Approximate solutions and scaling transformations for quadratic solitons

We study quadratic solitons supported by two- and three-wave parametric interactions in chi-2 nonlinear media. Both planar and two-dimensional cases are considered. We obtain very accurate, 'almost exact', explicit analytical solutions, matching the actual bright soliton profiles, with the help of a specially-developed approach, based on analysis of the scaling properties. Additionally, we use these approximations to describe the linear tails of solitary waves which are related to the properties of the soliton bound states.Comment: 11 pages, 9 figures; submitted for publicatio

Analysis of the optimization of resources with Learning Analytics techniques

This paper presents an empirical study based on the learning environment through different data analysis tools. The study is applied to the subject of Theory of Machines and Materials Resistance of the Chemical Engineering degree at the Universitat Politècnica de València (Spain), with the aim of being able to understand and optimise with greater knowledge the way of learning taught, to know what is more difficult for the students and to create a more personalised learning environment. In order to achieve this, it is important to have as much information as possible about the use and usefulness of the resources provided to the students as a teacher. Knowing this data will allow us to provide more efficient resources and to change those that, through data analysis, are not being useful to students. The results of this research show how, through applications such as Learning Analytics, greater performance can be obtained in both teaching and learning

Instabilities of Higher-Order Parametric Solitons. Filamentation versus Coalescence

We investigate stability and dynamics of higher-order solitary waves in quadratic media, which have a central peak and one or more surrounding rings. We show existence of two qualitatively different behaviours. For positive phase mismatch the rings break up into filaments which move radially to initial ring. For sufficient negative mismatches rings are found to coalesce with central peak, forming a single oscillating filament.Comment: 5 pages, 7 figure

Solutions to the Optical Cascading Equations

Group theoretical methods are used to study the equations describing \chi^{(2)}:\chi^{(2)} cascading. The equations are shown not to be integrable by inverse scattering techniques. On the other hand, these equations do share some of the nice properties of soliton equations. Large families of explicit analytical solutions are obtained in terms of elliptic functions. In special cases, these periodic solutions reduce to localized ones, i.e., solitary waves. All previously known explicit solutions are recovered, and many additional ones are obtainedComment: 21 page

Quantitative Analysis Procedure for Building Materials in Historic Buildings by Applying Infrared Thermography

