Fast coarsening in unstable epitaxy with desorption

Homoepitaxial growth is unstable towards the formation of pyramidal mounds when interlayer transport is reduced due to activation barriers to hopping at step edges. Simulations of a lattice model and a continuum equation show that a small amount of desorption dramatically speeds up the coarsening of the mound array, leading to coarsening exponents between 1/3 and 1/2. The underlying mechanism is the faster growth of larger mounds due to their lower evaporation rate.Comment: 4 pages, 4 PostScript figure

Coarsening of Surface Structures in Unstable Epitaxial Growth

We study unstable epitaxy on singular surfaces using continuum equations with a prescribed slope-dependent surface current. We derive scaling relations for the late stage of growth, where power law coarsening of the mound morphology is observed. For the lateral size of mounds we obtain $\xi \sim t^{1/z}$ with $z \geq 4$. An analytic treatment within a self-consistent mean-field approximation predicts multiscaling of the height-height correlation function, while the direct numerical solution of the continuum equation shows conventional scaling with z=4, independent of the shape of the surface current.Comment: 15 pages, Latex. Submitted to PR

Coarsening Dynamics of Crystalline Thin Films

The formation of pyramid-like structures in thin-film growth on substrates with a quadratic symmetry, e.g., {001} surfaces, is shown to exhibit anisotropic scaling as there exist two length scales with different time dependences. Analytical and numerical results indicate that for most realizations coarsening of mounds is described by an exponent n=0.2357. However, depending on material parameters, n may lie between 0 (logarithmic coarsening) and 1/3. In contrast, growth on substrates with triangular symmetries ({111} surfaces) is dominated by a single length scale and an exponent n=1/3.Comment: RevTeX, 4 pages, 3 figure

Asymptotic step profiles from a nonlinear growth equation for vicinal surfaces

We study a recently proposed nonlinear evolution equation describing the collective step meander on a vicinal surface subject to the Bales-Zangwill growth instability [O. Pierre-Louis et al., Phys. Rev. Lett. (80), 4221 (1998)]. A careful numerical analysis shows that the dynamically selected step profile consists of sloped segments, given by an inverse error function and steepening as sqrt(t), which are matched to pieces of a stationary (time-independent) solution describing the maxima and minima. The effect of smoothening by step edge diffusion is included heuristically, and a one-parameter family of evolution equations is introduced which contains relaxation by step edge diffusion and by attachment-detachment as special cases. The question of the persistence of an initially imposed meander wavelength is investigated in relation to recent experiments.Comment: 4 pages, 5 included figures. Typo in Eq.(5) corrected, section headlines added and Ref.[12] update

Competing mechanisms for step meandering in unstable growth

The meander instability of a vicinal surface growing under step flow conditions is studied within a solid-on-solid model. In the absence of edge diffusion the selected meander wavelength agrees quantitatively with the continuum linear stability analysis of Bales and Zangwill [Phys. Rev. B {\bf 41}, 4400 (1990)]. In the presence of edge diffusion a local instability mechanism related to kink rounding barriers dominates, and the meander wavelength is set by one-dimensional nucleation. The long-time behavior of the meander amplitude differs in the two cases, and disagrees with the predictions of a nonlinear step evolution equation [O. Pierre-Louis et al., Phys. Rev. Lett. {\bf 80}, 4221 (1998)]. The variation of the meander wavelength with the deposition flux and with the activation barriers for step adatom detachment and step crossing (the Ehrlich-Schwoebel barrier) is studied in detail. The interpretation of recent experiments on surfaces vicinal to Cu(100) [T. Maroutian et al., Phys. Rev. B {\bf 64}, 165401 (2001)] in the light of our results yields an estimate for the kink barrier at the close packed steps.Comment: 8 pages, 7 .eps figures. Final version. Some errors in chapter V correcte

Numerical test of the damping time of layer-by-layer growth on stochastic models

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.Comment: 4 pages, source LaTeX file and 5 PS figure

