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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

SU-E-T-643: Pure Alanine Dosimeter for Verification Dosimetry in IMRT

Purpose: The objective of this study was evaluation of accuracy of pure alanine dosimeters measuring intensity-modulated radiation therapy (IMRT) dose distributions in a thorax phantom. Methods: Alanine dosimeters were prepared in the form of 110 mg pure L-α-alanine powder filled into clear tissue-equivalent polymethylmethacrylate (PMMA) plastic tubes with the dimensions 25 mm length, 3 mm inner diameter, and 1 mm wall thickness. A dose-response calibration curve was established for the alanine by placing the dosimeters at 1.5 cm depth in a 30×30×30 cm{sup 3} solid water phantom and then irradiating on a linac with 6 MV photon beam at 10×10 cm{sup 2} field size to doses ranging from 1 to 5 Gy. Electron paramagnetic resonance (EPR) spectroscopy was used to determine the absorbed dose in alanine. An IMRT treatment plan was designed for a commercial heterogeneous CIRS thorax phantom and the dose values were calculated at three different points located in tissue, lung, and bone equivalent materials. A set of dose measurements was carried out to compare measured and calculated dose values by placing the alanine dosimeters at those selected locations inside the thorax phantom and delivering the IMRT to the phantom. Results: The alanine dose measurements and the IMRT plan dose calculations were found to be in agreement within ±2%. Specifically, the deviations were −0.5%, 1.3%, and −1.7% for tissue, lung, and bone; respectively. The slightly large deviations observed for lung and bone may be attributed to tissue inhomogeneity, steep dose gradients in these regions, and uncontrollable changes in spectrometer conditions. Conclusion: The results described herein confirmed that pure alanine dosimeter was suitable for in-phantom dosimetry of IMRT beams because of its high sensitivity and acceptable accuracy. This makes the dosimeter a promising option for quality control of the therapeutic beams, complementing the commonly used ionization chambers, TLDs, and films.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

MO-F-CAMPUS-T-03: Data Driven Approaches for Determination of Treatment Table Tolerance Values for Record and Verification Systems

Purpose: To determine appropriate couch tolerance values for modern radiotherapy linac R&V systems with indexed patient setup. Methods: Treatment table tolerance values have been the most difficult to lower, due to many factors including variations in patient positioning and differences in table tops between machines. We recently installed nine linacs with similar tables and started indexing every patient in our clinic. In this study we queried our R&V database and analyzed the deviation of couch position values from the acquired values at verification simulation for all patients treated with indexed positioning. Mean and standard deviations of daily setup deviations were computed in the longitudinal, lateral and vertical direction for 343 patient plans. The mean, median and standard error of the standard deviations across the whole patient population and for some disease sites were computed to determine tolerance values. Results: The plot of our couch deviation values showed a gaussian distribution, with some small deviations, corresponding to setup uncertainties on non-imaging days, and SRS/SRT/SBRT patients, as well as some large deviations which were spot checked and found to be corresponding to indexing errors that were overriden. Setting our tolerance values based on the median + 1 standard error resulted in tolerance values of 1cm lateral and longitudinal, and 0.5 cm vertical for all non- SRS/SRT/SBRT cases. Re-analizing the data, we found that about 92% of the treated fractions would be within these tolerance values (ignoring the mis-indexed patients). We also analyzed data for disease site based subpopulations and found no difference in the tolerance values that needed to be used. Conclusion: With the use of automation, auto-setup and other workflow efficiency tools being introduced into radiotherapy workflow, it is very essential to set table tolerances that allow safe treatments, but flag setup errors that need to be reassessed before treatments.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Moderate deviations-based importance sampling for stochastic recursive equations

Subsolutions to the Hamilton–Jacobi–Bellman equation associated with a moderate deviations approximation are used to design importance sampling changes of measure for stochastic recursive equations. Analogous to what has been done for large deviations subsolution-based importance sampling, these schemes are shown to be asymptotically optimal under the moderate deviations scaling. Here, we present various implementations and numerical results to contrast their performance, and also discuss the circumstances under which a moderate deviation scaling might be appropriate.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

