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Diffusion coefficients of Fokker-Planck equation for rotating dust grains in a fusion plasma

In the fusion devices, ions, H atoms, and H{sub 2} molecules collide with dust grains and exert stochastic torques which lead to small variations in angular momentum of the grain. By considering adsorption of the colliding particles, thermal desorption of H atoms and normal H{sub 2} molecules, and desorption of the recombined H{sub 2} molecules from the surface of an oblate spheroidal grain, we obtain diffusion coefficients of the Fokker-Planck equation for the distribution function of fluctuating angular momentum. Torque coefficients corresponding to the recombination mechanism show that the nonspherical dust grains may rotate with a suprathermal angular velocity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A whole-path importance-sampling scheme for Feynman path integral calculations of absolute partition functions and free energies

Using Feynman path integrals, a molecular partition function can be written as a double integral with the inner integral involving all closed paths centered at a given molecular configuration, and the outer integral involving all possible molecular configurations. In previous work employing Monte Carlo methods to evaluate such partition functions, we presented schemes for importance sampling and stratification in the molecular configurations that constitute the path centroids, but we relied on free-particle paths for sampling the path integrals. At low temperatures, the path sampling is expensive because the paths can travel far from the centroid configuration. In this paper, we now present a scheme for importance sampling of whole Feynman paths based on harmonic information from an instantaneous normal mode calculation at the centroid configuration, which we refer to as harmonically guided whole-path importance sampling (WPIS). We obtain paths conforming to our chosen importance function by rejection sampling from a distribution of free-particle paths. Sample calculations on CH 4 demonstrate that at a temperature of 200 K, about 99.9% of the free-particle paths can be rejected without integration, and at 300 K, about 98% can be rejected. Finally, we also show that it is typically possible to reduce the overhead associated with the WPIS scheme by sampling the paths using a significantly lower-order path discretization than that which is needed to converge the partition function.

74 ATOMIC AND MOLECULAR PHYSICS↗

Reconnection from a turbulence perspective

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power law behavior, with a slope near −5/3 at wave numbers smaller than the inverse ion inertial length and a slope steeper than −8/3 for larger wave numbers up to the inverse electron inertial length. This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is the fact that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70° to about 48° (nearly isotropic) by the end of the simulation. The distribution of energy over length scales is further analyzed by dividing the domain into spatial subregions and employing structure functions.

Adhikari, S. (ORCID:0000000321607066)↗

Velocity-space signatures of shock-drift acceleration at quasi-perpendicular collisionless shocks

The shock-drift acceleration of ions at quasi-perpendicular shocks is a well-known kinetic mechanism for the acceleration of a small fraction of incoming ions to high energy. Here, we use a suite of sixteen hybrid simulations of quasi-perpendicular collisionless shocks over the range of Alfvén Mach number 4.3 ≤ M A ≤ 15.8 (corresponding to a range of fast magnetosonic Mach numbers 2.6 ≤ M f ≤ 9.4) and shock-normal angle 45°≤ θ Bn ≤ 90° to identify the velocity-space signature of shock-drift acceleration using the field-particle correlation technique. We show that the features of the ion velocity distribution in the shock foot and ramp regions can be clearly interpreted by analysis of the single-particle trajectory of a reflected ion through the full 3D-3V phase space. The characteristic features of the velocity-space signature of shock-drift acceleration remain qualitatively robust over the full parameter range of our simulations, providing a potential means for its identification using single-point spacecraft measurements. At higher Alfvén Mach numbers M A ≳8 (M f ≳5), kinetic instabilities generate fluctuations of the electromagnetic fields within the shock transition region, leading to fluctuations in and smearing out of the resulting velocity-space signatures, but the signature remains generally robust and identifiable. The results on the shock-drift acceleration of ions presented here represent a novel means to determine more completely the partitioning of upstream bulk flow kinetic energy into plasma heating, particle acceleration, and electromagnetic fields in collisionless shocks.

