We develop a nonlinear theory of the weak single bunch instability in electron and positron circular accelerators and damping rings. A nonlinear equation is derived that governs the evolution of the amplitude of unstable oscillations with account of quantum diffusion effects due to the synchrotron radiation. Numerical solutions to this equation show a large variety of nonlinear regimes dependin...

It is widely accepted that, on ensemble average, the transmission T of guided modes decays exponentially with the waveguide length L due to small imperfections, leading to the important figure of merit defined as the attenuation−rate coefficient α = −/L. In this letter, we evidence that the exponential−damping law is not valid in general for periodic monomode waveguides, especially as th...

Abstract. Differential equations involving derivatives of non-integer order have shown to be adequate models for various physical phenomena in areas like damping laws, diffusion processes, etc. A small number of algorithms for the numerical solution of these equations has been suggested, but mainly without any error estimates. In this paper, we propose an implicit algorithm for the approximate ...

The optimal damping control for nonlinear time-delay systems with persistent disturbances is considered. Based on successive approximation approach (SAA), the optimal damping control (ODC) law is achieved by solving a decoupled sequence of inhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The ODC law of the original problem consists of accu...

A method of estimating damping parameters for multidegree-of-freedom vibration systems is outlined, involving a balance of dissipated and supplied energies over a cycle of periodic vibration. The power is formulated as the inner product between velocity and force terms, and integrated over a cycle. Conservative terms (mass and stiffness) drop out of the formulation. The displacement response an...

The halting scale of the inverse energy cascade and the partition between kinetic and potential energy are considered for the case of forced quasigeostrophic turbulence in the regime of intermediate Rossby deformation length, for which the deformation length is comparable to the energy-containing scales of the flow. Phenomenological estimates for the halting scale and equilibrated energy of the...

We consider a mathematical model of a linear vibrational system described by the second-order system of differential equations Mẍ +Dẋ+Kx = 0, where M, K and D are positive definite matrices, called mass, stiffness and damping, respectively. We are interested in finding an optimal damping matrix which will damp a certain part of the undamped eigenfrequencies. For this we use a minimization crite...

The primary objective was to develop field-verified models for the evolution of surfacegravity waves propagating over a muddy seafloor, allowing more skillful predictions of wave fields on continental shelves, and enabling the estimation of characteristics of the seafloor from wave observations. The approach was to investigate empirical and theoretical expressions for mud-induced damping by com...

A method of physical parameter system identification (SI) is proposed here for threedimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time domain m...

The effectiveness of viscous elements in introducing damping in a structure is a function of several variables, including their number, their location in the structure, and their physical properties. This paper addresses the questions of the placement of these elements and the selection of their physical parameters via optimization techniques. The paper investigates various metrics to define th...