Dynamics of multidimensional Césaro operators

[EN] We study the dynamics of the multi-dimensional Cesar degrees integral operator on L-P (I-n), for I the unit interval, 1 = 2, that is defined as C(f)(x(1),...,x(n)) = 1/x(1)x(2)...x(n) integral(x1)(0) ... integral(x1)(0) f(u(1),...,u(n))du(1)...du(n) for f is an element of L-p(I-n). This operator is already known to be bounded. As a consequence of the Eigenvalue Criterion, we show that it is hypercyclic as well. Moreover, we also prove that it is Devaney chaotic and frequently hypercyclic.The first author was supported by MEC, grant MTM201675963-P. The third author was supported by grant MTM2015-65825-P.Conejero, JA.; Mundayadan, A.; Seoane-Sepúlveda, JB. (2019). Dynamics of multidimensional Césaro operators. Bulletin of the Belgian Mathematical Society Simon Stevin. 26(1):11-20. http://hdl.handle.net/10251/159145S112026

Chaos for the Hyperbolic Bioheat Equation

The Hyperbolic Heat Transfer Equation describes heat processes in which extremely short periods of time or extreme temperature gradients are involved. It is already known that there are solutions of this equation which exhibit a chaotic behaviour, in the sense of Devaney, on certain spaces of analytic functions with certain growth control. We show that this chaotic behaviour still appears when we add a source term to this equation, i.e. in the Hyperbolic Bioheat Equation. These results can also be applied for the Wave Equation and for a higher order version of the Hyperbolic Bioheat Equation.The authors are supported in part by MEC and FEDER, Projects MTM2010-14909 and MTM2013-47093-P.Conejero, JA.; Ródenas Escribá, FDA.; Trujillo Guillen, M. (2015). Chaos for the Hyperbolic Bioheat Equation. Discrete and Continuous Dynamical Systems - Series A. 35(2):653-668. doi:10.3934/dcds.2015.35.653S65366835

Nonlinear resonance reflection from and transmission through a dense glassy system built up of oriented linear Frenkel chains: two-level models

A theoretical study of the resonance optical response of assemblies of oriented short (as compared to an optical wavelength) linear Frenkel chains is carried out using a two-level model. We show that both transmittivity and reflectivity of the film may behave in a bistable fashion and analyze how the effects found depend on the film thickness and on the inhomogeneous width of the exciton optical transition.Comment: 26 pages, 9 figure

Divisibility networks of the rational numbers in the unit interval

[EN] Divisibility networks of natural numbers present a scale-free distribution as many other process in real life due to human interventions. This was quite unexpected since it is hard to find patterns concerning anything related with prime numbers. However, it is by now unclear if this behavior can also be found in other networks of mathematical nature. Even more, it was yet unknown if such patterns are present in other divisibility networks. We study networks of rational numbers in the unit interval where the edges are defined via the divisibility relation. Since we are dealing with infinite sets, we need to define an increasing covering of subnetworks. This requires an order of the numbers different from the canonical one. Therefore, we propose the construction of four different orders of the rational numbers in the unit interval inspired in Cantor's diagonal argument. We motivate why these orders are chosen and we compare the topologies of the corresponding divisibility networks showing that all of them have a free-scale distribution. We also discuss which of the four networks should be more suitable for these analysesJAC was funded by MEC grant number MTM2016-75963-P. PASH acknowledges the support of MESCyT-RD, Casa Brugal, and Fundacion Proyecto Escuela Hoy Inc. for his PhD grants. MAGM acknowledges funding from the Spanish Ministry of Education and Vocational Training (MEFP) through the Beatriz Galindo program 2018 (BEAGAL18/00203) and Spanish Ministry MINECO FIDEUA PID2019-106901GB-I00/10.13039/501100011033.Solares-Hernández, PA.; Garcia March, MA.; Conejero, JA. (2020). Divisibility networks of the rational numbers in the unit interval. Symmetry (Basel). 12(11):1-12. https://doi.org/10.3390/sym12111879S112121

A bremsstrahlung gamma-ray source based on stable ionization injection of electrons into a laser wakefield accelerator

Laser wakefield acceleration permits the generation of ultra-short, high-brightness relativistic electron beams on a millimeter scale. While those features are of interest for many applications, the source remains constraint by the poor stability of the electron injection process. Here we present results on injection and acceleration of electrons in pure nitrogen and argon. We observe stable, continuous ionization-induced injection of electrons into the wakefield for laser powers exceeding a threshold of 7 TW. The beam charge scales approximately linear with the laser energy and is limited by beam loading. For 40 TW laser pulses we measure a maximum charge of almost 1 nC per shot, originating mostly from electrons of less than 10 MeV energy. The relatively low energy, the high charge and its stability make this source well-suited for applications such as non-destructive testing. Hence, we demonstrate the production of energetic radiation via bremsstrahlung conversion at 1 Hz repetition rate. In accordance with Geant4 Monte-Carlo simulations, we measure a gamma-ray source size of less than 100 microns for a 0.5 mm tantalum converter placed at 2 mm from the accelerator exit. Furthermore we present radiographs of image quality indicators

