Totally Asymmetric Exclusion Process with Hierarchical Long-Range Connections

A non-equilibrium particle transport model, the totally asymmetric exclusion process, is studied on a one-dimensional lattice with a hierarchy of fixed long-range connections. This model breaks the particle-hole symmetry observed on an ordinary one-dimensional lattice and results in a surprisingly simple phase diagram, without a maximum-current phase. Numerical simulations of the model with open boundary conditions reveal a number of dynamic features and suggest possible applications.Comment: 10 pages, revtex4, reorganized, with some new analytical results. For related articles, see http://www.physics.emory.edu/faculty/boettcher

Low-Temperature Excitations of Dilute Lattice Spin Glasses

A new approach to exploring low-temperature excitations in finite-dimensional lattice spin glasses is proposed. By focusing on bond-diluted lattices just above the percolation threshold, large system sizes $L$ can be obtained which lead to enhanced scaling regimes and more accurate exponents. Furthermore, this method in principle remains practical for any dimension, yielding exponents that so far have been elusive. This approach is demonstrated by determining the stiffness exponent for dimensions $d=3$, $d=6$ (the upper critical dimension), and $d=7$. Key is the application of an exact reduction algorithm, which eliminates a large fraction of spins, so that the reduced lattices never exceed $\sim10^3$ variables for sizes as large as L=30 in $d=3$, L=9 in $d=6$, or L=8 in $d=7$. Finite size scaling analysis gives $y_3=0.24(1)$ for $d=3$, significantly improving on previous work. The results for $d=6$ and $d=7$, $y_6=1.1(1)$ and $y_7=1.24(5)$, are entirely new and are compared with mean-field predictions made for d>=6.Comment: 7 pages, LaTex, 7 ps-figures included, added result for stiffness in d=7, as to appear in Europhysics Letters (see http://www.physics.emory.edu/faculty/boettcher/ for related information

Numerical Results for Ground States of Mean-Field Spin Glasses at low Connectivities

An extensive list of results for the ground state properties of spin glasses on random graphs is presented. These results provide a timely benchmark for currently developing theoretical techniques based on replica symmetry breaking that are being tested on mean-field models at low connectivity. Comparison with existing replica results for such models verifies the strength of those techniques. Yet, we find that spin glasses on fixed-connectivity graphs (Bethe lattices) exhibit a richer phenomenology than has been anticipated by theory. Our data prove to be sufficiently accurate to speculate about some exact results.Comment: 4 pages, RevTex4, 5 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

pH-Independent, 520 mV Open-Circuit Voltages of Si/Methyl Viologen^(2+/+) Contacts Through Use of Radial n^+p-Si Junction Microwire Array Photoelectrodes

The effects of introducing an n^+-doped emitter layer have been evaluated for both planar Si photoelectrodes and for radial junction Si microwire-array photoelectrodes. In contact with the pH-independent, one-electron, outer-sphere, methyl viologen redox system (denoted MV^(2+/+)), both planar and wire array p-Si photoelectrodes yielded open-circuit voltages, V_(oc), that varied with the pH of the solution. The highest V_(oc) values were obtained at pH = 2.9, with V_(oc) = 0.53 V for planar p-Si electrodes and V_(oc) = 0.42 V for vapor−liquid−solid catalyzed p-Si microwire array samples, under 60 mW cm^(−2) of 808 nm illumination. Increases in the pH of the electrolyte produced a decrease in V_(oc) by approximately −44 mV/pH unit for planar electrodes, with similar trends observed for the Si microwire array electrodes. In contrast, introduction of a highly doped, n^+ emitter layer produced V_(oc) = 0.56 V for planar Si electrodes and V_(oc) = 0.52 V for Si microwire array electrodes, with the photoelectrode properties in each system being essentially independent of pH over six pH units (3 < pH < 9). Hence, formation of an n^+ emitter layer not only produced nearly identical photovoltages for planar and Si microwire array photoelectrodes, but decoupled the band energetics of the semiconductor (and hence the obtainable photovoltage) from the value of the redox potential of the solution. The formation of radial junctions on Si microwire arrays thus provides an approach to obtaining Si-based photoelectrodes with high-photovoltages that can be used for a variety of photoelectrochemical processes, including potentially the hydrogen evolution reaction, under various pH conditions, regardless of the intrinsic barrier height and flat-band properties of the Si/liquid contact

