Numerical resolution of Emden's equation using Adomian polynomials

Purpose: In this paper the authors aim to show the advantages of using the decomposition method introduced by Adomian to solve Emden's equation, a classical non‐linear equation that appears in the study of the thermal behaviour of a spherical cloud and of the gravitational potential of a polytropic fluid at hydrostatic equilibrium. Design/methodology/approach: In their work, the authors first review Emden's equation and its possible solutions using the Frobenius and power series methods; then, Adomian polynomials are introduced. Afterwards, Emden's equation is solved using Adomian's decomposition method and, finally, they conclude with a comparison of the solution given by Adomian's method with the solution obtained by the other methods, for certain cases where the exact solution is known. Findings: Solving Emden's equation for n in the interval [0, 5] is very interesting for several scientific applications, such as astronomy. However, the exact solution is known only for n=0, n=1 and n=5. The experiments show that Adomian's method achieves an approximate solution which overlaps with the exact solution when n=0, and that coincides with the Taylor expansion of the exact solutions for n=1 and n=5. As a result, the authors obtained quite satisfactory results from their proposal. Originality/value: The main classical methods for obtaining approximate solutions of Emden's equation have serious computational drawbacks. The authors make a new, efficient numerical implementation for solving this equation, constructing iteratively the Adomian polynomials, which leads to a solution of Emden's equation that extends the range of variation of parameter n compared to the solutions given by both the Frobenius and the power series methods.

A high-resolution binocular video-oculography system: assessment of pupillary light reflex and detection of an early incomplete blink and an upward eye movement

Background: The pupillary light reflex characterizes the direct and consensual response of the eye to the perceived brightness of a stimulus. It has been used as indicator of both neurological and optic nerve pathologies. As with other eye reflexes, this reflex constitutes an almost instantaneous movement and is linked to activation of the same midbrain area. The latency of the pupillary light reflex is around 200 ms, although the literature also indicates that the fastest eye reflexes last 20 ms. Therefore, a system with sufficiently high spatial and temporal resolutions is required for accurate assessment. In this study, we analyzed the pupillary light reflex to determine whether any small discrepancy exists between the direct and consensual responses, and to ascertain whether any other eye reflex occurs before the pupillary light reflex. Methods: We constructed a binocular video-oculography system two high-speed cameras that simultaneously focused on both eyes. This was then employed to assess the direct and consensual responses of each eye using our own algorithm based on Circular Hough Transform to detect and track the pupil. Time parameters describing the pupillary light reflex were obtained from the radius time-variation. Eight healthy subjects (4 women, 4 men, aged 24–45) participated in this experiment. Results: Our system, which has a resolution of 15 microns and 4 ms, obtained time parameters describing the pupillary light reflex that were similar to those reported in previous studies, with no significant differences between direct and consensual reflexes. Moreover, it revealed an incomplete reflex blink and an upward eye movement at around 100 ms that may correspond to Bell’s phenomenon. Conclusions: Direct and consensual pupillary responses do not any significant temporal differences. The system and method described here could prove useful for further assessment of pupillary and blink reflexes. The resolution obtained revealed the existence reported here of an early incomplete blink and an upward eye movement.

