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

Photoelectrochemical water splitting: silicon photocathodes for hydrogen evolution

The development of low cost, scalable, renewable energy technologies is one of today's most pressing scientific challenges. We report on progress towards the development of a photoelectrochemical water-splitting system that will use sunlight and water as the inputs to produce renewable hydrogen with oxygen as a by-product. This system is based on the design principle of incorporating two separate, photosensitive inorganic semiconductor/liquid junctions to collectively generate the 1.7-1.9 V at open circuit needed to support both the oxidation of H_2O (or OH^-) and the reduction of H^+ (or H_2O). Si microwire arrays are a promising photocathode material because the high aspect-ratio electrode architecture allows for the use of low cost, earth-abundant materials without sacrificing energy-conversion efficiency, due to the orthogonalization of light absorption and charge-carrier collection. Additionally, the high surfacearea design of the rod-based semiconductor array inherently lowers the flux of charge carriers over the rod array surface relative to the projected geometric surface of the photoelectrode, thus lowering the photocurrent density at the solid/liquid junction and thereby relaxing the demands on the activity (and cost) of any electrocatalysts. Arrays of Si microwires grown using the Vapor Liquid Solid (VLS) mechanism have been shown to have desirable electronic light absorption properties. We have demonstrated that these arrays can be coated with earth-abundant metallic catalysts and used for photoelectrochemical production of hydrogen. This development is a step towards the demonstration of a complete artificial photosynthetic system, composed of only inexpensive, earth-abundant materials, that is simultaneously efficient, durable, and scalable

d_c=4 is the upper critical dimension for the Bak-Sneppen model

Numerical results are presented indicating d_c=4 as the upper critical dimension for the Bak-Sneppen evolution model. This finding agrees with previous theoretical arguments, but contradicts a recent Letter [Phys. Rev. Lett. 80, 5746-5749 (1998)] that placed d_c as high as d=8. In particular, we find that avalanches are compact for all dimensions d<=4, and are fractal for d>4. Under those conditions, scaling arguments predict a d_c=4, where hyperscaling relations hold for d<=4. Other properties of avalanches, studied for 1<=d<=6, corroborate this result. To this end, an improved numerical algorithm is presented that is based on the equivalent branching process.Comment: 4 pages, RevTex4, as to appear in Phys. Rev. Lett., related papers available at http://userwww.service.emory.edu/~sboettc

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

Continuous extremal optimization for Lennard-Jones Clusters

In this paper, we explore a general-purpose heuristic algorithm for finding high-quality solutions to continuous optimization problems. The method, called continuous extremal optimization(CEO), can be considered as an extension of extremal optimization(EO) and is consisted of two components, one is with responsibility for global searching and the other is with responsibility for local searching. With only one adjustable parameter, the CEO's performance proves competitive with more elaborate stochastic optimization procedures. We demonstrate it on a well known continuous optimization problem: the Lennerd-Jones clusters optimization problem.Comment: 5 pages and 3 figure

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

Evaluation of Pt, Ni, and Ni–Mo electrocatalysts for hydrogen evolution on crystalline Si electrodes

The dark electrocatalytic and light photocathodic hydrogen evolution properties of Ni, Ni–Mo alloys, and Pt on Si electrodes have been measured, to assess the viability of earth-abundant electrocatalysts for integrated, semiconductor coupled fuel formation. In the dark, the activities of these catalysts deposited on degenerately doped p^+-Si electrodes increased in the order Ni < Ni–Mo ≤ Pt. Ni–Mo deposited on degenerately doped Si microwires exhibited activity that was very similar to that of Pt deposited by metal evaporation on planar Si electrodes. Under 100 mW cm^(−2) of Air Mass 1.5 solar simulation, the energy conversion efficiencies of p-type Si/catalyst photoelectrodes ranged from 0.2–1%, and increased in the order Ni ≈ Ni–Mo < Pt, due to somewhat lower photovoltages and photocurrents for p-Si/Ni–Mo relative to p-Si/Ni and p-Si/Pt photoelectrodes. Deposition of the catalysts onto microwire arrays resulted in higher apparent catalytic activities and similar photoelectrode efficiencies than were observed on planar p-Si photocathodes, despite lower light absorption by p-Si in the microwire structures

Universal persistence exponents in an extremally driven system

The local persistence R(t), defined as the proportion of the system still in its initial state at time t, is measured for the Bak--Sneppen model. For 1 and 2 dimensions, it is found that the decay of R(t) depends on one of two classes of initial configuration. For a subcritical initial state, R(t)\sim t^{-\theta}, where the persistence exponent \theta can be expressed in terms of a known universal exponent. Hence \theta is universal. Conversely, starting from a supercritical state, R(t) decays by the anomalous form 1-R(t)\sim t^{\tau_{\rm ALL}} until a finite time t_{0}, where \tau_{\rm ALL} is also a known exponent. Finally, for the high dimensional model R(t) decays exponentially with a non--universal decay constant.Comment: 4 pages, 6 figures. To appear in Phys. Rev.

10 µm minority-carrier diffusion lengths in Si wires synthesized by Cu-catalyzed vapor-liquid-solid growth

The effective electron minority-carrier diffusion length, L_(n,eff), for 2.0 µm diameter Si wires that were synthesized by Cu-catalyzed vapor-liquid-solid growth was measured by scanning photocurrent microscopy. In dark, ambient conditions, L_(n,eff) was limited by surface recombination to a value of ≤ 0.7 µm. However, a value of L_(n,eff) = 10.5±1 µm was measured under broad-area illumination in low-level injection. The relatively long minority-carrier diffusion length observed under illumination is consistent with an increased surface passivation resulting from filling of the surface states of the Si wires by photogenerated carriers. These relatively large L_(n,eff) values have important implications for the design of high-efficiency, radial-junction photovoltaic cells from arrays of Si wires synthesized by metal-catalyzed growth processes

Solar Water Splitting Cells

No abstract