Howes, Gregory G. [Univ. of Iowa, Iowa City, IA (U↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

The Multi-Isotope Process (MIP) Monitor Project: FY13 Final Report

The Multi-Isotope Process (MIP) Monitor provides an efficient approach to monitoring the process conditions in reprocessing facilities in support of the goal of “… (minimization of) the risks of nuclear proliferation and terrorism.” The MIP Monitor measures the distribution of the radioactive isotopes in product and waste streams of a nuclear reprocessing facility. These isotopes are monitored online by gamma spectrometry and compared, in near-real-time, to spectral patterns representing “normal” process conditions using multivariate analysis and pattern recognition algorithms. The combination of multivariate analysis and gamma spectroscopy allows us to detect small changes in the gamma spectrum, which may indicate changes in process conditions. By targeting multiple gamma-emitting indicator isotopes, the MIP Monitor approach is compatible with the use of small, portable, relatively high-resolution gamma detectors that may be easily deployed throughout an existing facility. The automated multivariate analysis can provide a level of data obscurity, giving a built-in information barrier to protect sensitive or proprietary operational data. Proof-of-concept simulations and experiments have been performed in previous years to demonstrate the validity of this tool in a laboratory setting for systems representing aqueous reprocessing facilities. However, pyroprocessing is emerging as an alternative to aqueous reprocessing techniques.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Partnership for Edge Physics Simulation

A major goal of our participation in the Edge Physics Simulation project has been to contribute to the understanding of the self-organization of tokamak turbulence fluctuations resulting in the formation of a staircase structure in the ion temperature. A second important goal is to demonstrate how small scale turbulence in plasmas self-organizes with dynamically driven quasi-stationary flow shear. These goals have been accomplished through the analyses of the statistical properties of XGC1 flux driven Gyrokinetic electrostatic ion temperature gradient (ITG) turbulence simulation data in which neutrals are included. The ITG turbulence data, and in particular fluctuation data, were obtained from a massively parallel flux-driven gyrokinetic full-f particle-in-cell simulation of a DIII-D like equilibrium. Below some the findings are summarized. It was observed that the emergence of staircase structure is related to the variations in the normalized temperature gradient length (R/LT) and the poloidal flow shear. Average turbulence intensity is found to be large in the vicinity of minima in R/LTi, where ITG growth is expected to be lower. The distributions of the occurrences of potential fluctuation are found to be Gaussian away from the staircase-step locations, but they are found to be non-Gaussian in the vicinity of staircase-step locations. The results of analytically derived expressions for the distribution of the occurrences of turbulence intensity and intensity flux were compared with the corresponding quantities computed using XGC1 simulation data and good agreement is found. The derived expressions predicts inward and outward propagation of turbulence intensity flux in an intermittent fashion. The outward propagation of turbulence intensity flux occurs at staircase-step locations and is related to the change in poloidal flow velocity shear and to the change in the ion temperature gradient. The standard deviation, skewness and kurtosis for turbulence quantities were computed and found to be large in the vicinity of the staircase-step structures. Large values of skewness and kurtosis can be explained by a temporary opening and closing of the structure which allows turbulence intensity events to propagate. The staircase patterns may reduce the ion heat transport and a manipulation of these patterns may be used to optimize heat transport in tokamaks. An additional objective of the research in support of the Edge Physics Simulation initiative has been to improve the understanding of scrape-off layer thermal transport. In planning experiments and designing future tokamaks, it is important to understand the physical effects that contribute to divertor heat-load fluxes. The research accomplished will contribute to developing new models for the scrape-off layer region. The XGC0 code was used to compute the heat fluxes and the heat-load width in the outer divertor plates of C-Mod and DIII-D tokamaks. It was observed that the width of the XGC0 neoclassical heat-load was approximately inversely proportional to the total plasma current. Anomalous transport in the H-mode pedestal region of five Alcator C-Mod discharges, representing a collisionality scan, was analyzed. The understanding of anomalous transport in the pedestal region is important for the development of a comprehensive model for the H-mode pedestal slope. It was found that the electron thermal anomalous diffusivities at the pedestal top increase with the electron collisionality. This dependence can point to the DRIBM as the modes that drive the anomalous transport in the plasma edge of highly collisional discharges. The effects of plasma shaping on the H-mode pedestal structure was also investigated. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities were discussed. For the discharges with higher elongation, it was found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states. In these simulations, the pedestal slowly continued to evolve to higher pedestal pressures and bootstrap currents until the peeling ballooning stability conditions were satisfied. The discharges with lower elongation do not reach the semi-steady state, and ELM crashes were triggered at earlier times. The plasma elongation was found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency was large, and the H-mode pedestal evolves rapidly. It was found that the temperature of neutrals in the scrape-off-layer region can affect the dynamics of the H-mode pedestal buildup. However, the final pedestal profiles were nearly independent of the neutral temperature. The elongation and triangularity affected the pedestal widths of plasma density and electron temperature profiles differently. This study illustrated a new mechanism for controlling the pedestal bootstrap current and the pedestal stability.

