An investigation of dynamic instability of stiffened rectangular plates

Boundaries of regions of parametric instability of simply supported stiffened rectangular plat

An investigation of the parametric resonance of rectangular plates reinforced with closely spaced stiffeners

Parametric resonance and structural stability model of uniformly reinforced flat plate

Single molecule conductance

This thesis represents an excursion into the world of molecular electronics, i.e. the field of research trying to use individual (organic) molecules as electronic components; in this work various experimental methods have been explored to connect individual molecules to metallic contacts and determine their electronic properties. The drive for this research is twofold. On the one hand there is the rush towards ever smaller electronics. Using individual molecules in integrated circuits would further shrink the size of electronic components. On the other hand, different theories have to be used (and developed) to describe the conductance of electrons through matter as the dimensions of the material in question become smaller and smaller. This is because the (conduction) properties of a material change with changing size. In other words, research into the field of molecular electronics yields new fundamental insights into the interaction of electrons with matter at the nanoscale. In this thesis two elementary models, namely a Self Consistent Field model and a Coulomb model, have been used to investigate the conduction properties of (a single energy level of) a single molecule between two metal contacts. Various parameters of these two models were systematically varied to see what their influence is on the conductance. In particular, the effect of the coupling (of the molecule to the metallic leads) on the conduction was studied carefully for both models. For the Self Consistent Field model it was shown, that, for symmetric coupling constants, the conductance reaches a maximum, namely the quantum of conductance, as the magnitude of the couplings becomes large. For highly non-symmetric coupling constants though the conductance drops to zero. In case of the Coulomb model it was observed that using coupling constants whose magnitudes have a ratio that is far from unity, resulted in a polarity dependent Coulomb blockade behavior: for one bias polarity Coulomb blockade occurred, while for the other polarity it did not. These model calculations were performed to back up the two kinds experiments that were designed and performed to measure the electrical properties of a single molecule between two metallic contacts. The first method consisted of pushing colloidal gold nanoparticles in between two lithographically defined metallic contacts (to reduce the size of the gap between these two electrodes to a few nanometers) with the tip of an atomic force microscopy (AFM) and subsequently apply molecules to the (in size reduced) gap. It was found that a fully connecting chain of colloids, so without any molecules yet added to the device, did not conduct at all. The reason for the lack of conduction turned out to be the presence of an electrically insulating shell (of citrate molecules) around each colloid. Using microwave radiation, it was attempted to remove this shell. While microwave irradiation removed the shell and even caused individual colloids to melt and coalesce, the process could not be controlled to the extent that metallic contacts with a separation of 1 to 2 nm could reliably be produced. In the second method the reverse was attempted: Instead of reducing the size of the gap, it was attempted to controllably create a gap of nanometer dimensions from a fully connected metallic structure, to which molecules could subsequently be applied. The process by which these gaps were created is called electromigration and basically consists of applying a high enough current(density) to a metallic wire to break it. It was found that to reliably create gaps with dimensions of 1 to 2 nm, it was necessary to add a series resistor to the system to obtain the correct overall resistance value. Too low a resistance value, i.e. no series resistor added, resulted in gaps that had size-distributions that were too large for the gaps to be of use. Too high a resistance value, namely too large a series resistor, resulted in gaps that were also useless, because for these gaps the exact gap size could not be determined, since the tunneling current flowing through these gap was too low to be determined. With the correct overall resistance, 30 for these particular kind of structures, gaps with dimensions of a few nanometers could be reliably made more than 85% of the time. Placing an individual molecule in such a gap turned out to be more troublesome, as none of the 76 created structures resulted in a electrical measurement on a single molecule. As an alternative to creating nanometer sized contacts, local probe oxidation has been performed on self-assembled monolayers (that consist of octadecyl trichlorosilane molecules on a silicon(oxide) substrate). With local probe oxidation, which is an AFM technique, an electric current is passed through a conductive tip (by applying a bias between tip and substrate), to selectively modify the surface area. In this fashion a pattern is written on the substrate as the tip is scanned across the surface. From literature it is known that such patterns could, for example, be used to selectively coat parts of the substrate with metals and in this fashion create nano-scale electronic contacts. Before this can be done effectively, however, it is necessary to control the oxidation process. Two processes can occur when a bias is applied, namely the modification of the methyl end-groups of the molecules that form the monolayer into carboxylic acid groups, which is desirable, and growth of silicon oxide underneath the monolayer, which is undesirable. It was found that, depending on the oxidation conditions, i.e. the applied bias and the duration over which it is applied, a distinction can be made between these two processes. It is also observed that, depending on the scan direction of the AFM, the end-group modification can be observed as either an increase or a decrease of the height of the modified areas due to cross-coupling, i.e. mixing, of the simultaneously recorded height and friction signals of the AFM. To truly measure the conduction properties of individual molecules, scanning tunneling microscopy was used to measure the conductivity of thiophenol molecules absorbed on a silver(111) substrate. It was found that the molecules form ordered monolayers on the substrate with a 3 p 3 × 3 unit cell. The performed conduction experiments revealed vibrational features that could be related to the presence of vibrational modes of the thiophenol molecule as well as to phonon modes of the silver substrate. By comparing these conduction experiments with computational simulations, it was determined that, depending on the exact position of the tip above the molecule, electrons can take different pathways through the molecule and thereby excite different atomic/molecular vibrations. The calculations also showed that the composition of the tip has an important effect on the obtained IET spectrum as well. Additionally, it has been observed that the conductance spectrum is asymmetric around 0 Volts, which is attributed to a realignment of the molecule due to its dipole interaction with the applied electric field, and has a characteristic dip for voltages below 40 mV that is thought to be caused by the interplay between the silver phonon modes and the thiophenol molecules

Thermal distortions of non-Gaussian beams in Fabry–Perot cavities

Thermal effects are already important in currently operating interferometric gravitational wave detectors. Planned upgrades of these detectors involve increasing optical power to combat quantum shot noise. We consider the ramifications of this increased power for one particular class of laser beams—wide, flat-topped, mesa beams. In particular we model a single mesa beam Fabry–Perot cavity having thermoelastically deformed mirrors. We calculate the intensity profile of the fundamental cavity eigenmode in the presence of thermal perturbations, and the associated changes in thermal noise. We also outline an idealized method of correcting for such effects. At each stage we contrast our results with those of a comparable Gaussian beam cavity. Although we focus on mesa beams the techniques described are applicable to any azimuthally symmetric system