Divalent and mixed divalent/monovalent conduction in β″-alumina: A Monte Carlo study

A Monte Carlo method is developed for simulation of mixed ionic conductivity in β″-alumina-type materials. The conduction plane of these materials is represented by a lattice gas model in which monovalent and divalent cation carriers diffuse via a vacancy mechanism and interact through a nearest-neighbor coulombic repulsion. By comparing experimental data for pure Na⁺ and pure Ba²⁺ β″-aluminas with simulation results, it is possible to estimate the near-neighbor interaction energies ε_i and jump barriers U_i for both kinds of ions. On the basis of these estimations the total ionic conductivity of Na⁺Ba²⁺ β″-alumina is calculated as a function of temperature and concentration of carriers. As Ba²⁺ replaces Na⁺, the conductivity initially increases as more vacancies become available. For very high temperatures, this increase continues until exchange is complete; but at lower temperatures, the conductivity reaches a peak for some optimal ${}^{\mathrm{<mtext>Ba2+</mtext>}}{}^{\mathrm{<mtext>Na+</mtext>}}$ composition, and then drops off as the number of Ba²⁺, and hence the strength of ionic correlation, goes up. The presence of ordering in the fully exchanged (all Ba²⁺) case manifests itself in substantial curvature of the Arrhenius plots for conductivity. The activation energy for conductivity as a function of Ba²⁺ mole fraction (X_Ba²⁺) shows a pronounced rise near an X value of $\text{2}\text{3}$, in agreement with recent experimental observations.     

Steady-state mode I cracks in a viscoelastic triangular lattice

We construct exact solutions for Mode I steady-state cracks in an ideally brittle viscoelastic triangular lattice model. Our analytic solutions for the infinite lattice are compared to numerical results for finite width systems. The issues we address include the crack velocity versus driving curve as well as the onset of additional bond breaking, signaling the emergence of complex spatio-temporal behavior. Somewhat surprisingly, the critical velocity for this transition becomes a decreasing function of the dissipation for sufficiently large values thereof. Lastly, we briefly discuss the possible relevance of our findings for experiments on mode I crack instabilities.     

Genomic tableaux

We explain how genomic tableaux [Pechenik–Yong ’15] are a semistandard complement to increasing tableaux [Thomas–Yong ’09]. From this perspective, one inherits genomic versions of jeu de taquin, Knuth equivalence, infusion and Bender–Knuth involutions, as well as Schur functions from (shifted) semistandard Young tableaux theory. These are applied to obtain new Littlewood–Richardson rules for K-theory Schubert calculus of Grassmannians (after [Buch ’02]) and maximal orthogonal Grassmannians (after [Clifford–Thomas–Yong ’14], [Buch–Ravikumar ’12]). For the unsolved case of Lagrangian Grassmannians, sharp upper and lower bounds using genomic tableaux are conjectured.     

A dual electrolyte H2/O2 planar membraneless microchannel fuel cell system with open circuit potentials in excess of 1.4 V

A dual electrolyte H2/O2 fuel cell system employing a planar microfluidic membraneless fuel cell has been investigated and compared to single electrolyte H2/O2 systems under analogous conditions. The fuel is H2 dissolved in 0.1 M KOH (pH 13), and the oxidant is O2 dissolved in 0.1 M H2SO4 (pH 0.9), comprising a system with a calculated thermodynamic potential of 1.943 V (when 1 M H2 and O2 concentrations are assumed). This value is well above the calculated thermodynamic maximum of 1.229 V for an acid, or alkaline, single electrolyte H2/O2 fuel cell. Experimentally, open-circuit potentials in excess of 1.4 V have been achieved with the dual electrolyte system. This is a 500 mV increase in the open circuit potentials observed for single electrolyte H2/O2 systems also studied. The dual electrolyte fuel cell system shows power generation of 0.6 mW/cm2 from a single device, which is nearly 0.25 mW/cm2)greater than the values obtained for single electrolyte H2/O2 fuel cell systems studied. Microchannels of varying dimensions have been employed to study both the single and dual electrolyte H2/O2 systems. Channel thickness variation and the flow rate dependences of power generation are also addressed.     

The Genomic Schur Function is Fundamental-Positive

Annals of Combinatorics - In work with A.&nbsp;Yong, the author introduced genomic tableaux to prove the first positive combinatorial rule for the Littlewood–Richardson coefficients in...