SU-F-T-588: Asymmetries in the CyberKnife Iris 2 Collimator

Purpose: The Iris 2 dodecahedral collimator in the CyberKnife unit can demonstrate visible asymmetry in the shaped radiation field, as seen on routine films. Specifically some edges of the collimator project longer than others. PDDs and output factors remain unaffected by this asymmetry. An in-house program was written to analyze the impact of this asymmetry on profiles. Methods: Two years of routine chromodynamic films were retrospectively analyzed using an in-house developed program. Films were obtained on a weekly basis in a plastic phantom on the vendor-provided mount. Profiles were obtained every degree. A dodecahedron was fitted to the 50% isodose line and the positions and sizes of the upper and lower hexagonal collimators were derived. The collimators’ profiles at every degree, symmetry and centering were calculated and trended over the months. Results: Asymmetries in the obtained profiles were apparent. The upper and lower collimators were off-centered (0.31 mm, p<10–8), they did not project the same field size at 80 cm (0.46 mm difference, p<10–31). Profiles as a function of angle demonstrate a periodicity, but short and long profiles are rarely 15° apart, but vary from 9° to 21°. In addition, a second, intermediate minimum is seen at every other short profile. A trend in the field size over time is noted and can be monitored to identify servicing needs. Conclusion: Despite its differences, the asymmetric Iris 2 collimator did not demonstrate large deviations in PDDs and output factors. Due to the asymmetry, the 15° apart profiles obtained at commissioning do not represent the true large and short blade profiles of the collimator. Averaging of the profiles in the commissioning process hides this difference.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2018

Towards district scale flood simulations using conventional and anisotropic porosity shallow water models with high-resolution topographic information

Current topographic survey technology provides high-resolution (HR) datasets for urban environments. Incorporating this HR information in models aiming to provide flood risk assessment is desirable because the flood wave propagation is depending on the urban topographic features, i.e. buildings, bridges and street networks. Conceptual, numerical and practical challenges arise from the application of shallow water models to HR urban flood modeling. For example, numerical challenges are occurrence of wet-dry fronts, geometric discontinuities in the urban environment and discontinuous solutions, i.e. shock waves. These challenges can be overcome by using a Godunov-type scheme. However, the computational cost of this type of schemes is high, such that HR two-dimensional shallow water simulations with practical relevance have to be run on supercomputers. The porous shallow water model is an alternative approach that aims to reduce computational cost by using a coarse resolution and accounting for unresolved processes by means of the porosity terms. Usually, a speedup between two and three orders of magnitude in comparison to HR simulations can be obtained. This study presents preliminary results of a practical test case concerning pluvial flooding in a district of the city of Nice, France, caused by the intense rainfall event on October 3rd, 2015. HR topography data set on a 1 m resolution is available for the district, whereby street features of infra-metric dimensions have been included. A reference solution is calculated by a HR shallow water model on a 1 m by 1 m structured computational grid. The porous shallow water model is run on a 10 m by 10 m grid and the influence of the drag source term is studied. The model calculations show a large deviation, which is caused by the poor meshing strategy of the porous shallow water (AP) model. The study also summarizes practical challenges that arise during the application of the AP and HR models to a large urban catchment. The main difficulty is to obtain a good mesh. In smaller scale investigations, the mesh is currently constructed by hand such that the cell edges align with buildings. This approach is not feasible for large scale urban catchments with a large number of buildings. Future steps that have to be taken, such as a strategy for automatic mesh generation, are reported on.