Studies in synthetic carbonatite systems: Solidus relationships for CaO-MgO-CO_2-H_2O to 40 kbar and CaO-MgO-SiO_2-CO_2-H_2O to 10 kbar

The system CaO-MgO-SiO_2-CO_2-H_2O is an important model for many igneous and metamorphic processes, including the generation and differentiation of carbonatite and associated silicate magmas. We have experimentally established the vapor-saturated solidus for the system CaO-MgO-CO_2-H_2O from 595°C/1 kbar to <500°C/40 kbar, about 25°C lower than the corresponding temperatures for the CaO-CO_2-H_2O system. Brucite replaces periclase on the vapor-saturated solidus at about 750 bars pressure, remaining as the stable phase to pressures of at least 40 kbar; no dolomite or magnesite was encountered. At a pressure between 35 and 40 kbar, the assemblage portlandite + brucite + aragonite + vapor changes to one containing phase W, a previously unreported Ca-Mg carbonate. At 20 kbar, the vapor-saturated liquid contains at least 24 wt % H_2O. The vapor-saturated solidus for the system CaO-MgO-SiO_2-CO_2-H_2O ranges from 613°C/1 kbar to 565°C/10 kbar, experimentally indistinguishable from that for CaO-MgO-CO_2-H_2O, about 10°C lower than that for CaO-CO_2-H_2O, and about 25°C lower than that for CaO-SiO_2-CO_2-H_2O. In the quinary system, monticellite is replaced by dellaite and an unidentified silicate on the vapor-saturated solidus above 4.1 kbar. MgO-poor liquids are similar in composition to the magma from which the Magnet Cove calcite carbonatite crystallized. More magnesian magmas would produce dolomite at moderate depths, such as at Alnö Island

Aging in Dense Colloids as Diffusion in the Logarithm of Time

The far-from-equilibrium dynamics of glassy systems share important phenomenological traits. A transition is generally observed from a time-homogeneous dynamical regime to an aging regime where physical changes occur intermittently and, on average, at a decreasing rate. It has been suggested that a global change of the independent time variable to its logarithm may render the aging dynamics homogeneous: for colloids, this entails diffusion but on a logarithmic time scale. Our novel analysis of experimental colloid data confirms that the mean square displacement grows linearly in time at low densities and shows that it grows linearly in the logarithm of time at high densities. Correspondingly, pairs of particles initially in close contact survive as pairs with a probability which decays exponentially in either time or its logarithm. The form of the Probability Density Function of the displacements shows that long-ranged spatial correlations are very long-lived in dense colloids. A phenomenological stochastic model is then introduced which relies on the growth and collapse of strongly correlated clusters ("dynamic heterogeneity"), and which reproduces the full spectrum of observed colloidal behaviors depending on the form assumed for the probability that a cluster collapses during a Monte Carlo update. In the limit where large clusters dominate, the collapse rate is ~1/t, implying a homogeneous, log-Poissonian process that qualitatively reproduces the experimental results for dense colloids. Finally an analytical toy-model is discussed to elucidate the strong dependence of the simulation results on the integrability (or lack thereof) of the cluster collapse probability function.Comment: 6 pages, extensively revised, final version; for related work, see http://www.physics.emory.edu/faculty/boettcher/ or http://www.fysik.sdu.dk/staff/staff-vip/pas-personal.htm

Die Ärzte-Botaniker des XVII. Jahrhunderts

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Solar Water Splitting Cells

No abstract