Green Roofs Over Time: A Spatially Explicit Method for Studying Green Roof Vegetative Dynamics and Performance

In the past decade, conventional green roof research methodology has emphasized performance measures that assume a static state condition of vegetative composition based on design intent and establishment conditions. Such research has predominantly been limited to short-term observations for low diversity, rigorously maintained systems. These conditions, however, are not the reality of many installed green roofs, and as a result knowledge of how these living systems change over time is limited. Given this perspective, this paper presents an ecologically grounded and spatially explicit methodology aimed at assessing the long-term performance and dynamics of green roof vegetation. The method allows for observations of plant composition and performance based on both statistical and graphical analysis of plant cover and diversity measures. Application of this methodology is presented through a multi-year case study of a single, six year-old, intensive green roof in Ithaca, New York. Applicable to any green roof, this method promotes an understanding of green roofs as adaptive, ecological systems, a perspective that will aid in better predicting green roof performance over time, and inform the design, construction, and maintenance of resilient, high-performance roofscapes

String Theory and Water Waves

We uncover a remarkable role that an infinite hierarchy of non-linear differential equations plays in organizing and connecting certain {hat c}<1 string theories non-perturbatively. We are able to embed the type 0A and 0B (A,A) minimal string theories into this single framework. The string theories arise as special limits of a rich system of equations underpinned by an integrable system known as the dispersive water wave hierarchy. We observe that there are several other string-like limits of the system, and conjecture that some of them are type IIA and IIB (A,D) minimal string backgrounds. We explain how these and several string-like special points arise and are connected. In some cases, the framework endows the theories with a non-perturbative definition for the first time. Notably, we discover that the Painleve IV equation plays a key role in organizing the string theory physics, joining its siblings, Painleve I and II, whose roles have previously been identified in this minimal string context.Comment: 49 pages, 4 figure

Modelling the spatial distribution of DEM Error

Assessment of a DEM’s quality is usually undertaken by deriving a measure of DEM accuracy – how close the DEM’s elevation values are to the true elevation. Measures such as Root Mean Squared Error and standard deviation of the error are frequently used. These measures summarise elevation errors in a DEM as a single value. A more detailed description of DEM accuracy would allow better understanding of DEM quality and the consequent uncertainty associated with using DEMs in analytical applications. The research presented addresses the limitations of using a single root mean squared error (RMSE) value to represent the uncertainty associated with a DEM by developing a new technique for creating a spatially distributed model of DEM quality – an accuracy surface. The technique is based on the hypothesis that the distribution and scale of elevation error within a DEM are at least partly related to morphometric characteristics of the terrain. The technique involves generating a set of terrain parameters to characterise terrain morphometry and developing regression models to define the relationship between DEM error and morphometric character. The regression models form the basis for creating standard deviation surfaces to represent DEM accuracy. The hypothesis is shown to be true and reliable accuracy surfaces are successfully created. These accuracy surfaces provide more detailed information about DEM accuracy than a single global estimate of RMSE

D-Branes and Fluxes in Supersymmetric Quantum Mechanics

Type 0A string theory in the (2,4k) superconformal minimal model backgrounds, with background ZZ D-branes or R-R fluxes can be formulated non-perturbatively. The branes and fluxes have a description as threshold bound states in an associated one-dimensional quantum mechanics which has a supersymmetric structure, familiar from studies of the generalized KdV system. The relevant bound state wavefunctions in this problem have unusual asymptotics (they are not normalizable in general, and break supersymmetry) which are consistent with the underlying description in terms of open and closed string sectors. The overall organization of the physics is very pleasing: The physics of the closed strings in the background of branes or fluxes is captured by the generalized KdV system and non-perturbative string equations obtained by reduction of that system (the hierarchy of equations found by Dalley, Johnson, Morris and Watterstam). Meanwhile, the bound states wavefunctions, which describe the physics of the ZZ D-brane (or flux) background in interaction with probe FZZT D-branes, are captured by the generalized mKdV system, and non-perturbative string equations obtained by reduction of that system (the Painleve II hierachy found by Periwal and Shevitz in this context).Comment: 41 pages, LaTe

Temperature dependence of mechanical stiffness and dissipation in ultrananocrystalline diamond

