Implementation of population balances in simulation of gas-liquid reactors using a CFD-PBM coupled approach

In bubbly flow simulations, bubble size distribution is an important factor in determination of hydrodynamics. Beside hydrodynamics, it is crucial in the prediction of interfacial area available for mass transfer and in the prediction of reaction rate in gas-liquid reactors such as bubble columns. Solution of population balance equations is a method which can help to model the size distribution by considering continuous bubble coalescence and breakage. Therefore, in Computational Fluid Dynamic simulations it is necessary to couple CFD and Population Balance Model (CFD-PBM) to get reliable distribution. In the current work a CFD-PBM coupled model is implemented as FORTRAN subroutines in ANSYS CFX 10 and it has been tested for bubbly flow. This model uses the idea of Multi Phase Multi Size Group approach which was previously presented by Sha et al. (2006) [18]. The current CFD-PBM coupled method considers inhomogeneous flow field for different bubble size groups in the Eulerian multi-dispersed phase systems. Considering different velocity field for bubbles can give the advantageof more accurate solution of hydrodynamics. It is also an improved method for prediction of bubble size distribution in multiphase flow compared to available commercial packages.

Demographic Modelling of Human Population Growth

This work presents models and methods that have been used in producing forecasts of population growth. The work is intended to emphasize the reliability bounds of the model forecasts. Leslie model and various versions of logistic population models are presented. References to literature and several studies are given. A lot of relevant methodology has been developed in biological sciences. The Leslie modelling approach involves the use of current trends in mortality,fertility, migration and emigration. The model treats population divided in age groups and the model is given as a recursive system. Other group of models is based on straightforward extrapolation of census data. Trajectories of simple exponential growth function and logistic models are used to produce the forecast. The work presents the basics of Leslie type modelling and the logistic models, including multi- parameter logistic functions. The latter model is also analysed from model reliability point of view. Bayesian approach and MCMC method are used to create error bounds of the model predictions.

Very High Energy Gamma-Rays emitting BL LAC's Population Study

Context: BL Lacs are the most numerous extragalactic objects which are detected in Very High Energy (VHE) gamma-rays band. They are a subclass of blazars. Large flux variability amplitude, sometimes happens in very short time scale, is a common characteristic of them. Significant optical polarization is another main characteristics of BL Lacs. BL Lacs' spectra have a continuous and featureless Spectral Energy Distribution (SED) which have two peaks. Among 1442 BL Lacs in the Roma-BZB catalogue, only 51 are detected in VHE gamma-rays band. BL Lacs are most numerous (more than 50% of 514 objects) objects among the sources that are detected above 10 GeV by FERMI-LAT. Therefore, many BL Lacs are expected to be discovered in VHE gamma-rays band. However, due to the limitation on current and near future technology of Imaging Air Cherenkov Telescope, astronomers are forced to predict whether an object emits VHE gamma-rays or not. Some VHE gamma-ray prediction methods are already introduced but still are not confirmed. Cross band correlations are the building blocks of introducing VHE gamma-rays prediction method. Aims: We will attempt to investigate cross band correlations between flux energy density, luminosity and spectral index of the sample. Also, we will check whether recently discovered MAGIC J2001+435 is a typical BL Lac. Methods: We select a sample of 42 TeV BL Lacs and collect 20 of their properties within five energy bands from literature and Tuorla blazar monitoring program database. All of the data are synchronized to be comparable to each other. Finally, we choose 55 pair of datasets for cross band correlations finding and investigating whether there is any correlation between each pair. For MAGIC J2001+435 we analyze the publicly available SWIFT-XRT data, and use the still unpublished VHE gamma-rays data from MAGIC collaboration. The results are compared to the other sources of the sample. Results: Low state luminosity of multiple detected VHE gamma-rays is strongly correlated luminosities in all other bands. However, the high state does not show such strong correlations. VHE gamma-rays single detected sources have similar behaviour to the low state of multiple detected ones. Finally, MAGIC J2001+435 is a typical TeV BL Lac. However, for some of the properties this source is located at the edge of the whole sample (e.g. in terms of X-rays flux). Keywords: BL Lac(s), Population study, Correlations finding, Multi wavelengths analysis, VHE gamma-rays, gamma-rays, X-rays, Optical, Radio