Nanoscale magnetic structure of ferromagnet/antiferromagnet manganite multilayers

Polarized Neutron Reflectometry and magnetometry measurements have been used to obtain a comprehensive picture of the magnetic structure of a series of La{2/3}Sr{1/3}MnO{3}/Pr{2/3}Ca{1/3}MnO{3} (LSMO/PCMO) superlattices, with varying thickness of the antiferromagnetic (AFM) PCMO layers (0<=t_A<=7.6 nm). While LSMO presents a few magnetically frustrated monolayers at the interfaces with PCMO, in the latter a magnetic contribution due to FM inclusions within the AFM matrix was found to be maximized at t_A~3 nm. This enhancement of the FM moment occurs at the matching between layer thickness and cluster size, where the FM clusters would find the optimal strain conditions to be accommodated within the "non-FM" material. These results have important implications for tuning phase separation via the explicit control of strain.Comment: 4 pages, submitted to PR

Gas-solid contactors and catalytic reactors with direct microwave heating: current status and perspectives

Microwave heating (MWH) transforms energy from an electromagnetic wave to heat. In contrast to conventional heating (CH) mechanisms that use slower heat transfer processes via conduction, convection or radiation, microwaves (MW) directly interact with MW susceptor materials and induce a rapid conversion of the electromagnetic energy into heat. This rapid heating provides MWH with distinct features that can be leveraged to increase conversion, selectivity and/or energy efficiency of chemical processes. Here we discuss recent significant advances reported in MWH processes involving gas-solid interactions. Special attention is devoted to key aspects such as the methodologies to accurately determine local temperatures under the influence of electromagnetic (EM). Other relevant aspects such as the consideration of the solid catalyst dielectric properties or the design of novel gas-solid contactor configurations will be discussed. Emerging aspects such as the potential of MWH to minimize secondary by-products in high temperature reactions or to efficiently perform in transient processes, e.g. adsorption-desorption cycles, are highlighted. Finally, current challenges and perspectives towards a wide application of MWH in gas solid contactors will be critically discussed

Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations

[EN] The benefits and properties of iterative splitting methods, which are based on serial versions, have been studied in recent years, this work, we extend the iterative splitting methods to novel classes of parallel versions to solve nonlinear fractional convection-diffusion equations. For such interesting partial differential examples with higher dimensional, fractional, and nonlinear terms, we could apply the parallel iterative splitting methods, which allow for accelerating the solver methods and reduce the computational time. Here, we could apply the benefits of the higher accuracy of the iterative splitting methods. We present a novel parallel iterative splitting method, which is based on the multi-splitting methods, The flexibilisation with multisplitting methods allows for decomposing large scale operator equations. In combination with iterative splitting methods, which use characteristics of waveform-relaxation (WR) methods, we could embed the relaxation behavior and deal better with the nonlinearities of the operators. We consider the convergence results of the parallel iterative splitting methods, reformulating the underlying methods with a summation of the individual convergence results of the WR methods. We discuss the numerical convergence of the serial and parallel iterative splitting methods with respect to the synchronous and asynchronous treatments. Furthermore, we present different numerical applications of fluid and phase field problems in order to validate the benefit of the parallel versions.This research was partially supported by Ministerio de Economia y Competitividad, Spain, under grant PGC2018-095896-B-C21-C22 and German Academic Exchange Service grant number 91588469.Geiser, J.; Martínez Molada, E.; Hueso, JL. (2020). Serial and Parallel Iterative Splitting Methods: Algorithms and Applications to Fractional Convection-Diffusion Equations. Mathematics. 8(11):1-42. https://doi.org/10.3390/math8111950S142811Farago, I., & Geiser, J. (2007). Iterative operator-splitting methods for linear problems. International Journal of Computational Science and Engineering, 3(4), 255. doi:10.1504/ijcse.2007.018264Frommer, A., & Szyld, D. B. (2000). On asynchronous iterations. Journal of Computational and Applied Mathematics, 123(1-2), 201-216. doi:10.1016/s0377-0427(00)00409-xO’Leary, D. P., & White, R. E. (1985). Multi-Splittings of Matrices and Parallel Solution of Linear Systems. SIAM Journal on Algebraic Discrete Methods, 6(4), 630-640. doi:10.1137/0606062White, R. E. (1986). Parallel Algorithms for Nonlinear Problems. SIAM Journal on Algebraic Discrete Methods, 7(1), 137-149. doi:10.1137/0607017Geiser, J. (2016). Picard’s iterative method for nonlinear multicomponent transport equations. Cogent Mathematics, 3(1), 1158510. doi:10.1080/23311835.2016.1158510Miekkala, U., & Nevanlinna, O. (1987). Convergence of Dynamic Iteration Methods for Initial Value Problems. SIAM Journal on Scientific and Statistical Computing, 8(4), 459-482. doi:10.1137/0908046Miekkala, U., & Nevanlinna, O. (1996). Iterative solution of systems of linear differential equations. Acta Numerica, 5, 259-307. doi:10.1017/s096249290000266xGeiser, J. (2010). Iterative operator-splitting methods for nonlinear differential equations and applications. Numerical Methods for Partial Differential Equations, 27(5), 1026-1054. doi:10.1002/num.20568He, D., Pan, K., & Hu, H. (2020). A spatial fourth-order maximum principle preserving operator splitting scheme for the multi-dimensional fractional Allen-Cahn equation. Applied Numerical Mathematics, 151, 44-63. doi:10.1016/j.apnum.2019.12.018Giona, M., Cerbelli, S., & Roman, H. E. (1992). Fractional diffusion equation and relaxation in complex viscoelastic materials. Physica A: Statistical Mechanics and its Applications, 191(1-4), 449-453. doi:10.1016/0378-4371(92)90566-9Nigmatullin, R. R. (1986). The realization of the generalized transfer equation in a medium with fractal geometry. physica status solidi (b), 133(1), 425-430. doi:10.1002/pssb.2221330150Allen, S. M., & Cahn, J. W. (1979). A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening. Acta Metallurgica, 27(6), 1085-1095. doi:10.1016/0001-6160(79)90196-2Yue, P., Feng, J. J., Liu, C., & Shen, J. (2005). Diffuse-interface simulations of drop coalescence and retraction in viscoelastic fluids. Journal of Non-Newtonian Fluid Mechanics, 129(3), 163-176. doi:10.1016/j.jnnfm.2005.07.002Sommacal, L., Melchior, P., Oustaloup, A., Cabelguen, J.-M., & Ijspeert, A. J. (2008). Fractional Multi-models of the Frog Gastrocnemius Muscle. Journal of Vibration and Control, 14(9-10), 1415-1430. doi:10.1177/1077546307087440Moshrefi-Torbati, M., & Hammond, J. K. (1998). Physical and geometrical interpretation of fractional operators. Journal of the Franklin Institute, 335(6), 1077-1086. doi:10.1016/s0016-0032(97)00048-3El-Nabulsi, R. A. (2009). Fractional Dirac operators and deformed field theory on Clifford algebra. Chaos, Solitons & Fractals, 42(5), 2614-2622. doi:10.1016/j.chaos.2009.04.002Kanney, J. F., Miller, C. T., & Kelley, C. T. (2003). Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems. Advances in Water Resources, 26(3), 247-261. doi:10.1016/s0309-1708(02)00162-8Geiser, J., Hueso, J. L., & Martínez, E. (2020). Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations. Mathematics, 8(3), 302. doi:10.3390/math8030302Meerschaert, M. M., Scheffler, H.-P., & Tadjeran, C. (2006). Finite difference methods for two-dimensional fractional dispersion equation. Journal of Computational Physics, 211(1), 249-261. doi:10.1016/j.jcp.2005.05.017Irreversibility, Least Action Principle and Causality. Preprint, HAL, 2008 https://hal.archives-ouvertes.fr/hal-00348123v1Cresson, J. (2007). Fractional embedding of differential operators and Lagrangian systems. Journal of Mathematical Physics, 48(3), 033504. doi:10.1063/1.2483292Meerschaert, M. M., & Tadjeran, C. (2004). Finite difference approximations for fractional advection–dispersion flow equations. Journal of Computational and Applied Mathematics, 172(1), 65-77. doi:10.1016/j.cam.2004.01.033Geiser, J. (2011). Computing Exponential for Iterative Splitting Methods: Algorithms and Applications. Journal of Applied Mathematics, 2011, 1-27. doi:10.1155/2011/193781Geiser, J. (2008). Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations. Journal of Computational and Applied Mathematics, 217(1), 227-242. doi:10.1016/j.cam.2007.06.028Ladics, T. (2015). Error analysis of waveform relaxation method for semi-linear partial differential equations. Journal of Computational and Applied Mathematics, 285, 15-31. doi:10.1016/j.cam.2015.02.003Yuan, D., & Burrage, K. (2003). Convergence of the parallel chaotic waveform relaxation method for stiff systems. Journal of Computational and Applied Mathematics, 151(1), 201-213. doi:10.1016/s0377-0427(02)00749-5Ladics, T., & Faragó, I. (2013). Generalizations and error analysis of the iterative operator splitting method. Open Mathematics, 11(8). doi:10.2478/s11533-013-0246-4Moler, C., & Van Loan, C. (2003). Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later. SIAM Review, 45(1), 3-49. doi:10.1137/s00361445024180Najfeld, I., & Havel, T. F. (1995). Derivatives of the Matrix Exponential and Their Computation. Advances in Applied Mathematics, 16(3), 321-375. doi:10.1006/aama.1995.1017Hochbruck, M., & Ostermann, A. (2010). Exponential integrators. Acta Numerica, 19, 209-286. doi:10.1017/s0962492910000048Casas, F., & Iserles, A. (2006). Explicit Magnus expansions for nonlinear equations. Journal of Physics A: Mathematical and General, 39(19), 5445-5461. doi:10.1088/0305-4470/39/19/s07Magnus, W. (1954). On the exponential solution of differential equations for a linear operator. Communications on Pure and Applied Mathematics, 7(4), 649-673. doi:10.1002/cpa.3160070404Jeltsch, R., & Pohl, B. (1995). Waveform Relaxation with Overlapping Splittings. SIAM Journal on Scientific Computing, 16(1), 40-49. doi:10.1137/0916004Faragó, I. (2008). A modified iterated operator splitting method. Applied Mathematical Modelling, 32(8), 1542-1551. doi:10.1016/j.apm.2007.04.018Li, J., Jiang, Y., & Miao, Z. (2019). A parareal approach of semi‐linear parabolic equations based on general waveform relaxation. Numerical Methods for Partial Differential Equations, 35(6), 2017-2043. doi:10.1002/num.22390Trotter, H. F. (1959). On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4), 545-545. doi:10.1090/s0002-9939-1959-0108732-6Strang, G. (1968). On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5(3), 506-517. doi:10.1137/0705041Geiser, J. (2009). Operator-splitting methods in respect of eigenvalue problems for nonlinear equations and applications for Burgers equations. Journal of Computational and Applied Mathematics, 231(2), 815-827. doi:10.1016/j.cam.2009.05.00

