A Class of Collisions of Plane Impulsive Light--Like Signals in General Relativity

We present a systematic study of collisions of homogeneous, plane--fronted, impulsive light--like signals which do not interact after head--on collision. For the head--on collision of two such signals, six real parameters are involved, three from each of the incoming signals. We find two necessary conditions to be satisfied by these six parameters for the signals to be non--interacting after collision. We then solve the collision problem in general when these necessary conditions hold. After collision the two signals focus each other at Weyl curvature singularities on each others signal front. Our family of solutions contains some known collision solutions as special cases.Comment: 14 pages, late

Evaporation and growth of crystals - propagation of step density compression waves at vicinal surfaces

We studied the step dynamics during crystal sublimation and growth in the limit of fast surface diffusion and slow kinetics of atom attachment-detachment at the steps. For this limit we formulate a model free of the quasi-static approximation in the calculation of the adatom concentration on the terraces at the crystal surface. Such a model provides a relatively simple way to study the linear stability of a step train in a presence of step-step repulsion and an absence of destabilizing factors (as Schwoebel effect, surface electromigration etc.). The central result is that a critical velocity of the steps in the train exists which separates the stability and instability regimes. When the step velocity exceeds its critical value the plot of these trajectories manifests clear space and time periodicity (step density compression waves propagate on the vicinal surface). This ordered motion of the steps is preceded by a relatively short transition period of disordered step dynamics.Comment: 18 pages, 6 figure

Synthesis and characterization of biodegradable lignin nanoparticles with tunable surface properties

Lignin nanoparticles can serve as biodegradable carriers of biocidal actives with minimal environmental footprint. Here we describe the colloidal synthesis and interfacial design of nanoparticles with tunable surface properties using two different lignin precursors, Kraft (Indulin AT) lignin and Organosolv (high-purity lignin). The green synthesis process is based on flash precipitation of dissolved lignin polymer, which enabled the formation of nanoparticles in the size range of 45–250 nm. The size evolution of the two types of lignin particles is fitted on the basis of modified diffusive growth kinetics and mass balance dependencies. The surface properties of the nanoparticles are fine-tuned by coating them with a cationic polyelectrolyte, poly(diallyldimethylammonium chloride). We analyze how the colloidal stability and dispersion properties of these two types of nanoparticles vary as a function of pH and salinities. The data show that the properties of the nanoparticles are governed by the type of lignin used and the presence of polyelectrolyte surface coating. The coating allows the control of the nanoparticles’ surface charge and the extension of their stability into strongly basic regimes, facilitating their potential application at extreme pH conditions

Short Term Flux and Colour Variations in Low-Energy Peaked Blazars

We have measured multi-band optical flux and colour variations for a sample of 12 low energy peaked blazars on short, day-to-month, timescales. Our sample contains six BL Lacertae objects and six flat spectrum radio quasars. These photometric observations, made during September 2008 to June 2009, used five optical telescopes, one in India and four in Bulgaria. We detected short term flux variations in eleven of these blazars and colour variability in eight of them. Our data indicate that six blazars (3C 66A, AO 0235+164, S5 0716+714, PKS 0735+178, OJ 287 and 3C 454.3) were observed in pre- or post-outburst states, that five (PKS 0420-014, 4C 29.45, 3C 279, PKS 1510-089 and BL Lac) were in a low state, while one (3C 273) was in an essentially steady state. The duty cycles for flux and colour variations on short timescales in these low energy peaked blazars are ~ 92 percent and ~ 33 percent, respectively. The colour vs magnitude correlations seen here support the hypothesis that BL Lac objects tend to become bluer with increase in brightness; however, flat spectrum radio quasars may show the opposite trend, and there are exceptions to these trends in both categories of blazar. We briefly discuss emission models for active galactic nuclei that might explain our results.Comment: 34 pages, 5 tables, 15 figures, accepted for publication in MNRA

Global rigid registration of CT to video in laparoscopic liver surgery

PURPOSE: Image-guidance systems have the potential to aid in laparoscopic interventions by providing sub-surface structure information and tumour localisation. The registration of a preoperative 3D image with the intraoperative laparoscopic video feed is an important component of image guidance, which should be fast, robust and cause minimal disruption to the surgical procedure. Most methods for rigid and non-rigid registration require a good initial alignment. However, in most research systems for abdominal surgery, the user has to manually rotate and translate the models, which is usually difficult to perform quickly and intuitively. METHODS: We propose a fast, global method for the initial rigid alignment between a 3D mesh derived from a preoperative CT of the liver and a surface reconstruction of the intraoperative scene. We formulate the shape matching problem as a quadratic assignment problem which minimises the dissimilarity between feature descriptors while enforcing geometrical consistency between all the feature points. We incorporate a novel constraint based on the liver contours which deals specifically with the challenges introduced by laparoscopic data. RESULTS: We validate our proposed method on synthetic data, on a liver phantom and on retrospective clinical data acquired during a laparoscopic liver resection. We show robustness over reduced partial size and increasing levels of deformation. Our results on the phantom and on the real data show good initial alignment, which can successfully converge to the correct position using fine alignment techniques. Furthermore, since we can pre-process the CT scan before surgery, the proposed method runs faster than current algorithms. CONCLUSION: The proposed shape matching method can provide a fast, global initial registration, which can be further refined by fine alignment methods. This approach will lead to a more usable and intuitive image-guidance system for laparoscopic liver surgery

Electromigration-Induced Propagation of Nonlinear Surface Waves

Due to the effects of surface electromigration, waves can propagate over the free surface of a current-carrying metallic or semiconducting film of thickness h_0. In this paper, waves of finite amplitude, and slow modulations of these waves, are studied. Periodic wave trains of finite amplitude are found, as well as their dispersion relation. If the film material is isotropic, a wave train with wavelength lambda is unstable if lambda/h_0 < 3.9027..., and is otherwise marginally stable. The equation of motion for slow modulations of a finite amplitude, periodic wave train is shown to be the nonlinear Schrodinger equation. As a result, envelope solitons can travel over the film's surface.Comment: 13 pages, 2 figures. To appear in Phys. Rev.

Intelligent viewpoint selection for efficient CT to video registration in laparoscopic liver surgery

PURPOSE: Minimally invasive surgery offers advantages over open surgery due to a shorter recovery time, less pain and trauma for the patient. However, inherent challenges such as lack of tactile feedback and difficulty in controlling bleeding lower the percentage of suitable cases. Augmented reality can show a better visualisation of sub-surface structures and tumour locations by fusing pre-operative CT data with real-time laparoscopic video. Such augmented reality visualisation requires a fast and robust video to CT registration that minimises interruption to the surgical procedure. METHODS: We propose to use view planning for efficient rigid registration. Given the trocar position, a set of camera positions are sampled and scored based on the corresponding liver surface properties. We implement a simulation framework to validate the proof of concept using a segmented CT model from a human patient. Furthermore, we apply the proposed method on clinical data acquired during a human liver resection. RESULTS: The first experiment motivates the viewpoint scoring strategy and investigates reliable liver regions for accurate registrations in an intuitive visualisation. The second experiment shows wider basins of convergence for higher scoring viewpoints. The third experiment shows that a comparable registration performance can be achieved by at least two merged high scoring views and four low scoring views. Hence, the focus could change from the acquisition of a large liver surface to a small number of distinctive patches, thereby giving a more explicit protocol for surface reconstruction. We discuss the application of the proposed method on clinical data and show initial results. CONCLUSION: The proposed simulation framework shows promising results to motivate more research into a comprehensive view planning method for efficient registration in laparoscopic liver surgery