The incorporation of matter into characteristic numerical relativity

A code that implements Einstein equations in the characteristic formulation in 3D has been developed and thoroughly tested for the vacuum case. Here, we describe how to incorporate matter, in the form of a perfect fluid, into the code. The extended code has been written and validated in a number of cases. It is stable and capable of contributing towards an understanding of a number of problems in black hole astrophysics.Comment: 15 pages + 4 (eps) figure

Ground State Energy of the One-Dimensional Discrete Random Schr\"{o}dinger Operator with Bernoulli Potential

In this paper, we show the that the ground state energy of the one dimensional Discrete Random Schroedinger Operator with Bernoulli Potential is controlled asymptotically as the system size N goes to infinity by the random variable \ell_N, the length the longest consecutive sequence of sites on the lattice with potential equal to zero. Specifically, we will show that for almost every realization of the potential the ground state energy behaves asymptotically as $\frac{\pi^2}{\ell_N+1)^2}$ in the sense that the ratio of the quantities goes to one

The Extended Coupled Cluster Treatment of Correlations in Quantum Magnets

The spin-half XXZ model on the linear chain and the square lattice are examined with the extended coupled cluster method (ECCM) of quantum many-body theory. We are able to describe both the Ising-Heisenberg phase and the XY-Heisenberg phase, starting from known wave functions in the Ising limit and at the phase transition point between the XY-Heisenberg and ferromagnetic phases, respectively, and by systematically incorporating correlations on top of them. The ECCM yields good numerical results via a diagrammatic approach, which makes the numerical implementation of higher-order truncation schemes feasible. In particular, the best non-extrapolated coupled cluster result for the sublattice magnetization is obtained, which indicates the employment of an improved wave function. Furthermore, the ECCM finds the expected qualitatively different behaviours of the linear chain and the square lattice cases.Comment: 22 pages, 3 tables, and 15 figure

Machine-learning-based calving prediction from activity, lying, and ruminating behaviors in dairy cattle

The objective of this study was to use automated activity, lying, and rumination monitors to characterize prepartum behavior and predict calving in dairy cattle. Data were collected from 20 primiparous and 33 multiparous Holstein dairy cattle from September 2011 to May 2013 at the University of Kentucky Coldstream Dairy. The HR Tag (SCR Engineers Ltd., Netanya, Israel) automatically collected neck activity and rumination data in 2-h increments. The IceQube (IceRobotics Ltd., South Queensferry, United Kingdom) automatically collected number of steps, lying time, standing time, number of transitions from standing to lying (ly-. ing bouts), and total motion, summed in 15-min increments. IceQube data were summed in 2-h increments to match HR Tag data. All behavioral data were collected for 14 d before the predicted calving date. Retrospective data analysis was performed using mixed linear models to examine behavioral changes by day in the 14 d before calving. Bihourly behavioral differences from baseline values over the 14 d before calving were also evaluated using mixed linear models. Changes in daily rumination time, total motion, lying time, and lying bouts occurred in the 14 d before calving. In the bihourly analysis, extreme values for all behaviors occurred in the final 24 h, indicating that the monitored behaviors may be useful in calving prediction. To determine whether technologies were useful at predicting calving, random forest, linear discriminant analysis, and neural network machine -learning techniques were constructed and implemented using R version 3.1.0 (R Foundation for Statistical Computing, Vienna, Austria). These methods were used on variables from each technology and all combined variables from both technologies. A neural network analysis that combined variables from both technologies at the daily level yielded 100.0% sen-sitivity and 86.8% specificity. A neural network analysis that combined variables from both technologies in bihourly increments was used to identify 2-h periods in the 8 h before calving with 82.8% sensitivity and 80.4% specificity. Changes in behavior and machine-learning alerts indicate that commercially marketed behavioral monitors may have calving prediction potential

Remote practicals in the time of coronavirus, a multidisciplinary approach

Due to the COVID-19 pandemic, universities across the world have curtailed face to face teaching. Associated with this is the halt to the delivery of the practical experience required of engineering students. The Multidisciplinary Engineering Education (MEE) team at The University of Sheffield have responded to this problem in an efficient and effective way by recording laboratory experiences and putting videos, quizzes and data online for students to engage with. The focus of this work was on ensuring all Learning Outcomes (LOs) for modules and courses were preserved. Naturally, practical skills cannot be easily provided using this approach, but it is an effective way of getting students to interact with real data, uncertainty and equipment which they cannot access directly. A number of short case studies from across the range of engineering disciplines are provided to inspire and guide other educators in how they can move experiments on line in an efficient and effective manner. No student feedback is available at the time of writing, but anecdotal evidence is that this approach is at least acceptable for students and a way of collecting future feedback is suggested. The effort expended on this approach and the artefacts produced will support student learning after the initial disruption of the lockdown has passed

