Numerical solution of degenerate stochastic Kawarada equations via a semi-discretized approach

The numerical solution of a highly nonlinear two-dimensional degenerate stochastic Kawarada equation is investigated. A semi-discretized approximation in space is comprised on arbitrary nonuniform grids. Exponential splitting strategies are then applied to advance solutions of the semi-discretized scheme over adaptive grids in time. It is shown that key quenching solution features including the positivity and monotonicity are well preserved under modest restrictions. The numerical stability of the underlying splitting method is also maintained without any additional restriction. Computational experiments are provided to not only illustrate our results, but also provide further insights into the global nonlinear convergence of the numerical solution.Comment: 22 pages, 9 figures, article accepted (being uploaded to arXiv to create repository of all work

Improvements of the shock arrival times at the Earth model STOA

Prediction of the shocks' arrival times (SATs) at the Earth is very important for space weather forecast. There is a well-known SAT model, STOA, which is widely used in the space weather forecast. However, the shock transit time from STOA model usually has a relative large error compared to the real measurements. In addition, STOA tends to yield too much `yes' prediction, which causes a large number of false alarms. Therefore, in this work, we work on the modification of STOA model. First, we give a new method to calculate the shock transit time by modifying the way to use the solar wind speed in STOA model. Second, we develop new criteria for deciding whether the shock will arrive at the Earth with the help of the sunspot numbers and the angle distances of the flare events. It is shown that our work can improve the SATs prediction significantly, especially the prediction of flare events without shocks arriving at the Earth.Comment: Submitted to JG

Modulation of galactic cosmic rays during the unusual solar minimum between cycles 23 and 24

During the recent solar minimum between cycles 23 and 24 (solar minimum $P_{23/24}$) the intensity of Galactic Cosmic Rays (GCRs) measured at the Earth was the highest ever recorded since space age. It is the purpose of this paper to resolve the most plausible mechanism for this unusually high intensity. A GCR transport model in three-dimensional heliosphere based on a simulation of Markov stochastic process is used to find the relation of cosmic ray modulation to various transport parameters, including solar wind (SW) speed, distance of heliospheric boundary, magnitude of interplanetary magnetic field (IMF) at the Earth, tilt angle of heliospheric current sheet (HCS), values of parallel and perpendicular diffusion coefficients. We calculate GCR proton energy spectra at the Earth for the last three solar minima $P_{21/22}$, $P_{22/23}$, and $P_{23/24}$, with the transport parameters obtained from observations. Besides weak IMF magnitude and slow SW speed, we find that a possible low magnetic turbulence, which increases the parallel diffusion and reduces the perpendicular diffusion in the polar direction, might be an additional possible mechanism for the high GCR intensity in the solar minimum $P_{23/24}$.Comment: Accepted for publication in JGR space physic

Representation in Econometrics: A Historical Perspective

Measurement forms the substance of econometrics. This chapter outlines the history of econometrics from a measurement perspective - how have measurement errors been dealt with and how, from a methodological standpoint, did econometrics evolve so as to represent theory more adequately in relation to data? The evolution is organized in terms of four phases: 'theory and measurement', 'measurement and theory', 'measurement with theory' and 'measurement without theory'. The question of how measurement research has helped in the advancement of knowledge advance is discussed in the light of this history.Econometrics, History, Measurement error

Maximizing the Probability of Delivery of Multipoint Relay Broadcast Protocol in Wireless Ad Hoc Networks with a Realistic Physical Layer

