Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain

We find approximations to travelling breather solutions of the one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright breather and dark breather solutions are found. We find that the existence of localised (bright) solutions depends upon the coefficients of cubic and quartic terms of the potential energy, generalising an earlier inequality derived by James [CR Acad Sci Paris 332, 581, (2001)]. We use the method of multiple scales to reduce the equations of motion for the lattice to a nonlinear Schr{\"o}dinger equation at leading order and hence construct an asymptotic form for the breather. We show that in the absence of a cubic potential energy term, the lattice supports combined breathing-kink waveforms. The amplitude of breathing-kinks can be arbitrarily small, as opposed to traditional monotone kinks, which have a nonzero minimum amplitude in such systems. We also present numerical simulations of the lattice, verifying the shape and velocity of the travelling waveforms, and confirming the long-lived nature of all such modes

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice

Using asymptotic methods, we investigate whether discrete breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional Fermi-Pasta-Ulam lattice is shown to model the charge stored within an electrical transmission lattice. A third-order multiple-scale analysis in the semi-discrete limit fails, since at this order, the lattice equations reduce to the (2+1)-dimensional cubic nonlinear Schrödinger (NLS) equation which does not support stable soliton solutions for the breather envelope. We therefore extend the analysis to higher order and find a generalised $(2+1)$-dimensional NLS equation which incorporates higher order dispersive and nonlinear terms as perturbations. We find an ellipticity criterion for the wave numbers of the carrier wave. Numerical simulations suggest that both stationary and moving breathers are supported by the system. Calculations of the energy show the expected threshold behaviour whereby the energy of breathers does {\em not} go to zero with the amplitude; we find that the energy threshold is maximised by stationary breathers, and becomes arbitrarily small as the boundary of the domain of ellipticity is approached

A synchronous multimedia annotation system for secure collaboratories

In this paper, we describe the Vannotea system - an application designed to enable collaborating groups to discuss and annotate collections of high quality images, video, audio or 3D objects. The system has been designed specifically to capture and share scholarly discourse and annotations about multimedia research data by teams of trusted colleagues within a research or academic environment. As such, it provides: authenticated access to a web browser search interface for discovering and retrieving media objects; a media replay window that can incorporate a variety of embedded plug-ins to render different scientific media formats; an annotation authoring, editing, searching and browsing tool; and session logging and replay capabilities. Annotations are personal remarks, interpretations, questions or references that can be attached to whole files, segments or regions. Vannotea enables annotations to be attached either synchronously (using jabber message passing and audio/video conferencing) or asynchronously and stand-alone. The annotations are stored on an Annotea server, extended for multimedia content. Their access, retrieval and re-use is controlled via Shibboleth identity management and XACML access policies

Effects of temperature on the ion-induced bending of germanium and silicon nanowires

Nanowires can be manipulated using an ion beam via a phenomenon known as ion-induced bending (IIB). While the mechanisms behind IIB are still the subject of debate, accumulation of point defects or amorphisation are often cited as possible driving mechanisms. Previous results in the literature on IIB of Ge and Si nanowires have shown that after irradiation the aligned nanowires are fully amorphous. Experiments were recently reported in which crystalline seeds were preserved in otherwise-amorphous ion-beam-bent Si nanowires which then facilitated solid-phase epitaxial growth (SPEG) during subsequent annealing. However, the ion-induced alignment of the nanowires was lost during the SPEG. In this work, in situ ion irradiations in a transmission electron microscope at 400°C and 500°C were performed on Ge and Si nanowires, respectively, to supress amorphisation and the build-up of point defects. Both the Ge and Si nanowires were found to bend during irradiation thus drawing into question the role of mechanisms based on damage accumulation under such conditions. These experiments demonstrate for the first time a simple way of realigning single-crystal Ge and Si nanowires via IIB whilst preserving their crystal structure

Employing Automated Experimental Evolution to Understand Survival Strategies of Lab-Grown Extremophiles

Experimental evolution (EE) exposes microbes to intentional stressors to improve resistance through artificial mutation. The resulting changes to metabolic pathways, protein structure, and genetic sequences, along with traditional genetic engineering tools, to can help understand the mechanisms of improved tolerance. An automated experimental set-up -- the Automated Adaptive Directed Evolution Chamber (AADEC) -- with minimal scope for human interference was developed at NASA Ames. A second- generation device integrating more real-time biochemical sensors has been developed recently. Added sensors include pH for indicating metabolic products, oxidation-reduction potential (ORP) for indicating available/consumed metabolic energy, dissolved oxygen (DO) for indicating aerobic/anaerobic growth cycles, and electrical conductivity (EC) as an additional indicator of metabolic products. With four additional sensors, the system is biochemically more informative in real-time. More importantly, each sensor parameter can be used as a selection pressure, individually or in combination with others, to artificially create and control inhospitable environments analogous to extremophile habitats for microbial growth in the lab. Potential stressors to be added in the future include thermal, reactive oxygen species, metal-ion concentrations, and varying nutrient availability

