Transitional random matrix theory nearest-neighbor spacing distributions

This paper presents a study of the properties of a matrix model that was introduced to describe transitions between all Wigner surmises of Random Matrix theory. New results include closed-form exact analytical expressions for the transitional probability density functions, as well as suitable analytical approximations for cases not amenable to explicit representation

Instrument-Dependent Cadherin Monolayer Interactions

We introduce two theoretical models for predicting forces between cadherin-coated sphere and plane. The first model is based on a continuum theory previously developed for the interaction of large objects embedded in liquids. The second model takes into account size effects, which are relevant in the cadherin measurements, as the size of the tip is frequently comparable to the size of geometrical features of the cadherin. We use the models to compare force–separation curves in atomic force microscopy and surface force apparatus

The emergence of multifrequency force microscopy

Atomic force microscopy uses the deflection of a cantilever with a sharp tip to examine surfaces, and conventional dynamic force microscopy involves the excitation and detection of a single frequency component of the tip’s motion. Information about the properties of a sample is, however, encoded in the motion of the probe and the dynamics of the cantilever are highly nonlinear. Therefore, information included in the other frequency components is irreversibly lost. Multifrequency force microscopy involves the excitation and/or detection of several frequencies of the probe’s oscillation, and has the potential to overcome limitations in spatial resolution and acquisition times of conventional force microscopes. It could also provide new applications in fields such as energy storage and nanomedicine. Here we review the development of multifrequency force microscopy methods, highlighting the five most prominent approaches. We also examine the range of applications offered by the technique, which include mapping the flexibility of proteins, imaging the mechanical vibrations of carbonbased resonators, mapping ion diffusion, and imaging the subsurface of cells.We are grateful for financial support from the Ministerio de Ciencia e Innovación (CSD2010-00024, MAT2009-08650).Peer reviewe