Three water sites in upper mantle olivine and the role of titanium in the water weakening mechanism

Infrared spectroscopy on synthetic olivines has established that there are at least four different mechanisms by which hydrogen is incorporated into the crystal structure. Two mechanisms occur in the system MgO-SiO2-H2O associated with silicon and magnesium vacancies, respectively. A third mechanism is associated with trivalent cation substitution, commonly Fe3+ in natural olivine, while the fourth mechanism, which is the one most prevalent in natural olivines from the spinel-peridotite facies of the Earth’s upper mantle, is associated with Ti4+ [Berry et al., 2005]. Here first principles calculations based on density functional theory are used to derive the structure and relative energies of the two defects in the pure MgO-SiO2-H2O system, and possible hydrogen-bearing and hydrogen-free point defects in Ti4+-doped forsterite. Calculated structures are used to compare the predicted orientation of the O-H bonds with the experimentally determined polarization. The energies are used to discuss how different regimes of chemical environment, temperature (T), pressure (P), and both water content and water fugacity ( fH2O), impact on which of the different hydroxyl substitution mechanisms are thermodynamically stable. We find that given the presence of Ti impurities, the most stable mechanism involves the formation of silicon vacancies containing two protons charge balanced by a Ti4+ cation occupying an adjacent octahedral site. This mechanism leads to the water-mediated formation of silicon vacancies. As silicon is known to be the most slowly diffusing species in olivine, this provides a credible explanation of the observed water weakening effect in olivine

Vatican Condemnation of Nazi War Crimes: Pope Pius XII’s Denunciation of Wartime Atrocities

The debate on the silence of Pope Pius XII has been rekindled by recent close examination of the Pope’s 1942 Christmas Message denouncing totalitarianism and the killing of persons “only because of their nationality and race,” along with a particular condemnation of Marxist Socialism and a call for national and international relations to be based on natural law principles guaranteeing justice, order, and peace. In particular, Michael Phayer, a historian writing on the Vatican’s relation to the Holocaust, suggested a need for renewed attention to the 1942 Christmas Message. According to Phayer: Historians . . . have been rather too dismissive of his 1942 Christmas address. Since Pius never spoke out again in a comparable way, the Christmas address has been judged by the Pope’s critics as falling short of the mark, given the enormity of the Holocaust. This judgment rests on hindsight. Most of those who heard or read the Christmas message viewed the statement in a different light, precisely because it was the Pope’s initial comment about wartime atrocities. Considering views such as Phayer’s, this Article will assess the 1942 Christmas Message to determine whether it in fact provided a response to the Holocaust, thus defeating the charge of “silence” which has been directed against Pius XII by revisionist historians and critics

High-order noise filtering in nontrivial quantum logic gates

Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization errors that must be accounted for in order to understand total average error rates. We develop a treatment based on effective Hamiltonian theory that allows us to efficiently model the effect of classical noise on nontrivial single-bit quantum logic operations composed of arbitrary control sequences. We present a general method to calculate the ensemble-averaged entanglement fidelity to arbitrary order in terms of noise filter functions, and provide explicit expressions to fourth order in the noise strength. In the weak noise limit we derive explicit filter functions for a broad class of piecewise-constant control sequences, and use them to study the performance of dynamically corrected gates, yielding good agreement with brute-force numerics.Comment: Revised and expanded to include filter function terms beyond first order in the Magnus expansion. Related manuscripts available from http://www.physics.usyd.edu.au/~mbiercu

Noise-induced behaviors in neural mean field dynamics

The collective behavior of cortical neurons is strongly affected by the presence of noise at the level of individual cells. In order to study these phenomena in large-scale assemblies of neurons, we consider networks of firing-rate neurons with linear intrinsic dynamics and nonlinear coupling, belonging to a few types of cell populations and receiving noisy currents. Asymptotic equations as the number of neurons tends to infinity (mean field equations) are rigorously derived based on a probabilistic approach. These equations are implicit on the probability distribution of the solutions which generally makes their direct analysis difficult. However, in our case, the solutions are Gaussian, and their moments satisfy a closed system of nonlinear ordinary differential equations (ODEs), which are much easier to study than the original stochastic network equations, and the statistics of the empirical process uniformly converge towards the solutions of these ODEs. Based on this description, we analytically and numerically study the influence of noise on the collective behaviors, and compare these asymptotic regimes to simulations of the network. We observe that the mean field equations provide an accurate description of the solutions of the network equations for network sizes as small as a few hundreds of neurons. In particular, we observe that the level of noise in the system qualitatively modifies its collective behavior, producing for instance synchronized oscillations of the whole network, desynchronization of oscillating regimes, and stabilization or destabilization of stationary solutions. These results shed a new light on the role of noise in shaping collective dynamics of neurons, and gives us clues for understanding similar phenomena observed in biological networks

Jahn-Teller Distortions and the Supershell Effect in Metal Nanowires

A stability analysis of metal nanowires shows that a Jahn-Teller deformation breaking cylindrical symmetry can be energetically favorable, leading to stable nanowires with elliptic cross sections. The sequence of stable cylindrical and elliptical nanowires allows for a consistent interpretation of experimental conductance histograms for alkali metals, including both the shell and supershell structures. It is predicted that for gold, elliptical nanowires are even more likely to form since their eccentricity is smaller than for alkali metals. The existence of certain metastable ``superdeformed'' nanowires is also predicted