The local cyclicity problem : Melnikov method using Lyapunov constants

In 1991, Chicone and Jacobs showed the equivalence between the computation of the first-order Taylor developments of the Lyapunov constants and the developments of the first Melnikov function near a non-degenerate monodromic equilibrium point, in the study of limit cycles of small-amplitude bifurcating from a quadratic centre. We show that their proof is also valid for polynomial vector fields of any degree. This equivalence is used to provide a new lower bound for the local cyclicity of degree six polynomial vector fields, so M(6) ≥ 44. Moreover, we extend this equivalence to the piecewise polynomial class. Finally, we prove that Mcp(4) ≥ 43 and Mcp(5) ≥ 65

Shock absorbing reception surfaces for collecting fruit during the mechanical harvesting of citrus

Damage to fresh citrus caused by impact of fruits onto collecting surfaces has restricted the adoption of mechanical harvesting. Two different experiments were carried out: investigating free-falling citrus and investigating the shock absorbing capacity of various surfaces. In free-falling experiment damage to mandarin, orange and lemon was studied. Three collecting surfaces were studied: a concrete floor, an elevated canvas provided with a frame and wheels, and a concrete floor covered with a shock absorbing canvases. Three dropping heights were used. In the shock absorbing experiment, an electronic sphere and a triaxial accelerometer were used to measure the shock capacity of seven receiving surfaces: earth, earth covered with a shock absorbing canvas, earth covered with weeds, earth covered with a mulch and an elevated canvas provided with a frame and wheels. The elevated canvases had a higher shock absorbing capacity compared to the other surfaces (260 m s−2 maximum acceleration compared with 1753 m s−2 to 2772 m s−2). Weeds, mulch and the shock absorbing canvases showed significantly higher shock absorbing capacity than the bare earth. Also, the shock absorbing canvas covering the concrete floor reduce impact and fruit damage (1866 m s−2 maximum acceleration compared to 2477 m s−2). Citrus damage susceptibility during harvest depended on variety. Weeds, mulch and shock absorbing canvases were shown to reduce impact when they cover earth during the mechanical harvesting of citrus. Elevated canvases could be used as collection systems for the mechanical harvesting of fresh citrus.This study was funded by the Ministerio de Ciencia e Innovacion (research project RTA2009-00118-C02-02) and FEDER. The authors are most grateful to the following collaborators: Maria del Mar Lopez Quevedo, Montano Perez, Juan Jose Pena and Angel Perez.Ortiz Sánchez, MC.; Blasco, J.; Balasch Parisi, S.; Torregrosa Mira, A. (2011). Shock absorbing reception surfaces for collecting fruit during the mechanical harvesting of citrus. Biosystems Engineering. 110(1):2-9. https://doi.org/10.1016/j.biosystemseng.2011.05.006S29110

A sparse mesh for Compact Finite Difference Fourier solvers with radius-dependent spectral resolution in circular domains

This paper presents a new method for the resolution of elliptic and parabolic equations in circular domains. It can be trivially extended to cylindrical domains. The algorithm uses a mixed Fourier-Compact Finite Difference method. The main advantage of the method is achieved by a new concept of mesh. The topology of the new grid keeps constant the aspect ratio of the cells, avoiding the typical clustering for radial structured meshes at the center. The reduction of the number of nodes has as a consequence the reduction in memory consumption. In the case of fluid mechanics problems, this technique also increases the time step for a constant Courant number. Several examples are given in the paper which show the potential of the method. (C) 2014 Elsevier Ltd. All rights reservedThis work was supported by the Spanish Government in the frame of the Project "Metodos LES para la simulacion de chorros multifasicos", grant ENE2010-18542. We also are very grateful to one of the referees for his/her work.Torregrosa, AJ.; Hoyas, S.; Gil, A.; García Galache, JP. (2014). A sparse mesh for Compact Finite Difference Fourier solvers with radius-dependent spectral resolution in circular domains. Computers and Mathematics with Applications. 67(6):1309-1318. https://doi.org/10.1016/j.camwa.2014.01.020S1309131867

Multiplicity anomalies of an optimal fourth-order class of iterative methods for solving nonlinear equations

