Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Laplace Operators on Fractals and Related Functional Equations

We give an overview over the application of functional equations, namely the classical Poincar\'e and renewal equations, to the study of the spectrum of Laplace operators on self-similar fractals. We compare the techniques used to those used in the euclidean situation. Furthermore, we use the obtained information on the spectral zeta function to define the Casimir energy of fractals. We give numerical values for this energy for the Sierpi\'nski gasket

Identification of a Methane Oxidation Intermediate on Solid Oxide Fuel Cell Anode Surfaces with Fourier Transform Infrared Emission

Fuel interactions on solid oxide fuel cell (SOFC) anodes are studied with in situ Fourier transform infrared emission spectroscopy (FTIRES). SOFCs are operated at 800 °C with CH₄ as a representative hydrocarbon fuel. IR signatures of gas-phase oxidation products, CO_2(g) and CO_(g), are observed while cells are under load. A broad feature at 2295 cm^–1 is assigned to CO₂ adsorbed on Ni as a CH₄ oxidation intermediate during cell operation and while carbon deposits are electrochemically oxidized after CH₄ operation. Electrochemical control provides confirmation of the assignment of adsorbed CO₂. FTIRES has been demonstrated as a viable technique for the identification of fuel oxidation intermediates and products in working SOFCs, allowing for the elucidation of the mechanisms of fuel chemistry

Methanol and Ethanol Fuels in Solid Oxide Fuel Cells: A Thermal Imaging Study of Carbon Deposition

Near-infrared (NIR) thermal imaging is used to study anodes of anode-supported solid oxide fuel cells (SOFCs) when operating with alcohol fuels. Relative propensities for carbon formation can be determined from surface cooling under fuel flows and subsequent heating under oxidizing conditions at temperatures between 700 and 800 °C. Ethanol forms considerable amounts of carbon at all temperatures and voltages studied as evidenced by substantial cooling related to carbon reactions and heating under oxidizing conditions. Methanol operation depends greatly on cell temperature and voltage. At 700 °C, temperature changes resemble those with ethanol, suggesting carbon deposition is occurring. At 800 °C, there is less cooling, which indicates that the oxide flux at higher polarizations mitigates the effects of endothermic carbon reactions. Under oxidizing conditions after fuel exposure, the small observed temperature increase demonstrates that little carbon is formed. At 750 °C the cooling depends on voltage, revealing a set of conditions where cooling from endothermic reactions and heating from exothermic reactions are balanced. The results show that while dry ethanol is not a clean fuel under any of our conditions, methanol can be at higher temperatures. NIR thermal imaging proves a valuable stand-off technique for identifying cell deterioration in situ, with potential for process monitoring in operating SOFCs

Toward a Working Mechanism of Fuel Oxidation in SOFCs: In Situ Optical Studies of Simulated Biogas and Methane

Solid-oxide fuel cells (SOFCs) have potential as highly efficient, clean, and sustainable electricity sources. However, the current, limited state of understanding of the complex electrochemical processes that occur at the anode in these systems, particularly those that lead to anode carbon formation and degradation, are roadblocks to effective cell design and operation. A suite of noninvasive, in situ optical techniques has been developed to help identify these processes. Vibrational Raman spectroscopy, Fourier-transform infrared emission spectroscopy (FTIRES), and near-infrared thermal (NIR) imaging, along with electrochemical measurements, provide surface and gas-phase molecular-specific diagnostics with the requisite temporal, spatial, and thermal resolution to correlate in operando observations with model chemical mechanisms associated with oxidation and carbon formation on Ni-based, anode-supported cells. This present work expands upon earlier in operando studies to fully assess the performance of commercially available Ni-YSZ anode SOFCs from 700 to 800 °C and to provide a more comprehensive description of the anode chemistry involved. Methane and simulated biogas (BG) are used as fuel. Raman measurements show that carbon grows minimally only at the lower operational temperatures for BG; however under methane, carbon formation occurs at all temperatures. Subsequent electrochemical oxidation of deposited carbon revealed that carbon formation under both fuels varies differently as a function of temperature. FTIRES measurements show that CO_<i>x</i> constituents increase with cell polarization only under methane fuel; this effect changes with temperature. NIR imaging indicates that the Ni anode surface cools significantly when cells are operated at 800 °C relative to 700 °C under BG, and only minimal cooling is observed when operating with methane

Hydrogen-Bond-Assisted Excited-State Deactivation at Liquid/Water Interfaces

The excited-state dynamics of eosin B (EB) at dodecane/water and decanol/water interfaces has been investigated with polarization-dependent and time-resolved surface second harmonic generation. The results of the polarization-dependent measurements vary substantially with (1) the EB concentration, (2) the age of the sample, and (3) the nature of the organic phase. All of these effects are ascribed to the formation of EB aggregates at the interface. Aggregation also manifests itself in the time-resolved measurements as a substantial shortening of the excited-state lifetime of EB. However, independently of the dye concentration used, the excited-state lifetime of EB at both dodecane/water and decanol/water interfaces is much longer than in bulk water, where the excited-state population undergoes hydrogen-bond-assisted non-radiative deactivation in a few picoseconds. These results indicate that hydrogen bonding between EB and water molecules at liquid/water interfaces is either much less efficient than in bulk water or does not enhance non-radiative deactivation. This strong increase of the excited-state lifetime of EB at liquid/water interfaces opens promising avenues of applying this molecule as a fluorescent interfacial probe