Bending Instabilities in Magnetized Accretion Discs

We study the global bending modes of a thin annular disc subject to both an internally generated magnetic field and a magnetic field due to a dipole embedded in the central star with axis aligned with the disc rotation axis. When there is a significant inner region of the disc corotating with the star, we find spectra of unstable bending modes. These may lead to elevation of the disc above the original symmetry plane facilitating accretion along the magnetospheric field lines. The resulting non-axisymmetric disc configuration may result in the creation of hot spots on the stellar surface and the periodic photometric variations observed in many classical T Tauri stars (CTTS). Time-dependent behaviour may occur including the shadowing of the central source in magnetic accretors even when the dipole and rotation axes are aligned.Comment: Accepted by MNRAS. 18 pages, 11 figures. LaTeX2e in the MN style. PostScript and HTML files are also available from http://www-star.qmw.ac.uk/~va/ or by e-mail: [email protected]

Plant-based Protein Food Products: Perceptions from the Greek Food Industry

The food industry is under pressure to improve food production and reduce its impact on the environment. Furthermore, consumers today are increasingly shifting to more sustainable diets. In this context, plant-based protein sources appear as a promising solution. This study investigates the perceptions of company representatives operating in Greece who produce or intend to produce, food products containing plant-based proteins. Based on 360 responses, this quantitative analysis a) identifies the main drivers and barriers for consumer acceptance of these products, b) ascertains the most popular choice (word and phrase) on their labels, and c) explores variations in key marketing factors such as organoleptic characteristics, price, and promotion of plant protein-based products versus those with animal protein sources. According to the findings, “human health” is the prevailing incentive to shift to the consumption of plant-based protein food products. Additionally, “reluctance” is the predominant barrier for consumers to change their eating habits. Regarding the use of words and phrases on labels, the word “plant-protein” and the phrase “high in vegetable protein” were found to be the most popular. Furthermore, there is an agreement that both the organoleptic characteristics and the promotional strategies of plant-based protein products and animal-based protein products, are or should be similar. Interestingly, the majority of respondents noted that the price of plant protein products is or will be higher compared to animal protein products. This study provides meaningful insights into the food and beverage industry and companies that either have or will have products with plant-based sources of protein. Keywords: alternative proteins, alternative products, plant-based proteins, plant-based substitutes, food industry, business perception

«Διδακτική – Μαθησιακή Ακολουθία: Διδακτική προσέγγιση για τους συγκλίνοντες φακούς στην Πρωτοβάθμια Εκπαίδευση»