[EN] Historic buildings have a great cultural and architectural value. It is necessary to analyze their state of conservation, but sometimes it is difficult to perform laboratory tests without damaging this heritage. In the field of architecture, infrared thermography is usually used to provide descriptive information about the surface temperature of building materials. This current research presents a methodology widely applicable to historic buildings. As an example of application, the study is focused in the Seminary-School of Corpus Christi of Valencia (Spain), a very outstanding building from the 16th Century. This research presents an analytical study to be able to differentiate the temperature distribution of all pixels of a thermographic image. Thermal images are a matrix of data and their study helps us in decision-making based on objective data.Lerma Elvira, C.; Mas Tomas, MDLA.; Gil Benso, E.; Vercher Sanchis, JM.; Torner-Feltrer, MEM. (2018). Quantitative Analysis Procedure for Building Materials in Historic Buildings by Applying Infrared Thermography. Russian Journal of Nondestructive Testing. 54(8):601-609. https://doi.org/10.1134/S1061830918080065S601609548Avdelidis, N.P. and Moropoulou, A., Applications of infrared thermography for the investigation of historic structures, J. Cult. Heritage, 2004, no. 5, pp. 119–127. doi 10.1016/j.culher.2003.07.002Barreira, E. and Freitas, V., Evaluation of building materials using infrared thermography, Constr. Build. Mater., 2007, vol. 21, pp. 218–224. doi 10.1016/j.conbuildmat.2005.06.049Bauer, E., Pavón, E., Barreira, E., and Kraus, E., Analysis of building façade defects using infrared thermography: Laboratory studies, J. Build. Eng., 2016, no. 6, pp. 93–104. doi /doi 10.1016/j.jobe.2016.02.012Binda, L., Cardani, G., and Zanzi, L., Nondestructive testing evaluation of drying process in flooded full-scale masonry walls, J. Perform. Constr. Facil., 2010, pp. 473–483. doi 10.1061/(ASCE)CF.1943-5509.0000097Cañas, I., Martín, S., and González, I., Thermal-physical aspects of materials used for the construction of rural buildings in Soria (Spain), Construct. Build. Mater., 2005, vol. 19, pp. 197–211. doi 10.1016/j.conbuildmat. 2004.05.016Carlomagno, G.M., Maio, R., Fedi, M., Meola, C., Integration of infrared thermography and high-frequency electromagnetic methods in archaeological surveys, J. Geophys. Eng., 2011, vol. 8, pp. 93–105. doi 10.1088/1742-2132/8/3/S09Cerdeira, F., Vázquez, ME, Collado, J., and Granada, E., Applicability of infrared thermography to the study of the behavior of Stone panels as building envelopes, Energy Build., 2011, vol. 43, pp. 1845–1851. doi 10.1016/j.enbuild.2011.03.029EN 13187:1998. Thermal performance of buildings. Qualitative detection of thermal irregularities in building envelopes. Infrared method (ISO 6781:1983 modified).Galarza Tortajada, M., La tapia valenciana: una técnica constructiva poco conocida, Proc. First Natl. Congr. Construct. Hist., Madrid, 1996.Grinzato, E., Bison, P.G., and Marinetti, S., Monitoring of ancient buildings by the thermal method, J. Cult. Heritage, 2002, vol. 3, pp. 21–29. doi 10.1016/S1296-2074(02)01159-7Ibarra-Castanedo C., Sfarra, S., Ambrosini, D., Paoletti, D., Bendada, A, and Maldague, X., Diagnostics of panel paintings using holographic interferometry and pulsed thermography, Quant. Infrared Thermogr. J., 2010, vol. 7, no. 1. doi 10.3166/qirt.7.85-114Lagüela, S., Martínez, J., Armesto, J., and Arias, P., Energy efficiency studies through 3D laser scanning and thermographic technologies, Energy Build., 2011, vol. 43, pp. 1216–1221. doi 10.1016/j.enbuild.2010.12.031Lerma, C., Mas, Á., Gil, E., and Galiana, M., An analytical procedure for the study of the documented construction process of the Seminary-School of Corpus Christi in Valencia (Spain), Inf. Constr., 2014, vol. 66 (533), e007. doi 10.3989/ic.12.117Lerma, C., Mas, A., Gil, E., Vercher, J., and Penalver, M.J., Pathology of building materials in historic buildings. Relationship between laboratory testing and infrared thermography, Mater. Constr., 2014, vol. 64 (313), e009. doi 10.3989/mc.2013.06612Lerma, J.L., Cabrelles, M., and Portalés, C., Multitemporal thermal analysis to detect moisture on a building façade, Construct. Build. Mater., 2011, vol. 25, pp. 2190–2197. doi 10.1016/j.conbuildmat.2010.10.007Madruga, F.J., Ibarra-Castanedo, C., Conde, O., López-Higuera, J.M., and Maldague, X., Infrared thermography processing based on higher-order statistics, NDT&E Int., 2010, vol. 43, pp. 661–666. doi 10.1016/j.ndteint.2010.07.002Meola, C., Infrared thermography of masonry structures, Infrared Phys. Technol., 2007, vol. 49, no. 3, pp. 228–33. doi 10.1016/j.infraredPosta, J., Dolejs, J., Non-destructive assessment of timber elements with an emphasis on radiometry., Intern. J. Arch. Herit., 2015, vol. 9, no.6.Válek, J., Kruschwitz, S., Wöstmann, J., Kind, T., Valach, J., Köpp, C., and Lesák, J., Nondestructive investigation of wet building material: Multimethodological approach, J. of performance of Constructed Facilities, pp. 462–472. doi 10.1061/(ASCE)CF.1943-5509.000005

Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

We demonstrate that weak parametric interaction of a fundamental beam with its third harmonic field in Kerr media gives rise to a rich variety of families of non-fundamental (multi-humped) solitary waves. Making a comprehensive comparison between bifurcation phenomena for these families in bulk media and planar waveguides, we discover two novel types of soliton bifurcations and other interesting findings. The later includes (i) multi-humped solitary waves without even or odd symmetry and (ii) multi-humped solitary waves with large separation between their humps which, however, may not be viewed as bound states of several distinct one-humped solitons.Comment: 9 pages, 17 figures, submitted to Phys. Rev.

Parametric localized modes in quadratic nonlinear photonic structures

We analyze two-color spatially localized modes formed by parametrically coupled fundamental and second-harmonic fields excited at quadratic (or chi-2) nonlinear interfaces embedded into a linear layered structure --- a quasi-one-dimensional quadratic nonlinear photonic crystal. For a periodic lattice of nonlinear interfaces, we derive an effective discrete model for the amplitudes of the fundamental and second-harmonic waves at the interfaces (the so-called discrete chi-2 equations), and find, numerically and analytically, the spatially localized solutions --- discrete gap solitons. For a single nonlinear interface in a linear superlattice, we study the properties of two-color localized modes, and describe both similarities and differences with quadratic solitons in homogeneous media.Comment: 9 pages, 8 figure