Stabilité et renforcement des fronts de taille des tunnels : une approche analytique en contraintes-déformations

National audienceConstruction process of tunnels involve more and more frequently a full face excavation, with high faces. Therefore engineers have to analyse the face stability and to design reinforcement by longitudinal fibreglass bolts. The current methods are mainly based on stability analysis, but they scarcely allow an evaluation of the deformations, except when using numerical modelling, in which the consideration of reinforcements induces very heavy models, much difficult to use in engineering practice. This paper describes a new stress-strain approach, based on a spherical principle, and allowing the calculation of face deformations, including when bolts reinforcement is used. We present the general principles of the methods and its validation, then various parametric analysis, and finally some cases of practical use: evaluation of a safety factor, design of face reinforcement, effect of the confining pressure on the face deformations when using a TBM.Les tunnels sont de plus en plus réalisés en pleine section, ce qui conduit à des hauteurs du front de taille parfois très importantes. C'est pourquoi les ingénieurs sont fréquemment appelés à examiner la tenue du front, et à prévoir son renforcement par des boulons longitudinaux en fibre de verre. Les approches actuelles privilégient les analyses en stabilité, mais ne permettent guère une évaluation des déformations du front, sauf à utiliser des méthodes numériques, dans lesquels la prise en compte des renforcements conduit à des modèles très lourds et peu utilisables en pratique courante. Cet article présente une nouvelle approche analytique en contraintes-déformations, basée sur un principe de symétrie sphérique, et permettant d'évaluer les déformations d'extrusion du front, et ce même lorsque le front est renforcé par des boulons. Nous présentons en premier lieu les principes de la méthode ainsi que sa validation, puis différentes études paramétriques, ainsi que quelques cas possibles d'utilisation : évaluation d'un coefficient de sécurité, dimensionnement d'un renforcement par boulonnage, effet de la pression de confinement sur l'extrusion lors de l'utilisation de boucliers

Determination of the Fermion Pair Size in a Resonantly Interacting Superfluid

Fermionic superfluidity requires the formation of pairs. The actual size of these fermion pairs varies by orders of magnitude from the femtometer scale in neutron stars and nuclei to the micrometer range in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in BCS-BEC crossover theories, describing the crossover from a Bardeen-Cooper-Schrieffer (BCS) type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensation (BEC) of tightly bound molecules. Such a crossover superfluid has been realized in ultracold atomic gases where high temperature superfluidity has been observed. The microscopic properties of the fermion pairs can be probed with radio-frequency (rf) spectroscopy. Previous work was difficult to interpret due to strong and not well understood final state interactions. Here we realize a new superfluid spin mixture where such interactions have negligible influence and present fermion-pair dissociation spectra that reveal the underlying pairing correlations. This allows us to determine the spectroscopic pair size in the resonantly interacting gas to be 2.6(2)/kF (kF is the Fermi wave number). The pairs are therefore smaller than the interparticle spacing and the smallest pairs observed in fermionic superfluids. This finding highlights the importance of small fermion pairs for superfluidity at high critical temperatures. We have also identified transitions from fermion pairs into bound molecular states and into many-body bound states in the case of strong final state interactions.Comment: 8 pages, 7 figures; Figures updated; New Figures added; Updated discussion of fit function

From Cavity Electromechanics to Cavity Optomechanics

We present an overview of experimental work to embed high-Q mesoscopic mechanical oscillators in microwave and optical cavities. Based upon recent progress, the prospect for a broad field of "cavity quantum mechanics" is very real. These systems introduce mesoscopic mechanical oscillators as a new quantum resource and also inherently couple their motion to photons throughout the electromagnetic spectrum.Comment: 8 pages, 6 figures, ICAP proceedings submissio

Broad Feshbach resonance in the 6Li-40K mixture

We study the widths of interspecies Feshbach resonances in a mixture of the fermionic quantum gases 6Li and 40K. We develop a model to calculate the width and position of all available Feshbach resonances for a system. Using the model we select the optimal resonance to study the 6Li/40K mixture. Experimentally, we obtain the asymmetric Fano lineshape of the interspecies elastic cross section by measuring the distillation rate of 6Li atoms from a potassium-rich 6Li/40K mixture as a function of magnetic field. This provides us with the first experimental determination of the width of a resonance in this mixture, Delta B=1.5(5) G. Our results offer good perspectives for the observation of universal crossover physics using this mass-imbalanced fermionic mixture.Comment: 4 pages, 2 figure