[EN] There is a few number of optimal fourth-order iterative methods for obtaining the multiple roots of nonlinear equations. But, in most of the earlier studies, scholars gave the flexibility in their proposed schemes only at the second step (not at the first step) in order to explore new schemes. Unlike what happens in existing methods, the main aim of this manuscript is to construct a new fourth-order optimal scheme which will give the flexibility to the researchers at both steps as well as faster convergence, smaller residual errors and asymptotic error constants. The construction of the proposed scheme is based on the mid-point formula and weight function approach. From the computational point of view, the stability of the resulting class of iterative methods is studied by means of the conjugacy maps and the analysis of strange fixed points. Their basins of attractions and parameter planes are also given to show their dynamical behavior around the multiple roots. Finally, we consider a real-life problem and a concrete variety of standard test functions for numerical experiments and relevant results are extensively treated to confirm the theoretical development.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and Generalitat Valenciana PROMETEO/2016/089.Behl, R.; Cordero Barbero, A.; Motsa, SS.; Torregrosa Sánchez, JR. (2018). Multiplicity anomalies of an optimal fourth-order class of iterative methods for solving nonlinear equations. Nonlinear Dynamics. 91(1):81-112. https://doi.org/10.1007/s11071-017-3858-6S81112911Behl, R., Cordero, A., Motsa, S.S., Torregrosa, J.R., Kanwar, V.: An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algorithms 71(4), 775–796 (2016)Blanchard, P.: Complex analytic dynamics on the Riemann sphere. Bull. Am. Math. Soc. 11(1), 85–141 (1984)Chicharro, F., Cordero, A., Torregrosa, J.R.: Drawing dynamical and parameter planes of iterative families and methods. Sci. World J. 2013(2013), 1–11 (2013)Devaney, R.L.: The Mandelbrot Set, the Farey Tree and the Fibonacci sequence. Am. Math. Mon. 106(4), 289–302 (1999)Dong, C.: A family of multipoint iterative functions for finding multiple roots of equations. Int. J. Comput. Math. 21, 363–367 (1987)Hueso, J.L., Martínez, E., Teruel, C.: Determination of multiple roots of nonlinear equations and applications. J. Math. Chem. 53, 880–892 (2015)Kung, H.T., Traub, J.F.: Optimal order of one-point and multipoint iteration. J. Assoc. Comput. Mach. 21, 643–651 (1974)Li, S.G., Cheng, L.Z., Neta, B.: Some fourth-order nonlinear solvers with closed formulae for multiple roots. Comput. Math. Appl. 59, 126–135 (2010)Li, S., Liao, X., Cheng, L.: A new fourth-order iterative method for finding multiple roots of nonlinear equations. Appl. Math. Comput. 215, 1288–1292 (2009)Petković, M.S., Neta, B., Petković, L.D., Dz̆unić, J.: Multipoint Methods for Solving Nonlinear Equations. Academic Press, New York (2013)Sbibih, D., Serghini, A., Tijini, A., Zidna, A.: A general family of third order method for finding multiple roots. AMC 233, 338–350 (2014)Schröder, E.: Über unendlichviele Algorithm zur Auffosung der Gleichungen. Math. Ann. 2, 317–365 (1870)Sharifi, M., Babajee, D.K.R., Soleymani, F.: Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012)Soleymani, F., Babajee, D.K.R.: Computing multiple zeros using a class of quartically convergent methods. Alex. Eng. J. 52, 531–541 (2013)Soleymani, F., Babajee, D.K.R., Lofti, T.: On a numerical technique forfinding multiple zeros and its dynamic. J. Egypt. Math. Soc. 21, 346–353 (2013)Traub, J.F.: Iterative Methods for the Solution of Equations. Prentice-Hall, Englewood Cliffs (1964)Zhou, X., Chen, X., Song, Y.: Families of third and fourth order methods for multiple roots of nonlinear equations. Appl. Math. Comput. 219, 6030–6038 (2013)Zhou, X., Chen, X., Song, Y.: Constructing higher-order methods for obtaining the muliplte roots of nonlinear equations. J. Comput. Math. Appl. 235, 4199–4206 (2011

Design and multidimensional extension of iterative methods for solving nonlinear problems

[EN] In this paper, a three-step iterative method with sixth-order local convergence for approximating the solution of a nonlinear system is presented. From Ostrowski¿s scheme adding one step of Newton with ¿frozen¿ derivative and by using a divided difference operator we construct an iterative scheme of order six for solving nonlinear systems. The computational efficiency of the new method is compared with some known ones, obtaining good conclusions. Numerical comparisons are made with other existing methods, on standard nonlinear systems and the classical 1D-Bratu problem by transforming it in a nonlinear system by using finite differences. From this numerical examples, we confirm the theoretical results and show the performance of the presented scheme.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C2-2-P and FONDOCYT 2014-1C1-088 Republica Dominicana.Artidiello, S.; Cordero Barbero, A.; Torregrosa Sánchez, JR.; Vassileva, MP. (2017). Design and multidimensional extension of iterative methods for solving nonlinear problems. Applied Mathematics and Computation. 293:194-203. https://doi.org/10.1016/j.amc.2016.08.034S19420329

