Instabilities in Zakharov Equations for Laser Propagation in a Plasma

F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov system arising in the study of Laser-plasma interaction, is locally well posed in the whole space, for fields vanishing at infinity. Here we show that in the periodic case, seen as a model for fields non-vanishing at infinity, the system develops strong instabilities of Hadamard's type, implying that the Cauchy problem is strongly ill-posed

On the spectrum of the Laplace operator of metric graphs attached at a vertex -- Spectral determinant approach

We consider a metric graph $\mathcal{G}$ made of two graphs $\mathcal{G}_1$ and $\mathcal{G}_2$ attached at one point. We derive a formula relating the spectral determinant of the Laplace operator $S_\mathcal{G}(\gamma)=\det(\gamma-\Delta)$ in terms of the spectral determinants of the two subgraphs. The result is generalized to describe the attachment of $n$ graphs. The formulae are also valid for the spectral determinant of the Schr\"odinger operator $\det(\gamma-\Delta+V(x))$.Comment: LaTeX, 8 pages, 7 eps figures, v2: new appendix, v3: discussions and ref adde

Millisecond spin-flip times of donor-bound electrons in GaAs

We observe millisecond spin-flip relaxation times of donor-bound electrons in high-purity n-GaAs . This is three orders of magnitude larger than previously reported lifetimes in n-GaAs . Spin-flip times are measured as a function of magnetic field and exhibit a strong power-law dependence for fields greater than 4 T . This result is in qualitative agreement with previously reported theory and measurements of electrons in quantum dots.Comment: 4 pages, 4 figure

Upper critical field divergence induced by mesoscopic phase separation in the organic superconductor (TMTSF)2ReO4

Due to the competition of two anion orders, (TMTSF)2ReO4, presents a phase coexistence between semiconducting and metallic (superconducting) regions (filaments or droplets) in a wide range of pressure. In this regime, the superconducting upper critical field for H parallel to both c* and b' axes present a linear part at low fields followed by a divergence above a cross-over field. This cross-over corresponds to the 3D-2D decoupling transition expected in filamentary or granular superconductors. The sharpness of the transition also demonstrates that all filaments are of similar sizes and self organize in a very ordered way. The distance between the filaments and their cross-section are estimated.Comment: 4 pages, 4 figure

Bar imprints on the inner gas kinematics of M33

We present measurements of the stellar and gaseous velocities in the central 5' of the Local Group spiral M33. The data were obtained with the ARC 3.5m telescope. Blue and red spectra with resolutions from 2 to 4\AA covering the principal gaseous emission and stellar absorption lines were obtained along the major and minor axes and six other position angles. The observed radial velocities of the ionized gas along the photometric major axis of M33 remain flat at ~22 km s^{-1} all the way into the center, while the stellar velocities show a gradual rise from zero to 22 km s^{-1} over that same region. The central star cluster is at or very close to the dynamical center, with a velocity that is in accordance with M33's systemic velocity to within our uncertainties. Velocities on the minor axis are non-zero out to about 1' from the center in both the stars and gas. Together with the major axis velocities, they point at significant deviations from circular rotation. The most likely explanation for the bulk of the velocity patterns are streaming motions along a weak inner bar with a PA close to that of the minor axis, as suggested by previously published IR photometric images. The presence of bar imprints in M33 implies that all major Local Group galaxies are barred. The non-circular motions over the inner 200 pc make it difficult to constrain the shape of M33's inner dark matter halo profile. If the non-circular motions we find in this nearby Sc galaxy are present in other more distant late-type galaxies, they might be difficult to recognize.Comment: 20 pages, 12 figures, ApJ in pres

Contamination of indoor air by toxic soil vapours: the effects of subfloor ventilation and other protective measures

A steady-state analytical model is derived for estimating the concentration of vapour-phase contaminants in indoor air in houses with subfloor voids, given the contaminant concentration in bulk soil. The model includes the key mechanisms of transport and dispersion—contaminant partitioning into the soil-vapour phase, molecular diffusion, suction flow, stack effect, and ventilation, including contaminant transport by ventilation flow between subfloor void and living space. Using the model, different construction styles are examined from the point of view of their resistance to ingress of soil gases. Model results indicate that indoor air concentration depends strongly on wind velocity and on geometrical parameters of void and living space. Worked examples for houses of different construction styles illustrate the effects of wind velocity and house parameters on the concentration of benzene in soil that would give rise to its maximum permissible concentration in indoor air. Brief consideration is also given to concrete raft foundations and clean cover systems

Recent progress in the theory of railway-generated ground vibrations

Recent progress in the theory of railway-generated ground vibration

Generation of surface acoustic waves by moving trains

The theory of generation of ground surface acoustic waves by trains is developed using the Green's function formalism. Mechanical properties of the rail track and parameters of train and soil (including contact nonlinearity of track-soil system) are taken into account. It's shown that generated ground vibration spectra depend strongly on the geometrical parameters of track and train, on the mechanical properties of soil, and on the axle loads of the carriages. Simple practical methods are suggested to modify, the spectra of railway-generated surface elastic waves and to reduce their level at chosen frequency bands