Σκοπός της παρούσας έρευνας ήταν ο σχεδιασμός, η ανάπτυξη, η εφαρμογή και η αξιολόγηση μίας Διδακτικής – Μαθησιακής Ακολουθίας (ΔΜΑ), για τη σύγκλιση των φωτεινών ακτινών μίας αυτόφωτης πηγής, όταν αυτές προσπίπτουν σε έναν συγκλίνον φακό, σε παιδιά Ε’ τάξης του Δημοτικού Σχολείου (10-11 ετών). Απώτερος στόχος ήταν η καταγραφή των μαθησιακών μονοπατιών των μαθητών, κατά την οικοδόμηση της επιστημονικά αποδεκτής εξήγησης του εν λόγω φαινομένου. Πιο συγκεκριμένα, το βασικό ερώτημα που επιδιώχθηκε να απαντηθεί ήταν το εξής: «Μπορούν μαθητές Ε’ τάξης του Δημοτικού Σχολείου να οικοδομήσουν στοιχεία του επιστημονικά αποδεκτού μοντέλου για τη σύγκλιση φωτεινών ακτινών που ξεκινούν από ένα αυτόφωτο αντικείμενο, όταν αυτές συναντήσουν έναν συγκλίνοντα φακό;» Συμμετέχοντες στην, παρούσα, έρευνα ήταν 4 μαθητές (4 αγόρια) Ε’ Δημοτικού σχολείου, χωρισμένοι σε δύο δυάδες. Όλοι οι μαθητές φοιτούσαν σε δημόσια σχολεία του δήμου Αχαρνών. Η παρακάτω έρευνα αποτελεί συνέχεια μιας ΔΜΑ η οποία ξεκίνησε με την έρευνα των Δημητράκου & Κοτταρά (2021), προκειμένου να μελετηθούν τα μονοπάτια μάθησης (learning pathways) των μαθητών πρωτοβάθμιας εκπαίδευσης για την διαπραγμάτευση φαινομένων σχετικά με τους συγκλίνοντες φακούς. Η έρευνα πραγματοποιήθηκε με τη μέθοδο του Διδακτικού Πειράματος (ΔΠ), όπως αυτή προτείνεται από τους Komorek & Duit (2004). Η μέθοδος αυτή συνδυάζει στοιχεία κλασικής κλινικής συνέντευξης και τυπικής διδασκαλίας. Κατά την εφαρμογή ενός ΔΠ δίνεται η δυνατότητα στον ερευνητή να λειτουργήσει σε δύο επίπεδα, καθώς μπορεί είναι συνεντευκτής αλλά και διδάσκων, αναλόγως την τροπή που παίρνει κάθε φορά η διαδικασία συλλογής των δεδομένων. Για τις ανάγκες της παρούσας έρευνας σχεδιάστηκαν δύο Διδακτικά Πειράματα. Πριν την πραγματοποίηση του (2ου) Διδακτικού Πειράματος σχετικά με τους συγκλίνοντες φακούς κρίθηκε απαραίτητο να προηγηθεί ένα Διδακτικό Πείραμα για τα χαρακτηριστικά των διαφανών και αδιαφανών σωμάτων. Η παραπάνω απόφαση λήφθηκε αφού, σύμφωνα με σχετική βιβλιογραφία, ορισμένοι μαθητές δυσκολεύονται να αντιληφθούν το φως ως μία οντότητα που ταξιδεύει στον χώρο και έχουν δυσκολία να ερμηνεύσουν λεκτικά την διαφορά μεταξύ διαφανών και αδιαφανών αντικειμένων (Christidou & Hatzinikita, 2013, Δημητράκου & Κοτταρά, 2021). Τα δεδομένα της έρευνας προήλθαν από την ανάλυση των βιντεοσκοπημένων Διδακτικών Πειραμάτων. Για την ανάλυση αυτή χρησιμοποιήθηκαν ποιοτικές μεθόδους ανάλυσης περιεχομένου (Erickson, 1998). Αναφορικά με την διάδοση του φωτός σε διαφανή και αδιαφανή σώματα (1ο διδακτικό πείραμα), πριν την παρέμβαση οι μαθητές έδειχναν διχασμένοι αφού οι μισοί μαθητές ισχυρίστηκαν ότι οι φωτεινές ακτίνες θα σταματήσουν την πορεία τους στο αδιαφανές σώμα, ενώ οι άλλοι μισοί υπέθεσαν πως οι φωτεινές ακτίνες της αυτόφωτης πηγής θα το διαπεράσουν. Ταυτόχρονα, η πλειοψηφία των μαθητών θεωρούσε, ότι το φως μπορεί να διαπεράσει το διαφανές σώμα. Μετά την διεξαγωγή του Διδακτικού Πειράματος, όλοι οι μαθητές κατάφεραν να φτάσουν στην επιστημονικά αποδεκτή άποψη ότι το φως διαπερνά μέσα από διαφανή σώματα και όχι μέσα από αδιαφανή. Όταν ζητήθηκε από τους μαθητές να προβλέψουν ποια πορεία θα ακολουθήσουν οι φωτεινές ακτίνες που ξεκινούν από μία αυτόφωτη πηγή και στη συνέχεια προσπίπτουν σε έναν συγκλίνοντα φακό (2ο διδακτικό πείραμα), τρεις από τους τέσσερις μαθητές ισχυρίστηκαν πως το φως θα ταξιδέψει ευθύγραμμα μέσα από το βάζο και θα χτυπήσει στον τοίχο στην απέναντι πλευρά, ενώ ο τελευταίος μαθητής υπέθεσε πως οι ακτίνες θα διασκορπιστούν προς όλες τις κατευθύνσεις, ο οποίος διατήρησε την ίδια άποψη ακόμη και μετά το πέρας της παρούσας έρευνας. Μετά την περάτωση του 2ου Διδακτικού Πειράματος, οι μαθητές δεν κατάφεραν να φτάσουν στο επιστημονικά αποδεκτό συμπέρασμα, δηλαδή στην σύγκλιση των ακτινών, αντίθετα διαμορφώθηκαν οι παρακάτω απόψεις: Α) οι φωτεινές ακτίνες ξεκινούν από τη φωτεινή πηγή, διαδίδονται ευθύγραμμα μέχρι τον συγκλίνοντα φακό και συνεχίζουν σε απόκλιση δημιουργώντας ένα V. Β) οι ακτίνες μετά τον συγκλίνοντα φακό θα ταξιδέψουν προς όλες τις κατευθύνσεις. Σημαντικό εμπόδιο προς την πορεία τους για το επιθυμητό συμπέρασμα αποτέλεσε η εστίαση της προσοχής τους, κατά την διεξαγωγή των σχετικών πειραματικών διατάξεων, στα όρια των σκιάς που δημιουργούνταν στο «σκηνικό» των πειραμάτων, τα οποία ταυτίστηκαν από τη μεριά των μαθητών με τα όρια των φωτεινών δεσμών που συνεχίζουν την πορεία τους μετά τον συγκλίνοντα φακό. Στο πλαίσιο αυτό αναδείχθηκαν