We present a theoretical framework for the dynamic calibration of the higher eigenmode parameters (stiffness and optical lever inverse responsivity) of a cantilever. The method is based on the tip-surface force reconstruction technique and does not require any prior knowledge of the eigenmode shape or the particular form of the tip-surface interaction. The calibration method proposed requires a...

For a distribution advected by a simple chaotic map with diffusion, the "strange eigenmode" is investigated from the Lagrangian (material) viewpoint and compared to its Eulerian (spatial) counterpart. The eigenmode embodies the balance between diffusion and exponential stretching by a chaotic flow. It is not strictly an eigenmode in Lagrangian coordinates, because its spectrum is rescaled expon...

The inward momentum flux driven by the off-diagonal pressure gradient in a fluid model for ion temperature gradient turbulence with large Richardson number is significantly reduced by the excitation of stable eigenmodes. This is accomplished primarily through the amplitude autocorrelation of the damped eigenmode, which, in the flux, directly counteracts the quasilinear contribution of the unsta...

Introduction Eddy currents have long been the bane of MRI. Particularly since the mid 1980s when imaging sequences became more rapid [1] and superconducting magnets became routinely used. When gradient coils are switched rapidly, eddy currents are induced in the cryostat vessel and other surrounding conducting structures. Two principal solutions have been adopted into standard practice for deal...

We demonstrate an optical cavity that supports an eigenmode with a flattop spatial profile--a profile that has been proposed for the cavities in the Advanced Laser Interferometer Gravitational Wave Observatory, the second-generation laser interferometric gravitational wave observatory--because it provides better averaging of the spatially dependent displacement noise on the surface of the mirro...

Energy stored in a resonant medium may be used to amplify the Cerenkov radiation generated by a small driving bunch. The hybrid eigenmode of the system is a combination of Cerenkov radiation and eigenmode of the resonant medium. In the vicinity of the resonant frequency of the medium and when Cerenkov condition is satisfied, the eigenfrequency has an imaginary part. The latter occurs in a relat...

We examine the decay of passive scalars with small, but non zero, diffusivity in bounded 2D domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the scalar field with r...

We examine the decay of passive scalars with small, but nonzero, diffusivity in bounded two-dimensional (2D) domains. The velocity fields responsible for advection are smooth (i.e., they have bounded gradients) and of a single large scale. Moreover, the scale of the velocity field is taken to be similar to the size of the entire domain. The importance of the initial scale of variation of the sc...

Bimodal atomic force microscopy uses a cantilever that is simultaneously driven at two of its eigenmodes (resonant modes). Parameters associated with both resonances can be measured and used to extract quantitative nanomechanical information about the sample surface. Driving the first eigenmode at a large amplitude and a higher eigenmode at a small amplitude simultaneously provides four indepen...