Singularities in speckled speckle: Statistics

Random optical fields with two widely different correlation lengths generate far field speckle spots that are themselves highly speckled. We call such patterns speckled speckle, and study their critical points (singularities and stationary points) using analytical theory and computer simulations. We find anomalous spatial arrangements of the critical points and orders of magnitude anomalies in their relative number densities, and in the densities of the associated zero crossings.     

Ionization of methane in strong and ultrastrong relativistic fields

The photoionization of methane is reported for intensities up to 10(19) W/cm2 with linear and circular polarized light. While fragmental ions (e.g., CH3+, CH+, C+, C2+) created from 10(14) W/cm2 to 10(15) W/cm2 are formed by Coulomb explosion, ionization to form C3+ and C4+ involves Coulomb explosion and tunneling ionization. In ultrastrong fields, removal of a carbon K-shell electron from methane proceeds via tunneling and rescattering ionization, without the influence of molecular channels. Photoelectrons from methane at 10(19) W/cm2 extend up to kinetic energies of 0.6 MeV.     

Bulk and shear mechanical loss of titania-doped tantala

We report on the mechanical loss from bulk and shear stresses in thin film, ion beam deposited, titania-doped tantala. The numerical values of these mechanical losses are necessary to fully calculate the Brownian thermal noise in precision optical cavities, including interferometric gravitational wave detectors like LIGO. We found the values from measuring the normal mode mechanical quality factors, Q's, in the frequency range of about 2000-10,000 Hz, of silica disks coated with titania-doped tantala coupled with calculating the elastic energy in shear and bulk stresses in the coating using a finite element model. We fit the results to both a frequency independent and frequency dependent model and find ${?}_{\mathrm{shear}}=(8.3\pm 1.1)\times {10}^{?4}$, ${?}_{\mathrm{bulk}}=(6.6\pm 3.8)\times {10}^{?4}$ with a frequency independent model and ${?}_{\mathrm{shear}}\left(f\right)=(5.0\pm 0.7)\times {10}^{?4}+(5.4\pm 1.1)\times {10}^{?8}f$, ${?}_{\mathrm{bulk}}\left(f\right)=(11\pm 2.8)\times {10}^{?4}?(8.7\pm 4.7)\times {10}^{?8}f$ with a frequency dependent (linear) model. The ratio of these values suggest that modest improvement in the coating thermal noise may be possible in future gravitational wave detector optics made with titania-doped tantala as the high index coating material by optimizing the coating design to take advantage of the two different mechanical loss angles.     

Golem: an algorithm for robust experiment and process optimization

Numerous challenges in science and engineering can be framed as optimization tasks, including the maximization of reaction yields, the optimization of molecular and materials properties, and the fine-tuning of automated hardware protocols. Design of experiment and optimization algorithms are often adopted to solve these tasks efficiently. Increasingly, these experiment planning strategies are coupled with automated hardware to enable autonomous experimental platforms. The vast majority of the strategies used, however, do not consider robustness against the variability of experiment and process conditions. In fact, it is generally assumed that these parameters are exact and reproducible. Yet some experiments may have considerable noise associated with some of their conditions, and process parameters optimized under precise control may be applied in the future under variable operating conditions. In either scenario, the optimal solutions found might not be robust against input variability, affecting the reproducibility of results and returning suboptimal performance in practice. Here, we introduce Golem, an algorithm that is agnostic to the choice of experiment planning strategy and that enables robust experiment and process optimization. Golem identifies optimal solutions that are robust to input uncertainty, thus ensuring the reproducible performance of optimized experimental protocols and processes. It can be used to analyze the robustness of past experiments, or to guide experiment planning algorithms toward robust solutions on the fly. We assess the performance and domain of applicability of Golem through extensive benchmark studies and demonstrate its practical relevance by optimizing an analytical chemistry protocol under the presence of significant noise in its experimental conditions.

Numerous challenges in science and engineering can be framed as optimization tasks. Golem is an uncertain-input algorithm that ensures the reproducible performance of optimized experimental protocols and processes.     

Pointwise a priori bounds for a strongly coupled system of reaction–diffusion equations with a balance law

We consider a reaction–diffusion system with a full matrix of diffusion coefficients satisfying a balance law on a bounded domain with no-flux boundary conditions. We demonstrate that global solutions exist for polynomial reaction terms provided some conditions on the diffusion coefficients are satisfied. The proof makes use of comparison results and Solonnikov's estimates concerning linear parabolic equations in Banach spaces. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Synthesis and electrochemical properties of new cobalt and manganese phthalocyanine complexes tetra-substituted with 3,4-(methylendioxy)-phenoxy

The synthesis and electrochemical properties of new cobalt and manganese phthalocyanine complexes, tetra-substituted with 3,4-(methylendioxy)-phenoxy at the peripheral (complexes 3 and 5) and non-peripheral (complexes 4 and 6) positions, are reported. Complexes 3 and 4 showed Q-band absorption, in DMF, at 668 and 686 nm, respectively while Q-band due to complexes 5 and 6 appeared at 732 and 760 nm, respectively in CHCl₃. All the complexes showed well resolved redox processes attributed to both metal and ring based processes. Complexes 3 and 4 showed four redox processes, labeled I, II, III and IV. For complex 3, process I (Co^IPc⁻²/Co^IPc⁻³) was observed at −1.45 V, II (Co^IIPc⁻²/Co^IPc⁻²) at −0.38 V, III (Co^IIIPc⁻²/Co^IIPc⁻²) at +0.49 V and IV (Co^IIIPc⁻¹/Co^IIIPc⁻²) at +0.97 V versus Ag|AgCl. Similar processes were observed for complex 4 at −1.36 V, −0.27 V, +0.56 V, +1.03 V versus Ag|AgCl, respectively. Complexes 5 and 6 showed two redox processes (I and II). For complex 5, these processes appeared at −0.79 V (Mn^IIPc⁻²/Mn^IIPc⁻³, I) and −0.07 V versus Ag|AgCl (Mn^IIIPc⁻²/Mn^IIPc⁻², II), while for complex 6, they were observed at −0.86 V and −0.04 V versus Ag|AgCl. Spectroelectrochemistry was used to probe and confirm the origin of these processes.     

Anodic and Cathodic Platinum Dissolution Processes Involve Different Oxide Species

The degradation of Pt-containing oxygen reduction catalysts for fuel cell applications is strongly linked to the electrochemical surface oxidation and reduction of Pt. Here, we study the surface restructuring and Pt dissolution mechanisms during oxidation/reduction for the case of Pt(100) in 0.1 M HClO₄ by combining operando high-energy surface X-ray diffraction, online mass spectrometry, and density functional theory. Our atomic-scale structural studies reveal that anodic dissolution, detected during oxidation, and cathodic dissolution, observed during the subsequent reduction, are linked to two different oxide phases. Anodic dissolution occurs predominantly during nucleation and growth of the first, stripe-like oxide. Cathodic dissolution is linked to a second, amorphous Pt oxide phase that resembles bulk PtO₂ and starts to grow when the coverage of the stripe-like oxide saturates. In addition, we find the amount of surface restructuring after an oxidation/reduction cycle to be potential-independent after the stripe-like oxide has reached its saturation coverage.