Generalized doubling meets Poincaré

We establish a modified segment inequality on metric spaces that satisfy a generalized volume doubling property. This leads to Sobolev and Poincaré inequalities for such spaces. We also give several examples of spaces that satisfy the generalized doubling condition.     

A moving zone of quiet for narrowband noise in a one-dimensional duct using virtual sensing

A frequent problem in active noise control is that the zone of quiet created at the error sensor tends to be very small. This means that the error sensor generally needs to be located close to an observer's ear, which might not always be a convenient or feasible solution. Virtual sensing is a method that can move the zone of quiet away from the error sensor to a desired location that is spatially fixed. This method has been investigated previously, and has shown potential to improve the performance of an active noise control system. However, it is very likely that the desired location of the zone of quiet is not spatially fixed. An active noise control system incorporating a virtual sensing method thus has to be able to create a moving zone of quiet that tracks the observer's ears. This paper presents a method for creating a moving zone of quiet based on the LMS virtual microphone technique. To illustrate the proposed method, it is implemented in an acoustic duct and narrowband control results are presented. These results show that a moving zone of quiet was effectively created inside the duct for narrowband noise.     

On eigenvalue pinching in positive Ricci curvature

We shall show that for manifolds with Ric≥n−1 the radius is close to π iff the (n+1)st eigenvalue is close to n. This extends results of Cheng and Croke which show that the diameter is close to π iff the first eigenvalue is close to n. We shall also give a new proof of an important theorem of Colding to the effect that if the radius is close to π, then the volume is close to that of the sphere and the manifold is Gromov-Hausdorff close to the sphere. From work of Cheeger and Colding these conditions imply that the manifold is diffeomorphic to a sphere. Oblatum 29-V-1998 & 4-II-1999 / Published online: 21 May 1999     

Measurement of the rate coefficient of the reaction CH+O2 → products in the temperature range 2200 to 2600 K

The rate coefficient of the reaction CH+O₂ → products was determined by measuring CH-radical concentration profiles in shock-heated 100–150 ppm ethane/1000 ppm O₂ mixtures in Ar using cw, narrow-linewidth laser absorption at 431.131 nm. Comparing the measured CH concentration profiles to ones calculated using a detailed kinetics model, yielded the following average value for the rate coefficient independent of temperature over the range 2200–2600 K: The experimental conditions were chosen such that the calculated profiles were sensitive mainly to the reactions CH+O₂ → products and CH₃+M → CH+H₂+M. For the methyl decomposition reaction channel, the following rate-coefficient expression provided the best fit of the measured CH profiles: Additionally, the rate coefficient of the reaction CH₂+H→CH+ H₂ was determined indirectly in the same system: © 1997 John Wiley & Sons, Inc.     

A computational investigation of the finite-time blow-up of the 3D incompressible Euler equations based on the Voigt regularization

We report the results of a computational investigation of two blow-up criteria for the 3D incompressible Euler equations. One criterion was proven in a previous work, and a related criterion is proved here. These criteria are based on an inviscid regularization of the Euler equations known as the 3D Euler–Voigt equations, which are known to be globally well-posed. Moreover, simulations of the 3D Euler–Voigt equations also require less resolution than simulations of the 3D Euler equations for fixed values of the regularization parameter \(\alpha >0\). Therefore, the new blow-up criteria allow one to gain information about possible singularity formation in the 3D Euler equations indirectly, namely by simulating the better-behaved 3D Euler–Voigt equations. The new criteria are only known to be sufficient criterion for blow-up. Therefore, to test the robustness of the inviscid-regularization approach, we also investigate analogous criteria for blow-up of the 1D Burgers equation, where blow-up is well known to occur.     

In situ bioconjugation—Novel laser based approach to pure nanoparticle-conjugates

The generation and characterization of nanoparticulate carrier systems is important for drug delivery, biosensing and in vivo or in vitro diagnostics. Conventional nanoparticle generation is based on chemical synthesis methods requiring time intensive reaction and additive design for each material. Successive purification and surface functionalisation is often required after the nanoparticle generation to achieve pure nanoparticle-bioconjugates. We established a novel single step method, which allows the generation of pure nanoparticles and their in situ conjugation with biomolecules bearing electron donating moieties using pulsed laser ablation in liquids. For comparison between unspecific binding and binding through strong dative bonds (here: S-Au), we applied this preparation method to the conjugation of gold nanoparticles with unmodified and thiolated oligonucleotides. In order to determine optimal parameters (laser pulse energy, focus diameter), the influence on productivity of nanoparticle generation and their interaction with oligonucleotides is studied. We report quenching of nanoparticle growth and modification of the surface plasmon resonance as evidence of a successful functionalisation. Their stability in ionic solutions is evidenced with relevance to biological and medical assays. Negligible differences between the two model bioconjugations evidence the universality of the established in situ bioconjugation method.     

Elliptic flow in an integrated (3+1)d microscopic + macroscopic approach with fluctuating initial conditions

The elliptic flow excitation function calculated in a Boltzmann approach with an intermediate hydrodynamic stage for heavy-ion reactions from GSI-SIS to the highest CERN-SPS energies is discussed in the context of the experimental data. The specific setup with initial conditions and freeze-out from a non-equilibrium transport model allows for a direct comparison between ideal fluid dynamics and hadronic transport simulations. At higher SPS energies, where the pure transport calculation cannot account for the high elliptic flow values, the smaller mean free path in the hydrodynamic evolution leads to higher elliptic flow values. The lower mean free path leads to higher pressure gradients in the early stage and as a consequence to higher elliptic flow values even without a phase transition. Special emphasis is put on the influence of the initial conditions on the results of the hybrid model calculation. Event-by-event fluctuations are directly taken into account via event-wise non-equilibrium initial conditions generated by the primary collisions and string fragmentations in the microscopic UrQMD model. This leads to non-trivial velocity and energy density distributions for the hydrodynamical initial conditions. Due to the more realistic initial conditions and the incorporated hadronic rescattering the results are in line with the experimental data almost over the whole energy range from E _lab=2–160A GeV.     

A new approach to asymmetric feedback in a segmented broad area diode laser

We present the demonstration of a non-critical setup for asymmetric feedback in a segmented broad area diode laser. We compare the dependence of the beam quality on the position of the dispersive element for standard spectral beam combining and our new non-critical setup. We find that our new approach is significantly less critical to the position of the dispersive element. It is shown that we can displace the dispersive element by at least 50% of the focal length of the collimating lens away from the Fourier plane without compromising performance. Furthermore, our approach provides the same high beam quality as is possible using off-axis spectral beam combining. This provides the possibility of achieving a high beam quality in a more compact setup than previously possible.