Coherent combining in an Yb-doped double-core fiber laser

Coherent combining is demonstrated in a clad-pumped Yb-doped double-core fiber laser. A slope efficiency of more than 70% is achieved with 96% of the total output power in the fundamental mode of one of the two cores. This high combining efficiency is obtained when both cores are coupled via a biconical fused taper in a Michelson interferometer configuration.     

Fluctuations for Kawasaki Dynamics

In this paper Kawasaki dynamics are considered. Lower bounds are obtained for the variance of the occupation time of a site in any dimension and for temperature above critical temperature. These lower bounds are expressed in terms of the density correlation function and hence relate the fluctuations to some phase transition quantities. At critical temperature, under a reasonable assumption of the static structure function, lower bounds for the variance of the occupation time are obtained. These lower bounds are consistent with the supposed value of the critical exponent. This paper also examines the same problem for Glauber dynamics and shows that the phase transition may not be of importance for the behavior of fluctuations.     

Delayed fracture in porous media

The fracture of porous media subjected to a constant load is studied. Contrary to homogeneous solids in which fracture usually happens instantaneously at a well-defined breaking strength, the fracture of a porous medium can occur with a delay, allowing us to quantify the average lifetime of the unbroken material. We show that the average fracture probability, a key property for risk analysis in civil engineering, is given by the probability of crack nucleation. The nucleation process can be understood qualitatively by calculating the activation energy for crack nucleation, taking into account the porosity of the medium.     

On the asymptotic completeness of the Volterra calculus

The Volterra calculus is a simple and powerful pseudodifferential tool for inverting parabolic equations which has found many applications in geometric analysis. An important property in the theory of pseudodifferential operators is asymptotic completeness, which allows the construction of parametrices modulo smoothing operators. In this paper, we present new and fairly elementary proofs of the asymptotic completeness of the Volterra calculus. The author was partially supported by the European RT NetworkGeometric Analysis HPCRN-CT-1999-00118.     

On Tate-Shafarevich groups over galois extensions

LetA be an abelian variety defined over a number fieldK. LetL be a finite Galois extension ofK with Galois groupG and let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups ofA overK and ofA overL. Assuming these groups are finite, we compute [III(A/L) ^G ]/[III(A/K)] and [III(A/K)]/[N(III(A/L))], where [X] is the order of a finite abelian groupX. Especially, whenL is a quadratic extension ofK, we derive a simple formula relating [III(A/L)], [III(A/K)], and [III(A ^x/K)] whereA x is the twist ofA by the non-trivial characterχ ofG.     

Nonalgebraizable real analytic tubes in ℂ<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We give necessary conditions for certain real analytic tube generic submanifolds in ⁿ to be locally algebraizable. As an application, we exhibit families of real analytic non locally algebraizable tube generic submanifolds in ⁿ. During the proof, we show that the local CR automorphism group of a minimal, finitely nondegenerate real algebraic generic submanifold is a real algebraic local Lie group. We may state one of the main results as follows. Let M be a real analytic hypersurface tube in ⁿ passing through the origin, having a defining equation of the form v= (y), where (z,w)=(x+iy,u+iv)^n–1×. Assume that M is Levi nondegenerate at the origin and that the real Lie algebra of local infinitesimal CR automorphisms of M is of minimal possible dimension n, i.e. generated by the real parts of the holomorphic vector fields _z1,...,_{z n–1},_w. Then M is locally algebraizable only if every second derivative ²_{yky l}; is an algebraic function of the collection of first derivatives _y1,,_ym.Mathematics Subject Classification (2000): 32V40, 32V25, 32H02, 32H40, 32V10     

On periodic points under the iteration of additive polynomials

Let F be a field and f(X) F[X]. An element P of F is called a (pre)periodic point of f if the sequence P, f(P), f(f(P)), is (eventually) periodic. In the case where F is a function field of characteristic p>0 and f(X)=aX ^q +bX or f(X)=aX ^{q 2}+bX ^q +cX with q a power of p, we try to give effective upper bounds (depending only on q and F) for the number of (pre)periodic points of f in F. Mathematics Subject Classification (2000):primary: 11C08, secondary: 11G09, 37E15     

Measurement of the generalized polarizabilities of the proton in virtual Compton scattering at Q2=0.92 and 1.76 GeV2

We report a virtual Compton scattering study of the proton at low c.m. energies. We have determined the structure functions P(LL)-P(TT)/epsilon and P(LT), and the electric and magnetic generalized polarizabilities (GPs) alpha(E)(Q2) and beta(M)(Q2) at momentum transfer Q(2)=0.92 and 1.76 GeV2. The electric GP shows a strong falloff with Q2, and its global behavior does not follow a simple dipole form. The magnetic GP shows a rise and then a falloff; this can be interpreted as the dominance of a long-distance diamagnetic pion cloud at low Q2, compensated at higher Q2 by a paramagnetic contribution from piN intermediate states.     

Hanbury Brown-Twiss correlations to probe the population statistics of GHz photons emitted by conductors

We present the first study of the statistics of GHz photons in quantum circuits, using Hanbury Brown and Twiss correlations. The super-Poissonian and Poissonian photon statistics of thermal and coherent sources, respectively, made of a resistor and a radio frequency generator, are measured down to the quantum regime at milli-Kelvin temperatures. As photon correlations are linked to the second and fourth moments of current fluctuations, this experiment, which is based on current cryogenic electronics, may become a standard for probing electron/photon statistics in quantum conductors.     

Observation of laser driven supercritical radiative shock precursors

We present a supercritical radiative shock experiment performed with the LULI nanosecond laser facility. Using targets filled with xenon gas at low pressure, the propagation of a strong shock with a radiative precursor is evidenced. The main measured shock quantities (electronic density and propagation velocity) are shown to be in good agreement with theory and numerical simulations.