Number of cyclic square-tiled tori

We study cyclic square-tiled tori in $\mathcal{H}(0)$, answering a question by M. Bolognesi (by personal communication to A. Zorich). We give the exact number of cyclic tori tiled by $n\in\mathbb{N}$ squares. We also give the asymptotic proportion of cyclic square-tiled tori over all square-tiled tori.Comment: 6 pages, 1 figur

Cone types and asymptotic invariants for the random walk on the modular group

We compute the cone types of the Cayley graph of the modular group $\mathrm{PSL}(2,\mathbf{Z})$ associated with the standard system of generators ${\small\left\{\left(\begin{smallmatrix} 0 & -1 \\ 1 & 0 \end{smallmatrix}\right),\left(\begin{smallmatrix} 1 & 1 \\ 0 & 1 \end{smallmatrix}\right)\right\}}$. We do this by showing that, in general, there is a set of suffixes of each element that completely determines the cone type of the element, and such suffixes are subwords of primitive relators. Then, using J. W. Cannon's seminal ideas (1984), we compute its growth function. We estimate from above and below the spectral radius of the random walk using ideas from T. Nagnibeda (1999) and S. Gou\"ezel (2015). Finally, using results of Y. Guivarc'h (1980) and S. Gou\"ezel, F. Math\'{e}us and F. Maucourant (2015), we estimate other asymptotic invariants of the random walk, namely, the entropy and the drift.Comment: 31 pages, 6 figures, 11 table

Counting problem on wind-tree models

We study periodic wind-tree models, billiards in the plane endowed with $\mathbb{Z}^2$-periodically located identical connected symmetric right-angled obstacles. We show asymptotic formulas for the number of (isotopy classes of) closed billiard trajectories (up to $\mathbb{Z}^2$-translations) on the wind-tree billiard. We also compute explicitly the associated Siegel-Veech constant for generic wind-tree billiards depending on the number of corners on the obstacle.Comment: 41 pages, 15 figures. arXiv admin note: substantial text overlap with arXiv:1502.06405 by other author

Standalone Photovoltaic Direct Pumping in Urban Water Pressurized Networks with Energy Storage in Tanks or Batteries

