Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

Fractional commensurate, composition, and adding schemes: Learning trajectories of Jason and Laura: Grade 5

A case study of two 5th-Grade children, Jason and Laura, is presented who participated in the teaching experiment, Children’s Construction of the Rational Numbers of Arithmetic. The case study begins on the 29th of November of their 5th-Grade in school and ends on the 5th of April of the same school year. Two basic problems were of interest in the case study. The first was to provide an analysis of the concepts and operations that are involved in the construction of three fractional schemes: a commensurate fractional scheme, a fractional composition scheme, and a fractional adding scheme. The second was to provide an analysis of the contribution of interactive mathematical activity in the construction of these schemes. The phrase, “commensurate factional scheme” refers to the concepts and operations that are involved in transforming a given fraction into another fraction that are both measures of an identical quantity. Likewise, “fractional composition scheme” refers to the concepts and operations that are involved in finding how much, say, 1/3 of 1/4 of a quantity is of the whole quantity, and “fractional adding scheme” refers to the concepts and operations involved in finding how much, say, 1/3 of a quantity joined to 1/4 of a quantity is of the whole quantity. Critical protocols were abstracted from the teaching episodes with the two children that illustrate what is meant by the schemes, changes in the children’s concepts and operations, and the interactive mathematical activity that was involved. The body of the case study consists of an on-going analysis of the children’s interactive mathematical activity and changes in that activity. The last section of the case study consists of an analysis of the constitutive aspects of the children’s constructive activity, including the role of social interaction and nonverbal interactions of the children with each other and with the computer software we used in teaching the children.     

Tunable laser Stark-difference spectra of CD3OH

We present Doppler resolution limited spectra of the P(J) and R(J) multiplets for J ≦ 10 of the 10-μm CO stretch band of ¹²CD₃¹⁶OH using a tunable diode laser. Relative frequencies within the multiplets accurate to ±0.0002–0.0005 cm^?1 are obtained, but no absolute frequencies are given. We are able to assign most of the hindered rotation and K substructure in these multiplets. The assignments are based on analyses of Stark-difference spectra combined with the ground-state microwave data and the intensity variations which are expected theoretically. The ground and excited state A, K = 1 asymmetry splitting parameters are measured to be δ₁″ = (8.5450 ± 0.0080) × 10^?3cm^?1 and δ₁′ = (9.7706 ± 0.0080) × 10^?3cm^?1, respectively. The ground-state value agrees well with the microwave results. A rapid-scan system for recording data and a computer-aided technique for calibrating and plotting the spectra are described.     

Calculation of the rotation-vibration spectrum of NH+

Ab initio molecular orbital calculations have been used to compute potential energy and dipole moment functions for the X²II and a⁴Σ^? states of NH⁺. These functions have been used to compute rotational-vibrational energy levels, including the interaction between the two states. Transition moments have been calculated for transitions between these levels, using either the results of numerical diagonalization of the Hamiltonian, or more approximately by fitting analytic functions. Good agreement with experimental data is found, and our results have also been used to interpret previously unassigned spectral lines.     

Visual Speech Recognition with Lightweight Psychologically Motivated Gabor Features

Extraction of relevant lip features is of continuing interest in the visual speech domain. Using end-to-end feature extraction can produce good results, but at the cost of the results being difficult for humans to comprehend and relate to. We present a new, lightweight feature extraction approach, motivated by human-centric glimpse-based psychological research into facial barcodes, and demonstrate that these simple, easy to extract 3D geometric features (produced using Gabor-based image patches), can successfully be used for speech recognition with LSTM-based machine learning. This approach can successfully extract low dimensionality lip parameters with a minimum of processing. One key difference between using these Gabor-based features and using other features such as traditional DCT, or the current fashion for CNN features is that these are human-centric features that can be visualised and analysed by humans. This means that it is easier to explain and visualise the results. They can also be used for reliable speech recognition, as demonstrated using the Grid corpus. Results for overlapping speakers using our lightweight system gave a recognition rate of over 82%, which compares well to less explainable features in the literature.     

