Special functions for engineers and applied mathematicians

A simple model is used to describe how radiation damping limits the resonant oscillations of a cantilever or strut. In the low‐frequency limit, radiation damping is equivalent to a fictitious internal dissipation, with a loss factor ηrad slightly higher than typical mechanical loss factors, showing that resonant response is limited only by radiation loss, even for thin struts for which k0a 1 it is found that ηrad is much larger than any internal loss factor and therefore that high‐frequency resonances are heavily damped, regardless of internal dissipation. The pressure field near the strut is also examined, and in the case k0a<1 is found at resonance to exceed the driving pressure by the large factor (k0a)−2. The farfield pressure at resonance may, under some conditions, also greatly exceed the off‐resonance scattered field, and this great scattering efficiency of a thin strut at resonance is demonstrated by detailed examination of a particular case.

Resonant oscillations of fluid‐loaded struts

Antibiotic resistance is a rapidly emerging global health problem as year on year more drugs are rendered ineffective and fewer new antibiotics developed to meet the demand. This is exemplified by Vancomycin, the `antibiotic of last resort' for decades, now facing growing resistance among bacteria. Interest around modifying existing drugs to improve their antibiotic action and stabilise them against resistance is raising the need for detailed understanding of the modes of action of antibiotics. Nanocantilevers provide a complementary method for exploring both the binding process and the mechanical mode of action by which Vancomycin and its derivatives weaken and destroy bacterial cell wall. When functionalised with monolayers of peptides analogous to cell wall precursors the cantilevers measure the build up of surface stresses in-plane, on a surface, representative of the antibacterial interactions in-situ. This thesis reports the first steps towards a comprehensive theoretical model of stress induction on a nanocantilever, focusing on elucidating the chemical and geometric nature of experimentally observed responses to Vancomycin. The chemical origins of stress generation are explored within, using a monolayer of decanethiol as a model system and looking at contributions from both adsorbate-adsorbate and adsorbate-substrate interactions. How those individual molecular contributions combine across the cantilever to produce the eventual deflection is investigated by varying the coverage of Vancomycin binding events across an appropriately functionalised cantilever, using an interaction potential extrapolated from molecular dynamics simulations and a lattice model developed in this thesis to return the corresponding stress and deflection. The elastic response of the beam itself is also examined in some detail, as is the effect of the operating medium on the cantilever's action. All findings provide the first steps to a truly representative, and quantitatively predictive, model of nanocantilever operation and insight into the technology's unique merit in the race to discover a new generation of antibiotics.

AC Dejardin

Papers

Modelling the nanocantilever response to stressed networks of antibiotic binding events