42 ENGINEERING↗
DOE OSTI2016

TIDAL STIRRING OF SATELLITES WITH SHALLOW DENSITY PROFILES PREVENTS THEM FROM BEING TOO BIG TO FAIL

The “too big to fail” problem is revisited by studying the tidal evolution of populations of dwarf satellites with different density profiles. The high-resolution cosmological ΛCDM “ErisMod” set of simulations is used. These simulations can model both the stellar and dark matter components of the satellites, and their evolution under the action of the tides of a Milky Way (MW)-sized host halo at a force resolution better than 10 pc. The stronger tidal mass loss and re-shaping of the mass distribution induced in satellites with γ = 0.6 dark matter density distributions, as those resulting from the effect of feedback in hydrodynamical simulations of dwarf galaxy formation, are sufficient to bring the circular velocity profiles in agreement with the kinematics of MW’s dSphs. In contrast, in simulations in which the satellites retain cusps at z = 0 there are several “massive failures” with circular velocities in excess of the observational constraints. Various sources of deviations in the conventionally adopted relation between the circular velocity at the half-light radius and the one-dimensional line of sight velocity dispersions are found. Such deviations are caused by the response of circular velocity profiles to tidal effects, which also varies depending on the initially assumed inner density profile and by the complexity of the stellar kinematics, which include residual rotation and anisotropy. In addition, tidal effects naturally induce large deviations in the stellar mass–halo mass relation for halo masses below 10{sup 9} M {sub ⊙}, preventing any reliable application of the abundance matching technique to dwarf galaxy satellites.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

An Hp-Adaptive Minimum Action Method Based on a Posteriori Error Estimate

In this work, we develop an hp-adaptive minimum action method (MAM). MAM plays an important role to minimize the Freidlin-Wentzell action functional, which is the central object of the Freidlin-Wentzell theory of large deviations for transitions induced by small random perturbations. Because of the demanding computation cost, especially in spatially extended systems, numerical efficiency is a critical issue for MAM. Difficulties come from discretizations of both time and space. One hurdle for the application of MAM to large scale systems is the global reparametrization in time direction, which is required by most versions of MAM. We recently introduced a new version of MAM in [25], called tMAM, where we used some simple heuristic criteria to demonstrate that tMAM can be effectively coupled with h-adaptivity. The target of this paper is to integrate hp-adaptivity into tMAM using a posterior error estimation techniques. More specifically, we use the arc length constraint given by geometric minimum action method (gMAM) to define an indicator of the effect of linear time scaling in tMAM, and the derivative recovery technique to construct an error indicator and a regularity indicator for hp-refinement. Numerical results are presented.

Wan, Xiaoliang↗
DOE OSTI2020

Beam energy dependence of net- Λ fluctuations measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider

The measurements of particle multiplicity distributions have generated considerable interest in understanding the fluctuations of conserved quantum numbers in the quantum chromodynamics (QCD) hadronization regime, in particular near a possible critical point and near the chemical freeze-out. Net-protons and net-kaons have been used as proxies for the net-baryon number and net-strangeness, respectively. We report the measurement of efficiency- and centrality-bin width-corrected cumulant ratios (C 2 /C 1 , C 3 /C 2 ) of net- Λ distributions, in the context of both strangeness and baryon number conservation, as a function of collision energy, centrality, and rapidity. The results are for Au + Au collisions at five beam energies ( √s NN = 19.6 , 27, 39, 62.4, and 200 GeV) recorded with the Solenoidal Tracker at RHIC (STAR). We compare our results to the Poisson and negative binomial (NBD) expectations, as well as to ultrarelativistic quantum molecular dynamics (UrQMD) and hadron resonance gas (HRG) model predictions. Both NBD and Poisson baselines agree with data within the statistical and systematic uncertainties. UrQMD describes the measured net- Λ C 1 and C 3 at 200 GeV reasonably well but deviates from C 2 , and the deviation increases as a function of collision energy. The ratios of the measured cumulants show no features of critical fluctuations. The chemical freeze-out temperatures extracted from a recent HRG calculation, which was successfully used to describe the net-proton, net-kaon, and net-charge data, indicate Λ freeze-out conditions similar to those of kaons. However, large deviations are found when comparing with temperatures obtained from net-proton fluctuations. The net- Λ cumulants show a weak but finite dependence on the rapidity coverage in the acceptance of the detector, which can be attributed to quantum number conservation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Constructing auxiliary dynamics for nonequilibrium stationary states by variance minimization

We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study the interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D weakly asymmetric simple exclusion process. We show that with modest resources, we can capture the features of the susceptibility in large systems that mark the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Electric field and turbulence in global Braginskii simulations across the ASDEX Upgrade edge and scrape-off layer