σημαντικά ευρήματα τα οποία μπορούν να αξιοποιηθούν για τον εμπλουτισμό της ΔΜΑ σε μία πιθανή μελλοντική εφαρμογή της.The purpose of this research was the design, development, implementation and evaluation of a Teaching-Learning Sequence (TLS), for the convergent of the light rays that come from a self-luminous source, when they come across a converging lens, to students attending the 5th grade of elementary school (10-11 years old). Ultimate goal was the record of the students’ learning pathways, during the building of the scientifically accepted view on the matter at hand. More specifically, the main question that was attempted to be answered was the following: «Can 5th grade students understand the scientifically accepted data needed for the convergence of rays, when they go through a Convergent Lenses». In this particular research, participated 4 students (4 boys) in the 5th grade of elementary school, partied in two pairs. All students were studying in public schools in Acharnai. The following research is part of a TLS which started from the research of Δημητράκου & Κοτταρά (2021), in order to study the learning pathways of students in primary education to discuss phenomena related to converging lenses. The research was carried out using the Teaching Experiment (TE) method as recommended by Komorek & Duit (2004). This method combines elements of classic clinical interviewing and formal teaching. During the application of a TE, the researcher is given the possibility to operate on two levels, as he can be an interviewer as well as a teacher, depending on the turn that the data collection process takes each time. For the needs of this particular research, two teaching experiments were designed. Before carrying out the (2nd) Teaching Experiment on converging lenses it was deemed necessary to precede a Teaching Experiment on the characteristics of transparent and non-transparent bodies. The above decision was made since, according to relevant literature, some students have difficulty perceiving light as an entity that travels through space and have difficulty verbally interpreting the difference between transparent and non-transparent objects (Christidou & Hatzinikita, 2013, Δημητράκου & Κοτταρά, 2021). The research data came from the analysis of videotaped Teaching Experiments. Qualitative methods of content analysis were used for this analysis (Erickson, 1998). Regarding the propagation of light in transparent and non-transparent bodies (1st teaching experiment), before the intervention the students seemed divided since half of the students claimed that the light rays would stop their course in the non-transparent body, while the other half assumed that the light rays of the self-luminous source would penetrate it. At the same time, the majority of students believed that light can penetrate the transparent body. After conducting the Teaching Experiment, all students managed to reach the scientifically accepted view that light penetrates through transparent bodies and not through opaque ones. When the students were asked to predict the path of light rays that start from a self-illuminating source and then hit a converging lens (2nd teaching experiment), three of the four students claimed that the light would travel straight through the jar and hit the wall on the opposite side, while the last student assumed that the rays would be scattered in all directions, who maintained the same opinion even after the end of the present research. After the completion of the 2nd Teaching Experiment, the students did not manage to reach the scientifically acceptable conclusion, that is the convergence of the rays, instead the following opinions were formed: A) light rays start from the light source, propagate in a straight line to the converging lens and continue diverging creating a V. B) the rays after the converging lens will travel in all directions. An important obstacle to their progress towards the desired conclusion was the focus of their attention, during the conduct of the relevant experimental arrangements, on the boundaries of the shadows that were created in the "stage" of the experiments, which were identified by the students with the boundaries of the light beams that continue their path after the converging lens. In this context, important findings emerged, which can be used to enrich the TLS in a possible future application