An alternative analysis for the local convergence of iterative methods for multiple roots including when the multiplicity is unknown

[EN] In this paper we propose an alternative for the study of local convergence radius and the uniqueness radius for some third-order methods for multiple roots whose multiplicity is known. The main goal is to provide an alternative that avoids the use of sophisticated properties of divided differences that are used in already published papers about local convergence for multiple roots. We defined the local study by using a technique taking into consideration a bounding condition for the derivative of the function with i=1,2. In the case that the method uses first and second derivative in its iterative expression and i=1 in case the method only uses first derivative. Furthermore we implement a numerical analysis in the following sense. Since the radius of local convergence for high-order methods decreases with the order, we must take into account the analysis of ITS behaviour when we introduce a new iterative method. Finally, we have used these iterative methods for multiple roots for the case where the multiplicity m is unknown, so we estimate this factor by different strategies comparing the behaviour of the corresponding estimations and how this fact affect to the original method.This work was supported by Secretaria de Educacion Superior, Ciencia, Tecnologia e Innovacion (Convocatoria Abierta 2015 fase II).Alarcon, D.; Hueso, JL.; Martínez Molada, E. (2020). An alternative analysis for the local convergence of iterative methods for multiple roots including when the multiplicity is unknown. International Journal of Computer Mathematics. 97(1-2):312-329. https://doi.org/10.1080/00207160.2019.1589460S312329971-2Argyros, I. (2003). On The Convergence And Application Of Newton’s Method Under Weak HÖlder Continuity Assumptions. International Journal of Computer Mathematics, 80(6), 767-780. doi:10.1080/0020716021000059160Hueso, J. L., Martínez, E., & Teruel, C. (2014). Determination of multiple roots of nonlinear equations and applications. Journal of Mathematical Chemistry, 53(3), 880-892. doi:10.1007/s10910-014-0460-8McNamee, J. M. (1998). A comparison of methods for accelerating convergence of Newton’s method for multiple polynomial roots. ACM SIGNUM Newsletter, 33(2), 17-22. doi:10.1145/290590.290592Ortega, J. M. (1974). Solution of Equations in Euclidean and Banach Spaces (A. M. Ostrowski). SIAM Review, 16(4), 564-564. doi:10.1137/1016102Osada, N. (1994). An optimal multiple root-finding method of order three. Journal of Computational and Applied Mathematics, 51(1), 131-133. doi:10.1016/0377-0427(94)00044-1Schr�der, E. (1870). Ueber unendlich viele Algorithmen zur Aufl�sung der Gleichungen. Mathematische Annalen, 2(2), 317-365. doi:10.1007/bf01444024Vander Stracten, M., & Van de Vel, H. (1992). Multiple root-finding methods. Journal of Computational and Applied Mathematics, 40(1), 105-114. doi:10.1016/0377-0427(92)90045-yZhou, X., Chen, X., & Song, Y. (2013). On the convergence radius of the modified Newton method for multiple roots under the center–Hölder condition. Numerical Algorithms, 65(2), 221-232. doi:10.1007/s11075-013-9702-

Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations

[EN] This article proposes adaptive iterative splitting methods to solve Multiphysics problems, which are related to convection-diffusion-reaction equations. The splitting techniques are based on iterative splitting approaches with adaptive ideas. Based on shifting the time-steps with additional adaptive time-ranges, we could embedded the adaptive techniques into the splitting approach. The numerical analysis of the adapted iterative splitting schemes is considered and we develop the underlying error estimates for the application of the adaptive schemes. The performance of the method with respect to the accuracy and the acceleration is evaluated in different numerical experiments. We test the benefits of the adaptive splitting approach on highly nonlinear Burgers' and Maxwell-Stefan diffusion equations.This research was funded by German Academic Exchange Service grant number 91588469. We acknowledge support by the DFG Open Access Publication Funds of the Ruhr-Universität of Bochum, Germany and by Ministerio de Economía y Competitividad, Spain, under grant PGC2018-095896-B-C21-C22.Geiser, J.; Hueso, JL.; Martínez Molada, E. (2020). Adaptive Iterative Splitting Methods for Convection-Diffusion-Reaction Equations. Mathematics. 8(3):1-22. https://doi.org/10.3390/math8030302S12283Auzinger, W., & Herfort, W. (2014). Local error structures and order conditions in terms of Lie elements for exponential splitting schemes. Opuscula Mathematica, 34(2), 243. doi:10.7494/opmath.2014.34.2.243Auzinger, W., Koch, O., & Quell, M. (2016). Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions. Numerical Algorithms, 75(1), 261-283. doi:10.1007/s11075-016-0206-8Descombes, S., & Massot, M. (2004). Operator splitting for nonlinear reaction-diffusion systems with an entropic structure : singular perturbation and order reduction. Numerische Mathematik, 97(4), 667-698. doi:10.1007/s00211-003-0496-3Descombes, S., Dumont, T., Louvet, V., & Massot, M. (2007). On the local and global errors of splitting approximations of reaction–diffusion equations with high spatial gradients. International Journal of Computer Mathematics, 84(6), 749-765. doi:10.1080/00207160701458716McLachlan, R. I., & Quispel, G. R. W. (2002). Splitting methods. Acta Numerica, 11, 341-434. doi:10.1017/s0962492902000053Trotter, H. F. (1959). On the product of semi-groups of operators. Proceedings of the American Mathematical Society, 10(4), 545-545. doi:10.1090/s0002-9939-1959-0108732-6Strang, G. (1968). On the Construction and Comparison of Difference Schemes. SIAM Journal on Numerical Analysis, 5(3), 506-517. doi:10.1137/0705041Jahnke, T., & Lubich, C. (2000). Bit Numerical Mathematics, 40(4), 735-744. doi:10.1023/a:1022396519656Nevanlinna, O. (1989). Remarks on Picard-Lindelöf iteration. BIT, 29(2), 328-346. doi:10.1007/bf01952687Farago, I., & Geiser, J. (2007). Iterative operator-splitting methods for linear problems. International Journal of Computational Science and Engineering, 3(4), 255. doi:10.1504/ijcse.2007.018264DESCOMBES, S., DUARTE, M., DUMONT, T., LOUVET, V., & MASSOT, M. (2011). ADAPTIVE TIME SPLITTING METHOD FOR MULTI-SCALE EVOLUTIONARY PARTIAL DIFFERENTIAL EQUATIONS. Confluentes Mathematici, 03(03), 413-443. doi:10.1142/s1793744211000412Geiser, J. (2008). Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations. Journal of Computational and Applied Mathematics, 217(1), 227-242. doi:10.1016/j.cam.2007.06.028Dimov, I., Farago, I., Havasi, A., & Zlatev, Z. (2008). Different splitting techniques with application to air pollution models. International Journal of Environment and Pollution, 32(2), 174. doi:10.1504/ijep.2008.017102Karlsen, K. H., Lie, K.-A., Natvig, J. ., Nordhaug, H. ., & Dahle, H. . (2001). Operator Splitting Methods for Systems of Convection–Diffusion Equations: Nonlinear Error Mechanisms and Correction Strategies. Journal of Computational Physics, 173(2), 636-663. doi:10.1006/jcph.2001.6901Geiser, J. (2010). Iterative operator-splitting methods for nonlinear differential equations and applications. Numerical Methods for Partial Differential Equations, 27(5), 1026-1054. doi:10.1002/num.20568Geiser, J., & Wu, Y. H. (2015). Iterative solvers for the Maxwell–Stefan diffusion equations: Methods and applications in plasma and particle transport. Cogent Mathematics, 2(1), 1092913. doi:10.1080/23311835.2015.1092913Geiser, J., Hueso, J. L., & Martínez, E. (2017). New versions of iterative splitting methods for the momentum equation. Journal of Computational and Applied Mathematics, 309, 359-370. doi:10.1016/j.cam.2016.06.002Boudin, L., Grec, B., & Salvarani, F. (2012). A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations. Discrete & Continuous Dynamical Systems - B, 17(5), 1427-1440. doi:10.3934/dcdsb.2012.17.1427Duncan, J. B., & Toor, H. L. (1962). An experimental study of three component gas diffusion. AIChE Journal, 8(1), 38-41. doi:10.1002/aic.69008011