Bifurcation Diversity in an Annular Pool Heated from Below: Prandtl and Biot Numbers Effects

In this article the instabilities appearing in a liquid layer are studied numerically by means of the linear stability method. The fluid is confined in an annular pool and is heated from below with a linear decreasing temperature profile from the inner to the outer wall. The top surface is open to the atmosphere and both lateral walls are adiabatic. Using the Rayleigh number as the only control parameter, many kind of bifurcations appear at moderately low Prandtl numbers and depending on the Biot number. Several regions on the Prandtl-Biot plane are identified, their boundaries being formed from competing solutions at codimension-two bifurcation points.The code developed for this article was finished during a visit of S. Hoyas to the Lehrstuhl fur Stromungsmechanik of the University of Erlangen-Nurnberg, funded by the Government of Valencia and the Universitat Politecnica de Valencia. S. Hoyas would like to thank to Prof. Delgado and Dr. Ausmeier for their support and kindness. Last, but not least, S. Hoyas is and always will be, in debt with his PhD advisors, Prof. Herrero, Prof. Mancho and Prof. Pardo.Torregrosa, AJ.; Hoyas, S.; Pérez Quiles, MJ.; Mompó Laborda, JM. (2013). Bifurcation Diversity in an Annular Pool Heated from Below: Prandtl and Biot Numbers Effects. Communications in Computational Physics. 13(2):428-441. doi:10.4208/cicp.090611.170212aS428441132Shi, W., Ermakov, M. K., Li, Y.-R., Peng, L., & Imaishi, N. (2009). Influence of Buoyancy Force on Thermocapillary Convection Instability in the Differentially Heated Annular Pools of Silicon Melt. Microgravity Science and Technology, 21(S1), 289-297. doi:10.1007/s12217-009-9118-8SCHWABE, D., ZEBIB, A., & SIM, B.-C. (2003). Oscillatory thermocapillary convection in open cylindrical annuli. Part 1. Experiments under microgravity. Journal of Fluid Mechanics, 491, 239-258. doi:10.1017/s002211200300541xPelacho, M. A., & Burguete, J. (1999). Temperature oscillations of hydrothermal waves in thermocapillary-buoyancy convection. Physical Review E, 59(1), 835-840. doi:10.1103/physreve.59.835Mercier, J. F., & Normand, C. (1996). Buoyant‐thermocapillary instabilities of differentially heated liquid layers. Physics of Fluids, 8(6), 1433-1445. doi:10.1063/1.868920Herrero, H., & Mancho, A. M. (1998). Influence of aspect ratio in convection due to nonuniform heating. Physical Review E, 57(6), 7336-7339. doi:10.1103/physreve.57.7336Shi, W., Liu, X., Li, G., Li, Y.-R., Peng, L., Ermakov, M. K., & Imaishi, N. (2010). Thermocapillary Convection Instability in Shallow Annular Pools by Linear Stability Analysis. Journal of Superconductivity and Novel Magnetism, 23(6), 1185-1188. doi:10.1007/s10948-010-0661-8Daviaud, F., & Vince, J. M. (1993). Traveling waves in a fluid layer subjected to a horizontal temperature gradient. Physical Review E, 48(6), 4432-4436. doi:10.1103/physreve.48.4432Canuto, C., Hussaini, M. Y., Quarteroni, A., & Zang, T. A. (1988). Spectral Methods in Fluid Dynamics. doi:10.1007/978-3-642-84108-8Burguete, J., Mukolobwiez, N., Daviaud, F., Garnier, N., & Chiffaudel, A. (2001). Buoyant-thermocapillary instabilities in extended liquid layers subjected to a horizontal temperature gradient. Physics of Fluids, 13(10), 2773-2787. doi:10.1063/1.1398536Mancho, A. M., & Herrero, H. (2000). Instabilities in a laterally heated liquid layer. Physics of Fluids, 12(5), 1044-1051. doi:10.1063/1.870359Smith, M. K., & Davis, S. H. (1983). Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. Journal of Fluid Mechanics, 132, 119-144. doi:10.1017/s0022112083001512Hoyas, S., Mancho, A. M., Herrero, H., Garnier, N., & Chiffaudel, A. (2005). Bénard–Marangoni convection in a differentially heated cylindrical cavity. Physics of Fluids, 17(5), 054104. doi:10.1063/1.1876892Peng, L., Li, Y.-R., Shi, W.-Y., & Imaishi, N. (2007). Three-dimensional thermocapillary–buoyancy flow of silicone oil in a differentially heated annular pool. International Journal of Heat and Mass Transfer, 50(5-6), 872-880. doi:10.1016/j.ijheatmasstransfer.2006.08.015Herrero, H., Hoyas, S., Donoso, A., Mancho, A. M., Chacón, J. M., Portugués, R. F., & Yeste, B. (2003). Journal of Scientific Computing, 18(3), 315-328. doi:10.1023/a:1022678124929Hoyas, S., Herrero, H., & Mancho, A. M. (2002). Thermal convection in a cylindrical annulus heated laterally. Journal of Physics A: Mathematical and General, 35(18), 4067-4083. doi:10.1088/0305-4470/35/18/306Hoyas, S., Herrero, H., & Mancho, A. M. (2002). Bifurcation diversity of dynamic thermocapillary liquid layers. Physical Review E, 66(5). doi:10.1103/physreve.66.057301Ganier N. , PhD thesis, http://nicolasgarnier.free.fr/these-garnier.pdf, 2002.RILEY, R. J., & NEITZEL, G. P. (1998). Instability of thermocapillary–buoyancy convection in shallow layers. Part 1. Characterization of steady and oscillatory instabilities. Journal of Fluid Mechanics, 359, 143-164. doi:10.1017/s0022112097008343Mancho, A., Herrero, H., & Burguete, J. (1997). Primary instabilities in convective cells due to nonuniform heating. Physical Review E, 56(3), 2916-2923. doi:10.1103/physreve.56.2916Ezersky, A. B., Garcimartín, A., Burguete, J., Mancini, H. L., & Pérez-García, C. (1993). Hydrothermal waves in Marangoni convection in a cylindrical container. Physical Review E, 47(2), 1126-1131. doi:10.1103/physreve.47.1126Pardo, R., Herrero, H., & Hoyas, S. (2011). Theoretical study of a Bénard–Marangoni problem. Journal of Mathematical Analysis and Applications, 376(1), 231-246. doi:10.1016/j.jmaa.2010.10.06