Low-cost inorganic cation exchange membrane for electrodialysis: optimum processing temperature for the cation exchanger

The optimum temperature for fixing zirconium phosphate, obtained by precipitation, on a low-cost ceramic support was determined in order to obtain an inorganic cation exchange membrane for electrodialysis. Zirconium phosphate ion exchange capacity maximised between 450 and 550°C, thus it was considered the optimum processing temperature. The origin of this maximum was investigated by means of X-ray diffraction and termogravimetry and evolved gas analysis. Zirconium phosphate formation by precipitation in the porous network of the support was verified by scanning electron microscopy and energy dispersive X-ray analysis and mercury intrusion porosimetry. The membrane obtained after thermal treatment at 450°C displayed selectivity to the cations present in the spent rinse water of the chromium plating process. This property allows the recovery of chromium by removing the cations through the cation exchange ceramic membrane.The authors wish to express their gratitude to the Spanish Ministry of Science and Innovation for the support given to the research study (National Basic Research Programme, Ref. CTQ2008-06750-C02-02), as well as for the FPU student grant awarded to one of the authors (Ref.: AP2009-4409).Mestre, S.; Sales, S.; Palacios, M.; Lorente, M.; Mallol, G.; Pérez-Herranz, V. (2013). Low-cost inorganic cation exchange membrane for electrodialysis: optimum processing temperature for the cation exchanger. Desalination and Water Treatment. 51(16-18):3317-3324. https://doi.org/10.1080/19443994.2012.749177S331733245116-18Strathmann, H. (2010). Electromembrane Processes: Basic Aspects and Applications. Comprehensive Membrane Science and Engineering, 391-429. doi:10.1016/b978-0-08-093250-7.00048-7Drioli, E., & Fontananova, E. (s. f.). Integrated Membrane Processes. 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(1966). Inorganic ion-exchange membranes and their application to electrodialysis. Desalination, 1(3), 231-246. doi:10.1016/s0011-9164(00)80255-6INAMUDDIN, KHAN, S., SIDDIQUI, W., & KHAN, A. (2007). Synthesis, characterization and ion-exchange properties of a new and novel ‘organic–inorganic’ hybrid cation-exchanger: Nylon-6,6, Zr(IV) phosphate. Talanta, 71(2), 841-847. doi:10.1016/j.talanta.2006.05.042HELEN, M., VISWANATHAN, B., & MURTHY, S. (2007). Synthesis and characterization of composite membranes based on α-zirconium phosphate and silicotungstic acid. Journal of Membrane Science, 292(1-2), 98-105. doi:10.1016/j.memsci.2007.01.018Yu.S. Dzyaz’ko, V.N. Belyakov, N.V. Stefanyak, S.L. Vasilyuk, Anion-exchange properties of composite ceramic membranes containing hydrated zirconium dioxide, Russ. J. Appl. Chem. 79 (2006) 769–773.Linkov, V. ., & Belyakov, V. . (2001). Novel ceramic membranes for electrodialysis. Separation and Purification Technology, 25(1-3), 57-63. doi:10.1016/s1383-5866(01)00090-9Linkov, V. M., Dzyaz’ko, Y. S., Belyakov, V. N., & Atamanyuk, V. Y. (2007). Inorganic composite membranes for electrodialytic desaltination. Russian Journal of Applied Chemistry, 80(4), 576-581. doi:10.1134/s1070427207040118El-Sourougy, M. R., Zaki, E. E., & Aly, H. F. (1997). Transport characteristics of ceramic supported zirconium phosphate membrane. Journal of Membrane Science, 126(1), 107-113. doi:10.1016/s0376-7388(96)00273-6Sánchez, E., Mestre, S., Pérez-Herranz, V., & García-Gabaldón, M. (2005). Síntesis de membranas cerámicas para la regeneración de baños de cromado agotados. Boletín de la Sociedad Española de Cerámica