[EN] Photovoltaic energy production is nowadays one of the hottest topics in the water industry as this green energy source is becoming more and more workable in countries like Spain, with high values of irradiance. In water pressurized systems supplying urban areas, they distribute energy consumption in pumps throughout the day, and it is not possible to supply electromechanical devices without energy storages such as batteries. Additionally, it is not possible to manage energy demand for water consumption. Researchers and practitioners have proven batteries to be reliable energy storage systems, and are undertaking many efforts to increase their performance, capacity, and useful life. Water pressurized networks incorporate tanks as devices used for accumulating water during low consumption hours while releasing it in peak hours. The compensation tanks work here as a mass and energy source in water pressurized networks supplied with photovoltaic arrays (not electricity grids). This work intends to compare which of these two energy storage systems are better and how to choose between them considering that these two systems involve running the network as a standalone pumping system without being connected to electricity grids. This work also calculates the intermediate results, considering both photovoltaic arrays and electricity grids for supplying electricity to pumping systems. We then analyzed these three cases in a synthetic network (used in earlier research) considering the effect of irradiation and water consumption, as we did not state which should be the most unfavorable month given that higher irradiance coincides with higher water consumption (i.e., during summer). Results show that there is no universal solution as energy consumption depends on the network features and that energy production depends very much on latitude. We based the portfolio of alternatives on investments for purchasing different equipment at present (batteries, pipelines, etc.) based on economic criteria so that the payback period is the indicator used for finding the best alternative, which is the one with the lowest value.This work was supported by the research project "GESAEN" through the 2016 call of the Vicerrectorado de Investigacion, Desarrollo e Innovacion from the University of Alicante, GRE-16-08.Pardo, MA.; Cobacho Jordán, R.; Bañón, L. (2020). Standalone Photovoltaic Direct Pumping in Urban Water Pressurized Networks with Energy Storage in Tanks or Batteries. Sustainability. 12(2):1-20. https://doi.org/10.3390/su12020738S120122Bijl, D. L., Bogaart, P. W., Kram, T., de Vries, B. J. M., & van Vuuren, D. P. (2016). Long-term water demand for electricity, industry and households. Environmental Science & Policy, 55, 75-86. doi:10.1016/j.envsci.2015.09.005Breadsell, J. K., Byrne, J. J., & Morrison, G. M. (2019). Household Energy and Water Practices Change Post-Occupancy in an Australian Low-Carbon Development. Sustainability, 11(20), 5559. doi:10.3390/su11205559Watson, K. J. (2015). Understanding the role of building management in the low-energy performance of passive sustainable design: Practices of natural ventilation in a UK office building. Indoor and Built Environment, 24(7), 999-1009. doi:10.1177/1420326x15601478Berry, S., & Davidson, K. (2015). Zero energy homes – Are they economically viable? Energy Policy, 85, 12-21. doi:10.1016/j.enpol.2015.05.009Wittenberg, I., & Matthies, E. (2016). Solar policy and practice in Germany: How do residential households with solar panels use electricity? Energy Research & Social Science, 21, 199-211. doi:10.1016/j.erss.2016.07.008Alghamdi, A., Haider, H., Hewage, K., & Sadiq, R. (2019). Inter-University Sustainability Benchmarking for Canadian Higher Education Institutions: Water, Energy, and Carbon Flows for Technical-Level Decision-Making. Sustainability, 11(9), 2599. doi:10.3390/su11092599Hardy, L., Garrido, A., & Juana, L. (2012). Evaluation of Spain’s Water-Energy Nexus. International Journal of Water Resources Development, 28(1), 