Assessment of acoustic reciprocity and conservativeness in exhaust aftertreatment systems

[EN] Tightening emission standards limiting gas and aerosol emissions from internal combustion engines have led to the extensive use of exhaust aftertreatment systems (EATS) with different chemical functions as a solution to meet standards requirements. Incidentally, the placement of aftertreatment monolithic devices into the exhaust line also plays a key role on the exhaust noise emission. Their presence disturbs the pattern of the pressure waves and sets the boundary conditions for the silencer design. The impact of the EATS on wave transmission can be analyzed by means of the transmission or scattering matrix. The present work discusses the implications of acoustic reciprocity and conservativeness on the definition of the scattering matrix elements. The fulfillment of these properties in real operating conditions was evaluated against a set of experimental data obtained for several exhaust aftertreatment monolithic bricks in an impulse test rig. The influence of different excitation amplitudes and superimposed mean flows was also considered. Once it was shown that the devices are reciprocal, the need to account for dissipation phenomena was evidenced. Finally, the application of reciprocity and conservativeness together with dissipation provided simple expressions allowing to predict the response of the EATS in the inverse direction, i.e. from outlet to inlet, from the transmission and reflection properties obtained in the direct direction. Thus, the proposed procedure becomes useful to reduce both the required number of tests and the gas dynamics modelling work in methodologies driven to assess the acoustic response of EATS based on the use of experimental and computational tools. (C) 2018 Elsevier Ltd. All rights reserved.This research has been partially supported by FEDER and the Government of Spain through project TRA2016-79185-R. Additionally, the Ph.D. student Enrique José Sanchis has been funded by a grant from Universitat Politècnica de València with reference FPI-2016-S2-1355.Torregrosa, AJ.; Piqueras, P.; Sanchis-Pacheco, EJ.; Guilain, S.; Dubarry, M. (2018). Assessment of acoustic reciprocity and conservativeness in exhaust aftertreatment systems. Journal of Sound and Vibration. 436:46-61. https://doi.org/10.1016/j.jsv.2018.08.032S466143

