Theoretical guidelines to create and tune electric skyrmion bubbles

Researchers have long wondered whether ferroelectrics may present topological textures akin to magnetic skyrmions and chiral bubbles, the results being modest thus far. An electric equivalent of a typical magnetic skyrmion would rely on a counterpart of the Dzyaloshinskii-Moriya interaction and seems all but impossible; further, the exotic ferroelectric orders reported to date rely on specific composites and superlattices, limiting their generality and properties. Here, we propose an original approach to write topological textures in simple ferroelectrics in a customary manner. Our second-principles simulations of columnar nanodomains, in prototype material PbTiO3, show we can harness the Bloch-type structure of the domain wall to create objects with the usual skyrmion-defining features as well as unusual ones?including isotopological and topological transitions driven by external fields and temperature?and potentially very small sizes. Our results suggest countless possibilities for creating and manipulating such electric textures, effectively inaugurating the field of topological ferroelectrics.We were also funded by the Spanish Ministry of Economy and Competitiveness through grants FIS2015-64886-C5-2-P (to P.G.-F. and J.J.) and RyC-2013-12515 (to P.G.-F.)

Fórmulas para el coeficiente de arrastre y la ecuación Navier-Stokes fraccional

Se quiere encontrar la relación entre la ecuación de Navier-Stokes fraccional y las fórmulas para el coeficiente de arrastre, como las de Kármán-Schoenherr, Prandtl- Kármán, y Nikuradse. Los cambios de escala producen una renormalización para las ecuaciones de la capa límite, que contiene la hipótesis esencial de la delgadez de dicha capa, y da lugar a una descripción multifractal. Se obtiene una generalización del resultado experimental de Blasius para el factor de fricción. Si se reajustan las relaciones del número de rasgos del multifractal, se infieren las fórmulas, objeto de este estudio, y se las representa como un bi-multifractal, lo que permite un camino analítico para el número de Reynolds crítico y señala a la de Kármán-Schoenherr como la fórmula apropiada para el límite a la derecha de la subcapa viscosa. Los reajustes se traducen en matizar las aproximaciones de la relación entre los números de Euler y Reynolds, o bien en los decaimientos relativos del coeficiente de arrastre. Se aplican los resultados a la descripción de la capa límite turbulenta y a las interacciones entre corrientes y fondos (en ríos, desiertos y huracanes)

El coeficiente de descarga y la densidad beta

Se estudia el coeficiente de descarga y la distribución de intensidades de la turbulencia. Con el teorema de Torricelli y la teoría de probabilidades se formulan el caudal y el coeficiente de descarga, siguiendo una densidad beta unimodal, renormalizada, con dos parámetros de forma. Se había construido un modelo multifractal para la cascada de la energía cinética en la turbulencia, partiendo de los métodos de Pearson y de Kolmogorov. Para la intensidad de la turbulencia, con el primero se creó una distribución beta; para el segundo, una ley en potencia. Se completa el modelo multifractal, reconociendo la función de estructura como la función Kummer. Se busca la compatibilidad entre los dos modelos y la identificación de sus parámetros. Se encuentra que los dos parámetros de forma determinan la resolución del modelo de cascada. Se determina la dimensión local y el espectro de dimensiones para los estados que producen el teorema de Torricelli. Redefiniendo la función de estructura, la resolución queda determinada por el tirante para el cambio de régimen. Análogamente, pueden identificarse diversos prototipos, a los que hemos denominado: cuatro experimentales, tres canales, Kolmogorov, Kármán, Taylor, Verhulst (logística), Cauchy-Manning y Euclides (áurea). Se concluye que el coeficiente de descarga es una beta renormalizada; la distribución de intensidades de la turbulencia es una beta; el prototipo Torricelli resulta representativo para los cuatro experimentales y el de Euclides, quedando lejos de la distribución Gaussiana, que está contenida en el de Kármán; en tanto, el de Taylor produce la delta de Dirac