151-170. doi:10.1080/07900627.2012.642240Cucchiella, F., D’Adamo, I., Gastaldi, M., & Stornelli, V. (2018). Solar Photovoltaic Panels Combined with Energy Storage in a Residential Building: An Economic Analysis. Sustainability, 10(9), 3117. doi:10.3390/su10093117Zsiborács, H., Hegedűsné Baranyai, N., Vincze, A., Háber, I., & Pintér, G. (2018). Economic and Technical Aspects of Flexible Storage Photovoltaic Systems in Europe. Energies, 11(6), 1445. doi:10.3390/en11061445Roncero-Sánchez, P., Parreño Torres, A., & Vázquez, J. (2018). Control Scheme of a Concentration Photovoltaic Plant with a Hybrid Energy Storage System Connected to the Grid. Energies, 11(2), 301. doi:10.3390/en11020301Chen, J., Li, J., Zhang, Y., Bao, G., Ge, X., & Li, P. (2018). A Hierarchical Optimal Operation Strategy of Hybrid Energy Storage System in Distribution Networks with High Photovoltaic Penetration. Energies, 11(2), 389. doi:10.3390/en11020389Reca, J., Torrente, C., López-Luque, R., & Martínez, J. (2016). Feasibility analysis of a standalone direct pumping photovoltaic system for irrigation in Mediterranean greenhouses. Renewable Energy, 85, 1143-1154. doi:10.1016/j.renene.2015.07.056Senol, R. (2012). An analysis of solar energy and irrigation systems in Turkey. Energy Policy, 47, 478-486. doi:10.1016/j.enpol.2012.05.049Tarjuelo, J. M., Rodriguez-Diaz, J. A., Abadía, R., Camacho, E., Rocamora, C., & Moreno, M. A. (2015). Efficient water and energy use in irrigation modernization: Lessons from Spanish case studies. Agricultural Water Management, 162, 67-77. doi:10.1016/j.agwat.2015.08.009Chandel, S. S., Nagaraju Naik, M., & Chandel, R. (2015). Review of solar photovoltaic water pumping system technology for irrigation and community drinking water supplies. Renewable and Sustainable Energy Reviews, 49, 1084-1099. doi:10.1016/j.rser.2015.04.083Córcoles, J., Gonzalez Perea, R., Izquiel, A., & Moreno, M. (2019). Decision Support System Tool to Reduce the Energy Consumption of Water Abstraction from Aquifers for Irrigation. Water, 11(2), 323. doi:10.3390/w11020323Betka, A., & Attali, A. (2010). Optimization of a photovoltaic pumping system based on the optimal control theory. Solar Energy, 84(7), 1273-1283. doi:10.1016/j.solener.2010.04.004Elkholy, M. M., & Fathy, A. (2016). Optimization of a PV fed water pumping system without storage based on teaching-learning-based optimization algorithm and artificial neural network. Solar Energy, 139, 199-212. doi:10.1016/j.solener.2016.09.022Narvarte, L., Fernández-Ramos, J., Martínez-Moreno, F., Carrasco, L. M., Almeida, R. H., & Carrêlo, I. B. (2018). Solutions for adapting photovoltaics to large power irrigation systems for agriculture. Sustainable Energy Technologies and Assessments, 29, 119-130. doi:10.1016/j.seta.2018.07.004Mohanty, A., Ray, P. K., Viswavandya, M., Mohanty, S., & Mohanty, P. P. (2018). Experimental analysis of a standalone solar photo voltaic cell for improved power quality. Optik, 171, 876-885. doi:10.1016/j.ijleo.2018.06.139Mérida García, A., Fernández García, I., Camacho Poyato, E., Montesinos Barrios, P., & Rodríguez Díaz, J. A. (2018). Coupling irrigation scheduling with solar energy production in a smart irrigation management system. Journal of Cleaner Production, 175, 670-682. doi:10.1016/j.jclepro.2017.12.093Pardo Picazo, M., Juárez, J., & García-Márquez, D. (2018). Energy Consumption Optimization in Irrigation Networks Supplied by a Standalone Direct Pumping Photovoltaic System. Sustainability, 10(11), 4203. doi:10.3390/su10114203González Perea, R., Mérida García, A., Fernández García, I., Camacho Poyato, E., Montesinos, P., & Rodríguez Díaz, J. A. (2019). Middleware to Operate Smart Photovoltaic Irrigation Systems in Real Time. Water, 11(7), 1508. doi:10.3390/w11071508Wetzel, T., & Borchers, S. (2014). Update of energy payback time and greenhouse gas emission data for crystalline silicon photovoltaic modules. Progress in Photovoltaics: Research and Applications, 23(10), 1429-1435. doi:10.1002/pip.2548Kou, Q., Klein, S. A., & Beckman, W. A. (1998). A method for estimating the long-term performance of