Heterogeneous-driven glutathione oxidation: defining the catalytic role of chalcopyrite nanoparticles

Transition-metal nanocatalysis represents a novel alternative currently experiencing flourishing progress to tackle the tumor microenvironment (TME) in cancer therapy. These nanomaterials aim at attacking tumor cells using the intrinsic selectivity of inorganic catalysts. In addition, special attention to tune and control the release of these transition metals is also required. Understanding the chemical reactions behind the catalytic action of the transition-metal nanocatalysts and preventing potential undesired side reactions caused by acute cytotoxicity of the released ionic species represent another important field of research. Specifically, copper-based oxides may suffer from acute leaching that potentially may induce toxicity not only to target cancer cells but also to nearby cells and tissues. In this work, we propose the synthesis of chalcopyrite (CuFeS2) nanostructures capable of triggering two key reactions for an effective chemodynamic therapy (CDT) in the heterogeneous phase: (i) glutathione (GSH) oxidation and (ii) oxidation of organic substrates using H2O2, with negligible leaching of metals under TME-like conditions. This represents an appealing alternative toward the development of safer copper–iron-based nanocatalytic materials with an active catalytic response without incurring leaching side phenomena

Ethylene epoxidation in microwave heated structured reactors

In the present work we show the microwave-induced heating of monolithic reactors containing a thin-layered catalyst that exhibits a strong and selective heating susceptibility under microwave irradiation. The combination of microwave radiation and structured reactors has been successfully applied for the intensification of the selective oxidation of ethylene to ethylene oxide (epoxidation) while operating at lower power consumptions and with higher energy efficiencies than in conventional heating conditions. The microwave radiation selectively heats the catalyst and the monolith walls while maintaining a relatively colder gas stream thereby creating a gas/solid temperature gradient of up to ~70 °C at a reaction temperature of 225 °C. Moreover, the influence of different parameters such as the distribution of the catalyst onto the structured monoliths or the temperature measurement techniques employed to determine the heating profiles (Optic Fibers and/or IR thermography) have been also thoroughly evaluated to justify the obtained catalytic results