Gender and grade level differences in self-concept dimensions: study with a Spanish adolescent sample

Este estudio analizó las diferencias de género y curso y el papel predictivo de estas variables en las dimensiones del autoconcepto medidas por el SDQ-II. El cuestionario fue administrado a 2.022 estudiantes de 1º a 4º de ESO. Los resultados revelaron que los chicos puntuaron significativamente más alto en las dimensiones Habilidades Físicas, Apariencia Física, Estabilidad Emocional y Matemáticas, mientras las chicas presentaron puntuaciones más altas en Relaciones con el Mismo Sexo, Relaciones con los Padres, Sinceridad-Veracidad y Verbal, no encontrándose diferencias estadísticamente significativas en la puntuación total del SDQ-II. Además, no se hallaron diferencias de curso estadísticamente significativas en Habilidades Físicas, Relaciones con el Mismo Sexo, Estabilidad Emocional, Matemáticas, Autoestima y Sinceridad-Veracidad, existiendo variaciones en el resto de escalas así como en la puntuación total. Los análisis de regresión logística revelaron que el género y el curso fueron predictores significativos del autoconcepto, aunque los resultados variaron para cada dimensión.This study analyzed gender and grade differences and the predictive role of these variables in the self-concept domains measured by the SDQ-II. The questionnaire was administered to 2.022 secondary school students from Grades 7 to 10. Results revealed that boys scored significantly higher in Physical Ability, Physical Appearance, Emotional Stability and Maths, whereas girls showed higher scores in Same Sex Relations, Parents Relations, Honesty-Trustworthiness and Verbal. No statistically significant differences were found in the total score. Likewise, statistically significant differences were not found in grade level regarding Physical Abilities, Same Sex Relations, Emotional Stability, Maths, General Self and Honesty-Trustworthiness. Statistically significant differences were reported in the remaining domains and in the total score. Logistic regression analyses revealed that gender and grade were significant predictors of self-concept, although results varied for each dimension

Large-scale production of somatic embryos as a source of hypocotyl explants for Vitis vinifera micrografting

To the standard methods currently used to make grapevine virus-free, apex micrografting on hypocotyls of somatic embryos is proposed as an alternative procedure. The study defines optimal conditions to produce hypocotyl fragments suitable for micrografting. Interruption of the process by storage of tissues or embryos at low temperature (+ 4 °C) was assessed at different stages and for durations up to 6 months. Best procedure to produce somatic embryos were: long-term maintenance of embryogenic cultures on C1 medium (5 μM 2.4-D + 1 μM BAP, solidified with 4 g·l-1 agar and 4 g·l-1 Phytagel) ; differentiation of embryogenic callus for 2 months on C2 medium (5 μM NOA + 1 μM BAP, gelling agents same as above) ; transfer of single embryos on plant growth regulator-free medium for 2-3 weeks for germination. At different steps of the process, embryogenic tissues or differentiated embryos can be stored for up to 180 d for some cultivars. Micrografting assays were performed with various types of embryo and with apices from several V. vinifera cultivars. White to slightly coloured hypocotyls, excised from embryos germinated in darkness, gave best results for micrografting, while hypocotyl shape had little influence. For all genotypes tested the success rate ranged from 18 to 30 %.

Frecuencia del consumo de drogas legales: Diferencias de edad en la adolescencia

El consumo de drogas es especialmente relevante por sus efectos negativos sobre la salud psicofísica y el funcionamiento social de los jóvenes. El objetivo de este estudio fue analizar las diferencias de edad respecto a las frecuencias de consumo de alcohol y tabaco en una muestra de 354 escolares (50.85% varones) de 12 a 18 años (M = 14.66; DT = 1.08) que cumplimentaron el Questionnarie about Consume of Alcohol and Tobacco (TNT). Los resultados muestran que el 82.4% de los adolescentes ha consumido bebidas alcohólicas en alguna ocasión y el 25.6% es consumidor actualmente. Respecto al consumo de tabaco, el 40.4% de estudiantes afirma haber fumado en alguna ocasión, siendo consumidores actuales el 8.2%. Asimismo, se hallaron diferencias estadísticamente significativas entre la adolescencia temprana y tardía, observándose un aumento sustancial del consumo actual de ambas sustancias con la edad. Estos resultados resaltan la importancia de la variable edad a la hora de planificar medidas preventivas y de promoción de la salud en población adolescente