Abstract:
Today reactor neutrino experiments are at the cutting edge of fundamental research in particle physics. Understanding the neutrino is far from complete, but thanks to the impressive progress in this field over the last 15 years, a few research groups are seriously considering that neutrinos could be useful for society. The International Atomic Energy Agency (IAEA) works with its Member States to promote safe, secure and peaceful nuclear technologies. In a context of international tension and nuclear renaissance, neutrino detectors could help IAEA to enforce the Treaty on the Non-Proliferation of Nuclear Weapons (NPT). In this article we discuss a futuristic neutrino application to detect and localize an undeclared nuclear reactor from across borders. The SNIF (Secret Neutrino Interactions Finder) concept proposes to use a few hundred thousand tons neutrino detectors to unveil clandestine fission reactors. Beyond previous studies we provide estimates of all known background sources as a function of the detector's longitude, latitude and depth, and we discuss how they impact the detectability.

Abstract:
Several observed anomalies in neutrino oscillation data can be explained by a hypothetical fourth neutrino separated from the three standard neutrinos by a squared mass difference of a few eV^2. We show that this hypothesis can be tested with a PBq (ten kilocurie scale) 144Ce or 106Ru antineutrino beta-source deployed at the center of a large low background liquid scintillator detector. In particular, the compact size of such a source could yield an energy-dependent oscillating pattern in event spatial distribution that would unabiguously determine neutrino mass differences and mixing angles.

Abstract:
We present a new approach to constrain the spectral energy distribution of the intergalactic UV background observationally by studying metal absorption systems. We study single-component metal line systems exhibiting various well-measured species. Among the observed transitions at least two ratios of ionization stages from the same element are required, e.g. CIII/CIV and SiIII/SiIV. For each system photoionization models are constructed varying the spectrum of the ionizing radiation. The spectral energy distribution can then be constrained by comparing the models with the observed column density ratios. Extensive tests with artificial absorbers show that the spectrum of the ionizing radiation cannot be reconstructed unambiguously, but it is possible to constrain the main characteristics of the spectrum. Furthermore, the resulting physical parameters of the absorber, such as ionization parameter, metallicity, and relative abundances, may depend strongly on the adopted ionizing spectrum. Even in case of well-fitting models the uncertainties can be as high as ~0.5 dex for the ionization parameter and up to ~1.5 dex for the metallicity. Therefore, it is essential to know the hardness of the UV background when estimating the metallicity of the intergalactic medium. Applying the procedure to a small sample of 3 observed single-component metal line systems yields a soft ionizing radiation at z > 2 and a slightly harder spectrum at z < 2. The resulting energy distributions exhibit strong HeII Ly alpha re-emission features suggesting that reprocessing by intergalactic HeII is important. Comparing to UV background spectra from the literature indicates that the recent model of Madau & Haardt (2009) including sawtooth modulation due to reprocessing by intergalactic HeII with delayed helium reionization fits the investigated systems very well.

Abstract:
Water scarcity in developing countries has forced farmers to use sewage as an alternative source of irrigation water. However, the usage of sewage for vegetable production has been known to cause excessive and often-unbalanced addition of nutrients hence posing a threat to food safety. The objective of this study was to determine the efficacy of slow sand filter and wetland plant in domestic wastewater treatment. To achieve this objective, samples were collected from the domestic wastewater collection pond within Jomo Kenyatta University of Agriculture and Technology (JKUAT). Laboratory tests were conducted on the collected samples and they revealed the presence of BOD, DO, pH, TDS, Sulfates, Chloride, Turbidity, Salinity, Conductivity, Alkalinity？and Coliform; whose values varied when compared with that of the parameters for standard irrigation water. This gave insight to the kind of treatments and filtration medium that were required to transform domestic wastewater into water fit for irrigation. A slow sand filter bed was designed and constructed using precisely six samples materials; sand, sand and wetland plants, gravel, gravel and wetland plants, mixture of gravel and sand, mixture of gravel and sand with wetland plants. These materials were used to identify the chemical and biological changes in domestic wastewater within a seven-day period. The water collected from the slow sand filter was tested, results showed that, of all six samples, slow sand filter using the mixture of gravel, sand with wetland plants had an average percentage efficient of 90% in removing all impurities from domestic wastewater thereby turning it into water suitable for irrigation. It is hoped that this study will provide a safe, easy, eco-friendly and cheap method of wastewater treatment while ensuring the sustainability of wastewater for irrigation and the expansion of green spaces in urban and peri-urban areas.

