Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd.     

Almost-Sure Central Limit Theorem for Directed Polymers and Random Corrections

We consider a general model of directed polymers on the lattice , weakly coupled to a random environment. We prove that the central limit theorem holds almost surely for the discrete time random walk X _T associated to the polymer. Moreover we show that the random corrections to the cumulants of X _T are finite, starting from some dimension depending on the index of the cumulants, and that there are corresponding random corrections of order , , in the asymptotic expansion of the expectations of smooth functions of X _T . Full proofs are carried out for the first two cumulants. We finally prove a kind of local theorem showing that the ratio of the probabilities of the events to the corresponding probabilities with no randomness, in the region of “moderate” deviations from the average drift bT, are, for almost all choices of the environment, uniformly close, as , to a functional of the environment “as seen from (T,y)$”. Received: 14 October 1996 / Accepted: 28 March 1997     

Resonance enhancement of diffuse scattering of x-rays in a waveguide heterostructure

The diffuse scattering of x rays in a four-layer waveguide-type heterostructure is investigated. The dynamic enhancement of diffuse scattering is detected experimentally in regions corresponding to the excitation of waveguide modes for both the incident and scattered waves. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 219–223 (25 August 1997)     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.     

Magnetic properties of amorphous alloys

The magnetic properties of existing amorphous iron based materials, i.e., Fe--metalloid, Fe--early transition metals and Fe--rare earth alloys, are briefly discussed for some representative alloys. The spin orientation of amorphous Fe--metalloid alloys has been determined by the angular dependence of hyperfine interactions. It is shown that in iron--early transition metals ferromagnetic order is not long-ranged, but determined by magnetic clusters. The magnetic hyperfine field distributions of Fe-rich iron--early transition metals consist of a high and a low field tail. The magnetic structure has been investigated for two representative Fe--RE (RE = Er, Ce) amorphous alloys. For the first time, the magnetic coupling phenomenon in amorphous/crystalline multilayers has been discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Laser systems specialized for laser spectroscopy at storage rings

Laser spectroscopy at storage rings often suffers from a limited resolution due to Doppler-broadened resonances. Broadening is caused by the velocity spread of the ions stored in the beam. In the following, the present status of our work on laser systems specialized on the specific needs of laser spectroscopy at storage rings is reported. Two pulsed laser systems were developed. One is a dye laser whose spectral bandwidth can be switched by inserting different Littrow-prisms into the resonator. An increase in bandwidth up to a factor of 45 was achieved. This laser was used for fast qualitative scans and high resolution measurements. The other laser system is a Nd : YAG laser pumped optical parametric oscillator. It is a tunable laser system covering the spectral range from 410 to 4000 nm. Furthermore, a continuous wave laser with a frequency shifted feedback cavity is described. It shows broadband emission with an adjustable bandwidth of up to 4.5 GHz. This laser can be advantageous for laser cooling of ion beams. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinetics of benzonitrile nitration with mixed acid under homogeneous conditions

Chemical kinetics of benzonitrile nitration with mixed acid is investigated in the temperature range 283–299 K. Pseudo-first-order rate constants are evaluated by means of rate experiments on homogeneous reacting mixtures having large stoichiometric excesses of nitric acid. The second-order kinetic constants for nitronium ion attack to the aromatic substrate are derived on the basis of the assessed nitration mechanism. An activation energy of 604 ± 37 kJ mol^?1 is calculated for this reaction step. © 1993 John Wiley & Sons, Inc.