Modelo Multifractal Aplicado al Riego

We define the binomial multifractal distribution as an expression of a law of small numbers. We studied a form of evaluation or design of a distribution system in an irrigation district by determining its conduction capacity with the desired flexibility knowing the following parameters: flow, frequency, and irrigation time. The method consists of the approximation of the binomial distribution through the Gaussian, an inverse relation of probability, two estimations of Gaussian parameters, and the application of the multifractal distribution. We present the mathematical reformulation of Boltzmann relation in the statistical mechanics, which gives origin to the multifractal model. In particular, we illustrate its application in the problems of irrigation,  pointing out that it is also possible to apply it to multifractal models: variogram, exponential, gamma, and Gaussian.Definimos la distribución multifractal binomial, como expresión de una ley de los pequeños números. Estudiamos una forma de evaluación o de diseño de un sistema de distribución en un distrito de riego, al determinar su capacidad de conducción con la flexibilidad deseada, conociendo los parámetros de gasto, frecuencia y tiempo de riego. El método es la aproximación de la distribución binomial por la Gaussiana, una relación inversa de probabilidad, dos estimaciones de parámetros Gaussianos, y la aplicación de la distribución multifractal. Presentamos la reformulación matemática de la relación de Boltzmann en la mecánica estadística, que da origen al modelo multifractal. En particular, ilustramos su aplicación en el problema del riego. Pero también es posible aplicarlo a los modelos multifractales: variograma, exponencial, gama, y Gaussiano

Chiral structures of electric polarization vectors quantified by X-ray resonant scattering

Resonant elastic X-ray scattering (REXS) offers a unique tool to investigate solid-state systems providing spatial knowledge from diffraction combined with electronic information through the enhanced absorption process, allowing the probing of magnetic, charge, spin, and orbital degrees of spatial order together with electronic structure. A new promising application of REXS is to elucidate the chiral structure of electrical polarization emergent in a ferroelectric oxide superlattice in which the polarization vectors in the REXS amplitude are implicitly described through an anisotropic tensor corresponding to the quadrupole moment. Here, we present a detailed theoretical framework and analysis to quantitatively analyze the experimental results of Ti L-edge REXS of a polar vortex array formed in a PbTiO3/SrTiO3 superlattice. Based on this theoretical framework, REXS for polar chiral structures can become a useful tool similar to x-ray resonant magnetic scattering (XRMS), enabling a comprehensive study of both electric and magnetic REXS on the chiral structures.K.T.K., S.Y.P., and D.R.L acknowledge financial support by National Research Foundation of Korea (Grant No. NRF-2020R1A2C1009597, NRF-2019K1A3A7A09033387, and NRF-2021R1C1C1009494). M.M. and R.R. were supported by the Quantum Materials program from the Office of Basic Energy Sciences, US Department of Energy (DE-AC02-05CH11231). V.A.S., J.W.F., and L.W.M. acknowledge the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC-0012375 for support to study complex-oxide heterostructure with X-ray scattering. L.W.M. and R.R. acknowledge partial support from the Army Research Office under the ETHOS MURI via cooperative agreement W911NF-21-2-0162. J.Í. acknowledges financial support from the Luxembourg National Research Fund through project FNR/C18/MS/12705883/REFOX. M.A.P.G. was supported by the Czech Science Foundation (project no. 19-28594X). Diamond Light Source, UK, is acknowledged for beamtime on beamline I10 under proposal NT24797. Use of the Advanced Light Source, Lawrence Berkeley National Laboratory, was supported by the U.S. Department of Energy (DOE) under contract no. DE-AC02-05CH11231, and use of the Advanced Photon Source was supported by DOE’s Office of Science under contract DE-AC02-06CH11357

Structural chirality of polar skyrmions probed by resonant elastic x-ray scattering