97 MATHEMATICS AND COMPUTING↗

Seeing through noise in power laws

Despite widespread claims of power laws across the natural and social sciences, evidence in data is often equivocal. Modern data and statistical methods reject even classic power laws such as Pareto’s law of wealth and the Gutenberg–Richter law for earthquake magnitudes. We show that the maximum-likelihood estimators and Kolmogorov–Smirnov (K-S) statistics in widespread use are unexpectedly sensitive to ubiquitous errors in data such as measurement noise, quantization noise, heaping and censorship of small values. This sensitivity causes spurious rejection of power laws and biases parameter estimates even in arbitrarily large samples, which explains inconsistencies between theory and data. We show that logarithmic binning by powers of λ > 1 attenuates these errors in a manner analogous to noise averaging in normal statistics and that λ thereby tunes a trade-off between accuracy and precision in estimation. Binning also removes potentially misleading within-scale information while preserving information about the shape of a distribution over powers of λ, and we show that some amount of binning can improve sensitivity and specificity of K-S tests without any cost, while more extreme binning tunes a trade-off between sensitivity and specificity. We therefore advocate logarithmic binning as a simple essential step in power-law inference.

97 MATHEMATICS AND COMPUTING↗

High-resolution Statistics of Solar Wind Turbulence at Kinetic Scales Using the Magnetospheric Multiscale Mission

Using data from the Magnetospheric Multiscale (MMS) and Cluster missions obtained in the solar wind, we examine second-order and fourth-order structure functions at varying spatial lags normalized to ion inertial scales. The analysis includes direct two-spacecraft results and single-spacecraft results employing the familiar Taylor frozen-in flow approximation. Several familiar statistical results, including the spectral distribution of energy, and the sale-dependent kurtosis, are extended down to unprecedented spatial scales of ∼6 km, approaching electron scales. The Taylor approximation is also confirmed at those small scales, although small deviations are present in the kinetic range. The kurtosis is seen to attain very high values at sub-proton scales, supporting the previously reported suggestion that monofractal behavior may be due to high-frequency plasma waves at kinetic scales.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-E-T-632: Preliminary Study On Treating Nose Skin Using Energy and Intensity Modulated Electron Beams with Monte Carlo Based Dose Calculations

Purpose: Uneven nose surfaces and air cavities underneath and the use of bolus present complexity and dose uncertainty when using a single electron energy beam to plan treatments of nose skin with a pencil beam-based planning system. This work demonstrates more accurate dose calculation and more optimal planning using energy and intensity modulated electron radiotherapy (MERT) delivered with a pMLC. Methods: An in-house developed Monte Carlo (MC)-based dose calculation/optimization planning system was employed for treatment planning. Phase space data (6, 9, 12 and 15 MeV) were used as an input source for MC dose calculations for the linac. To reduce the scatter-caused penumbra, a short SSD (61 cm) was used. Our previous work demonstrates good agreement in percentage depth dose and off-axis dose between calculations and film measurement for various field sizes. A MERT plan was generated for treating the nose skin using a patient geometry and a dose volume histogram (DVH) was obtained. The work also shows the comparison of 2D dose distributions between a clinically used conventional single electron energy plan and the MERT plan. Results: The MERT plan resulted in improved target dose coverage as compared to the conventional plan, which demonstrated a target dose deficit at the field edge. The conventional plan showed higher dose normal tissue irradiation underneath the nose skin while the MERT plan resulted in improved conformity and thus reduces normal tissue dose. Conclusion: This preliminary work illustrates that MC-based MERT planning is a promising technique in treating nose skin, not only providing more accurate dose calculation, but also offering an improved target dose coverage and conformity. In addition, this technique may eliminate the necessity of bolus, which often produces dose delivery uncertainty due to the air gaps that may exist between the bolus and skin.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Interindividual registration and dose mapping for voxelwise population analysis of rectal toxicity in prostate cancer radiotherapy

