Equational Reasoning as a Tool for Data Analysis

A combination of deductive reasoning, clustering, and inductive learning is given as an example of a hybrid system for exploratory data analysis. Visualization is replaced by a dialogue with the data.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

XSophe-Sophe-XeprView (R). A computer simulation software suite (v. 1.1.3) for the analysis of continuous wave EPR spectra

The XSophe-Sophe-XeprView((R)) computer simulation software suite enables scientists to easily determine spin Hamiltonian parameters from isotropic, randomly oriented and single crystal continuous wave electron paramagnetic resonance (CW EPR) spectra from radicals and isolated paramagnetic metal ion centers or clusters found in metalloproteins, chemical systems and materials science. XSophe provides an X-windows graphical user interface to the Sophe programme and allows: creation of multiple input files, local and remote execution of Sophe, the display of sophelog (output from Sophe) and input parameters/files. Sophe is a sophisticated computer simulation software programme employing a number of innovative technologies including; the Sydney OPera HousE (SOPHE) partition and interpolation schemes, a field segmentation algorithm, the mosaic misorientation linewidth model, parallelization and spectral optimisation. In conjunction with the SOPHE partition scheme and the field segmentation algorithm, the SOPHE interpolation scheme and the mosaic misorientation linewidth model greatly increase the speed of simulations for most spin systems. Employing brute force matrix diagonalization in the simulation of an EPR spectrum from a high spin Cr(III) complex with the spin Hamiltonian parameters g(e) = 2.00, D = 0.10 cm(-1), E/D = 0.25, A(x) = 120.0, A(y) = 120.0, A(z) = 240.0 x 10(-4) cm(-1) requires a SOPHE grid size of N = 400 (to produce a good signal to noise ratio) and takes 229.47 s. In contrast the use of either the SOPHE interpolation scheme or the mosaic misorientation linewidth model requires a SOPHE grid size of only N = 18 and takes 44.08 and 0.79 s, respectively. Results from Sophe are transferred via the Common Object Request Broker Architecture (CORBA) to XSophe and subsequently to XeprView((R)) where the simulated CW EPR spectra (1D and 2D) can be compared to the experimental spectra. Energy level diagrams, transition roadmaps and transition surfaces aid the interpretation of complicated randomly oriented CW EPR spectra and can be viewed with a web browser and an OpenInventor scene graph viewer.

Experimental Analysis of Froude Number Effect on Air Entrainment in the Hydraulic Jump

A hydraulic jump is characterized by strong energy dissipation and mixing, large-scale turbulence, air entrainment, waves and spray. Despite recent pertinent studies, the interaction between air bubbles diffusion and momentum transfer is not completely understood. The objective of this paper is to present experimental results from new measurements performed in rectangular horizontal flume with partially-developed inflow conditions. The vertical distributions of void fraction and air bubbles count rate were recorded for inflow Froude number Fr1 in the range from 5.2 to 14.3. Rapid detrainment process was observed near the jump toe, whereas the structure of the air diffusion layer was clearly observed over longer distances. These new data were compared with previous data generally collected at lower Froude numbers. The comparison demonstrated that, at a fixed distance from the jump toe, the maximum void fraction Cmax increases with the increasing Fr1. The vertical locations of the maximum void fraction and bubble count rate were consistent with previous studies. Finally, an empirical correlation between the upper boundary of the air diffusion layer and the distance from the impingement point was provided.

Clustering Process Analysis in a Large-Size Dropshaft and in a Hydraulic Jump

Recent efforts in the characterization of air-water flows properties have included some clustering process analysis. A cluster of bubbles is defined as a group of two or more bubbles, with a distinct separation from other bubbles before and after the cluster. The present paper compares the results of clustering processes two hydraulic structures. That is, a large-size dropshaft and a hydraulic jump in a rectangular horizontal channel. The comparison highlighted some significant differences in clustering production and structures. Both dropshaft and hydraulic jump flows are complex turbulent shear flows, and some clustering index may provide some measure of the bubble-turbulence interactions and associated energy dissipation.

