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Observability estimates for the Schrödinger equation on the equilateral triangle
No full textWe prove observability estimates for the Schrödinger equation posed on the equilateral triangle in the plane, under both Neumann and Dirichlet boundary conditions. No geometric control condition is required on the rough localization functions that we consider. This is the first result of this kind on a non-toric domain in the compact setting. Our strategy is to exploit Pinsky's tiling argument to deduce this result from observability estimates on rational twisted tori. These are obtained via propagation of singularities, adapting arguments from Burq and Zworski. The later require Strichartz estimates on such twisted rational tori, that we derive from Zygmund inequalities in the same geometric setting, also providing the sharp constant. Strichartz estimates on the equilateral triangle are also derived from this analysis
On Regional Sampled-Data Control of Nonlinear Time-Delay Systems with Input Saturation Constraints
No full textInternational audienceIn this paper, we deal with the stabilization problem of nonlinear time-delay systems affected by input saturation constraints via sampled-data dynamic output feedback controllers. Nonlinear time-delay systems not necessarily affine in the control input are studied. A new approach for the design of sampled-data dynamic output feedback controllers is provided taking into account the effects of input saturation constraints. In particular, it is shown that the digital implementation via suitable approximation functions of dynamic output steepest descent feedback (continuous or not) with amplitude bounds yields the practical stability, with arbitrarily small final target ball, of the related sampled-data closed-loop system limited to suitably small regions. The case of time-varying sampling intervals and the stability analysis of the inter-sampling system behavior are included in the theory here developed. The provided results can be applied also for nonlinear delay-free systems which are here addressed as a special case. An example is presented which validates the theoretical results
Light-based 3D printing and post-treatments of moulds for PDMS soft lithography
No full textInternational audiencePolydimethylsiloxane (PDMS) chips are still the workhorses of academic microfluidics. Their production requires the fabrication of moulds, commonly produced using clean-room technologies. Light-based 3D printing and in particular, vat photopolymerization, material jetting and two-photon polymerization are rising techniques for the fabrication of moulds for PDMS replication, thanks to their accessibility, fast prototyping time, and improving resolution. Here, we are first reviewing the possibility opened by 3D printing for soft lithography, with a focus on mould designs. Then, inhibition of PDMS curing by photosensitive resins will be discussed as the main technical hurdle of 3D printed moulds. Fortunately, mould post-treatments are efficient solutions to eliminate this curing inhibition, which we gathered in a large database of post-treatment protocols from the literature
Cell cycle phases, their effect on cell mechanical properties and the impact on Candida-host cell interaction
No full textInternational audienceCell mechanics is essential in many biological phenomena such as cell division, and migration. Further, cell mechanobiological measurements can distinguish between healthy and diseases cells, thus, investigations of cell mechanics have led to the development of tools to study the elasticity and the viscosity of cells. Cell mechanics can be affected by factors such as cell morphology, and cytoskeletal remodelling and cell intrinsic factors and these are important in understanding disease progression. Here we use an atomic force microscopy (AFM)-microrheology with a colloidal probe for a dynamic mechanical analysis of host cell elasticity and viscosity at 6 frequencies ranging from 1 Hz to 200 Hz. Epithelial cells exhibit a more "liquid-like" behavior as the frequency increases, whereas cancerous cells transition into this viscous, fluid-like state at lower frequencies (48 and 63 Hz) compared to normal cells (92 Hz).Cell mechanical measurements inherently exhibit heterogeneity due to physical factors such as cell shape and the position of the probe on the cell surface. In addition to this physical variability, biological parameters -notably the cell cycle phases -also contribute to mechanical heterogeneity. In this study, we specifically investigated the influence of cell cycle phases on cell mechanical properties. Using chemically synchronized normal and cancerous cells in different phases of the cell cycle, shows that the actin cytoskeleton undergoes rapid reorganization as the cell cycle progresses.Results show that as actin becomes disorganized the elastic moduli decreases, the loss tangent is larger coupled with a lower phase shift frequency. Cells in the G1 and S phase had the lowest elastic moduli (G') meaning they were softer than cells in G2/M phase.During disease onset the pathogen adheres and invades the host, a process which leads to cytoskeleton arrangement and thus, changes in cell elasticity and thus, to understand the impact of the cell cycle on host invasion we probed the interaction of C. albicans with HeLa, HCT 116 and HaCaT cells using AFM in single cell force spectroscopy mode. There was a significant increase in force of interaction during the S phase which could be attributed to the disorganized cytoskeleton. This shows the importance of cytoskeletal organization and cell cycle phase in cell mechanical properties and pathogen-host interaction.</p