Purpose: Recent studies revealed a trend toward voxelwise population analysis in order to understand the local dose/toxicity relationships in prostate cancer radiotherapy. Such approaches require, however, an accurate interindividual mapping of the anatomies and 3D dose distributions toward a common coordinate system. This step is challenging due to the high interindividual variability. In this paper, the authors propose a method designed for interindividual nonrigid registration of the rectum and dose mapping for population analysis. Methods: The method is based on the computation of a normalized structural description of the rectum using a Laplacian-based model. This description takes advantage of the tubular structure of the rectum and its centerline to be embedded in a nonrigid registration-based scheme. The performances of the method were evaluated on 30 individuals treated for prostate cancer in a leave-one-out cross validation. Results: Performance was measured using classical metrics (Dice score and Hausdorff distance), along with new metrics devised to better assess dose mapping in relation with structural deformation (dose-organ overlap). Considering these scores, the proposed method outperforms intensity-based and distance maps-based registration methods. Conclusions: The proposed method allows for accurately mapping interindividual 3D dose distributions toward a single anatomical template, opening the way for further voxelwise statistical analysis.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRB-01: Coverage Evaluation and Probabilistic Treatment Planning as a Margin Alternative

The accepted clinical method to accommodate targeting uncertainties inherent in fractionated external beam radiation therapy is to utilize GTV-to-CTV and CTV-to-PTV margins during the planning process to design a PTV-conformal static dose distribution on the planning image set. Ideally, margins are selected to ensure a high (e.g. >95%) target coverage probability (CP) in spite of inherent inter- and intra-fractional positional variations, tissue motions, and initial contouring uncertainties. Robust optimization techniques, also known as probabilistic treatment planning techniques, explicitly incorporate the dosimetric consequences of targeting uncertainties by including CP evaluation into the planning optimization process along with coverage-based planning objectives. The treatment planner no longer needs to use PTV and/or PRV margins; instead robust optimization utilizes probability distributions of the underlying uncertainties in conjunction with CP-evaluation for the underlying CTVs and OARs to design an optimal treated volume. This symposium will describe CP-evaluation methods as well as various robust planning techniques including use of probability-weighted dose distributions, probability-weighted objective functions, and coverage optimized planning. Methods to compute and display the effect of uncertainties on dose distributions will be presented. The use of robust planning to accommodate inter-fractional setup uncertainties, organ deformation, and contouring uncertainties will be examined as will its use to accommodate intra-fractional organ motion. Clinical examples will be used to inter-compare robust and margin-based planning, highlighting advantages of robust-plans in terms of target and normal tissue coverage. Robust-planning limitations as uncertainties approach zero and as the number of treatment fractions becomes small will be presented, as well as the factors limiting clinical implementation of robust planning. Learning Objectives: To understand robust-planning as a clinical alternative to using margin-based planning. To understand conceptual differences between uncertainty and predictable motion. To understand fundamental limitations of the PTV concept that probabilistic planning can overcome. To understand the major contributing factors to target and normal tissue coverage probability. To understand the similarities and differences of various robust planning techniques To understand the benefits and limitations of robust planning techniques.

60 APPLIED LIFE SCIENCES↗

SU-D-BRE-02: Development and Commissioning of A Gated Spot Scanning Proton Beam Therapy System with Real-Time Tumor-Tracking

Purpose: A novel Proton Beam Therapy system has been developed by integrating Real-Time Tumor-Tracking (RTRT) and discrete spot scanning techniques. The system dedicated for spot scanning delivers significant advantages for both clinical and economical points of view. The system has the ability to control dose distribution with spot scanning beams and to gate the beams from the synchrotron to irradiate moving tumors only when the actual positions of them are within the planned position. Methods: The newly designed system consists of a synchrotron, beam transport systems, a compact and rotating gantry system with robotic couch and two orthogonal sets of X-ray fluoroscopes. The fully compact design of the system has been realized by reducing the maximum energy of the beam to 220MeV, corresponding to 30g/cm2 range and the number of circulating protons per synchrotron operation cycle, due to higher beam utilization efficiency in spot scanning. To improve the irradiation efficiency in the integration of RTRT and spot scanning, a new control system has been developed to enable multiple gated irradiation per operation cycle according to the gating signals. After the completion of the equipment installation, beam tests and commissioning has been successfully performed. Results: The basic performances and beam characteristics through the synchrotron accelerator to iso-center have been confirmed and the performance test of the irradiation nozzle and whole system has been appropriately completed. CBCT image has been checked and sufficient quality was obtained. RTRT system has been demonstrated and realized accurate dose distributions for moving targets. Conclusion: The gated spot scanning Proton Beam Therapy system with Real-Time Tumor-Tracking has been developed, successfully installed and tested. The new system enables us to deliver higher dose to the moving target tumors while sparing surrounding normal tissues and to realize the compact design of the system and facility by maximizing the efficiency of proton beam utilization. This research is granted by the Japan Society for the Promotion of Science(JSPS) through the “Funding Program for World-Leading Innovative R and D on Science and Technology(FIRST Program)”, initiated by the Council for Science and Technology Policy(CSTP)