An investigation of magnetic field distortions in accretion discs around neutron stars. I. Analysis of the poloidal field component

We report results from calculations investigating stationary magnetic field configurations in accretion discs around magnetised neutron stars. Our strategy is to start with a very simple model and then progressively improve it providing complementary insight into results obtained with large numerical simulations. In our first model, presented here, we work in the kinematic approximation and consider the stellar magnetic field as being a dipole aligned with the stellar rotation axis and perpendicular to the disc plane, while the flow in the disc is taken to be steady and axisymmetric. The behaviour in the radial direction is then independent of that in the azimuthal direction. We investigate the distortion of the field caused by interaction with the disc matter, solving the induction equation numerically in full 2D. The influence of turbulent diffusivity and fluid velocity on the poloidal field configuration is analysed, including discussion of outflows from the top and bottom of the disc. We find that the distortions increase with increasing magnetic Reynolds number R_m (calculated using the radial velocity). However, a single global parameter does not give an adequate description in different parts of the disc and we use instead a `magnetic distortion function' D_m(r,\theta) (a magnetic Reynolds number defined locally). Where D_m<<1 (near to the inner edge of the disc) there is little distortion, but where D_m>1 (most of the rest of the disc), there is considerable distortion and the field becomes weaker than the dipole would have been. Between these two regions, there is a transition zone where the field is amplified and can have a local minimum and maximum. The location of this zone depends sensitively on the diffusivity. The results depend very little on the boundary conditions at the top of the disc.Comment: Published in A&A; 10 pages and 8 figures; ver. 4: compactification of content

Warping modes in discs around accreting neutron stars

The origin and stability of a thin sheet of plasma in the magnetosphere of an accreting neutron star is investigated. First the radial extension of such a magnetospheric disc is explored. Then a mechanism for magnetospheric accretion is proposed, reconsidering the bending wave explored by Agapitou, Papaloizou & Terquem (1997), that was found to be stable in ideal MHD. We show that this warping becomes unstable and can reach high amplitudes, in a variant of Pringle's radiation-driven model for the warping of AGN accretion discs (Pringle (1996)). Finally we discuss how this mechanism might give a clue to explain the observed X-ray kHz QPO of neutron star binaries.Comment: Accepted for publication in MNRA

Wave Excitation in Disks Around Rotating Magnetic Stars

The accretion disk around a rotating magnetic star (neutron star, white dwarf or T Tauri star) is subjected to periodic vertical magnetic forces from the star, with the forcing frequency equal to the stellar spin frequency or twice the spin frequency. This gives rise bending waves in the disk that may influence the variabilities of the system. We study the excitation, propagation and dissipation of these waves using a hydrodynamical model coupled with a generic model description of the magnetic forces. The $m=1$ bending waves are excited at the Lindblad/vertical resonance, and propagate either to larger radii or inward toward the corotation resonance where dissipation takes place. While the resonant torque is negligible compared to the accretion torque, the wave nevertheless may reach appreciable amplitude and can cause or modulate flux variabilities from the system. We discuss applications of our result to the observed quasi-periodic oscillations from various systems, in particular neutron star low-mass X-ray binaries.Comment: Small changes/clarifications. To be published in ApJ, Aug.20,2008 issu