A Novel approach to open the world of silica-based AFM probes using selective laser etching
No full textInternational audienceAtomic force microscopy (AFM) cantilevers are indispensable for nanoscale imaging and force sensing of both materials and biological specimens. However, their traditional fabrication methods, which rely on silicon or silicon nitride bulk micromachining, suffer from high costs, low throughput, and limited geometric flexibility [1],[2]. These limitations have driven the development of innovative AFM cantilevers made of silica glass through a novel, cost-effective approach, offering benefits such as chemical inertness, biocompatibility, reduced fabrication time and design flexibility to accommodate a wide range of applications. Our innovative approach involves fabricating cantilevers using selective laser etching (SLE), a subtractive laser technology capable of producing complex 3D glass structures with micron-level precision. The process consists in 3 sequential steps that are i) laser irradiation, ii) KOH etching, and iii) Ti/Au metallization. It begins with irradiating the transparent material with a focused femtosecond (fs) laser beam at 1030 nm, inducing localized modifications. The laser then writes the desired structure spot by spot in three dimensions:Figure 1(a). Following fs Laser irradiation, the irradiated volume is etched in a 10 mol/l KOH solution at 90°C for 5 hours: Figure 1(b). Upon completion, a bi-layer metal deposition wiss performed, consisting in 10 nm of Titanium (Ti) and 30 nm of Gold (Au), for the AFM laser reflection.We fabricated cantilevers with spring constants ranging from 0.08 to 45 N/m, enabling the characterization of both material surfaces and biological specimens. Pyramidal and semi-spherical tips of various dimensions were developed for the tip design: Figure 1(c,d). Using pyramidal tips, topographic measurements were conducted on various calibration gratings Figure 1(e,f). In addition, force spectroscopy and imaging were performed on cells using the semi-spherical tips.[1]F. J. Giessibl, ‘Advances in atomic force microscopy’, Rev Mod Phys, vol. 75, no. 3, 2003.[2]A. S. Algamili et al., ‘A Review of Actuation and Sensing Mechanisms in MEMS-Based Sensor Devices’, Nanoscale Res. Lett., vol. 16, no. 1, p. 16, Jan. 2021, doi: 10.1186/s11671-021-03481-7
Local activation of Cxcl12a signaling controls olfactory placode morphogenesis in zebrafish embryos
No full textInternational audienceMorphogenesis and cell-type differentiation are highly coordinated in sensory organs to ensure their function. Morphogenesis of the olfactory placode in zebrafish provides a unique model to study this process as undifferentiated cells aligned around the anterior neural plate mature into clusters of early olfactory neurons across a short timescale. Although the Cxcl12a/Cxcr4b signaling pathway drives this process, what constraints on pathway activation apply during morphogenesis are unclear. We developed a mathematical model recapitulating Cxcl12a-mediated olfactory placode morphogenesis. Restoring Cxcl12a expression in mutants for the ligand rescues correct morphogenesis both in silico and in vivo. However, where expression of the ligand is restored is crucial for rescue, a point not predicted by our model and suggesting an unexpected level of pathway activation control. Analysis of a Cxcr4b activation reporter supports this idea. We concluded that mosaic and heterochronic Cxcl12a activation along the anteroposterior axis sculpts the olfactory placode
Topology of ultra-localized insulators and superconductors
No full textInternational audienceThe topology of an insulator can be defined even when all eigenstates of the system are localized - an extreme case of Anderson insulators that we call ultra-localized. We derive the classification of such ultra-localized insulators in all symmetry classes and dimensions. We clarify their bulk-boundary correspondence and show that ultra-localized systems are in many instances phases of matter not described by the known classification of topological insulators and superconductors
Kerr-Brillouin frequency combs in fiber Fabry-Perot resonators
No full textInternational audienceWe report the observation of broadband optical frequency combs in high-Q fiber Fabry-Perot resonators under CW pumping. We develop a new mean-field equation which permits to efficiently simulate the observed spectra and to unveil the physics underlying this phenomenon