Turbulence simulations in diverted geometry across the edge and scrape-off layer (SOL) of ASDEX Upgrade are performed with the GRILLIX code (Stegmeir et al 2019 Phys. Plasmas 26 052517). The underlying global (full-f) drift-reduced Braginskii model allows to concurrently study the self-consistent dynamics of the turbulence and the background as well as the evolution of toroidal and zonal flows. Different contributions to the radial electric field are identified. The dominant contribution on closed flux surfaces comes from the ion pressure gradient, due to the diamagnetic drift in the curved magnetic field. Large deviations can be induced, in particular, by the polarization particle flux, leading to zonal flows. The latter are driven by small-scale eddies, but do not exhibit much impact on the overall transport which is driven by ballooning modes at larger scales. Ion viscosity is found to be important in damping poloidal rotation through adjusting of the parallel velocity profile, but not via direct vorticity damping. The zonal flow drive peaks at the separatrix, where a strong shear layer forms due to the sheath-induced counter-propagating SOL flow, allowing for the formation of a transport barrier. The temperature profile across the separatrix is determined by the competition between cross-field transport and outflow in the SOL, the latter being largely controlled by the parallel heat conductivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Assessment of Model Hub Height Wind Speed Performance Using DOE Lidar Buoy Data

As the offshore wind industry continues to gain momentum both in the U.S. and globally, reanalysis products remain essential tools for the lifecycle of a wind farm. From project siting and production estimates to determining construction and maintenance windows, reanalysis products play an important role. These regional and global long-term models also serve as inputs to higher resolution models. With such wide-ranging impacts on the offshore wind industry, the need for validation of reanalysis products is strong, particularly at typical turbine hub heights. Pacific Northwest National Laboratory (PNNL) operates two AXYS WindSentinelTM buoys for the U.S. Department of Energy (DOE) in order to collect meteorological and oceanographic data, including hub height wind speed, in areas of interest for offshore wind development. This work uses DOE buoy observations off the coasts of New Jersey and Virginia to evaluate the performance of Modern Era Retrospective Analysis for Research and Applications-2 (MERRA-2), the North American Regional Reanalysis (NARR), the European Center for Medium-Range Weather Forecasts (ECMWF) Reanalysis 5th generation (ERA5), and the National Oceanic and Atmospheric Administration (NOAA) assimilation system Rapid Refresh (RAP). Biases and degrees of correspondence are determined for each reanalysis product in order to provide insights on the performance and uncertainty for long-term wind resource characterization. With the baseline metrics determined, this work proceeds with an investigation into the sources of large deviations between the modeled and observed hub height wind speeds during the East Coast lidar buoy deployments. Consistent sources of reanalysis model error include stably stratified flow conditions, high wind shear, flow parallel to the coastline, and tropical and winter storms. For the near shore New Jersey location, offshore winds (i.e. blowing from land to water) tend to be associated with model overestimation of observed hub height wind speed, while winds parallel to the coastline are correlated with model underestimation of wind speed. Similarly, near the Virginia buoy, during southerly winds (parallel to the coastline) models underestimate the observed wind speed due to coastal upwelling. Reanalysis model wind speeds underestimate the hub height winds with increasing stable atmospheric stratification. Reanalysis model biases are seen when the observed wind speeds approach or exceed typical turbine cut-out speeds (around 20 m s-1). Large model errors during winter and tropical storm events, high wind speed events, and ramp events are often the result of wind speed timing and magnitude offsets. Overall, ERA5 provides the most successful representation of observed offshore hub height wind speeds at the U.S. East Coast buoy locations and is therefore best suited as an input boundary condition for model case studies. ERA5 performs well for a variety of atmospheric phenomena, including storms and sea breezes, however RAP, the next most successful reanalysis model, performs best in capturing the frequency of ramp events.

