber reinforced polymer) possess many favorable characteristics suitable and applicable for construction industry when compared with steel reinforcement. there are new ideas to use frps as longitudinal or transverse reinforcement for new concrete elements particularly for bridge decks or beams. although high tensile strength of frp is main characteristic for applications at both areas, i...

In this article we derive error estimates for the Galerkin approximation of a general linear second order hyperbolic partial differential equation. The results can be applied to a variety of cases e.g. vibrating systems of linked elastic bodies. The results generalize the work of Baker [1] and also allow for viscous type damping. Splitting the proofs for the semidiscrete and fully discrete case...

This paper presents a solution to the boundary stabilization of a symmetric composite laminated plate in free transverse vibration. The symmetric composite laminated plate dynamics is presented by a linear fourth order partial differential equation (PDE). A linear control law is constructed to stabilize the plate. The control force consists of feedback of the velocity at the boundary of the pla...

It is shown how the linear Gouy phase of an ideal nondiffracting beam of ±(k − kz)z form, with kz being the projection of the wavevector of modulus k of the plane wave spectrum onto the propagation axis z, is built from a rigorous treatment based on the successive approximations to the Helmholtz equation. All of different families of nondiffracting beams with a continuum spectrum, as Bessel bea...