Complexity and chirality indices for molecular informatics::differential geometry approach

Novel molecular complexity measures are designed based on the quantum molecular kinematics. The Hamiltonian matrix constructed in a quasi-topological approximation describes the temporal evolution of the modelled electronic system and determined the time derivatives for the dynamic quantities. This allows to define the average quantum kinematic characteristics closely related to the curvatures of the electron paths, particularly, the torsion reflecting the chirality of the dynamic system. A special attention has been given to the computational scheme for this chirality measure. The calculations on realistic molecular systems demonstrate reasonable behaviour of the proposed molecular complexity indices.

Improved sampling, pre-concentration, and detection of hidden explosives and illicit drugs by a novel solid phase microextraction geometry coupled to ion mobility spectrometry

The 9/11 Act mandates the inspection of 100% of cargo shipments entering the U.S. by 2012 and 100% inspection of air cargo by March 2010. So far, only 5% of inbound shipping containers are inspected thoroughly while air cargo inspections have fared better at 50%. Government officials have admitted that these milestones cannot be met since the appropriate technology does not exist. This research presents a novel planar solid phase microextraction (PSPME) device with enhanced surface area and capacity for collection of the volatile chemical signatures in air that are emitted from illicit compounds for direct introduction into ion mobility spectrometers (IMS) for detection. These IMS detectors are widely used to detect particles of illicit substances and do not have to be adapted specifically to this technology. For static extractions, PDMS and sol-gel PDMS PSPME devices provide significant increases in sensitivity over conventional fiber SPME. Results show a 50–400 times increase in mass detected of piperonal and a 2–4 times increase for TNT. In a blind study of 6 cases suspected to contain varying amounts of MDMA, PSPME-IMS correctly detected 5 positive cases with no false positives or negatives. One of these cases had minimal amounts of MDMA resulting in a false negative response for fiber SPME-IMS. A La (dihed) phase chemistry has shown an increase in the extraction efficiency of TNT and 2,4-DNT and enhanced retention over time. An alternative PSPME device was also developed for the rapid (seconds) dynamic sampling and preconcentration of large volumes of air for direct thermal desorption into an IMS. This device affords high extraction efficiencies due to strong retention properties under ambient conditions resulting in ppt detection limits when 3.5 L of air are sampled over the course of 10 seconds. Dynamic PSPME was used to sample the headspace over the following: MDMA tablets (12–40 ng detected of piperonal), high explosives (Pentolite) (0.6 ng detected of TNT), and several smokeless powders (26–35 ng of 2,4-DNT and 11–74 ng DPA detected). PSPME-IMS technology is flexible to end-user needs, is low-cost, rapid, sensitive, easy to use, easy to implement, and effective. ^

On the study of train-track dynamic interactions caused by rail welds on discrete supported rails

The paper studies the influence of rail weld dip on wheel-rail contact dynamics, with particular reference to freight trains where it is important to increase the operating speed and also the load transported. This has produced a very precise model, albeit simple and cost-effective, which has enabled train-track dynamic interactions over rail welds to be studied to make it possible to quantify the influence on dynamic forces and displacements of the welding geometry; of the position of the weld relative to the sleeper; of the vehicle's speed; and of the axle load and wheelset unsprung mass. It is a vertical model on the spatial domain and is drawn up in a simple fashion from vertical track receptances. For the type of track and vehicle used, the results obtained enable the quantification of increases in wheel-rail contact forces due to the new speed and load conditions.

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode.

Visual Insight in Geometry

According to a traditional rationalist proposal, it is possible to attain knowledge of certain necessary truths by means of insight—an epistemic mental act that combines the 'presentational' character of perception with the a priori status usually reserved for discursive reasoning. In this dissertation, I defend the insight proposal in relation to a specific subject matter: elementary Euclidean plane geometry, as set out in Book I of Euclid's Elements. In particular, I argue that visualizations and visual experiences of diagrams allow human subjects to grasp truths of geometry by means of visual insight. In the first two chapters, I provide an initial defense of the geometrical insight proposal, drawing on a novel interpretation of Plato's Meno to motivate the view and to reply to some objections. In the remaining three chapters, I provide an account of the psychological underpinnings of geometrical insight, a task that requires considering the psychology of visual imagery alongside the details of Euclid's geometrical system. One important challenge is to explain how basic features of human visual representations can serve to ground our intuitive grasp of Euclid's postulates and other initial assumptions. A second challenge is to explain how we are able to grasp general theorems by considering diagrams that depict only special cases. I argue that both of these challenges can be met by an account that regards geometrical insight as based in visual experiences involving the combined deployment of two varieties of 'dynamic' visual imagery: one that allows the subject to visually rehearse spatial transformations of a figure's parts, and another that allows the subject to entertain alternative ways of structurally integrating the figure as a whole. It is the interplay between these two forms of dynamic imagery that enables a visual experience of a diagram, suitably animated in visual imagination, to justify belief in the propositions of Euclid’s geometry. The upshot is a novel dynamic imagery account that explains how intuitive knowledge of elementary Euclidean plane geometry can be understood as grounded in visual insight.