Abstract:
The iron-chromium alloy and its derivatives are widely used for their remarkable resistance to corrosion, which only occurs in a narrow concentration range around 9 to 13 atomic percent chromium. Although known to be due to chromium enrichment of a few atoms thick layer at the surfaces, the understanding of its complex atomistic origin has been a remaining challenge. We report an investigation of the thermodynamics of such surfaces at the atomic scale by means of Monte Carlo simulations. We use a Hamiltonian which provides a parameterization of previous ab initio results and successfully describes the alloy's unusual thermodynamics. We report a strong enrichment in Cr of the surfaces for low bulk concentrations, with a narrow optimum around 12 atomic percent chromium, beyond which the surface composition decreases drastically. This behavior is explained by a synergy between (i) the complex phase separation in the bulk alloy, (ii) local phase transitions that tune the layers closest to the surface to an iron-rich state and inhibit the bulk phase separation in this region, and (iii) its compensation by a strong and non-linear enrichment in Cr of the next few layers. Implications with respect to the design of prospective nanomaterials are briefly discussed.

Abstract:
Ferritic steels possibly strengthened by oxide dispersion are candidates as structural materials for generation IV and fusion nuclear reactors. Their use is limited by incomplete knowledge of the iron-chromium phase diagram at low temperatures and of the phenomena inducing preferential segregation of one element at grain boundaries or at surfaces. In this context, this work contributes to the multi-scale study of the model iron-chromium alloy and their free surfaces by numerical simulations. This study begins with ab initio calculations of properties related to the mixture of atoms of iron and chromium. We highlight complex dependency of the magnetic moments of the chromium atoms on their local chemical environment. Surface properties are also proving sensitive to magnetism. This is the case of impurity segregation of chromium in iron and of their interactions near the surface. In a second step, we construct a simple energy model for high numerical efficiency. It is based on pair interactions on a rigid lattice to which are given local chemical environment and temperature dependencies. With this model, we reproduce the ab initio results at zero temperature and experimental results at high temperature. We also deduce the solubility limits at all intermediate temperatures with mean field approximations that we compare to Monte Carlo simulations. The last step of our work is to introduce free surfaces in our model. We then study the effect of ab initio calculated bulk and surface properties on surface segregation. Finally, we calculate segregation isotherms. We therefore propose an evolution model of surface composition of iron-chromium alloys as a function of bulk composition.

Abstract:
Network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by the destinations can be transmitted. In this paper, we introduce a new approach to this problem. We define a closure operator on a digraph closely related to the network coding instance and we show that the constraints for network coding can all be expressed according to that closure operator. Thus, a solution for the network coding problem is equivalent to a so-called solution of the closure operator. We can then define the closure solvability problem in general, which surprisingly reduces to finding secret-sharing matroids when the closure operator is a matroid. Based on this reformulation, we can easily prove that any multiple unicast where each node receives at least as many arcs as there are sources is solvable by linear functions. We also give an alternative proof that any nontrivial multiple unicast with two source-receiver pairs is always solvable over all sufficiently large alphabets. Based on singular properties of the closure operator, we are able to generalise the way in which networks can be split into two distinct parts; we also provide a new way of identifying and removing useless nodes in a network. We also introduce the concept of network sharing, where one solvable network can be used to accommodate another solvable network coding instance. Finally, the guessing graph approach to network coding solvability is generalised to any closure operator, which yields bounds on the amount of information that can be transmitted through a network.

Abstract:
The entropy of a digraph is a fundamental measure which relates network coding, information theory, and fixed points of finite dynamical systems. In this paper, we focus on the entropy of undirected graphs. We prove that for any integer $k$ the number of possible values of the entropy of an undirected graph up to $k$ is finite. We also determine all the possible values for the entropy of an undirected graph up to the value of four.

Abstract:
A finite dynamical system is a system of multivariate functions over a finite alphabet. The main feature of a finite dynamical system is its interaction graph, which indicates which local functions depend on which variables. The rank of a finite dynamical system is the cardinality of its image; the asymptotic rank is the number of its periodic points. In this paper, we determine the maximum rank and the maximum asymptotic rank of a finite dynamical system with a given interaction graph over any non-Boolean alphabet. We also obtain a similar result for Boolean finite dynamical systems whose interaction graphs are contained in a given digraph.

Abstract:
The entropy of a closure operator has been recently proposed for the study of network coding and secret sharing. In this paper, we study closure operators in relation to their entropy. We first introduce four different kinds of rank functions for a given closure operator, which determine bounds on the entropy of that operator. This yields new axioms for matroids based on their closure operators. We also determine necessary conditions for a large class of closure operators to be solvable. We then define the Shannon entropy of a closure operator, and use it to prove that the set of closure entropies is dense. Finally, we justify why we focus on the solvability of closure operators only.