direct-coupled PV pumping systems. Solar Energy, 64(1-3), 33-40. doi:10.1016/s0038-092x(98)00049-8Meah, K., Fletcher, S., & Ula, S. (2008). Solar photovoltaic water pumping for remote locations. Renewable and Sustainable Energy Reviews, 12(2), 472-487. doi:10.1016/j.rser.2006.10.008Child, M., Haukkala, T., & Breyer, C. (2017). The Role of Solar Photovoltaics and Energy Storage Solutions in a 100% Renewable Energy System for Finland in 2050. Sustainability, 9(8), 1358. doi:10.3390/su9081358Wong, J., Lim, Y. S., Tang, J. H., & Morris, E. (2014). Grid-connected photovoltaic system in Malaysia: A review on voltage issues. Renewable and Sustainable Energy Reviews, 29, 535-545. doi:10.1016/j.rser.2013.08.087Arab, A. H., Chenlo, F., Mukadam, K., & Balenzategui, J. L. (1999). Performance of PV water pumping systems. Renewable Energy, 18(2), 191-204. doi:10.1016/s0960-1481(98)00780-0Muhsen, D. H., Khatib, T., & Abdulabbas, T. E. (2018). Sizing of a standalone photovoltaic water pumping system using hybrid multi-criteria decision making methods. Solar Energy, 159, 1003-1015. doi:10.1016/j.solener.2017.11.044Khatib, T., Ibrahim, I. A., & Mohamed, A. (2016). A review on sizing methodologies of photovoltaic array and storage battery in a standalone photovoltaic system. Energy Conversion and Management, 120, 430-448. doi:10.1016/j.enconman.2016.05.011Li, C.-H., Zhu, X.-J., Cao, G.-Y., Sui, S., & Hu, M.-R. (2009). Dynamic modeling and sizing optimization of stand-alone photovoltaic power systems using hybrid energy storage technology. Renewable Energy, 34(3), 815-826. doi:10.1016/j.renene.2008.04.018Ru, Y., Kleissl, J., & Martinez, S. (2013). Storage Size Determination for Grid-Connected Photovoltaic Systems. IEEE Transactions on Sustainable Energy, 4(1), 68-81. doi:10.1109/tste.2012.2199339Narvarte, L., Almeida, R. H., Carrêlo, I. B., Rodríguez, L., Carrasco, L. M., & Martinez-Moreno, F. (2019). On the number of PV modules in series for large-power irrigation systems. Energy Conversion and Management, 186, 516-525. doi:10.1016/j.enconman.2019.03.001Yu, C., Khoo, Y., Chai, J., Han, S., & Yao, J. (2019). Optimal Orientation and Tilt Angle for Maximizing in-Plane Solar Irradiation for PV Applications in Japan. Sustainability, 11(7), 2016. doi:10.3390/su11072016Hailu, & Fung. (2019). Optimum Tilt Angle and Orientation of Photovoltaic Thermal System for Application in Greater Toronto Area, Canada. Sustainability, 11(22), 6443. doi:10.3390/su11226443Mérida García, A., Gallagher, J., McNabola, A., Camacho Poyato, E., Montesinos Barrios, P., & Rodríguez Díaz, J. A. (2019). Comparing the environmental and economic impacts of on- or off-grid solar photovoltaics with traditional energy sources for rural irrigation systems. Renewable Energy, 140, 895-904. doi:10.1016/j.renene.2019.03.122Seme, S., Lukač, N., Štumberger, B., & Hadžiselimović, M. (2017). Power quality experimental analysis of grid-connected photovoltaic systems in urban distribution networks. Energy, 139, 1261-1266. doi:10.1016/j.energy.2017.05.088Sugihara, H., Yokoyama, K., Saeki, O., Tsuji, K., & Funaki, T. (2013). Economic and Efficient Voltage Management Using Customer-Owned Energy Storage Systems in a Distribution Network With High Penetration of Photovoltaic Systems. IEEE Transactions on Power Systems, 28(1), 102-111. doi:10.1109/tpwrs.2012.2196529Pardo, M. Á., Manzano, J., Valdes-Abellan, J., & Cobacho, R. (2019). Standalone direct pumping photovoltaic system or energy storage in batteries for supplying irrigation networks. Cost analysis. Science of The Total Environment, 673, 821-830. doi:10.1016/j.scitotenv.2019.04.050Batchabani, E., & Fuamba, M. (2014). Optimal Tank Design in Water Distribution Networks: Review of Literature and Perspectives. Journal of Water Resources Planning and Management, 140(2), 136-145. doi:10.1061/(asce)wr.1943-5452.0000256Kurek, W., & Ostfeld, A. (2013). Multi-objective optimization of water quality, pumps operation, and storage sizing of water distribution systems. Journal of Environmental Management, 115, 