Enabling Experimental Evolution: Multi-Parameter Sensor System Integration into a Culture/Stressor Biofluidics System

Experimental evolution (EE) exposes microbial communities to ecological stressors, simulating dynamics up to near-extinction events. Combined with comparative sequencing and other molecular tools, such data can inform the genetic and other biological mechanisms underlying extremophile adaptation, and other observed effects. Automating this type of experiment using biofluidics can mitigate many traditional obstacles, including delays in assay results and environment adjustment and the need for many replicates. A first-generation device for automating EE procedures, the Automated Adaptive Directed Evolution Chamber (AADEC), was developed at NASA Ames. UV-C radiation was the stressor, an LED-photodiode array measured optical density, magnetic agitation and peristaltic pump systems ensured nutrient availability, and Arduino microcontrollers provided control. Escherichia coli in LB kanamycin media was used for testing and performance verification. A manual laboratory procedure with timed exposure to UV-C was performed to typify tolerance acquisition. Approximately a 106 factor increase in survival ratio was recorded over multiple iterations. Currently, a second-generation device is being developed integrating more real-time sensors: redox potential (ORP), indicating available/consumed metabolic energy; dissolved oxygen (DO), indicating aerobic/anaerobic growth; pH, indicating metabolic products; and electrical conductivity (EC), another indicator of metabolic products. The EC sensor system was constructed and calibrated in-house and matched commercial sensors in the required range. A Raspberry Pi computer automated the electrical system, allowing real-time data acquisition. The fluidics card was made of CNC-milled polycarbonate for biocompatibility. Each sensor parameter can also be used as a selection pressure alone or in combination with others to create extreme microbial environments. As a proof of concept, this work demonstrated sensor operation in one pair of growth-sensor chambers. It can be expanded to a multi-chamber system to enable inter-culture comparisons and multi-population studies. The prior Arduino system will be ported to the RPi system. Future stressors to be added include thermal, reactive oxygen species, and varying nutrient availability

An imaging-based platform for high-content, quantitative evaluation of therapeutic response in 3D tumour models

While it is increasingly recognized that three-dimensional (3D) cell culture models recapitulate drug responses of human cancers with more fidelity than monolayer cultures, a lack of quantitative analysis methods limit their implementation for reliable and routine assessment of emerging therapies. Here, we introduce an approach based on computational analysis of fluorescence image data to provide high-content readouts of dose-dependent cytotoxicity, growth inhibition, treatment-induced architectural changes and size-dependent response in 3D tumour models. We demonstrate this approach in adherent 3D ovarian and pancreatic multiwell extracellular matrix tumour overlays subjected to a panel of clinically relevant cytotoxic modalities and appropriately designed controls for reliable quantification of fluorescence signal. This streamlined methodology reads out the high density of information embedded in 3D culture systems, while maintaining a level of speed and efficiency traditionally achieved with global colorimetric reporters in order to facilitate broader implementation of 3D tumour models in therapeutic screening

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice with hexagonal symmetry. Using asymptotic methods based on small amplitude ansatz, at third order we obtain a reduction to a cubic nonlinear Schrodinger equation (NLS) for the breather envelope. However, this does not support stable soliton solutions, so we pursue a higher-order analysis yielding a generalised NLS, which includes known stabilising terms. We present numerical results which suggest that long-lived stationary and moving breathers are supported by the lattice. We find breather solutions which move in an arbitrary direction, an ellipticity criterion for the wavenumbers of the carrier wave, asymptotic estimates for the breather energy, and a minimum threshold energy below which breathers cannot be found. This energy threshold is maximised for stationary breathers, and becomes vanishingly small near the boundary of the elliptic domain where breathers attain a maximum speed. Several of the results obtained are similar to those obtained for the square FPU lattice (Butt & Wattis, J Phys A, 39, 4955, (2006)), though we find that the square and hexagonal lattices exhibit different properties in regard to the generation of harmonics, and the isotropy of the generalised NLS equation.Comment: 29 pages, 14 Figure