Warping of Accretion Disks with Magnetically Driven Outflows: A Possible Origin for Jet Precession

Current theoretical models for the outflows/jets from AGN, X-ray binaries and young stellar objects involve large-scale magnetic fields threading an underlying accretion disk. We suggest that such a disk is subjected to warping instability and retrograde precession driven by magnetic torques associated with the outflow. The growth timescale for the disk warp and the precession period are of order the radial infall time of the disk. These effects may be relevant to jet precession and other variabilities observed in many systems.Comment: 4 pages with 2 figures. ApJL in pres

Accretion disc-stellar magnetosphere interaction: field line inflation and the effect on the spin-down torque

We calculate the structure of a force-free magnetosphere which is assumed to corotate with a central star and which interacts with an embedded differentially rotating accretion disc. The magnetic and rotation axes are aligned and the stellar field is assumed to be a dipole. We concentrate on the case when the amount of field line twisting through the disc-magnetosphere interaction is large and consider different outer boundary conditions. In general the field line twisting produces field line inflation (eg. Bardou & Heyvaerts 1996) and in some cases with large twisting many field lines can become open. We calculate the spin-down torque acting between the star and the disc and we find that it decreases significantly for cases with large field line twisting. This suggests that the oscillating torques observed for some accreting neutron stars could be due to the magnetosphere varying between states with low and high field line inflation. Calculations of the spin evolution of T Tauri stars may also have to be revised in light of the significant effect that field line twisting has on the magnetic torque resulting from star-disc interactions.Comment: Accepted by MNRAS. 21 pages, 15 figures. LaTeX2e in the MN style. PostScript files are also available from http://www-star.qmw.ac.uk/~va/ or by e-mail: [email protected]

Stellar dynamo driven wind braking instead of disc coupling

Star-disc coupling is considered in numerical models where the stellar field is not an imposed perfect dipole, but instead a more irregular self-adjusting dynamo-generated field. Using axisymmetric simulations of the hydromagnetic mean-field equations, it is shown that the resulting stellar field configuration is more complex, but significantly better suited for driving a stellar wind. In agreement with recent findings by a number of people, star-disc coupling is less efficient in braking the star than previously thought. Moreover, stellar wind braking becomes equally important. In contrast to a perfect stellar dipole field, dynamo-generated stellar fields favor field-aligned accretion with considerably higher velocity at low latitudes, where the field is weaker and originating in the disc. Accretion is no longer nearly periodic (as it is in the case of a stellar dipole), but it is more irregular and episodic.Comment: 19 pages, 15 figures, some errors corrected, Astron. Nach. (submitted). For higher quality images, see http://www.nordita.dk/~brandenb/papers/stellardyn

Three-dimensional Simulations of Disk Accretion to an Inclined Dipole: I. Magnetospheric Flow at Different Theta

We present results of fully three-dimensional MHD simulations of disk accretion to a rotating magnetized star with its dipole moment inclined at an angle Theta to the rotation axis of the disk. We observed that matter accretes from the disk to a star in two or several streams depending on Theta. Streams may precess around the star at small Theta. The inner regions of the disk are warped. The warping is due to the tendency of matter to co-rotate with inclined magnetosphere. The accreting matter brings positive angular momentum to the (slowly rotating) star tending to spin it up. The corresponding torque N_z depends only weakly on Theta. The angular momentum flux to the star is transported predominantly by the magnetic field; the matter component contributes < 1 % of the total flux. Results of simulations are important for understanding the nature of classical T Tauri stars, cataclysmic variables, and X-ray pulsars.Comment: 26 pages, 22 figures, LaTeX, macros: emulapj.sty, avi simulations are available at http://www.astro.cornell.edu/us-rus/inclined.ht