Hodograph solutions of the dispersionless coupled KdV hierarchies, critical points and the Euler-Poisson-Darboux equation

It is shown that the hodograph solutions of the dispersionless coupled KdV (dcKdV) hierarchies describe critical and degenerate critical points of a scalar function which obeys the Euler-Poisson-Darboux equation. Singular sectors of each dcKdV hierarchy are found to be described by solutions of higher genus dcKdV hierarchies. Concrete solutions exhibiting shock type singularities are presented.Comment: 19 page

Radial glia in the proliferative ventricular zone of the embryonic and adult turtle, Trachemys scripta elegans.

To better understand the role of radial glial (RG) cells in the evolution of the mammalian cerebral cortex, we investigated the role of RG cells in the dorsal cortex and dorsal ventricular ridge of the turtle, Trachemys scripta elegans. Unlike mammals, the glial architecture of adult reptile consists mainly of ependymoradial glia, which share features with mammalian RG cells, and which may contribute to neurogenesis that continues throughout the lifespan of the turtle. To evaluate the morphology and proliferative capacity of ependymoradial glia (here referred to as RG cells) in the dorsal cortex of embryonic and adult turtle, we adapted the cortical electroporation technique, commonly used in rodents, to the turtle telencephalon. Here, we demonstrate the morphological and functional characteristics of RG cells in the developing turtle dorsal cortex. We show that cell division occurs both at the ventricle and away from the ventricle, that RG cells undergo division at the ventricle during neurogenic stages of development, and that mitotic Tbr2+ precursor cells, a hallmark of the mammalian SVZ, are present in the turtle cortex. In the adult turtle, we show that RG cells encompass a morphologically heterogeneous population, particularly in the subpallium where proliferation is most prevalent. One RG subtype is similar to RG cells in the developing mammalian cortex, while 2 other RG subtypes appear to be distinct from those seen in mammal. We propose that the different subtypes of RG cells in the adult turtle perform distinct functions

Experimental analysis of a flat plate solar collector with integrated latent heat thermal storage

In the present paper, an experimental analysis of a solar water heating collector with an integrated latent heat storage unit is presented. With the purpose to determine the performance of a device on a lab scale, but with commercial features, a flat plate solar collector with phase change material (PCM) containers under the absorber plate was constructed and tested. PCM used was a commercial semi-refined light paraffin with a melting point of 60°C. Tests were carried out in outdoor conditions from October 2016 to March 2017 starting at 7:00 AM until the collector does not transfer heat to the water after sunset. Performance variables as water inlet temperature, outlet temperature, mass flow and solar radiation were measured in order to determine a useful heat and collector efficiency. Furthermore, the operating temperatures of the glass cover, air gap, absorber plate, and PCM containers are presented. Other external variables as ambient temperature, humidity and wind speed were measured with a weather station located next to the collector. The developed prototype reached an average thermal efficiency of 24.11% and a maximum outlet temperature of 50°C. Results indicate that the absorber plate reached the PCM melting point in a few cases, this suggests that the use of a PCM with a lower melting point could be a potential strategy to increase thermal storage. Thermal analysis and conclusions of the device performance are discussed

Introducing spaced mosaic plots

Informe de com fer spaced mosaic plots en RRecent research has developed a group of likelihood-based finite mixture mod- els for a data matrix with ordinal data, establishing likelihood-based multivari- ate methods which applies fuzzy clustering via finite mixtures to the ordered stereotype model. There are many visualisation tools which depict reduction of dimensionality in matrices of ordinal data. This technical report introduces the spaced mosaic plot which is one new graphical tool for ordinal data when the or- dinal stereotype model is used. It takes advantage of the fitted score parameters to determine the spacing between two adjacent ordinal categories. We develop a function in R and its documentation is presented. Finally, the description of a spaced mosaic plot is shown.Preprin

Experimentally based testing of the enthalpy-porosity method for the numerical simulation of phase change of paraffin-type PCMs

The enthalpy-porosity method is generally applied as an economical resort for the numerical simulation of phase change materials (PCMs). However, having been developed strictly for metals, its suitability for the task is unclear, nor is the rationale for assigning its internal parameters, e.g., latent enthalpy and the constant of the momentum source term representing the “mushy” region. We first experimentally and exhaustively characterize a paraffin-type PCM, including differential scanning calorimetry (DSC) at several heating rates, T-history, and fusion visualization. Then, we develop a numerical model and systematically run simulations under different internal parameters and thermophysical properties of the PCM. Simulation results exhibit significant disagreement with experiments that cannot be reduced by any strategy for combining different material properties and model parameters. Among other effects, the constant of the momentum source term, which has to be assigned somewhat arbitrarily, has more relevance in the accuracy than any set of properties obtained by DSC and other experimental techniques. Thus, a rather negative, although interesting, conclusion is suggested: the enthalpy-porosity method may fail to model the phase change of paraffin-type PCMs. This is, of course, of paramount importance for the studies of their utilization in practical systems since it puts a fundamental point of uncertainty in any numerical study or lumped-type model derived thereof. The paper concludes with a tentative discussion of the possible causes of this failure and perspectives for developing more proper models