Tensile strained InxGa1−xPIn_{x}Ga_{1-x}P membranes for cavity optomechanics

We investigate the optomechanical properties of tensile-strained ternary InGaP nanomembranes grown on GaAs. This material system combines the benefits of highly strained membranes based on stoichiometric silicon nitride, with the unique properties of thin-film semiconductor single crystals, as previously demonstrated with suspended GaAs. Here we employ lattice mismatch in epitaxial growth to impart an intrinsic tensile strain to a monocrystalline thin film (approximately 30 nm thick). These structures exhibit mechanical quality factors of 2*10^6 or beyond at room temperature and 17 K for eigenfrequencies up to 1 MHz, yielding Q*f products of 2*10^12 Hz for a tensile stress of ~170 MPa. Incorporating such membranes in a high finesse Fabry-Perot cavity, we extract an upper limit to the total optical loss (including both absorption and scatter) of 40 ppm at 1064 nm and room temperature. Further reductions of the In content of this alloy will enable tensile stress levels of 1 GPa, with the potential for a significant increase in the Q*f product, assuming no deterioration in the mechanical loss at this composition and strain level. This materials system is a promising candidate for the integration of strained semiconductor membrane structures with low-loss semiconductor mirrors and for realizing stacks of membranes for enhanced optomechanical coupling.Comment: 10 pages, 3 figure

Production of cold molecules via magnetically tunable Feshbach resonances

Magnetically tunable Feshbach resonances were employed to associate cold diatomic molecules in a series of experiments involving both atomic Bose as well as two spin component Fermi gases. This review illustrates theoretical concepts of both the particular nature of the highly excited Feshbach molecules produced and the techniques for their association from unbound atom pairs. Coupled channels theory provides the rigorous formulation of the microscopic physics of Feshbach resonances in cold gases. Concepts of dressed versus bare energy states, universal properties of Feshbach molecules, as well as the classification in terms of entrance- and closed-channel dominated resonances are introduced on the basis of practical two-channel approaches. Their significance is illustrated for several experimental observations, such as binding energies and lifetimes with respect to collisional relaxation. Molecular association and dissociation are discussed in the context of techniques involving linear magnetic field sweeps in cold Bose and Fermi gases as well as pulse sequences leading to Ramsey-type interference fringes. Their descriptions in terms of Landau-Zener, two-level mean field as well as beyond mean field approaches are reviewed in detail, including the associated ranges of validity.Comment: 50 pages, 26 figures, to be published in Reviews of Modern Physics, final version with updated reference

Formation of a vortex lattice in a rotating BCS Fermi gas

We investigate theoretically the formation of a vortex lattice in a superfluid two-spin component Fermi gas in a rotating harmonic trap, in a BCS-type regime of condensed non-bosonic pairs. Our analytical solution of the superfluid hydrodynamic equations, both for the 2D BCS equation of state and for the 3D unitary quantum gas, predicts that the vortex free gas is subject to a dynamic instability for fast enough rotation. With a numerical solution of the full time dependent BCS equations in a 2D model, we confirm the existence of this dynamic instability and we show that it leads to the formation of a regular pattern of quantum vortices in the gas.Comment: 14 page

Superfluidity and binary-correlations within clusters of fermions

We propose a method for simulating the behaviour of small clusters of particles that explicitly accounts for all mean-field and binary-correlation effects. Our approach leads to a set of variational equations that can be used to study both the dynamics and thermodynamics of these clusters. As an illustration of this method, we explore the BCS-BEC crossover in the simple model of four fermions, interacting with finite-range potentials, in a harmonic potential. We find, in the crossover regime, that the particles prefer to occupy two distinct pair states as opposed to the one assumed by BCS theory

On Quartet Superfluidity of Fermionic Atomic Gas

Possibility of a quartet superfluidity in fermionic systems is studied as a new aspect of atomic gas at ultra low temperatures. The four-fold degeneracy of hyperfine state and moderate coupling is indispensable for the quartet superfluidity to occur. Possible superconductivity with quartet condensation in electron systems is discussed.Comment: 7 pages, 1 figure. J. Phys. Soc. Jpn. vol.74 (2005) No.7, in press; Note added for related previous works; some typographic errors revise