Coherence and wavefront characterization of Si‐111 monochromators using double‐grating interferometry

A study of the coherence and wavefront properties of a pseudo‐channel‐cut monochromator in comparison with a double‐crystal monochromator is presented. Using a double‐grating interferometer designed for the hard X‐ray regime, the complex coherence factor was measured and the wavefront distortions at the sample position were analyzed. A transverse coherence length was found in the vertical direction that was a factor of two larger for the channel‐cut monochromator owing to its higher mechanical stability. The wavefront distortions after different optical elements in the beam, such as monochromators and mirrors, were also quantified. This work is particularly relevant for coherent diffraction imaging experiments with synchrotron sources.     

Performance of a four‐element Si drift detector for X‐ray absorption fine‐structure spectroscopy: resolution, maximum count rate,and dead‐time correction with incorporation into the ATHENA data analysis software

The performance of a four‐element Si drift detector for energy‐dispersive fluorescence‐yield X‐ray absorption fine‐structure measurements is reported, operating at the National Institute of Standards and Technology beamline X23A2 at the National Synchrotron Light Source. The detector can acquire X‐ray absorption fine‐structure spectra with a throughput exceeding 4 × 10⁵ counts per second per detector element (>1.6 × 10⁶ total counts per second summed over all four channels). At this count rate the resolution at 6 keV is approximately 220 eV, which adequately resolves the Mn Kα and Kβ fluorescence lines. Accurate dead‐time correction is demonstrated, and it has been incorporated into the ATHENA data analysis program. To maintain counting efficiency and high signal to background, it is suggested that the incoming count rate should not exceed ～70% of the maximum throughput.     

Mid infrared interband cascade lasers for sensing applications

The growth of Interband Cascade Laser material to cover the wavelength range from 3–4 μm is presented along with the fabrication and characterization of Broad Area (BA) and Ridge Waveguide (RWG) devices based on this material. Pulsed operation slightly below room temperature is observed for both device types, and a strong reduction of threshold currents can be observed in the RWG lasers. Variation of the active Quantum Well width in the epitaxial structures enables laser emission in the 3–4 μm wavelength region.     

Experimental study of the stability and optimization of multipulse passive mode locking

We present an experimental study of the stability of passively mode-locked pulses against noise in multipulse operation of an erbium-doped fiber laser. The laser properties are determined by two dimensionless combinations of the laser parameters. Measurements of the pulses' destabilization threshold as a function of those laser parameters show the optimal regions that maximize the mode-locked pulse stability. We find good agreement between the experimental observations and the theoretical predictions.     

Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

A Gleason–Kahane–Żelazko theorem for the Dirichlet space

We show that every linear functional on the Dirichlet space that is non-zero on nowhere-vanishing functions is necessarily a multiple of a point evaluation. Continuity of the functional is not assumed. As an application, we obtain a characterization of weighted composition operators on the Dirichlet space as being exactly those linear maps that send nowhere-vanishing functions to nowhere-vanishing functions.We also investigate possible extensions to weighted Dirichlet spaces with superharmonic weights. As part of our investigation, we are led to determine which of these spaces contain functions that map the unit disk onto the whole complex plane.     

Existence of incomplete canonical Kirkman packing designs

For $u,v$ positive integers with $u\equiv v\equiv 4\left(mod6\right)$, let ICKPD$(u,v)$ denote a canonical Kirkman packing of order $u$ missing one of order $v$. In this paper, it is shown that the necessary condition for existence of an ICKPD$(u,v)$, namely $u\ge 3v+4$, is sufficient with a definite exception $(u,v)=(16,4)$, and except possibly when $v>76$, $v\equiv 4\left(mod12\right)$ and $u\in \{3v+4,3v+10\}$.     

Convergence in Wasserstein distance for self-stabilizing diffusion evolving in a double-well landscape

It is well-known (see Bolley et al. [3]) that there exists a contraction in Wasserstein distance between the solution to the granular media equation and its unique steady state, provided that the confining potential is strictly convex. Nevertheless, in the nonconvex case, just few is known. In particular, we do not have a unique steady state under easily checked assumptions if the diffusion coefficient is sufficiently small. Consequently, the method of Bolley, Gentil and Guillin can not be applied in this setting. However, here, we present a simple example (for the sake of the simplicity) of a double-well confining potential, and we show the convergence to 0 of the Wasserstein distance between the solution to the granular media equation and a related application (which characterizes the steady states) of this solution.