1-Million droplet array with wide-field fluorescence imaging for digital PCR

Digital droplet reactors are useful as chemical and biological containers to discretize reagents into picolitre or nanolitre volumes for analysis of single cells, organisms, or molecules. However, most DNA based assays require processing of samples on the order of tens of microlitres and contain as few as one to as many as millions of fragments to be detected. Presented in this work is a droplet microfluidic platform and fluorescence imaging setup designed to better meet the needs of the high-throughput and high-dynamic-range by integrating multiple high-throughput droplet processing schemes on the chip. The design is capable of generating over 1-million, monodisperse, 50 picolitre droplets in 2-7 minutes that then self-assemble into high density 3-dimensional sphere packing configurations in a large viewing chamber for visualization and analysis. This device then undergoes on-chip polymerase chain reaction (PCR) amplification and fluorescence detection to digitally quantify the sample's nucleic acid contents. Wide-field fluorescence images are captured using a low cost 21-megapixel digital camera and macro-lens with an 8-12 cm(2) field-of-view at 1× to 0.85× magnification, respectively. We demonstrate both end-point and real-time imaging ability to perform on-chip quantitative digital PCR analysis of the entire droplet array. Compared to previous work, this highly integrated design yields a 100-fold increase in the number of on-chip digitized reactors with simultaneous fluorescence imaging for digital PCR based assays.     

High rates of nitrogen cycling in volcanic soils from Chilean grasslands

There are over one million hectares of pasture in Chile, and 80% and 50% of the country's milk and meat comes from 72% of this area, situated in the lake region of southern Chile. The soils are volcanic and a major characteristic is that they have very high organic matter (OM) contents with the potential to support plant growth with only moderate levels of added nitrogen (N). To understand better the potential fertility of these soils in order to maximise production and minimise losses of N, we undertook studies using the stable isotope of N ((15)N) to resolve the rates of the main internal N cycling processes in three soils representing the two main volcanic soil types: Osorno and Chiloé (Andisol) and Cudico (Ultisol). We also assessed the longer-term potential of these soils to sustain N release using anaerobic incubation. Gross rates (μg N g(-1) day(-1)) of mineralisation were 27.9, 27.1 and 15.5 and rates of immobilisation were 5.9, 12.0 and 6.3 for Osorno, Chiloé and Cudico, respectively, implying high rates of net mineralisation in these soils. This was confirmed by anaerobic incubation which gave potential seasonal net mineralisation indices of 1225, 1059 and 450 kg N ha(-1) in the top 10 cm soil layers of the three soils. However, plant production may still benefit from added N, as the release of N from organic sources may not be closely synchronised with crop demand. The low rates of nitrification that we found with these acidic soils suggest that the more mobile N (viz. nitrate-N) would be in limited supply and plants would have to compete for the less mobile ammonium-N with the soil microbial biomass. Nitrogen was mineralised in appreciable amounts even down to 60 cm depth, so that leaching could become significant, particularly if the soils were limed, which could enhance nitrification and N mobility through the soil profile.     

A collocation method for high-frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.     

Divisibility tests for low-valued primes and their use as generators of simple proofs

This article considers a family of divisibility tests for low-valued primes and their place as activities which develop the use of proof both within school and in teacher training. The way in which these tests can be seen as developing one from another is seen as of value in encouraging students to produce their own proofs.     

Multiple Ring Discharges in a Cylindrical Resonant Cavity

Observations have been made of an rf multiple-ring discharge which is a variant of the well-known single-ring rf discharge described by J. J. Thomson. A set of discretely-located plasma rings (typically 2 to 5 in number) forms coaxially in the central portion of a cylindrical quartz tube on the axis of a cylindrical cavity excited in the TE011 mode. The rings fit closely inside the inner periphery of the quartz tube at pressures ranging from a few Torr to atmospheric, have a minor diameter of order 1/10 the tube diameter, and are spaced at intervals nearly equal to the tube diameter. Excitation of the degenerate companion TM111 mode results in asymmetrical tilting of the rings. Gas flow through the discharge tube results in a continuous unidirectional axial motion of the rings with new rings being abruptly formed toward the input end of the tube and contracting and vanishing abruptly as they move toward the exit end. A theory is developed which accounts for the observed phenomena.     

Concerning bent-crystal spectrometer measurements ofKαx-rays from radioactive sources

The wavelengths of severalKα x-rays emitted from elements in and neighboring the rare earth region which were contained in radioactive sources have been determined with the two-meter quartz bent-crystal spectrometer at the California Institute of Technology. The results of the measurements in XU are the following: SmKα₂, 313·043; SmKα₁, 308·390; EuKα₂, 302·477; EuKα₁, 297·824; GdKα₂, 292·432; GdKα₁, 287·746; TmKα₂, 248·592; TmKα₁, 243·859; YbKα₂, 240·934; YbKα₁, 236·184; LuKα₂, 233·610; LuKα₁, 228·834; HfKα₂, 226·605; HfKα₁, 221·805. The estimated maximal error for each measurement is ±0·015 XU. From comparing the present measurements with precise measurements of the corresponding x-rays from the naturally occurring elements, it can be concluded that there are no observable shifts in the x-rays from the radioactive sources within 0·017 XU. An upper limit of 2·5 eV is obtained for an observable shift due to the isotope shift or the isomeric shift in the GdKα x-rays from a radioactive Eu source. Upper limits for the observation of shifts due to the isomeric shift in theKα x-rays of 2·5 eV for Sm and of 4 eV for Tm and Lu are also obtained.     

Precision determination of energies of gamma rays in Sm152, Gd152, 154, 155, 156, Yb170, and Os188

With the help of the bent-crystal gamma-ray diffraction spectrometer the energies of 13 gamma rays, most of them belonging to rotational levels, have been determined with high precision. Rotational parameters are presented for the nuclei of Sm¹⁵², Gd¹⁵⁴, and Gd¹⁵⁶. A complete level scheme is given for Gd¹⁵⁵.     

Phase transitions and renormalization group hamiltonian densities in the 80 diperiodic space groups

Phase transitions for systems with diperiodic symmetry are discussed. Direct group-theoretical methods are employed to obtain a list of possible commensurate lower-symmetry phases (subgroups) which are induced by a single order parameter. The lower-symmetry phases for all 80 diperiodic space groups are given, along with specific details of the group-subgroup relationships. Results for the 17 two-dimensional space groups are also contained in our list. The renormalization-group Hamiltonian densities for the diperiodics are calculated. The 12 densities listed constitute the complete set of densities which may arise in the diperiodic space groups. Critical properties for the diperiodics can thus be obtained from analysis of these densities.