It is now commonly accepted that the unit disk graph used to model the physical layer in wireless networks does not reflect real radio transmissions, and that the lognormal shadowing model better suits to experimental simulations. Previous work on realistic scenarios focused on unicast, while broadcast requirements are fundamentally different and cannot be derived from unicast case. Therefore, broadcast protocols must be adapted in order to still be efficient under realistic assumptions. In this paper, we study the well-known multipoint relay protocol (MPR). In the latter, each node has to choose a set of neighbors to act as relays in order to cover the whole 2-hop neighborhood. We give experimental results showing that the original method provided to select the set of relays does not give good results with the realistic model. We also provide three new heuristics in replacement and their performances which demonstrate that they better suit to the considered model. The first one maximizes the probability of correct reception between the node and the considered relays multiplied by their coverage in the 2-hop neighborhood. The second one replaces the coverage by the average of the probabilities of correct reception between the considered neighbor and the 2-hop neighbors it covers. Finally, the third heuristic keeps the same concept as the second one, but tries to maximize the coverage level of the 2-hop neighborhood: 2-hop neighbors are still being considered as uncovered while their coverage level is not higher than a given coverage threshold, many neighbors may thus be selected to cover the same 2-hop neighbors

Gravitational lensing and modified Newtonian dynamics

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe.Comment: PASA (OzLens edition), in press; 5 pages, 1 figur

Gravitational lensing and modified Newtonian dynamics

Gravitational lensing is most often used as a tool to investigate the distribution of (dark) matter in the universe, but, if the mass distribution is known a priori, it becomes, at least in principle, a powerful probe of gravity itself. Lensing observations are a more powerful tool than dynamical measurements because they allow measurements of the gravitational field far away from visible matter. For example, modified Newtonian dynamics (MOND) has no relativistic extension, and so makes no firm lensing predictions, but galaxy-galaxy lensing data can be used to empirically the deflection law of a point-mass. MONDian lensing is consistent with general relativity, in so far as the deflection experienced by a photon is twice that experienced by a massive particle moving at the speed of light. With the deflection law in place and no invisible matter, MOND can be tested wherever lensing is observed. The implications are that either MONDian lensing is completely non-linear or that MOND is not an accurate description of the universe.Comment: PASA (OzLens edition), in press; 5 pages, 1 figur

Metabolomic Analysis Reveals Contributions of Citric and Citramalic Acids to Rare Earth Bioleaching by a Paecilomyces Fungus.

Conventional methods for extracting rare earth elements from monazite ore require high energy inputs and produce environmentally damaging waste streams. Bioleaching offers a potentially more environmentally friendly alternative extraction process. In order to better understand bioleaching mechanisms, we conducted an exo-metabolomic analysis of a previously isolated rare earth bioleaching fungus from the genus Paecilomyces (GenBank accession numbers KM874779 and KM 874781) to identify contributions of compounds exuded by this fungus to bioleaching activity. Exuded compounds were compared under two growth conditions: growth with monazite ore as the only phosphate source, and growth with a soluble phosphate source (K2HPO4) added. Overall metabolite profiling, in combination with glucose consumption and biomass accumulation data, reflected a lag in growth when this organism was grown with only monazite. We analyzed the relationships between metabolite concentrations, rare earth solubilization, and growth conditions, and identified several metabolites potentially associated with bioleaching. Further investigation using laboratory prepared solutions of 17 of these metabolites indicated statistically significant leaching contributions from both citric and citramalic acids. These contributions (16.4 and 15.0 mg/L total rare earths solubilized) accounted for a portion, but not all, of the leaching achieved with direct bioleaching (42 ± 15 mg/L final rare earth concentration). Additionally, citramalic acid released significantly less of the radioactive element thorium than did citric acid (0.25 ± 0.01 mg/L compared to 1.18 ± 0.01 mg/L), suggesting that citramalic acid may have preferable leaching properties for a monazite bioleaching process

Morphology and Orientation Selection of Non-Metallic Inclusions in Electrified Molten Metal

The effect of electric current on morphology and orientation selection of non-metallic inclusions in molten metal has been investigated using theoretical modelling and numerical calculation. Two geometric factors, namely the circularity (fc) and alignment ratio (fe) were introduced to describe the inclusions shape and configuration. Electric current free energy was calculated and the values were used to determine the thermodynamic preference between different microstructures. Electric current promotes the development of inclusion along the current direction by either expatiating directional growth or enhancing directional agglomeration. Reconfiguration of the inclusions to reduce the system electric resistance drives the phenomena. The morphology and orientation selection follows the routine to reduce electric free energy. The numerical results are in agreement with our experimental observations