An escalating challenge in condensed-matter research is the characterization of emergent order-parameter nanostructures such as ferroelectric and ferromagnetic skyrmions. Their small length scales coupled with complex, three-dimensional polarization or spin structures makes them demanding to trace out fully. Resonant elastic x-ray scattering (REXS) has emerged as a technique to study chirality in spin textures such as skyrmions and domain walls. It has, however, been used to a considerably lesser extent to study analogous features in ferroelectrics. Here, we present a framework for modeling REXS from an arbitrary arrangement of charge quadrupole moments, which can be applied to nanostructures in materials such as ferroelectrics. With this, we demonstrate how extended reciprocal space scans using REXS with circularly polarized x rays can probe the three-dimensional structure and chirality of polar skyrmions. Measurements, bolstered by quantitative scattering calculations, show that polar skyrmions of mixed chirality coexist, and that REXS allows valuation of relative fractions of right- and left-handed skyrmions. Our quantitative analysis of the structure and chirality of polar skyrmions highlights the capability of REXS for establishing complex topological structures toward future application exploits.M. R. M. and R. R. were supported by the Quantum Materials program from the Office of Basic Energy Sciences, U.S. Department of Energy (DE-AC02-05CH11231). V. A. S., J. W. F., and L. W. M. acknowledge the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award No. DE-SC-0012375 for support to study complex-oxide heterostructure with x-ray scattering. L. W. M. and R. R. acknowledge partial support from the Army Research Office under the ETHOS MURI via cooperative agreement W911NF-21-2-0162. J. Í. acknowledge financial support from the Luxembourg National Research Fund through project FNR/C18/MS/12705883/REFOX. Diamond Light Source, UK, is acknowledged for beam time on beam line I10 under proposal NT24797. K. T. K., S. Y. P., and D. R. L. acknowledge support from the National Research Foundation of Korea, under Grant No. NRF-2020R1A2C1009597, NRF-2019K1A3A7A09033387, and NRF-2021R1C1C1009494. M. A. P. G. acknowledges support by the Czech Science Foundation (Project No. 19-28594X). This research used resources of the Advanced Light Source, a U.S. DOE Office of Science User Facility under Contract No. DE-AC02-05CH11231. This research used resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility at Argonne National Laboratory and is based on research supported by the U.S. DOE Office of Science-Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. S. D. gratefully acknowledges a start-up grant from Indian Institute of Science, Bangalore, India. F. G.-O., P. G.-F., and J. J. acknowledge financial support from Grant No. PGC2018-096955-B-C41 funded by MCIN/AEI/10.13039/501100011033 and by ERDF “A way of making Europe,” by the European Union. F. G.-O. acknowledges financial support from Grant No. FPU18/04661 funded by MCIN/AEI/10.13039/50110001103

Methodology for estimation of integrated evapotranspiration and canal capacity in an irrigation zone

La capacidad de la red de canales en un sistema de riego depende de satisfacer la demanda hídrica máxima de los cultivos. Los métodos para determinar la capacidad del canal requieren de la estimación de la variable agronómica: evapotranspiración de los cultivos. En grandes áreas de riego, con un padrón diversificado de cultivos, diferentes fechas de siembra y varios ciclos agrícolas no existe un procedimiento integrado para estimar esta variable agronómica, lo cual genera incertidumbre al ser requerida en los métodos. En este trabajo se desarrolla una propuesta para estimar dicha variable para grandes zonas de riego. La propuesta inicia con el cálculo de la evapotranspiración de los cultivos por fecha de siembra, y termina con la obtención de una curva general integral para un año agrícola, encontrándose la variable evapotranspiración de una zona de riego (ETzr). Esta metodología se aplicó para el canal principal del módulo de riego Santa Rosa, Distrito de Riego 075, Sinaloa, México en que la ETzr resultó de 4,1 mm d-1. Por los resultados se concluye la veracidad de la propuesta en determinar la evapotranspiración para el cálculo en la capacidad del canal.Capacity of irrigation networks needs to satisfy peak crop water demands. The methods to size canal capacity require the estimation of an agronomic variable: crop evapotranspiration. There is not an integrated procedure to estimate crop evapotranspiration for large irrigation zones with a diversified crop pattern, different planting dates, and several crop seasons. Not having this procedure generates uncertainty in methods for canal capacity estimations. This paper presents a methodological proposal to estimate the ET variable for large irrigation zones. The procedure starts with calculating the ET for each planting date per crop and season. Next, it integrates a general ET curve for the water year that finds the evapotranspiration for the irrigation zone (ETzr). The methodology was applied to size the main canal that supplies the “Santa Rosa" Water Irrigation Association in the 075 Irrigation District located in the state of Sinaloa, Mexico. A value of 4.1 mm d-1 was estimated for ETzr. The results indicate the proposed method’s accuracy to estimate the ET variable to size irrigation canals.Fil: Íñiguez-Covarrubias, Mauro. Instituto Mexicano de Tecnología del Agua (Morelos, México).Fil: Ojeda-Bustamante, Waldo. Instituto Mexicano de Tecnología del Agua (Morelos, México).Fil: Rojano-Aguilar, Abraham. Universidad Autónoma Chapingo (México

A function for hydrosystemic management: irrigation distribution planning, demand and canal conduction capacity

"Introduction: The management of irrigation areas aims to achieve an efficient use of resources for full user satisfaction.Objectives: To propose a methodology for hydrosystemic management in which crop demand, irrigation planning in the allocation and d