Betterment Accounting: A Requiem by the SEC

The railroad industry, unlike almost every other industry, has a depreciation accounting system all its own known as betterment accounting. In sharp contrast to generally-accepted methods of depreciation, such as ratable depreciation, where the cost of the capital asset is systematically expensed over the useful life of the asset, under the betterment practice, the initial cost of track structures is recorded as a nondepreciable asset. Subsequent replacement costs are then charged directly to operating expense as an adequately reliable measure of depreciation. Justifications for this unique system of accounting relate primarily to the peculiar nature of railroad track structure-a large number of individual components that can be replaced on a scheduled basis. The American Institute of Certified Public Accountants, noting the historical acceptance of betterment accounting, continues to allow the betterment method in railroad financial reports to shareholders. The Interstate Commerce Commission (ICC) as grappled constantly with the issue since the agency was formed in 1887, but still finds the betterment method acceptable and even requires it in railroad reports submitted to the Commission. The Securities and Exchange Commission (SEC) has a chance to make a fresh, critical examination of the appropriateness of betterment accounting for shareholder reporting purposes. The Railroad Revitalization and Regulatory Reform Act of 1976 [4R Act] gives the SEC expanded authority to issue disclosure requirements for railroads in filings with the SEC and reports to investors. Pursuant to this grant of authority, the SEC in April of 1977 announced a proposed rulemaking to examine the standards for disclosure of railroad industry operations. The SEC requested public comment as to whether betterment accounting should continue to be an acceptable accounting principle for railroads for reporting their financial position and results of operations to shareholders and the SEC. The betterment method and the alternative ratable depreciation approach must be compared in light of the SEC\u27s role in ensuring proper disclosure of financial information to the public: which method yields a more accurate picture of a railroad\u27s operating results and over-all financial health? This article will closely examine these two accounting methods by reviewing the public comment received by the SEC under its rulemaking procedure. First the betterment method currently practiced by railroads will be discussed, followed by an analysis of the more widely-accepted ratable depreciation approach

Quantifying the Resilience Value of Distributed Energy Resources

Extreme weather events, which are occurring with increasing frequency as a result of climate change, threaten the reliability and resilience of the nation\u27s electricity grid. Increased flooding due to intense rainfall, hurricane damage fueled in part by a warmer atmosphere and warmer, higher seas, and widespread wildfires caused by extended drought conditions constitute potential hazards for utility infrastructure and delivery of essential electricity service. As a possible adaptation strategy, increased deployment of distributed energy resources (DERs), which are small-scale generating resources located near-and connected to-a load being served with or without grid interconnection, can improve the resilience of the electric system in the face of the increasing frequency of extreme weather events, by avoiding some of the systemic vulnerabilities of a centralized large grid. The experience of Hurricane Sandy (ultimately downgraded to Superstorm Sandy by the time it hit the coasts of New York and New Jersey in late October 2012) provides a case study of the resilience benefits of DERs, and the lessons that can be learned as utilities plan for increasingly frequent extreme weather events of the future. Superstorm Sandy was the deadliest and most destructive hurricane of the 2012 Atlantic hurricane season, resulting in 286 deaths and $68 billion in damages. The storm\u27s diameter extended almost 1,000 miles, and produced a storm surge of 14 feet at the Battery in lower Manhattan that was at least three feet higher than prior reported storm tides. Approximately 8.5 million utility customers along the eastern U.S. lost power during Sandy. Apart from the sheer magnitude of the disaster in terms of fatalities and destruction, Superstorm Sandy provided a wake up call for energy providers, and electric utilities in particular, on the need to adopt a different set of long-term planning tools to improve the resilience of the electric system to cope with the anticipated extreme weather events of the future. One such tool is an expanded role for DERs and microgrids. If the electrical grid is impaired, DERs can be configured to island from the grid, thereby ensuring an uninterrupted supplyof power to utility customers within a microgrid. That was the experience from Superstorm Sandy, where the use of microgrids and DERs enabled power to be provided to pockets of consumers in the face of widespread outages of central power plants and the associated transmission and distribution (T&D) systems. While extended power outages affected the region for days, many commercial and industrial facilities and educational institutions in the area (including Princeton University\u27s campus in New Jersey and New York University\u27s campus in lower Manhattan) were able to continue operating uninterrupted, due to on-site DG facilities, primarily cogeneration or combined heat and power (CHP) facilities. DG resources offer the opportunity to improve the resilience of the electrical grid, mitigating the impacts of an emergency by keeping critical facilities running without any interruption in service. At the same time, it is difficult to quantify the resilience value of DERs and microgrids. To what extent is the grid more resilient due to the presence of DERs? What are the tools available to place a value on this increased resilience? Is it possible to place a value on the continued availability of critical facilities during an extended grid outage? As states move away from compensating DERs through net metering-based on the serving utility\u27s retail rate toward a system based on paying DERs according to their actual contributions to the grid-it becomes increasingly important to try to place a value on the resilience benefits that DERs provide to the grid, to ensure that DER owners and operators receive accurate price signals to stimulate an economically efficient level of investment. This article describes the experience of Superstorm Sandy and the resilience benefits that were provided by DERs and mircrogrids during that particular extreme weather event. The article then discusses recent developments in the approaches for compensating DERs, which is driving the need to quantify the resilience benefits of DERs. Next, the article will review recent efforts to place a value on the resilience benefits of DERs, followed by some concluding observations