Atom-scale ptychographic electron diffractive imaging of boron nitride cones

Ptychographic coherent diffractive imaging (CDI) has been extensively applied using both x rays and electrons. The extension to atomic resolution has been elusive. This Letter demonstrates ptychographic electron diffractive imaging at atomic resolution, permitting identification of structure in a boron nitride helical cone at a resolution of order 1 ?, beyond that of comparative Z-contrast images. A scanning transmission electron microscope is used to create a diverging illumination in a defocused Fresnel CDI geometry, providing a robust strategy leading to a unique solution.     

Empirical analysis of the evolution of a scientific collaboration network

We present an analysis of the temporal evolution of a scientific coauthorship network, the genetic programming network. We find evidence that the network grows according to preferential attachment, with a slightly sublinear rate. We empirically find how a giant component forms and develops, and we characterize the network by several other time-varying quantities: the mean degree, the clustering coefficient, the average path length, and the degree distribution. We find that the first three statistics increase over time in the growing network; the degree distribution tends to stabilize toward an exponentially truncated power-law. We finally suggest an effective network interpretation that takes into account the aging of collaboration relationships.     

Precision branching ratio measurement for the superallowed beta+ emitter 62Ga and isospin-symmetry-breaking corrections in A>or=62 nuclei

A high-precision branching ratio measurement for the superallowed beta+ decay of 62Ga was performed at the Isotope Separator and Accelerator radioactive ion beam facility. Nineteen gamma rays emitted following beta+ decay of 62Ga were identified, establishing the dominant superallowed branching ratio to be (99.861+/-0.011)%. Combined with recent half-life and Q-value measurements, this branching ratio yields a superallowed ft value of 3075.6+/-1.4 s for 62Ga decay. These results demonstrate the feasibility of high-precision superallowed branching ratio measurements in the A>or=62 mass region and provide the first stringent tests of the large isospin-symmetry-breaking effects predicted for these decays.     

Multiple-quantum NMR spectra of partially oriented indene: a new approach to estimating order in a nematic phase

Cyclic J cross polarisation (CYCLCROP) is a sensitive method for the noninvasive monitoring of (13)C distributions and fluxes. The PRAWN rotating frame Hartmann-Hahn mixing sequence ameliorates problems associated with sensitivity to Hartmann-Hahn mismatch and reduces RF power deposition. The combination of CYCLCROP with echo planar imaging (EPI) for spatial encoding of the proton detected carbon signal allows efficient use of the available signal to be made, permitting a significant improvement in the temporal resolution of any study. We report here on some initial experiments to demonstrate the feasibility of echo planar proton detected (13)C imaging using CYCLCROP based upon the PRAWN module, including the application of the technique to the measurement of transport and accumulation of (13)C-labelled sucrose in a castor bean seedling. Two methods that can be used to eliminate the effect of the J-splitting in the EP images are presented. In addition, a fast, image-based B(1) field-mapping method which may be used to quantitatively map the low frequency RF field in a dual resonant ((13)C/(1)H) probe is presented. The technique utilises the above described imaging method, permitting fully quantitative, 64x64 axial field maps to be generated in about a minute.     

Exhaustive checking of sparse algebras

We checked the 107-dimensional alternative algebra constructed by E. Kleinfeld (On centers of alternative algebras, Comm. Algebra8(3) 1980, 289–297) and verified that it was alternative. To straightforwardly check the alternative law for the basis elements proved to be too time consuming for the computer. We developed a new algorithm which is much faster for sparse multiplication tables and which requires much less memory. Instead of testing the identities for all possible choices of basis elements, our algorithm is based on “factoring” the basis elements in all possible ways. The factorization algorithm took 5 minutes of C.P.U. time; it is estimated direct substitution with no consideration for sparseness would take 600 hours. Even when the substitution technique was improved to account for sparseness it is estimated it would take 12 hours of C.P.U. time. Substitution also requires 100 times as much memory space as factorization.