With the emergence of nanotechnology, mankind has obtained the capability to manipulate materials at nanoscale and this led to the invention of a new group of novel materials like carbon nanotubes, graphene and quantum nanodots. Silicene nanoribbons (SiNRs) are one of the newest members of this nanomaterial family which has been synthesized very recently by deposition on silver substrates. A SiNR sheet is made up of a layer of two dimensional honeycomb structure solely composed of silicon atoms. In this thesis, structural and mechanical properties of SiNR are being investigated with the help of classical empirical molecular dynamics simulation technique. In the first part of this thesis, structural properties of SiNR sheets have been investigated. This investigation has been carried out by performing classical molecular dynamics simulations using atomistic many-body potential energy functions at many different SiNR sheet lengths and widths, at low and room temperatures with and without periodic boundaries. It has been found that SiNR sheets do not have perfectly flat honeycomb geometry. It has also been found that finite length models are more likely to form tubular structures resembling distorted silicon nanotubes at room temperature. In the second part of this thesis, mechanical properties of SiNRs have been investigated. Mechanical properties of silicene nanoribbons of varying width have been investigated under 5% and 10% uniaxial strain via classical Molecular-Dynamics simulations at 1 K&deg / and 300 K&deg / temperatures by the aid of atomistic many-body potential energy functions. It has been found that under strain, SiNRs show such material properties: they are very ductile, they have considerable toughness and despite their low elasticity, they have a very long plastic range before fragmentation.

Our vision is as yet unsurpassed by machines because of the sophisticated representations of objects in our brains. This representation is vastly different from a pixel-based representation used in machine storages. It is this sophisticated representation that enables us to perceive two faces as very different, i.e, they are far apart in the “perceptual space”, even though they are close to each other in their pixel-based representations. Neuroscientists have proposed distances between responses of neurons to the images (as measured in macaque monkeys) as a quantification of the “perceptual distance” between the images. Let us call these neuronal dissimilarity indices of perceptual distances. They have also proposed behavioural experiments to quantify these perceptual distances. Human subjects are asked to identify, as quickly as possible, an oddball image embedded among multiple distractor images. The reciprocal of the search times for identifying the oddball is taken as a measure of perceptual distance between the oddball and the distractor. Let us call such estimates as behavioural dissimilarity indices. In this thesis, we describe a decision-theoretic model for visual search that suggests a connection between these two notions of perceptual distances. In the first part of the thesis, we model visual search as an active sequential hypothesis testing problem. Our analysis suggests an appropriate neuronal dissimilarity index which correlates strongly with the reciprocal of search times. We also consider a number of alternative possibilities such as relative entropy (Kullback-Leibler divergence), the Chernoff entropy and the L1-distance associated with the neuronal firing rate profiles. We then come up with a means to rank the various neuronal dissimilarity indices based on how well they explain the behavioural observations. Our proposed dissimilarity index does better than the other three, followed by relative entropy, then Chernoff entropy and then L1 distance. In the second part of the thesis, we consider a scenario where the subject has to find an oddball image, but without any prior knowledge of the oddball and distractor images. Equivalently, in the neuronal space, the task for the decision maker is to find the image that elicits firing rates different from the others. Here, the decision maker has to “learn” the underlying statistics and then make a decision on the oddball. We model this scenario as one of detecting an odd Poisson point process having a rate different from the common rate of the others. The revised model suggests a new neuronal dissimilarity index. The new dissimilarity index is also strongly correlated with the behavioural data. However, the new dissimilarity index performs worse than the dissimilarity index proposed in the first part on existing behavioural data. The degradation in performance may be attributed to the experimental setup used for the current behavioural tasks, where search tasks associated with a given image pair were sequenced one after another, thereby possibly cueing the subject about the upcoming image pair, and thus violating the assumption of this part on the lack of prior knowledge of the image pairs to the decision maker. In conclusion, the thesis provides a framework for connecting the perceptual distances in the neuronal and the behavioural spaces. Our framework can possibly be used to analyze the connection between the neuronal space and the behavioural space for various other behavioural tasks.