Simulating the Performance of Michelson- and Sagnac-based Laser Interferometric Gravitational Wave Detectors in the Presence of Mirror Tilt and Curvature Errors

We model the behaviour of single-bounce delay-line dual recycled Sagnac-based interferometer and compare its performance with that of single-bounce Michelson-based system. Geometric imperfections such as mirror tilt and curvature mismatch can strongly influence the performance of the Sagnac device due to the inherently smaller free spectral range (FSR) and higher order mode spacing. This leads to a greater number of higher order modes near, or within the signal band in the signal recycling cavity of the instrument. The important consequence of that is, in general, a greater sensitivity of a Sagnac system to nonideal parameters and imperfections of various kind affecting the performance of a real interferometer. A number of optical configurations have also been examined numerically to determine the best possible optical arrangement, in the presence of such geometric imperfections. We show that there is an optimum choice for the nominal radius of curvature of the end mirrors which results from balancing the loss due to mirror tilt against that due to curvature mismatch.     

Optical emission spectroscopy of the sputtering process in the triode system

The results of spectroscopic investigation of plane plasma discharge and sputtering processes in the triode system are presented. The forced electric discharge with currents of 1–4 A at an argon pressure of 1 mTorr was studied using the emission spectroscopy method. The spectra of plasma discharge were observed in the 200–1100 nm wavelength range. Two metal targets, gold and silver, were used for sputtering. It was found that a part of sputtered particles is ionized in plasma. The emission spectra of the ionized gold and silver species were observed as a function of target voltage while sputtering. It was shown that the number of ionized metal species depends on the energy of argon ions.     

Feshbach resonance management for Bose-Einstein condensates

An experimentally realizable scheme of periodic sign-changing modulation of the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because of controlling the scattering length via the Feshbach resonance, the scheme is named Feshbach-resonance management. The modulational-instability analysis of the quasiuniform condensate driven by this scheme leads to an analog of the Kronig-Penney model. The ensuing stable localized structures are found. These include breathers, which oscillate between the Thomas-Fermi and Gaussian configuration, or may be similar to the 2-soliton state of the nonlinear Schr?dinger equation, and a nearly static state ("odd soliton") with a nested dark soliton. An overall phase diagram for breathers is constructed, and full stability of the odd solitons is numerically established.     

A canonical frame for nonholonomic rank two distributions of maximal class

In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in ${\mathbb{R}}^5$. We solve the analogous problems for rank 2 distributions in ${\mathbb{R}}^n$ for arbitrary $n>5$. Our method is a kind of symplectification of the problem and it is completely different from the Cartan method of equivalence. To cite this article: B. Doubrov, I. Zelenko, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Open Channel Structure of MscL: A Patch-Clamp and Spectroscopic Study

MscL, the bacterial mechanosensitive (MS) channel of large conductance, has become a prototype channel to study structure–function relationship of the MS class of ion channels. Within a few years of cloning the mscL gene, the three-dimensional structure of the MscL protein was determined by X-ray crystallography, which allowed for detailed molecular studies of its structure and function. A combination of the (1) patch-clamp recording examining the function of MscL channels reconstituted into artificial liposomes, and (2) electron paramagnetic resonance (EPR) and fluorescence resonance energy transfer (FRET) spectroscopy examining structural changes occurring during gating of the reconstituted channels, provided a plausible molecular mechanism of gating of MS channels. This experimental approach helped to establish two physical mechanisms as triggers of the MscL channel gating by lipid bilayer deformation forces: (1) the energetic cost of protein-bilayer hydrophobic mismatch and (2) the geometric consequences of bilayer intrinsic curvature. The results of the EPR and FRET spectroscopic studies showed that the open state of MscL is highly dynamic, supporting a water-filled pore of at least 25 Å in diameter corresponding to an overall change in diameter of the channel protein of about 15 Å.     

Ray shooting and intersection searching amidst fat convex polyhedra in 3-space

We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in . The data structure uses O(n^2+ε) storage and preprocessing time, and queries can be answered in O(log²n) time. A trade-off between storage and query time is also possible: for any m with n<m<n², we can construct a structure that uses O(m^1+ε) storage and preprocessing time such that queries take time.We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in . For any m with n<m<n³, we can construct a structure that uses O(m^1+ε) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m^1/3)logn+k) time, where k is the number of answers.     

KAM theory and the 3D Euler equation

We prove that the dynamical system defined by the hydrodynamical Euler equation on any closed Riemannian 3-manifold M   is not mixing in the C^k$C^k$ topology (k>4$k>4$ and non-integer) for any prescribed value of helicity and sufficiently large values of energy. This can be regarded as a 3D version of Nadirashvili's and Shnirelman's theorems showing the existence of wandering solutions for the 2D Euler equation. Moreover, we obtain an obstruction for the mixing under the Euler flow of C^k$C^k$-neighborhoods of divergence-free vectorfields on M  . On the way we construct a family of functionals on the space of divergence-free C¹$C^1$ vectorfields on the manifold, which are integrals of motion of the 3D Euler equation. Given a vectorfield these functionals measure the part of the manifold foliated by ergodic invariant tori of fixed isotopy types. We use the KAM theory to establish some continuity properties of these functionals in the C^k$C^k$-topology. This allows one to get a lower bound for the C^k$C^k$-distance between a divergence-free vectorfield (in particular, a steady solution) and a trajectory of the Euler flow.     

On Spectral Polynomials of the Heun Equation. II

The well-known Heun equation has the form