Diophantine equations as a context for technology-enhanced training in conjecturing and proving

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

Ultra sensitive label free surface enhanced Raman spectroscopy method for the detection of biomolecules

We present a proof of concept for a novel nanosensor for the detection of ultra-trace amounts of bio-active molecules in complex matrices. The nanosensor is comprised of gold nanoparticles with an ultra-thin silica shell and antibody surface attachment, which allows for the immobilization and direct detection of bio-active molecules by surface enhanced Raman spectroscopy (SERS) without requiring a Raman label. The ultra-thin passive layer (~1.3 nm thickness) prevents competing molecules from binding non-selectively to the gold surface without compromising the signal enhancement. The antibodies attached on the surface of the nanoparticles selectively bind to the target molecule with high affinity. The interaction between the nanosensor and the target analyte result in conformational rearrangements of the antibody binding sites, leading to significant changes in the surface enhanced Raman spectra of the nanoparticles when compared to the spectra of the un-reacted nanoparticles. Nanosensors of this design targeting the bio-active compounds erythropoietin and caffeine were able to detect ultra-trace amounts the analyte to the lower quantification limits of 3.5×10−13 M and 1×10−9 M, respectively.

Privacy enhanced electronic cheque system

With the introduction of Check 21 law and the development of FSTC's echeck system, there has been an increasing usage of e-cheque conversions and acceptance among retailers, banks, and consumers. However, the current e-cheque system does not address issues concerning privacy, confidentiality, and traceability. We highlight the issues concerning the current electronic cheque system and provide a solution to overcome those drawbacks.

Enhanced electron field emission from plasma-nitrogenated carbon nanotips

Nitrogenated carbon nanotips (NCNTPs) are synthesized by plasma-enhanced hot filament chemical vapor deposition from the hydrogen, methane, and nitrogen gas mixtures with different flow rate ratios of hydrogen to nitrogen. The morphological, structural, compositional, and electron field emission (EFE) properties of the NCNTPs were investigated by field emissionscanning electron microscopy, Raman spectroscopy, x ray photoelectron spectroscopy, and EFE high-vacuum system. It is shown that the NCNTPs deposited at an intermediate flow rate ratio of hydrogen to nitrogen feature the best size/shape and pattern uniformity, the highest nanotip density, the highest nitrogen concentration, as well as the best electron field emission performance. Several factors that come into play along with the nitrogen incorporation, such as the combined effect of the plasma sputtering and etching, the transition of sp 3carbon clusters to sp 2carbon clusters, the increase of the size of the sp 2 clusters, as well as the reduction of the work function, have been examined to interpret these experimental findings. Our results are highly relevant to the development of the next generation electron field emitters, flat panel displays, atomic force microscope probes, and several other advanced applications.

Room-temperature photoluminescence from nitrogenated carbon nanotips grown by plasma-enhanced hot filament chemical vapor deposition

Nitrogenated carbon nanotips with a low atomic concentration of nitrogen have been synthesized by using a custom-designed plasma-enhanced hot-filament plasma chemical vapor deposition system. The properties (including morphology, structure, composition, photoluminescence, etc.) of the synthesized nitrogenated carbon nanotips are investigated using advanced characterization tools. The room-temperature photoluminescence measurements show that the nitrogenated carbon nanotips can generate two distinct broad emissions located at ∼405 and ∼507 nm, respectively. Through the detailed analysis, it is shown that these two emission bands are attributed to the transition between the lone pair valence and bands, which are related to the sp3 and sp2 C-N bonds, respectively. These results are highly relevant to advanced applications of nitrogenated carbon nanotips in light emitting optoelectronic devices.

Increasing the length of single-wall carbon nanotubes in a magnetically enhanced arc discharge

It is demonstrated that a magnetic field has a profound effect on the length of a single-wall carbon nanotube (SWCNT) synthesized in the arc discharge. The average length of SWCNT increases by a factor of 2 in discharge with magnetic field as compared with the discharge without magnetic field, and the yield of long nanotubes with lengths above 5 μm also increases. A model of SWCNT growth on metal catalyst in arc plasma was developed. Monte-Carlo simulations confirm that the increase of the plasma density in the magnetic field leads to an increase in the nanotube growth rate and thus leads to longer nanotubes.

The large-scale production of graphene flakes using magnetically-enhanced arc discharge between carbon electrodes

A novel approach to large-scale production of high-quality graphene flakes in magnetically-enhanced arc discharges between carbon electrodes is reported. A non-uniform magnetic field is used to control the growth and deposition zones, where the Y-Ni catalyst experiences a transition to the ferromagnetic state, which in turn leads to the graphene deposition in a collection area. The quality of the produced material is characterized by the SEM, TEM, AFM, and Raman techniques. The proposed growth mechanism is supported by the nucleation and growth model.

Analysis of photoluminescence background of Raman spectra of carbon nanotips grown by plasma-enhanced chemical vapor deposition

Carbon nanotips with different structures were synthesized by plasma-enhanced hot filament chemical vapor deposition and plasma-enhanced chemical vapor deposition using different deposition conditions, and they were investigated by scanning electron microscopy and Raman spectroscopy. The results indicate that the photoluminescence background of the Raman spectra is different for different carbon nanotips. Additionally, the Raman spectra of the carbon nanotips synthesized using nitrogen-containing gas precursors show a peak located at about 2120 cm-1 besides the common D and G peaks. The observed difference in the photoluminescence background is related to the growth mechanisms, structural properties, and surface morphology of a-C:H and a-C:H:N nanotips, in particular, the sizes of the emissive tips.