60 APPLIED LIFE SCIENCES↗

WE-AB-204-02: Molecular-Imaging Based Assessment of Liver Complications for Yttrium-90 Microsphere Treatments: Can Existing NTCP Models Explain Clinical Outcomes?

Purpose: To evaluate weather the current radiobiological models can predict the normal liver complications of radioactive Yttrium-90 ({sup 90}Y) selective-internal-radiation-treatment (SIRT) for metastatic liver lesions based on the post-infusion {sup 90}Y PET images. Methods: A total of 20 patients with metastatic liver tumors treated with SIRT that received a post-infusion {sup 90}Y-PET/CT scan were analyzed in this work. The 3D activity distribution of the PET images was converted into a 3D dose distribution via a kernel convolution process. The physical dose distribution was converted into the equivalent dose (EQ2) delivered at 2 Gy based on the linear-quadratic (LQ) model considering the dose rate effect. The biological endpoint of this work was radiation-induce liver disease (RILD). The NTCPs were calculated with four different repair-times (T1/2-Liver-Repair= 0,0.5,1.0,2.0 hr) and three published NTCP models (Lyman-external-RT, Lyman 90Y-HCC-SIRT, parallel model) were compared to the incidence of RILD of the recruited patients to evaluate their ability of outcome prediction. Results: The mean normal liver physical dose (avg. 51.9 Gy, range 31.9–69.8 Gy) is higher than the suggested liver dose constraint for external beam treatment (∼30 Gy). However, none of the patients in our study developed RILD after the SIRT. The estimated probability of ‘no patient developing RILD’ obtained from the two Lyman models are 46.3% to 48.3% (T1/2-Liver-Repair= 0hr) and <1% for all other repair times. For the parallel model, the estimated probability is 97.3% (0hr), 51.7% (0.5hr), 2.0% (1.0hr) and <1% (2.0hr). Conclusion: Molecular-images providing the distribution of {sup 90}Y enable the dose-volume based dose/outcome analysis for SIRT. Current NTCP models fail to predict RILD complications in our patient population, unless a very short repair-time for the liver is assumed. The discrepancy between the Lyman {sup 90}Y-HCC-SIRT model predicted and the clinically observed outcomes further demonstrates the need of an NTCP model specific to the metastatic liver SIRT.

60 APPLIED LIFE SCIENCES↗

Analysis of High-Penetration Levels of Photovoltaics into the Distribution Grid on Oahu, Hawaii: Detailed Analysis of HECO Feeder WF1

Renewable generation is growing at a rapid rate due to the incentives available and the aggressive renewable portfolio standard (RPS) targets implemented by state governments. Distributed generation in particular is seeing the fastest growth among renewable energy projects, and is directly related to the incentives. Hawaii has the highest electricity costs in the country due to the high percentage of oil burning steam generation, and therefore has some of the highest penetration of distributed PV in the nation. The High Penetration PV (HiP-PV) project on Oahu aims to understand the effects of high penetration PV on the distribution level, to identify penetration levels creating disturbances on the circuit, and to offer mitigating solutions based on model results. Power flow models are validated using data collected from solar resources and load monitors deployed throughout the circuit. Existing interconnection methods and standards such as IEEE 1547, Hawaii Rule 14H and California Rule 21 are evaluated in these emerging high penetration scenarios. A key finding is a shift in the level of detail to be considered and moving away from steady-state peak time analysis towards dynamic and time varying simulations. Each level of normal interconnection study is evaluated and enhanced to a new level of detail, allowing full understanding of each issue.