Smooth functions with uncountably many zeros

[EN] In this short note we show that there exist uncountably generated alge- bras every non-zero element of which is a smooth function having uncount- ably many zeros. This result complements some recent ones by Enflo et al. [7, 9].The authors would like to thank the anonymous referee, whose thorough analysis and insightful remarks improved the text. The authors were supported by CNPq Grant 401735/2013-3 (PVE - Linha 2), MTM2012-34341, MEC Project MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Referencia SP2012070. The third author is also supported by a FPU grant of MEC Project MTM2010-14909.Conejero, JA.; Muñoz-Fernández, GA.; Murillo Arcila, M.; Seoane Sepúlveda, JB. (2015). Smooth functions with uncountably many zeros. Bulletin of the Bengian Mathematical Society. 22:1-5. http://hdl.handle.net/10251/64844152

Monitoring dynamics of human adenovirus disassembly induced by mechanical fatigue

The standard pathway for virus infection of eukaryotic cells requires disassembly of the viral shell to facilitate release of the viral genome into the host cell. Here we use mechanical fatigue, well below rupture strength, to induce stepwise disruption of individual human adenovirus particles under physiological conditions, and simultaneously monitor disassembly in real time. Our data show the sequence of dismantling events in individual mature (infectious) and immature (noninfectious) virions, starting with consecutive release of vertex structures followed by capsid cracking and core exposure. Further, our experiments demonstrate that vertex resilience depends inextricably on maturation, and establish the relevance of penton vacancies as seeding loci for virus shell disruption. The mechanical fatigue disruption route recapitulates the adenovirus disassembly pathway in vivo, as well as the stability differences between mature and immature virionsWe acknowledge funding by grants from the Ministry of Science and Innovation of Spain, PIB2010US-00233, FIS2011-29493, Consolider CSD2010-00024 and CAM project and the Comunidad de Madrid No. S2009/MAT-1467 to P. J. P.; BFU2010-16382/BMC to C.S.M.; and FIS2011-16090-E to C.S.M. and P.J.P. S.J.F acknowledges funding from the National Institutes of Health, USA (GM037705 and AI1058172). A.J.P.-B. holds a Juan de la Cierva postdoctoral contract from the Ministry of Science and Innovation of Spain; A.O.-E. and R.M.-C. are recipients of predoctoral fellowships from the Ministry of Education and the Instituto de Salud Carlos III of Spain, respectivel

Automatic Classification of Winding Asymmetries in Wound Rotor Induction Motors based on Bicoherence and Fuzzy C-Means Algorithms of Stray Flux Signals

(c) 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.[EN] Wound rotor induction motors are used in a certain number of industrial applications due to their interesting advantages, such as the possibility of inserting external rheostats in series with the rotor winding to enhance the torque characteristics under starting and to decrease the high inrush currents. However, the more complex structure of the rotor winding, compared to cage induction motors, is a source for potential maintenance problems. In this regard, several anomalies can lead to the occurrence of asymmetries in the rotor winding that may yield terrible repercussions for the machine¿s integrity. Therefore, monitoring the levels of asymmetry in the rotor winding is of paramount importance to ensure the correct operation of the motor. This work proposes the use of Bicoherence of the stray flux signal, as an indicator to obtain an automatic classification of the rotor winding condition. For this, the Fuzzy C-Means machine learning algorithm is used, which starts with the Bicoherence calculation and generates the different clusters for grouping and classification, according to the level of winding asymmetry. In addition, an analysis regarding the influence of the flux sensor position on the automatic classification and the failure detection is carried out. The results are highly satisfactory and prove the potential of the method for its future incorporation in autonomous condition monitoring systems that can be satisfactorily applied to determine the health of these machines.This work was supported in part by Generalitat Valenciana, Conselleria de Innovacion, Universidades, Ciencia y Sociedad Digital, (project AICO/019/224) and in part by MEC under Project MTM2016-75963-P.Iglesias Martínez, ME.; Antonino-Daviu, JA.; Fernández De Córdoba, P.; Conejero, JA.; Dunai, L. (2021). Automatic Classification of Winding Asymmetries in Wound Rotor Induction Motors based on Bicoherence and Fuzzy C-Means Algorithms of Stray Flux Signals. IEEE Transactions on Industry Applications. 57(6):5876-5886. https://doi.org/10.1109/TIA.2021.3108413S5876588657

Distributionally chaotic families of operators on Fréchet spaces

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915