Ring-Pattern Dynamics in Smectic-C* and Smectic-C_A* Freely Suspended Liquid Crystal Films

Ring patterns of concentric 2pi-solitons in molecular orientation, form in freely suspended chiral smectic-C films in response to an in-plane rotating electric field. We present measurements of the zero-field relaxation of ring patterns and of the driven dynamics of ring formation under conditions of synchronous winding, and a simple model which enables their quantitative description in low polarization DOBAMBC. In smectic C_A* TFMHPOBC we observe an odd-even layer number effect, with odd number layer films exhibiting order of magnitude slower relaxation rates than even layer films. We show that this rate difference is due to much larger spontaneous polarization in odd number layer films.Comment: 4 RevTeX pgs, 4 eps figures, submitted to Phys. Rev. Let

Zig-zag instability of an Ising wall in liquid crystals

We present a theoretical explanation for the interfacial zigzag instability that appears in anisotropic systems. Such an instability has been experimentally highlighted for an Ising wall formed in a nematic liquid crystal cell under homeotropic anchoring conditions. From an envelope equation, relevant close to the Freedericksz transition, we have derived an asymptotic equation describing the interface dynamics in the vicinity of its bifurcation. The asymptotic limit used accounts for a strong difference between two of the elastic constants. The model is characterized by a conservative order parameter which satisfies a Cahn-Hilliard equation. It provides a good qualitative understanding of the experiments.Comment: 4 pagess, 4 figures, lette

The French Didactic Tradition in Mathematics

This chapter presents the French didactic tradition. It first describes theemergence and development of this tradition according to four key features (role ofmathematics and mathematicians, role of theories, role of design of teaching andlearning environments, and role of empirical research), and illustrates it through two case studies respectively devoted to research carried out within this traditionon algebra and on line symmetry-reflection. It then questions the influence of thistradition through the contributions of four researchers from Germany, Italy, Mexicoand Tunisia, before ending with a short epilogue

Conceptually driven and visually rich tasks in texts and teaching practice: the case of infinite series

The study we report here examines parts of what Chevallard calls the institutional dimension of the students’ learning experience of a relatively under-researched, yet crucial, concept in Analysis, the concept of infinite series. In particular, we examine how the concept is introduced to students in texts and in teaching practice. To this purpose, we employ Duval's Theory of Registers of Semiotic Representation towards the analysis of 22 texts used in Canada and UK post-compulsory courses. We also draw on interviews with in-service teachers and university lecturers in order to discuss briefly teaching practice and some of their teaching suggestions. Our analysis of the texts highlights that the presentation of the concept is largely a-historical, with few graphical representations, few opportunities to work across different registers (algebraic, graphical, verbal), few applications or intra-mathematical references to the concept's significance and few conceptually driven tasks that go beyond practising with the application of convergence tests and prepare students for the complex topics in which the concept of series is implicated. Our preliminary analysis of the teacher interviews suggests that pedagogical practice often reflects the tendencies in the texts. Furthermore, the interviews with the university lecturers point at the pedagogical potential of: illustrative examples and evocative visual representations in teaching; and, student engagement with systematic guesswork and writing explanatory accounts of their choices and applications of convergence tests

Simulating JWST deep extragalactic imaging surveys and physical parameter recovery

International audienceWe present a new prospective analysis of deep multi-band imaging with the James Webb Space Telescope (JWST). In this work, we investigate the recovery of high-redshift 5  6 and redshifts of 0   5 galaxy samples can be reduced to < 0.01 arcmin−2 with a limited impact on galaxy completeness. We investigate multiple high-redshift galaxy selection techniques and find that the best compromise between completeness and purity at 5 <  z <  10 using the full redshift posterior probability distributions. In the EGS field, the galaxy completeness remains higher than 50% at magnitudes mUV <  27.5 and at all redshifts, and the purity is maintained above 80 and 60% at z ≤ 7 and 10, respectively. The faint-end slope of the galaxy UV luminosity function is recovered with a precision of 0.1–0.25, and the cosmic star formation rate density within 0.1 dex. We argue in favor of additional observing programs covering larger areas to better constrain the bright end

european didactic traditions in mathematics aspects and examples from four selected cases

In this paper, we report on the presentations and activities from the strand on "European Didactic Traditions" during the Thematic Afternoon at ICME-13. The focal point of the first hour of this afternoon were four key features that were identified as common in all European traditions and the second and third hours were devoted to the presentation of concrete examples from four specific traditions, organised in four parallel sessions

GA-NIFS: co-evolution within a highly star-forming galaxy group at z=3.7 witnessed by JWST/NIRSpec IFS

We present NIRSpec IFS observations of a galaxy group around the massive GS_4891 galaxy at z=3.7 in GOODS-South that includes two other two systems, GS_4891_n to the north and GS_28356 to the east. These observations, obtained as part of the GTO GA-NIFS program, allow for the first time to study the spatially resolved properties of the interstellar medium (ISM) and ionized gas kinematics of a galaxy at this redshift. Leveraging the wide wavelength range spanned with the high-dispersion grating (with resolving power R=2700) observations, covering from [OII]$\lambda$$\lambda$3726,29 to [SII]$\lambda$$\lambda$6716,31, we explore the spatial distribution of star-formation rate, nebular attenuation and gas metallicity, together with the mechanisms responsible for the excitation of the ionized gas. GS_4891 presents a clear gradient of gas metallicity (as traced by 12 + log(O/H)) by more than 0.2dex from the south-east (where a star-forming clump is identified) to the north-west. The gas metallicity in the less-massive northern system, GS_4891_n, is also higher by 0.2 dex than at the center of GS_4891, suggesting that inflows of lower-metallicity gas might be favoured in higher-mass systems. The kinematic analysis shows that GS_4891 presents velocity gradients in the ionized gas consistent with rotation. The region between GS_4891 and GS_4891_n does not present high gas turbulence which, together with the difference in gas metallicities, suggests that these two systems might be in a pre-merger stage. Finally, GS_4891 hosts an ionized outflow that extends out to r_out=1.2 kpc from the nucleus and reaches maximum velocities v_out of approximately 400 km/s. Despite entraining an outflowing mass rate of M_out$\sim$2Msun/yr, the low associated mass-loading factor, $\eta$=0.05, implies that the outflow does not have a significant impact on the star-formation activity of the galaxy.Comment: Submitted to Astronomy & Astrophysics on September 25th, 202