Gaia-ESO Survey: Analysis of pre-main sequence stellar spectra

Context. The Gaia-ESO Public Spectroscopic Survey is obtaining high-quality spectroscopy of some 100 000 Milky Way stars using the FLAMES spectrograph at the VLT, down to V = 19 mag, systematically covering all the main components of the Milky Way and providing the first homogeneous overview of the distributions of kinematics and chemical element abundances in the Galaxy. Observations of young open clusters, in particular, are giving new insights into their initial structure, kinematics, and their subsequent evolution. Aims. This paper describes the analysis of UVES and GIRAFFE spectra acquired in the fields of young clusters whose population includes pre-main sequence (PMS) stars. The analysis is applied to all stars in such fields, regardless of any prior information on membership, and provides fundamental stellar atmospheric parameters, elemental abundances, and PMS-specific parameters such as veiling, accretion, and chromospheric activity. Methods. When feasible, different methods were used to derive raw parameters (e.g. line equivalent widths) fundamental atmospheric parameters and derived parameters (e.g. abundances). To derive some of these parameters, we used methods that have been extensively used in the past and new ones developed in the context of the Gaia-ESO survey enterprise. The internal precision of these quantities was estimated by inter-comparing the results obtained by these different methods, while the accuracy was estimated by comparison with independent external data, such as effective temperature and surface gravity derived from angular diameter measurements, on a sample of benchmarks stars. A validation procedure based on these comparisons was applied to discard spurious or doubtful results and produce recommended parameters. Specific strategies were implemented to resolve problems of fast rotation, accretion signatures, chromospheric activity, and veiling. Results. The analysis carried out on spectra acquired in young cluster fields during the first 18 months of observations, up to June 2013, is presented in preparation of the first release of advanced data products. These include targets in the fields of the ρ Oph, Cha I, NGC 2264, γ Vel, and NGC 2547 clusters. Stellar parameters obtained with the higher resolution and larger wavelength coverage from UVES are reproduced with comparable accuracy and precision using the smaller wavelength range and lower resolution of the GIRAFFE setup adopted for young stars, which allows us to provide stellar parameters with confidence for the much larger GIRAFFE sample. Precisions are estimated to be ≈120 K rms in Teff, ≈0.3 dex rms in log g, and ≈0.15 dex rms in [Fe/H] for the UVES and GIRAFFE setups.

Development of multidisciplinary workshops between different subjects as an innovative teaching methodology for the acquisition of professional skills of the future architect

The implantation of the new Architecture Degree and the important normative changes in the building sector imply the need to use new teaching methodologies that enhance skills and competences in order to response to the increasing requirements demanded by society to the future architect. The aim of this paper is to present, analyze and discuss the development of multidisciplinary workshops as a new teaching methodology used in several Construction subjects of the Architecture Degree in the University of Alicante. Workshops conceived with the aim to synthesize and complement the technical knowledge acquired by the students during the Degree and to enhance the skills and competencies necessary for the professional practice. With that purpose, we decided to experiment on current subjects of the degree during this academic year, by applying the requirements defined in the future Architecture Degree in a practical way, through workshops between different subjects, superposing the technical knowledge with the resolution of constructive problems in the development of an architectural project. Developing these workshops between subjects we can dissolve the traditional boundaries between different areas of the Degree. This multidisciplinary workshop methodology allows the use of all the global knowledge acquired by students during their studies and at the same time, it enhances students’ ability to communicate and discuss their ideas and solutions in public. It also increases their capacity of self-criticism, and it foments their ability to undertake learning strategies and research in an autonomous way. The used methodology is based on the development of a practical work common to several subjects of different knowledge areas within the "Technology Block" of the future Architecture Degree. Thus, students work approaching the problem in a global way discussing simultaneously with teachers from different areas. By using these new workshops we stimulate an interactive class versus a traditional lecture. Work is evaluated continuously, valuing the participative pupil´s attitude, working in groups in class time, reaching weekly objectives and stimulating the individual responsibility and positive interdependence of the pupil inside the working group. The exercises are designed to improve students’ ability to transmit their ideas and solutions in public, knowing how to discuss and defend their technical resolutions to peers and teachers (Peer Reviewing), their capacity for self-criticism and their capacity to undertake strategies and autonomous learning processes at the same time they develop a personal research into new technologies, systems and materials. Students have shown their majority preference for this teaching methodology by the multidisciplinary workshops offered in the last years, with very satisfactory academic results. In conclusion, it can be verified nowadays the viability of the introduction of new contents and new teaching methodologies necessary for the acquisition of the skills in the future Architecture Degree, through workshops between several subjects that have had a great acceptance in students and positive contrasted academic results.