y Vidrio, 44(6), 409-414. doi:10.3989/cyv.2005.v44.i6.340Sánchez, E., Mestre, S., Pérez-Herranz, V., Reyes, H., & Añó, E. (2006). Membrane electrochemical reactor for continuous regeneration of spent chromium plating baths. Desalination, 200(1-3), 668-670. doi:10.1016/j.desal.2006.03.475Alberti, G., Casciola, M., Costantino, U., & Vivani, R. (1996). Layered and pillared metal(IV) phosphates and phosphonates. Advanced Materials, 8(4), 291-303. doi:10.1002/adma.19960080405Alberti, G., & Torracca, E. (1968). Crystalline insoluble salts of polybasic metals - II. Synthesis of crystalline zirconium or titanium phosphate by direct precipitation. Journal of Inorganic and Nuclear Chemistry, 30(1), 317-318. doi:10.1016/0022-1902(68)80096-xTrobajo, C., Khainakov, S. A., Espina, A., & García, J. R. (2000). On the Synthesis of α-Zirconium Phosphate. Chemistry of Materials, 12(6), 1787-1790. doi:10.1021/cm0010093Alberti, G. (1978). Syntheses, crystalline structure, and ion-exchange properties of insoluble acid salts of tetravalent metals and their salt forms. Accounts of Chemical Research, 11(4), 163-170. doi:10.1021/ar50124a007Rajeh, A. O., & szirtes, L. (1995). Investigations of crystalline structure of gamma-zirconium phosphate. Journal of Radioanalytical and Nuclear Chemistry Articles, 196(2), 319-322. doi:10.1007/bf02038050Krogh Andersen, A. M., Norby, P., Hanson, J. C., & Vogt, T. (1998). Preparation and Characterization of a New 3-Dimensional Zirconium Hydrogen Phosphate, τ-Zr(HPO4)2. Determination of the Complete Crystal Structure Combining Synchrotron X-ray Single-Crystal Diffraction and Neutron Powder Diffraction. Inorganic Chemistry, 37(5), 876-881. doi:10.1021/ic971060hFeng, Y., He, W., Zhang, X., Jia, X., & Zhao, H. (2007). The preparation of nanoparticle zirconium phosphate. Materials Letters, 61(14-15), 3258-3261. doi:10.1016/j.matlet.2006.11.132Clearfield, A. (2000). INORGANIC ION EXCHANGERS, PAST, PRESENT, AND FUTURE. Solvent Extraction and Ion Exchange, 18(4), 655-678. doi:10.1080/07366290008934702Szirtes, L., Shakshooki, S. K., Szeleczky, A. M., & Rajeh, A. O. (1998). Thermoanalyncal Investigation of Some Layered Zirconium Salts and Their Various Derivatives I. Journal of Thermal Analysis and Calorimetry, 51(2), 503-515. doi:10.1007/bf03340188Al-Othman, A., Tremblay, A. Y., Pell, W., Letaief, S., Burchell, T. J., Peppley, B. A., & Ternan, M. (2010). Zirconium phosphate as the proton conducting material in direct hydrocarbon polymer electrolyte membrane fuel cells operating above the boiling point of water. Journal of Power Sources, 195(9), 2520-2525. doi:10.1016/j.jpowsour.2009.11.052Thakkar, R., Patel, H., & Chudasama, U. (2007). A comparative study of proton transport properties of zirconium phosphate and its metal exchanged phases. Bulletin of Materials Science, 30(3), 205-209. doi:10.1007/s12034-007-0036-3Jiang, P., Pan, B., Pan, B., Zhang, W., & Zhang, Q. (2008). A comparative study on lead sorption by amorphous and crystalline zirconium phosphates. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 322(1-3), 108-112. doi:10.1016/j.colsurfa.2008.02.035García-Gabaldón, M., Pérez-Herranz, V., García-Antón, J., & Guiñón, J. L. (2009). Use of ion-exchange membranes for the removal of tin from spent activating solutions. Desalination and Water Treatment, 3(1-3), 150-156. doi:10.5004/dwt.2009.453García-Gabaldón, M., Pérez-Herranz, V., García-Antón, J., & Guiñón, J. L. (2009). Effect of hydrochloric acid on the transport properties of tin through ion-exchange membranes. Desalination and Water Treatment, 10(1-3), 73-79. doi:10.5004/dwt.2009.69