Analysis of heat transfer and entropy generation for a thermally developing Brinkman–Brinkman forced convection problem in a rectangular duct with isoflux walls

Heat transfer and entropy generation analysis of the thermally developing forced convection in a porous-saturated duct of rectangular cross-section, with walls maintained at a constant and uniform heat flux, is investigated based on the Brinkman flow model. The classical Galerkin method is used to obtain the fully developed velocity distribution. To solve the thermal energy equation, with the effects of viscous dissipation being included, the Extended Weighted Residuals Method (EWRM) is applied. The local (three dimensional) temperature field is solved by utilizing the Green’s function solution based on the EWRM where symbolic algebra is being used for convenience in presentation. Following the computation of the temperature field, expressions are presented for the local Nusselt number and the bulk temperature as a function of the dimensionless longitudinal coordinate, the aspect ratio, the Darcy number, the viscosity ratio, and the Brinkman number. With the velocity and temperature field being determined, the Second Law (of Thermodynamics) aspect of the problem is also investigated. Approximate closed form solutions are also presented for two limiting cases of MDa values. It is observed that decreasing the aspect ratio and MDa values increases the entropy generation rate.

Characteristics of undular hydraulic jumps: Experiments and analysis

The writers measured velocity, pressure and energy distributions, wavelengths, and wave amplitudes along undular jumps in a smooth rectangular channel 0.25 m wide. In each case the upstream flow was a fully developed shear flow. Analysis of the data shows that the jump has strong three-dimensional features and that the aspect ratio of the channel is an important parameter. Energy dissipation on the centerline is far from negligible and is largely constrained to the reach between the start of the lateral shock waves and the first wave crest of the jump, in which the boundary layer develops under a strong adverse pressure gradient. A Boussinesq-type solution of the free-surface profile, velocity, and energy and pressure distributions is developed and compared with the data. Limitations of the two-dimensional analysis are discussed.

Thermogravimetric analysis of carbon deposition over Ni/gamma-Al2O3 catalysts in carbon dioxide reforming of methane

Carbon formation on Ni/gamma-Al2O3 catalysts and its kinetics during methane reforming with carbon dioxide was studied in the temperature range of 500-700 degrees C using a thermogravimetric analysis technique. The activation energies of methane cracking, carbon gasification in CO2, as well as carbon deposition in CO2-CH4 reforming were obtained. The results show that the activation energy for carbon gasification is larger than that of carbon formation in methane cracking and that the activation energy of coking in CO2-CH4 reforming is also larger than that of methane decomposition to carbon. The dependencies of coking rate on partial pressures of CH4 and CO2 indicate that methane decomposition is the main route for carbon deposition. A mechanism and kinetic model for carbon deposition is proposed.

Analysis of proximal femur DXA scans in growing children: Comparisons of different protocols for cross-sectional 8-month and 7-year longitudinal data

Dual-energy X-ray absorptiometry (DXA) is a widely used method for measuring bone mineral in the growing skeleton. Because scan analysis in children offers a number of challenges, we compared DXA results using six analysis methods at the total proximal femur (PF) and five methods at the femoral neck (FN), In total we assessed 50 scans (25 boys, 25 girls) from two separate studies for cross-sectional differences in bone area, bone mineral content (BMC), and areal bone mineral density (aBMD) and for percentage change over the short term (8 months) and long term (7 years). At the proximal femur for the short-term longitudinal analysis, there was an approximate 3.5% greater change in bone area and BMC when the global region of interest (ROI) was allowed to increase in size between years as compared with when the global ROI was held constant. Trend analysis showed a significant (p < 0.05) difference between scan analysis methods for bone area and BMC across 7 years. At the femoral neck, cross-sectional analysis using a narrower (from default) ROI, without change in location, resulted in a 12.9 and 12.6% smaller bone area and BMC, respectively (both p < 0.001), Changes in FN area and BMC over 8 months were significantly greater (2.3 %, p < 0.05) using a narrower FN rather than the default ROI, Similarly, the 7-year longitudinal data revealed that differences between scan analysis methods were greatest when the narrower FN ROI was maintained across all years (p < 0.001), For aBMD there were no significant differences in group means between analysis methods at either the PF or FN, Our findings show the need to standardize the analysis of proximal femur DXA scans in growing children.