An objective representation of the Gaussian integers

A rig is a riNg without Negatives. We analyse the free rig on a generator x subject to the equivalence x = 1 + x + x^2, showing that in it the non-constant polynomials form a ring. This ring can be identified with the Gaussian integers, which thus acquire objective meaning

Phase transition in conservative diffusive contact processes

We determine the phase diagrams of conservative diffusive contact processes by means of numerical simulations. These models are versions of the ordinary diffusive single-creation, pair-creation and triplet-creation contact processes in which the particle number is conserved. The transition between the frozen and active states was determined by studying the system in the subcritical regime and the nature of the transition, whether continuous or first order, was determined by looking at the fractal dimension of the critical cluster. For the single-creation model the transition remains continuous for any diffusion rate. For pair- and triplet-creation models, however, the transition becomes first order for high enough diffusion rate. Our results indicate that in the limit of infinite diffusion rate the jump in density equals 2/3 for the pair-creation model and 5/6 for the triplet-creation model

Realization and efficiency evaluation of a micro-photocatalytic cell prototype for real-time blood oxygenation

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.A novel approach to blood oxygenation is presented. Microfluidic channels molded out of PDMS (using standard soft lithography techniques) work as photocatalytic cells, where the coupling of anatase titanium dioxide (TiO2) thin films and platinum electrodes, allow an electrically assisted photocatalytic reaction to produce dissolved oxygen gas from the water content of the flowing blood. The thin films were deposited onto quartz glass substrates at room temperature (300K) using reactive RF sputtering with a Ti metal target. The results of the current study, as a proof of concept, have shown that the device can generate oxygen at a rate of 4.06×10-3 mM O2/(cm2 min) and oxygenate venous blood to the oxygen saturation level of arterial blood

Inhomogeneous critical current in nanowire superconducting single-photon detectors

A superconducting thin film with uniform properties is the key to realize nanowire superconducting single-photon detectors (SSPDs) with high performance and high yield. To investigate the uniformity of NbN films, we introduce and characterize simple detectors consisting of short nanowires with length ranging from 100nm to 15{\mu}m. Our nanowires, contrary to meander SSPDs, allow probing the homogeneity of NbN at the nanoscale. Experimental results, endorsed by a microscopic model, show the strongly inhomogeneous nature of NbN films on the sub-100nm scale.Comment: 10 pages, 4 figure

Hydration and anomalous solubility of the Bell-Lavis model as solvent

We address the investigation of the solvation properties of the minimal orientational model for water, originally proposed by Bell and Lavis. The model presents two liquid phases separated by a critical line. The difference between the two phases is the presence of structure in the liquid of lower density, described through orientational order of particles. We have considered the effect of small inert solute on the solvent thermodynamic phases. Solute stabilizes the structure of solvent, by the organization of solvent particles around solute particles, at low temperatures. Thus, even at very high densities, the solution presents clusters of structured water particles surrounding solute inert particles, in a region in which pure solvent would be free of structure. Solute intercalates with solvent, a feature which has been suggested by experimental and atomistic simulation data. Examination of solute solubility has yielded a minimum in that property, which may be associated with the minimum found for noble gases. We have obtained a line of minimum solubility (TmS) across the phase diagram, accompanying the line of maximum in density (TMD). This coincidence is easily explained for non-interacting solute and it is in agreement with earlier results in the literature. We give a simple argument which suggests that interacting solute would dislocate TmS to higher temperatures

Gravitational effects on a rigid Casimir cavity

Vacuum fluctuations produce a force acting on a rigid Casimir cavity in a weak gravitational field. Such a force is here evaluated and is found to have opposite direction with respect to the gravitational acceleration; the order of magnitude for a multi-layer cavity configuration is analyzed and experimental detection is discussed, bearing in mind the current technological resources.Comment: 7 pages, Latex. Talk given at the Fifth Leipzig Workshop on Quantum Field Theory under the Influence of External Conditions, September 200

Assessing the Ability of Instantaneous Aircraft and Sonde Measurements to Characterize Climatological Means and Long-Term Trends in Tropospheric Composition