189-197. doi:10.1016/j.jenvman.2012.11.030Sarbu, I. (2016). A Study of Energy Optimisation of Urban Water Distribution Systems Using Potential Elements. Water, 8(12), 593. doi:10.3390/w8120593Gómez, E., Cabrera, E., Balaguer, M., & Soriano, J. (2015). Direct and Indirect Water Supply: An Energy Assessment. Procedia Engineering, 119, 1088-1097. doi:10.1016/j.proeng.2015.08.941Hamidat, A., & Benyoucef, B. (2009). Systematic procedures for sizing photovoltaic pumping system, using water tank storage. Energy Policy, 37(4), 1489-1501. doi:10.1016/j.enpol.2008.12.014Ould Amrouche, S., Rekioua, D., Rekioua, T., & Bacha, S. (2016). Overview of energy storage in renewable energy systems. International Journal of Hydrogen Energy, 41(45), 20914-20927. doi:10.1016/j.ijhydene.2016.06.243Üçtuğ, F. G., & Azapagic, A. (2018). Environmental impacts of small-scale hybrid energy systems: Coupling solar photovoltaics and lithium-ion batteries. Science of The Total Environment, 643, 1579-1589. doi:10.1016/j.scitotenv.2018.06.290Rydh, C. J., & Sandén, B. A. (2005). Energy analysis of batteries in photovoltaic systems. Part I: Performance and energy requirements. Energy Conversion and Management, 46(11-12), 1957-1979. doi:10.1016/j.enconman.2004.10.003Todde, G., Murgia, L., Deligios, P. A., Hogan, R., Carrelo, I., Moreira, M., … Narvarte, L. (2019). Energy and environmental performances of hybrid photovoltaic irrigation systems in Mediterranean intensive and super-intensive olive orchards. Science of The Total Environment, 651, 2514-2523. doi:10.1016/j.scitotenv.2018.10.175Ghorbanian, V., Karney, B., & Guo, Y. (2016). Pressure Standards in Water Distribution Systems: Reflection on Current Practice with Consideration of Some Unresolved Issues. Journal of Water Resources Planning and Management, 142(8), 04016023. doi:10.1061/(asce)wr.1943-5452.0000665Giustolisi, O., Savic, D., & Kapelan, Z. (2008). Pressure-Driven Demand and Leakage Simulation for Water Distribution Networks. Journal of Hydraulic Engineering, 134(5), 626-635. doi:10.1061/(asce)0733-9429(2008)134:5(626)Cabrera, E., Pardo, M. A., Cabrera, E., & Arregui, F. J. (2012). Tap Water Costs and Service Sustainability, a Close Relationship. Water Resources Management, 27(1), 239-253. doi:10.1007/s11269-012-0181-3Vindel, J. M., Polo, J., & Zarzalejo, L. F. (2015). Modeling monthly mean variation of the solar global irradiation. Journal of Atmospheric and Solar-Terrestrial Physics, 122, 108-118. doi:10.1016/j.jastp.2014.11.008Balling, R. C., Gober, P., & Jones, N. (2008). Sensitivity of residential water consumption to variations in climate: An intraurban analysis of Phoenix, Arizona. Water Resources Research, 44(10). doi:10.1029/2007wr006722Hoekstra, A. Y., Mekonnen, M. M., Chapagain, A. K., Mathews, R. E., & Richter, B. D. (2012). Global Monthly Water Scarcity: Blue Water Footprints versus Blue Water Availability. PLoS ONE, 7(2), e32688. doi:10.1371/journal.pone.0032688Kleiner, Y., & Rajani, B. (2001). Comprehensive review of structural deterioration of water mains: statistical models. Urban Water, 3(3), 131-150. doi:10.1016/s1462-0758(01)00033-4Cabrera, E., Pardo, M. A., Cobacho, R., & Cabrera, E. (2010). Energy Audit of Water Networks. Journal of Water Resources Planning and Management, 136(6), 669-677. doi:10.1061/(asce)wr.1943-5452.0000077Ebara Grupos de Presión Automáticos http://www.ebara.e

Diffusion rate in non-generic directions in the wind-tree model

We show that any real number in [0,1) is a diffusion rate for the wind-tree model with rational parameters. We will also provide a criterion in order to describe the shape of the Lyapunov spectrum of cocycles obtained as suspension of a representation. As an application, we exhibit an infinite family of wind-tree billiards for which the interior of the Lyapunov spectrum is a big as possible: this is the full square (0,1)^2. To the best of the knowledge of the authors, these are the first complete descriptions where the interior of the Lyapunov spectrum is known explicitly in dimension two, even for general Fuchsian groups.Comment: 26 page