Ward identity and electrical conductivity in hot QED

We study the Ward identity for the effective photon-electron vertex summing the ladder diagrams contributing to the electrical conductivity in hot QED at leading logarithmic order. It is shown that the Ward identity requires the inclusion of a new diagram in the integral equation for the vertex that has not been considered before. The real part of this diagram is subleading and therefore the final expressions for the electrical conductivity at leading logarithmic order are not affected.Comment: 25 pages with 5 eps figures, discussion in section 3 improved; to appear in JHE

Experimental Analysis of a Flat Plate Solar Collector with Integrated Latent Heat Thermal Storage

In the present paper, an experimental analysis of a solar water heating collector with an integrated latent heat storage unit is presented. With the purpose to determine the performance of a device on a lab scale, but with commercial features, a flat plate solar collector with phase change material (PCM) containers under the absorber plate was constructed and tested. PCM used was a commercial semi-refined light paraffin with a melting point of 60°C. Tests were carried out in outdoor conditions from October 2016 to March 2017 starting at 7:00 AM until the collector does not transfer heat to the water after sunset. Performance variables as water inlet temperature, outlet temperature, mass flow and solar radiation were measured in order to determine a useful heat and the collector efficiency. Furthermore, operating temperatures of the glass cover, air gap, absorber plate, and PCM containers are presented. Other external variables as ambient temperature, humidity and wind speed were measured with a weather station located next to the collector. The developed prototype reached an average thermal efficiency of 24.11% and a maximum outlet temperature of 50°C. Results indicate that the absorber plate reached the PCM melting point in few cases, this suggests that the use of a PCM with a lower melting point could be a potential strategy to increase thermal storage. A thermal analysis and conclusions of the device performance are discussed

On the dbar-dressing method applicable to heavenly equation

The \dbar-dressing scheme based on local nonlinear vector \dbar-problem is developed. It is applicable to multidimensional nonlinear equations for vector fields, and, after Hamiltonian reduction, to heavenly equation. Hamiltonian reduction is described explicitely in terms of the \dbar-data. An analogue of Hirota bilinear identity for heavenly equation hierarchy is introduced, $\tau$-function for the hierarchy is defined. Addition formulae (generating equations) for the $\tau$-function are found. It is demonstrated that $\tau$-function for heavenly equation hierarchy is given by the action for \dbar-problem evaluated on the solution of this problem.Comment: 11 page

Bayesian model-based clustering for longitudinal ordinal data

Traditional cluster analysis methods used in ordinal data, for instance k-means and hierarchical clustering, are mostly heuristic and lack statistical inference tools to compare among competing models. To address this we propose a latent transitional model, a finite mixture model that includes both observed and latent covariates and apply it for the first time to the case of longitudinal ordinal data. This model-based clustering model is an extension of the proportional odds model and includes a first-order transitional term, occasion effects and interactions which provide flexible ways to capture different time patterns by cluster as well as time-heterogeneous transitions. We estimate model parameters within a Bayesian setting using a Markov chain Monte Carlo scheme and block-wise Metropolis–Hastings sampling. We illustrate the model using 2001–2011 self-reported health status (SRHS) from the Household, Income and Labour Dynamics in Australia survey. SRHS is recorded as an ordinal variable with five levels: poor, fair, good, very good and excellent. Using the Widely Applicable Information Criterion for model comparison, we find evidence for six latent groups. Transitions in the original data and the estimated groups are visualized using heatmaps.Peer ReviewedPostprint (author's final draft

Multi-resolution internal template cleaning: An application to the Wilkinson Microwave Anisotropy Probe 7-yr polarization data

Cosmic microwave background (CMB) radiation data obtained by different experiments contain, besides the desired signal, a superposition of microwave sky contributions. We present a fast and robust method, using a wavelet decomposition on the sphere, to recover the CMB signal from microwave maps. An application to \textit{WMAP} polarization data is presented, showing its good performance particularly in very polluted regions of the sky. The applied wavelet has the advantages of requiring little computational time in its calculations, being adapted to the \textit{HEALPix} pixelization scheme, and offering the possibility of multi-resolution analysis. The decomposition is implemented as part of a fully internal template fitting method, minimizing the variance of the resulting map at each scale. Using a $\chi^2$ characterization of the noise, we find that the residuals of the cleaned maps are compatible with those expected from the instrumental noise. The maps are also comparable to those obtained from the \textit{WMAP} team, but in our case we do not make use of external data sets. In addition, at low resolution, our cleaned maps present a lower level of noise. The E-mode power spectrum $C_{\ell}^{EE}$ is computed at high and low resolution; and a cross power spectrum $C_{\ell}^{TE}$ is also calculated from the foreground reduced maps of temperature given by \textit{WMAP} and our cleaned maps of polarization at high resolution. These spectra are consistent with the power spectra supplied by the \textit{WMAP} team. We detect the E-mode acoustic peak at $\ell \sim 400$, as predicted by the standard $\Lambda CDM$ model. The B-mode power spectrum $C_{\ell}^{BB}$ is compatible with zero.Comment: 8 pages, 6 figures. Some changes have been done from the original manuscript. This paper is accepted by MNRA