14 SOLAR ENERGY↗

COMPARATIVE MORPHOLOGY OF SOLAR RELATIVISTIC PARTICLE EVENTS

Time profiles of the 0.25–10 MeV electrons and the ∼(0.1–1) GeV nucleon{sup −1} protons and helium associated with two solar coronal mass ejections (CMEs) are analyzed with a newly formulated method based on modeling of the particle transport in the interplanetary medium. With the modeling, we fit the observed angular distribution of solar particles and infer, for a particular particle instrument and magnetic field orientation, the time delay of the particle registration at 1 AU in respect to the solar source. Then, after the time offset removal, intensity re-normalization and background equalization, the time–intensity profiles of high-energy protons, helium and electrons in different energy channels are superposed and compared. The comparison reveals episodes of remarkable coincidence of different profiles, as well as episodes of essentially different behavior. It implies at least three sources of solar high-energy particles operating in a single event. The first, short-duration source emits electrons next to the flare's impulsive phase and CME liftoff. The second source gradually rises and continues for more than an hour, emitting electrons and lower energy protons, which is consistent with shock acceleration on open magnetic field lines extending to solar wind. An another, third source is the main source of relativistic ions in space. It is retarded in respect to the flare's impulsive phase and may be associated with a structure encountered by the shock within a few solar radii from the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗

A Submillimeter Perspective on the GOODS Fields (SUPER GOODS). I. An Ultradeep SCUBA-2 Survey of the GOODS-N

In this first paper in the SUPER GOODS series on powerfully star-forming galaxies in the two GOODS fields, we present a deep SCUBA-2 survey of the GOODS-N at both 850 and 450 μm (central rms noise of 0.28 mJy and 2.6 mJy, respectively). In the central region, the 850 μm observations cover the GOODS-N to near the confusion limit of ∼1.65 mJy, while over a wider 450 arcmin{sup 2} region—well complemented by Herschel far-infrared imaging—they have a median 4σ limit of 3.5 mJy. We present ⩾4σ catalogs of 186 850 μm and 31 450 μm selected sources. We use interferometric observations from the Submillimeter Array (SMA) and the Karl G. Jansky Very Large Array (VLA) to obtain precise positions for 114 SCUBA-2 sources (28 from the SMA, all of which are also VLA sources). We present new spectroscopic redshifts and include all existing spectroscopic or photometric redshifts. We also compare redshifts estimated using the 20 cm/850 μm and the 250 cm/850 μm flux ratios. We show that the redshift distribution increases with increasing flux, and we parameterize the dependence. We compute the star formation history and the star formation rate (SFR) density distribution functions in various redshift intervals, finding that they reach a peak at z=2--3 before dropping to higher redshifts. We show that the number density per unit volume of SFR ≳500 M{sub ⊙} yr{sup −1} galaxies measured from the SCUBA-2 sample does not change much relative to that of lower SFR galaxies from UV selected samples over z=2--5, suggesting that, apart from changes in the normalization, the shape in the number density as a function of SFR is invariant over this redshift interval.

79 ASTRONOMY AND ASTROPHYSICS↗

Stochastic Modeling of Overtime Occupancy and Its Application in Building Energy Simulation and Calibration

Overtime is a common phenomenon around the world. Overtime drives both internal heat gains from occupants, lighting and plug-loads, and HVAC operation during overtime periods. Overtime leads to longer occupancy hours and extended operation of building services systems beyond normal working hours, thus overtime impacts total building energy use. Current literature lacks methods to model overtime occupancy because overtime is stochastic in nature and varies by individual occupants and by time. To address this gap in the literature, this study aims to develop a new stochastic model based on the statistical analysis of measured overtime occupancy data from an office building. A binomial distribution is used to represent the total number of occupants working overtime, while an exponential distribution is used to represent the duration of overtime periods. The overtime model is used to generate overtime occupancy schedules as an input to the energy model of a second office building. The measured and simulated cooling energy use during the overtime period is compared in order to validate the overtime model. A hybrid approach to energy model calibration is proposed and tested, which combines ASHRAE Guideline 14 for the calibration of the energy model during normal working hours, and a proposed KS test for the calibration of the energy model during overtime. The developed stochastic overtime model and the hybrid calibration approach can be used in building energy simulations to improve the accuracy of results, and better understand the characteristics of overtime in office buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