Holographic recording using two-photon-induced photopolymerization

Molecular excitation via the simultaneous absorption of two photons can lead to improved three-dimensional control of photochemical or photophysical processes due to the quadratic dependence of the absorption probability on the incident radiation intensity. This has lead to the development of improved three-dimensional fluorescence imaging, optical data storage, and microfabrication. The latter of these involves the fabrication of three-dimensional structures using a spatial variation in the incident intensity within a photopolymerizable resin. In the past, the translation of the focal plane of a tightly focused laser beam was used to induce localized photopolymerization and fabrication of three-dimensional structures. Here we report the first successful demonstration of large-area patterning via ultrafast holography-based two-photon polymerization of a commercially available optical resin and a large two-photon cross-section dye (AF380). This opens tremendous possibilities for the wide-spread use of two-photon absorption for the three-dimensional control of photoinduced processes. Received: 21 June 1999 / Accepted: 23 June 1999 / Published online: 8 September 1999     

Nano-electrocatalyst materials for low temperature fuel cells:A review

Low temperature fuel cells are an attractive technology for transportation and residential applica‐tions due to their quick start up and shut down capabilities. This review analyzed the current status ...     

Scaling up Studies on PEMFC Using a Modified Serpentine Flow Field Incorporating Porous Sponge Inserts to Observe Water Molecules

Flooding of the cathode flow channel is a major hindrance in achieving maximum performance from Proton Exchange Membrane Fuel Cells (PEMFC) during the scaling up process. Water accumulated between the interface region of Gas Diffusion Layer (GDL) and rib of the cathode flow field can be removed by the use of Porous Sponge Inserts (PSI) on the ribs. In the present work, the experimental investigations are carried out on PEMFC for the various reaction areas, namely 25, 50 and 100 cm². Stoichiometry value of 2 is maintained for all experiments to avoid variations in power density obtained due to differences in fuel utilization. The experiments include two flow fields, namely Serpentine Flow Field (SFF) and Modified Serpentine with Staggered provisions of 4 mm PSI (4 mm × 2 mm × 2 mm) Flow Field (MSSFF). The peak power densities obtained on MSSFF are 0.420 W/cm², 0.298 W/cm² and 0.232 W/cm² compared to SFF which yields 0.242 W/cm², 0.213 W/cm² and 0.171 W/cm² for reaction areas of 25, 50 and 100 cm² respectively. Further, the reliability of experimental results is verified for SFF and MSSFF on 25 cm² PEMFC by using Electrochemical Impedance Spectroscopy (EIS). The use of 4 mm PSI is found to improve the performance of PEMFC through the better water management.     

The full automorphism group of T‾

Let $\stackrel{￣}{G}$ be the wonderful compactification of a simple affine algebraic group G of adjoint type defined over $\mathbb{C}$. Let $\stackrel{￣}{T}?\stackrel{￣}{G}$ be the closure of a maximal torus $T?G$. We prove that the group of all automorphisms of the variety $\stackrel{￣}{T}$ is the semi-direct product $N_G(T)?D$, where $N_G(T)$ is the normalizer of T in G and D is the group of all automorphisms of the Dynkin diagram, if $G\ne \mathrm{PSL}(2,\mathbb{C})$. Note that if $G=\mathrm{PSL}(2,\mathbb{C})$, then $\stackrel{￣}{T}=\mathbb{C}{\mathbb{P}}^1$ and so in this case $\text{Aut}(\stackrel{￣}{T})=\mathrm{PSL}(2,\mathbb{C})$.     

The cluster problem in constrained global optimization

Deterministic branch-and-bound algorithms for continuous global optimization often visit a large number of boxes in the neighborhood of a global minimizer, resulting in the so-called cluster problem (Du and Kearfott in J Glob Optim 5(3):253–265, 1994). This article extends previous analyses of the cluster problem in unconstrained global optimization (Du and Kearfott 1994; Wechsung et al. in J Glob Optim 58(3):429–438, 2014) to the constrained setting based on a recently-developed notion of convergence order for convex relaxation-based lower bounding schemes. It is shown that clustering can occur both on nearly-optimal and nearly-feasible regions in the vicinity of a global minimizer. In contrast to the case of unconstrained optimization, where at least second-order convergent schemes of relaxations are required to mitigate the cluster problem when the minimizer sits at a point of differentiability of the objective function, it is shown that first-order convergent lower bounding schemes for constrained problems may mitigate the cluster problem under certain conditions. Additionally, conditions under which second-order convergent lower bounding schemes are sufficient to mitigate the cluster problem around a global minimizer are developed. Conditions on the convergence order prefactor that are sufficient to altogether eliminate the cluster problem are also provided. This analysis reduces to previous analyses of the cluster problem for unconstrained optimization under suitable assumptions.