Ultrananocrystalline diamond (UNCD) films are promising for radio frequency micro electro mechanical systems (RF-MEMS) resonators due to the extraordinary physical properties of diamond, such as high Young’s modulus, quality factor, and stable surface chemistry. UNCD films used for this study are grown on 150 mm silicon wafers using hot filament chemical vapor deposition (HFCVD) at 680°C. UNCD fixed free (cantilever) resonator structures designed for the resonant frequencies in the kHz range have been fabricated using conventional microfabrication techniques and are wet released. Resonant excitation and ring down measurements in the temperature range of 138 K to 300 K were conducted under ultra high vacuum (UHV) conditions in a custom built UHV AFM stage to determine the temperature dependence of Young’s Modulus and dissipation (quality factor) in these UNCD cantilever structures. We measured a temperature coefficient of frequency (TCF) of 121 and 133 ppm/K for the cantilevers of 350 ìm and 400 ìm length respectively. Young’s modulus of the cantilevers increased by about 3.1% as the temperature was reduced from 300 K to 138 K. This is the first such measurement for UNCD and suggests that the nanostructure plays a significant role in modifying the thermo-mechanical response of the material. The quality factor of these resonators showed a moderate increase as the cantilevers were cooled from 300 K to 138 K. The results suggest that surface and bulk defects significantly contribute to the observed dissipation in UNCD resonators

Interplay between spatially explicit sediment sourcing, hierarchical river-network structure, and in-channel bed material sediment transport and storage dynamics

Understanding how sediment moves along source to sink pathways through watersheds„from hillslopes to channels and in and out of floodplains„is a fundamental problem in geomorphology. We contribute to advancing this understanding by modeling the transport and in-channel storage dynamics of bed material sediment on a river network over a 600æyear time period. Specifically, we present spatiotemporal changes in bed sediment thickness along an entire river network to elucidate how river networks organize and process sediment supply. We apply our model to sand transport in the agricultural Greater Blue Earth River Basin in Minnesota. By casting the arrival of sediment to links of the network as a Poisson process, we derive analytically (under supply-limited conditions) the time-averaged probability distribution function of bed sediment thickness for each link of the river network for any spatial distribution of inputs. Under transport-limited conditions, the analytical assumptions of the Poisson arrival process are violated (due to in-channel storage dynamics) where we find large fluctuations and periodicity in the time series of bed sediment thickness. The time series of bed sediment thickness is the result of dynamics on a network in propagating, altering, and amalgamating sediment inputs in sometimes unexpected ways. One key insight gleaned from the model is that there can be a small fraction of reaches with relatively low-transport capacity within a nonequilibrium river network acting as ñbottlenecksî that control sediment to downstream reaches, whereby fluctuations in bed elevation can dissociate from signals in sediment supply. ©2017. American Geophysical Union. All Rights Reserved

Backlund Transformations, D-Branes, and Fluxes in Minimal Type 0 Strings

We study the Type 0A string theory in the (2,4k) superconformal minimal model backgrounds, focusing on the fully non-perturbative string equations which define the partition function of the model. The equations admit a parameter, Gamma, which in the spacetime interpretation controls the number of background D-branes, or R-R flux units, depending upon which weak coupling regime is taken. We study the properties of the string equations (often focusing on the (2,4) model in particular) and their physical solutions. The solutions are the potential for an associated Schrodinger problem whose wavefunction is that of an extended D-brane probe. We perform a numerical study of the spectrum of this system for varying Gamma and establish that when Gamma is a positive integer the equations' solutions have special properties consistent with the spacetime interpretation. We also show that a natural solution-generating transformation (that changes Gamma by an integer) is the Backlund transformation of the KdV hierarchy specialized to (scale invariant) solitons at zero velocity. Our results suggest that the localized D-branes of the minimal string theories are directly related to the solitons of the KdV hierarchy. Further, we observe an interesting transition when Gamma=-1.Comment: 17 pages, 3 figure

Dispersion force for materials relevant for micro and nanodevices fabrication

The dispersion (van der Waals and Casimir) force between two semi-spaces are calculated using the Lifshitz theory for different materials relevant for micro and nanodevices fabrication, namely, gold, silicon, gallium arsenide, diamond and two types of diamond-like carbon (DLC), silicon carbide, silicon nitride and silicon dioxide. The calculations were performed using recent experimental optical data available in the literature, usually ranging from the far infrared up to the extreme ultraviolet bands of the electromagnetic spectrum. The results are presented in the form of a correction factor to the Casimir force predicted between perfect conductors, for the separation between the semi-spaces varying from 1 nanometre up to 1 micrometre. The relative importance of the contributions to the dispersion force of the optical properties in different spectral ranges is analyzed. The role of the temperature for semiconductors and insulators is also addressed. The results are meant to be useful for the estimation of the impact of the Casimir and van der Waals forces on the operational parameters of micro and nanodevices