17 WIND ENERGY↗
DOE OSTI2023

Evidence of Mixed Scaling for Mean Profile Similarity in the Stable Atmospheric Surface Layer

A new mixed scaling parameter Z = z/(Lh)1/2 is proposed for similarity in the stable atmospheric surface layer, where z is the height, L is the Obukhov length, and h is the boundary layer depth. In comparison with the parameter ζ = z/L from Monin–Obukhov similarity theory (MOST), the new parameter Z leads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on both Z and ζ. The proposed mixed scaling of Z and relevance of h can be explained by physical arguments related to the limit of z-less stratification that is reached asymptotically above the surface layer. The presented evidence and fitted similarity relations are promising, but the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Here, corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Crystal structure refinements of tetragonal (OH,F)-rich spessartine and henritermierite garnets

Cubic garnet (space group Ia\overline 3 d) has the general formula X 3 Y 2 Z 3 O 12 , where X , Y and Z are cation sites. In the tetragonal garnet (space group I 4 1 / acd ), the corresponding cation sites are X 1 and X 2, Y , and Z 1 and Z 2. In both space groups only the Y site is the same. The crystal chemistry of a tetragonal (OH,F)-rich spessartine sample from Tongbei, near Yunxiao, Fujian Province, China, with composition X (Mn 2.82 Fe^{2+}_{0.14}Ca 0.04 ) Σ3 Y {Al 1.95 Fe^{3+}_{0.05}} Σ2 Z [(SiO 4 ) 2.61 (O 4 H 4 ) 0.28 (F 4 ) 0.11 ] Σ3 (Sps 94 Alm 5 Grs 1 ) was studied with single-crystal X-ray diffraction and space group I 4 1 / acd . The deviation of the unit-cell parameters from cubic symmetry is small [ a = 11.64463(1), c = 11.65481 (2) Å, c / a = 1.0009]. Point analyses and back-scattered electron images, obtained by electron-probe microanalysis, indicate a homogeneous composition. The Z 2 site is fully occupied, but the Z 1 site contains vacancies. The occupied Z 1 and Z 2 sites with Si atoms are surrounded by four O atoms, as in anhydrous cubic garnets. Pairs of split sites are O1 with F11 and O2 with O22. When the Z 1 site is vacant, a larger [(O 2 H 2 )F 2 ] tetrahedron is formed by two OH and two F anions in the O22 and F11 sites, respectively. This [(O 2 H 2 )F 2 ] tetrahedron is similar to the O 4 H 4 tetrahedron in hydrogarnets. These results indicate ^{X}{{\rm Mn}^ {2+}_{3}}\,^{Y}{\rm Al}_{2}^{Z}[({\rm SiO}_{4})_{2}({\rm O}_{2}{\rm H}_{2})_{0.5}({\rm F}_{2})_{0.5}]_{\Sigma3} as a possible end member, which is yet unknown. The H atom that is bonded to the O22 site is not located because of the small number of OH groups. In contrast, tetragonal henritermierite, ideally ^{X}{\rm Ca}_{3}\,^{Y}{\rm Mn}^{3+}_{2}\,^{Z}[({\rm SiO}_{4})_{2}({\rm O}_{4}{\rm H}_{4})_1]_{\Sigma3}, has a vacant Z 2 site that contains the O 4 H 4 tetrahedron. The H atom is bonded to an O3 atom [O3—H3 = 0.73 (2) Å]. Because of O2—Mn 3+ —O2 Jahn–Teller elongation of the Mn 3+ O 6 octahedron, a weak hydrogen bond is formed to the under-bonded O2 atom. This causes a large deviation from cubic symmetry ( c / a = 0.9534).

Antao, Sytle M.↗
DOE OSTI2020

Fisher for complements: extracting cosmology and neutrino mass from the counts-in-cells PDF

In this work, we comprehensively analyse the cosmology dependence of counts-in-cells statistics. Furthermore, we focus on the shape of the one-point probability distribution function (PDF) of the matter density field at mildly non-linear scales. Based on large-deviation statistics, we parametrize the cosmology dependence of the matter PDF in terms of the linear power spectrum, the growth factor, the spherical collapse dynamics, and the non-linear variance. We extend our formalism to include massive neutrinos, finding that the total matter PDF is highly sensitive to the total neutrino mass Mν and can disentangle it from the clustering amplitude σ 8 . Additionally, using more than a million PDFs extracted from the Quijote simulations, we determine the response of the matter PDF to changing parameters in the νΛCDM model and successfully cross-validate the theoretical model and the simulation measurements. We present the first νΛCDM Fisher forecast for the matter PDF at multiple scales and redshifts, and its combination with the matter power spectrum. We establish that the matter PDF and the matter power spectrum are highly complementary at mildly non-linear scales. The matter PDF is particularly powerful for constraining the matter density Ωm, clustering amplitude σ 8 and the total neutrino mass Mν. Adding the mildly non-linear matter PDF to the mildly non-linear matter power spectrum improves constraints on Ω m by a factor of 5 and σ 8 by a factor of 2 when considering the three lowest redshifts. In our joint analysis of the matter PDF and matter power spectrum at three redshifts, the total neutrino mass is constrained to better than 0.01 eV with a total volume of 6 (Gpc h -1 ) 3 . We discuss how density-split statistics can be used to translate those encouraging results for the matter PDF into realistic observables in galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Complete resolution across the neodymium/samarium isotopic envelope with a liquid sampling‐atmospheric pressure glow discharge — Orbitrap mass spectrometer