Over four decades of measurements exist that sample the 3-D composition of reactive trace gases in the troposphere from approximately weekly ozone sondes, instrumentation on civil aircraft, and individual comprehensive aircraft field campaigns. An obstacle to using these data to evaluate coupled chemistry-climate models (CCMs)the models used to project future changes in atmospheric composition and climateis that exact space-time matching between model fields and observations cannot be done, as CCMs generate their own meteorology. Evaluation typically involves averaging over large spatiotemporal regions, which may not reflect a true average due to limited or biased sampling. This averaging approach generally loses information regarding specific processes. Here we aim to identify where discrete sampling may be indicative of long-term mean conditions, using the GEOS-Chem global chemical-transport model (CTM) driven by the MERRA reanalysis to reflect historical meteorology from 2003 to 2012 at 2o by 2.5o resolution. The model has been sampled at the time and location of every ozone sonde profile available from the Would Ozone and Ultraviolet Radiation Data Centre (WOUDC), along the flight tracks of the IAGOSMOZAICCARABIC civil aircraft campaigns, as well as those from over 20 individual field campaigns performed by NASA, NOAA, DOE, NSF, NERC (UK), and DLR (Germany) during the simulation period. Focusing on ozone, carbon monoxide and reactive nitrogen species, we assess where aggregates of the in situ data are representative of the decadal mean vertical, spatial and temporal distributions that would be appropriate for evaluating CCMs. Next, we identically sample a series of parallel sensitivity simulations in which individual emission sources (e.g., lightning, biogenic VOCs, wildfires, US anthropogenic) have been removed one by one, to assess where and when the aggregated observations may offer constraints on these processes within CCMs. Lastly, we show results of an additional 31-year simulation from 1980-2010 of GEOS-Chem driven by the MACCity emissions inventory and MERRA reanalysis at 4o by 5o. We sample the model at every WOUDC sonde and flight track from MOZAIC and NASA field campaigns to evaluate which aggregate observations are statistically reflective of long-term trends over the period

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page

Mapping isoprene emissions over North America using formaldehyde column observations from space

We present a methodology for deriving emissions of volatile organic compounds (VOC) using space-based column observations of formaldehyde (HCHO) and apply it to data from the Global Ozone Monitoring Experiment (GOME) satellite instrument over North America during July 1996. The HCHO column is related to local VOC emissions, with a spatial smearing that increases with the VOC lifetime. Isoprene is the dominant HCHO precursor over North America in summer, and its lifetime (≃1 hour) is sufficiently short that the smearing can be neglected. We use the Goddard Earth Observing System global 3-D model of tropospheric chemistry (GEOS-CHEM) to derive the relationship between isoprene emissions and HCHO columns over North America and use these relationships to convert the GOME HCHO columns to isoprene emissions. We also use the GEOS-CHEM model as an intermediary to validate the GOME HCHO column measurements by comparison with in situ observations. The GEOS-CHEM model including the Global Emissions Inventory Activity (GEIA) isoprene emission inventory provides a good simulation of both the GOME data (r2 = 0.69, n = 756, bias = +11%) and the in situ summertime HCHO measurements over North America (r2 = 0.47, n = 10, bias = −3%). The GOME observations show high values over regions of known high isoprene emissions and a day-to-day variability that is consistent with the temperature dependence of isoprene emission. Isoprene emissions inferred from the GOME data are 20% less than GEIA on average over North America and twice those from the U.S. EPA Biogenic Emissions Inventory System (BEIS2) inventory. The GOME isoprene inventory when implemented in the GEOS-CHEM model provides a better simulation of the HCHO in situ measurements than either GEIA or BEIS2 (r2 = 0.71, n = 10, bias = −10%)

Electromechanical tuning of vertically-coupled photonic crystal nanobeams

We present the design, the fabrication and the characterization of a tunable one-dimensional (1D) photonic crystal cavity (PCC) etched on two vertically-coupled GaAs nanobeams. A novel fabrication method which prevents their adhesion under capillary forces is introduced. We discuss a design to increase the flexibility of the structure and we demonstrate a large reversible and controllable electromechanical wavelength tuning (> 15 nm) of the cavity modes.Comment: 11 pages, 4 figure