Carbon nanofiber growth in plasma-enhanced chemical vapor deposition

A theoretical model to describe the plasma-assisted growth of carbon nanofibers (CNFs) is proposed. Using the model, the plasma-related effects on the nanofiber growth parameters, such as the growth rate due to surface and bulk diffusion, the effective carbon flux to the catalyst surface, the characteristic residence time and diffusion length of carbon atoms on the catalyst surface, and the surface coverages, have been studied. The dependence of these parameters on the catalyst surface temperature and ion and etching gas fluxes to the catalyst surface is quantified. The optimum conditions under which a low-temperature plasma environment can benefit the CNF growth are formulated. These results are in good agreement with the available experimental data on CNF growth and can be used for optimizing synthesis of related nanoassemblies in low-temperature plasma-assisted nanofabrication. © 2008 American Institute of Physics.

Magnetic-field-enhanced synthesis of single-wall carbon nanotubes in arc discharge

The ability to control the properties of single-wall nanotubes (SWNTs) produced in the arc discharge is important for many practical applications. Our experiments suggest that the length of SWNTs significantly increases (up to 4000 nm), along with the purity of the carbon deposit, when the magnetic field is applied to arc discharge. Scanning electron microscopy and transmission electron microscopy analyses have demonstrated that the carbon deposit produced in the magnetic-field-enhanced arc mainly consists of the isolated and bunched SWNTs. A model of a carbon nanotube interaction and growth in the thermal plasma was developed, which considers several important effects such as anode ablation that supplies the carbon plasma in an anodic arc discharge technique, and the momentum, charge, and energy transfer processes between nanotube and plasma. It is shown that the nanotube charge with respect to the plasma as well as nanotube length depend on plasma density and electric field in the interelectrode gap. For instance, nanotube charge changes from negative to positive value with an electron density decrease. The numerical simulations based on the Monte Carlo technique were performed, which explain an increase in the nanotubes produced in the magnetic-field-enhanced arc discharge. © 2008 American Institute of Physics.

High-rate, room temperature plasma-enhanced deposition of aluminum-doped zinc oxide nanofilms for solar cell applications

A custom-designed inductively coupled plasma (ICP)-assisted radio-frequency magnetron sputtering deposition system has been employed to synthesize aluminium-doped zinc oxide (ZnO:Al) nanofilms on glass substrates at room temperature. The effects of film thickness and ZnO target (partially covered by Al chips) power on the structural, electrical and optical properties of the ZnO:Al nanofilms are studied. A high growth rate (∼41 nm/min), low electrical sheet resistance (as low as 30 Ω/□) and high optical transparency (>80%) over the visible spectrum has been achieved at a film thickness of ∼615 nm and ZnO target power of 150 W. The synthesis of ZnO:Al nanofilms at room temperature and with high growth rates is attributed to the unique features of the ICP-assisted radio-frequency magnetron sputtering deposition approach. The results are relevant to the development of photovoltaic thin-film solar cells and flat panel displays.

Ways to increase the length of single wall carbon nanotubes in a magnetically enhanced arc discharge

Ability to control the properties of single-wall nanotubes produced in the arc discharge is important for many practical applications. Our experiments suggest that the length and purity of single-wall nanotubes significantly increase when the magnetic field is applied to the arc discharge. A model of a single wall carbon nanotube interaction and growth in the thermal plasma was developed which considers several important effects such as anode ablation that supplies the carbon plasma in an anodic arc discharge technique, and the momentum, charge and energy transfer processes between nanotube and plasma. The numerical simulations based on Monte-Carlo technique were performed, which explain an increase of the nanotubes produced in the magnetic field - enhanced arc discharge.

Simulation of gas-phase nanoparticle dynamics in the plasma-enhanced chemical vapor deposition of carbon nanostructures

The results of 1D simulation of nanoparticle dynamics in the areas adjacent to nanostructured carbon-based films exposed to chemically active complex plasma of CH4 + H2 + Ar gas mixtures are presented. The nanoparticle-loaded near-substrate (including sheath and presheath) areas of a low-frequency (0.5 MHz) inductively coupled plasma facility for the PECVD growth of the ordered carbon-based nanotip structures are considered. The conditions allowing one to predict the size of particles that can pass through the plasma sheath and softly land onto the surface are formulated. The possibility of soft nano-cluster deposition without any additional acceleration common for some existing nano-cluster deposition schemes is demonstrated. The effect of the substrate heating power and the average atomic mass of neutral species is studied numerically and verified experimentally.

E and H regimes of plasma enhanced chemical vapor deposition of diamond-like carbon film in low frequency inductively coupled plasma reactor

This paper reports on the efficient deposition of hydrogenated diamond-like carbon (DLC) film in a plasma reactor that features both the capacitively and inductively coupled operation regimes. The hydrogenated DLC films have been prepared on silicon wafers using a low-frequency (500 kHz) inductively coupled plasma (ICP) chemical vapor deposition (CVD) system. At low RF powers, the system operates as an asymmetric capacitively coupled plasma source, and the film deposition process is undertaken in the electrostatic (E) discharge regime. Above the mode transition threshold, the high-density inductively coupled plasma is produced in the electromagnetic (H) discharge regime. It has been shown that the deposition rate and hardness of the DLC film are much higher in the H-mode deposition regime. For a 2.66-Pa H-mode CH4 + Ar gas mixture discharge, the deposited DLC film exhibits a mechanical hardness of 18 GPa, Young's modulus of 170 GPa, and compressive stress of 1.3 GPa.

Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.