Impact of plant shoot architecture on leaf cooling: a coupled heat and mass transfer model.

Plants display a range of striking architectural adaptations when grown at elevated temperatures. In the model plant Arabidopsis thaliana, these include elongation of petioles, and increased petiole and leaf angles from the soil surface. The potential physiological significance of these architectural changes remains speculative. We address this issue computationally by formulating a mathematical model and performing numerical simulations, testing the hypothesis that elongated and elevated plant configurations may reflect a leaf-cooling strategy. This sets in place a new basic model of plant water use and interaction with the surrounding air, which couples heat and mass transfer within a plant to water vapour diffusion in the air, using a transpiration term that depends on saturation, temperature and vapour concentration. A two-dimensional, multi-petiole shoot geometry is considered, with added leaf-blade shape detail. Our simulations show that increased petiole length and angle generally result in enhanced transpiration rates and reduced leaf temperatures in well-watered conditions. Furthermore, our computations also reveal plant configurations for which elongation may result in decreased transpiration rate owing to decreased leaf liquid saturation. We offer further qualitative and quantitative insights into the role of architectural parameters as key determinants of leaf-cooling capacity.

Improving the signal-to-noise ratio of high-speed contact mode atomic force microscopy.

During high-speed contact mode atomic force microscopy, higher eigenmode flexural oscillations of the cantilever have been identified as the main source of noise in the resultant topography images. We show that by selectively filtering out the frequencies corresponding to these oscillations in the time domain prior to transforming the data into the spatial domain, significant improvements in image quality can be achieved.

Modelling oscillatory flexure modes of an atomic force microscope cantilever in contact mode whilst imaging at high speed.

Understanding the modal response of an atomic force microscope is important for the identification of image artefacts captured using contact-mode atomic force microscopy (AFM). As the scan rate of high speed AFM increases, these modes present themselves as ever clearer noise patterns as the frequency of cantilever vibration falls under the frequency of pixel collection. An Euler-Bernoulli beam equation is used to simulate the flexural modes of the cantilever of an atomic force microscope as it images a hard surface in contact mode. Theoretical results are compared with experimental recordings taken in the high speed regime, as well as previous analytical results. It is shown that the model can capture the mode shapes and resonance properties of the first four eigenmodes.

High-speed atomic force microscopy in slow motion--understanding cantilever behaviour at high scan velocities.

Using scanning laser Doppler vibrometer we have identified sources of noise in contact mode high-speed atomic force microscope images and the cantilever dynamics that cause them. By analysing reconstructed animations of the entire cantilever passing over various surfaces, we identified higher eigenmode oscillations along the cantilever as the cause of the image artefacts. We demonstrate that these can be removed by monitoring the displacement rather than deflection of the tip of the cantilever. We compare deflection and displacement detection methods whilst imaging a calibration grid at high speed and show the significant advantage of imaging using displacement.

Nonlinear models of development, amplification and compression in the mammalian cochlea.

This paper reviews current understanding and presents new results on some of the nonlinear processes that underlie the function of the mammalian cochlea. These processes occur within mechano-sensory hair cells that form part of the organ of Corti. After a general overview of cochlear physiology, mathematical modelling results are presented in three parts. First, the dynamic interplay between ion channels within the sensory inner hair cells is used to explain some new electrophysiological recordings from early development. Next, the state of the art is reviewed in modelling the electro-motility present within the outer hair cells (OHCs), including the current debate concerning the role of cell body motility versus active hair bundle dynamics. A simplified model is introduced that combines both effects in order to explain observed amplification and compression in experiments. Finally, new modelling evidence is presented that structural longitudinal coupling between OHCs may be necessary in order to capture all features of the observed mechanical responses.

Experimental observation of contact mode cantilever dynamics with nanosecond resolution.

We report the use of a laser Doppler vibrometer to measure the motion of an atomic force microscope contact mode cantilever during continuous line scans of a mica surface. With a sufficiently high density of measurement points the dynamics of the entire cantilever beam, from the apex to the base, can be reconstructed. We demonstrate nanosecond resolution of both rectangular and triangular cantilevers. This technique permits visualization and quantitative measurements of both the normal and lateral tip sample interactions for the first and higher order eigenmodes. The ability to derive quantitative lateral force measurements is of interest to the field of microtribology/nanotribology while the comprehensive understanding of the cantilever's dynamics also aids new cantilever designs and simulations.