Rationale Nd and Sm isotope ratios play an important role in geological dating and as nuclear forensic signatures; however, the overlap of the respective 144, 148, 150 Nd/Sm isobars requires prior separations to be performed before analysis on typical MS platforms. The work presented here overcomes these isobaric interferences using ultrahigh‐mass resolution to alleviate interference without prior chemical separations. Methods A liquid sampling‐atmospheric pressure glow discharge ion source was coupled to a standard, QExactive Focus Orbitrap mass spectrometer, providing a mass resolution of ~80 k. A Spectroswiss FTMS booster X2 data acquisition package was used to collect extended transients, providing much higher mass resolution; ~230 k and ~600 k are employed here for Nd and Sm isotopes. Results While the standard Orbitrap resolution is far greater than typical “atomic” MS platforms, it was insufficient to alleviate all isobars. The use of a resolution of ~230 k resulted in baseline separation across the entire isotopic envelope for both Nd and Sm. Isotope ratios obtained from Nd:Sm mixtures using high‐resolution were equivalent to those found for individual‐element solutions, while isotope ratios obtained at a resolution of ~80 k (standard for the OEM data system) showed large deviations. Conclusions Use of ultrahigh‐resolution is an attractive alternative to extensive chemical separations to alleviate severe isobaric interferences. Sufficient mass resolution greatly reduces/eliminates the need for sample manipulations (separations) before analysis while reducing costs and total analysis times.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A Characterization of the Reflected Quasipotential

Recent interest in the reflected quasipotential comes from the queueing theory literature, specifically the analysis of so-called (b,A,D) reflected Brownian motion where it is the large deviation rate function for the stationary distribution. Our purpose here is to characterize the reflected quasipotential in terms of a first-order Hamilton–Jacobi equation. Using conventional dynamic programming ideas, along with a complementarity problem formulation of the effect of the Skorokhod map on absolutely continuous paths, we will derive necessary conditions in the form of viscosity-sense boundary conditions. It turns out that even with these boundary conditions solutions are not unique. Thus a unique characterization needs to refer to some additional property of V(⋅). We establish such a characterization in two dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Asymptotic Properties of the Density of Particles in β-Ensembles

We extend recent results on the asymptotic equipartition property for the density of n particles in β-ensembles, as n tends to infinity. We prove the large deviation principle of the log-density for a general potential and the mod-Gaussian convergence in the classical examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Cluster Tails for Critical Power-Law Inhomogeneous Random Graphs

Recently, the scaling limit of cluster sizes for critical inhomogeneous random graphs of rank-1 type having finite variance but infinite third moment degrees was obtained in Bhamidi et al. (Ann Probab 40:2299–2361, 2012). It was proved that when the degrees obey a power law with exponent τ∈(3,4), the sequence of clusters ordered in decreasing size and multiplied through by n{sup −(τ−2)/(τ−1)} converges as n→∞ to a sequence of decreasing non-degenerate random variables. Here, we study the tails of the limit of the rescaled largest cluster, i.e., the probability that the scaling limit of the largest cluster takes a large value u, as a function of u. This extends a related result of Pittel (J Combin Theory Ser B 82(2):237–269, 2001) for the Erdős–Rényi random graph to the setting of rank-1 inhomogeneous random graphs with infinite third moment degrees. We make use of delicate large deviations and weak convergence arguments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