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...

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=-⟨ln(T)⟩/L. In this Letter, we evidence that the exponential-damping law is not valid in general for periodic monomode waveguides, especially as the ...

For precise measurement of the moment inertia (MOI) asymmetric objects, using an air bearing torsional pendulum, nonlinearity torsion bar and damping effect caused by interaction between sample need to be included in analysis. The instantaneous undamped natural frequency coefficient motion are obtained from Hilbert transform angular displacement signal used for data fitting calculate MOI. Measu...

Using a linear optical diffraction method, we have experimentally studied the long predicted diffusion anomalous behavior for H/W(100) near the reconstructive phase transition of the W(100) substrate. This anomaly manifests itself in the form of a strong dip in the diffusion coefficient D at the transition temperature T(C). We interpret the strong reduction of D as a result of the diverging fri...

We consider a class of ordinary differential equations describing one-dimensional quasiperiodically forced systems in the presence of large damping. We give a fully constructive proof of the existence of response solutions, that is quasi-periodic solutions which have the same frequency vector as the forcing. This requires dealing with a degenerate implicit function equation: we prove that the l...

The characterization and modeling of the dynamic behavior of many built-up structures under vibration conditions is still a subject of current research. The present study emphasizes the theoretical investigation of slip damping in layered and jointed welded cantilever structures using finite element approach. Application of finite element method in damping analysis is relatively recent, as such...

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...