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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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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Optimal scheduling for profit maximization of energy storage merchants considering market impact based on dynamic programming

This paper analyzes how electricity merchants' market impact affects merchants' profit. Energy storage has long been studied for its role in maximizing profit, and merchant decisions are assumed to have no impact on market prices. However, the trading decisions of large-scale energy storage merchants (e.g., pumped storage hydro) will affect the market prices. This paper employs dynamic programming theory to investigate merchants' optimal economic dispatch considering the market impact and physical characteristics of storage systems. Our findings show that the State-of-Charge (SOC) based analytical solution significantly facilitates energy storage merchants' decision-making. The SOC range is segmented into three regions by two optimal SOC reference points, which depend on the available energy in storage, given prices, and market impact. By comparing the current storage SOC with the reference points, the merchant can get the corresponding optimal actions. We analytically show that if the merchant neglects the market impact on the power market, she will exaggerate her expected profit when the price-taker and price-maker merchants have the same generating and pumping upper limits offered to Independent System Operators (ISOs). Furthermore, the profit-maximizing merchant must, therefore, assay to balance the trade-off correctly between the intensity of market impact and the dispatched power. Our findings are verified by numerical simulation, and results demonstrate the ramifications for electricity merchants in energy arbitrage decisions.

25 ENERGY STORAGE↗
DOE OSTI2022

Natural gas maximal load delivery for multi-contingency analysis

An increasing dependence on natural gas has amplified existing vulnerabilities to the power grid, including disruptions to gas transmission networks from natural and man-made disasters. To address the operational challenges arising from these disruptions, we, in this study, consider the problem of estimating the steady-state operating capacity of a damaged gas pipeline network while ensuring the maximal delivery of load. Specifically, we formulate the mixed-integer nonconvex maximal load delivery (MLD) problem, which proves difficult to solve on large-scale networks. To address this challenge, we present a relaxation of the MLD problem and use it to determine bounds on the transport capacity of a gas pipeline system. A rigorous computational evaluation over network models ranging in size from 11 to 4,197 junctions shows that the relaxation-based method is suitable for analyzing the impacts of multi-contingency network disruptions, often converging to the optimal solution of the relaxation in less than ten seconds.

03 NATURAL GAS↗
DOE OSTI2023

Ce nanoparticles and sol-gel hybrid organic-inorganic coatings maximize corrosion protection in the anodized AA2024-T3

Herein we demonstrate that the corrosion resistance of the AA2024-T3 alloy can be maximized with the application of top protective sol-gel hybrid organic-inorganic coatings. Samples combining Ce nanoparticles within the pores of the anodic layer with the top sol-gel coatings were observed to outperform samples featuring only the coating. This research unravels the self-healing capability against corrosion of the sol-gel coating when Ce nanoparticles are present, as well as a good coverage of defective regions within the oxide by the hybrid layer. This research opens a paradigm aiming at maximizing the corrosion resistance for non-ferrous anodized alloys.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Maximizing oil production from water alternating gas (CO 2 ) injection into residual oil zones: The impact of oil saturation and heterogeneity

Residual oil zones (ROZs) are widespread reservoirs, characterized by oil at residual saturation, either underlying oil fields (brownfield) or lateral (greenfield) to such fields. These reservoirs have the potential to produce volumes of oil sufficiently significant to make appreciable impacts on the US’s oil reserves and associated incidental CO 2 sequestration. The objective of this study is to improve our understanding the impact of heterogeneous and low oil saturations, in brownfield ROZs, on the effectiveness of water alternating gas (WAG) injection strategies. ROZs occur in the Permian Basin and elsewhere, and operators are using CO 2 injection for enhanced oil recovery (EOR) in these zones. The consensus model for the formation of ROZs is that they were formed by the effect of faster regional aquifer flow, acting over millions of years. Both the magnitude of oil saturation and the spatial distribution of oil differ from water-flooded main pay zones (MPZs). To explore the most effective injection strategies, we conducted simulations of CO 2 injection into synthetic geologic reservoirs. These simulations focused on injection into reservoirs subject to either man-made waterflooding or long-term natural waterflooding. By exploring the impact of varying: oil saturation; well patterns; reservoir heterogeneity; and permeability anisotropy, we attempt to quantify the factors that most influence the effectiveness of WAG injection. WAG ratios (the ratio of injected water and CO 2 , in reservoir volumes) of interest are those that either minimize the net CO 2 utilization ratios or maximize oil production rates. In general, the most effective WAG ratios for ROZs, are consistently less than those observed undergoing CO 2 injection in the same geologic reservoir models after traditional (man-made) waterflooding. This work demonstrates that most favorable WAG ratios for oil production in ROZs are different from those in traditional MPZs because of oil saturation differences. Therefore, CO 2 injection into both zones or directly copying WAG injection designs from MPZs to ROZs might not maximize oil production.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2017

Multi-mode evaluation of power-maximizing cross-flow turbine controllers

A general method for predicting and evaluating the performance of three candidate cross-flow turbine power-maximizing controllers is presented in this paper using low-order dynamic simulation, scaled laboratory experiments, and full-scale field testing. For each testing mode and candidate controller, performance metrics quantifying energy capture (ability of a controller to maximize power), variation in torque and rotation rate (related to drive train fatigue), and variation in thrust loads (related to structural fatigue) are quantified for two purposes. First, for metrics that could be evaluated across all testing modes, we considered the accuracy with which simulation or laboratory experiments could predict performance at full scale. Second, we explored the utility of these metrics to contrast candidate controller performance. For these turbines and set of candidate controllers, energy capture was found to only differentiate controller performance in simulation, while the other explored metrics were able to predict performance of the full-scale turbine in the field with various degrees of success. Finally, effects of scale between laboratory and full-scale testing are considered, along with recommendations for future improvements to dynamic simulations and controller evaluation.

13 HYDRO ENERGY↗
DOE OSTI2012

Long-Term Outcomes After Maximal Surgical Resection and Intraoperative Electron Radiotherapy for Locoregionally Recurrent or Locoregionally Advanced Primary Renal Cell Carcinoma

Purpose: To report outcomes of a multimodality therapy combining maximal surgical resection and intraoperative electron radiotherapy (IOERT) for patients with locoregionally (LR) recurrent renal cell carcinoma (RCC) after radical nephrectomy or LR advanced primary RCC. Methods and Materials: From 1989 through 2005, a total of 22 patients with LR recurrent (n = 19) or LR advanced primary (n = 3) RCC were treated with this multimodality approach. The median patient age was 63 years (range 46-78). Twenty-one patients (95%) received perioperative external beam radiotherapy (EBRT) with a median dose of 4,500 cGy (range, 4,140-5,500). Surgical resection was R0 (negative margins) in 5 patients (23%) and R1 (residual microscopic disease) in 17 patients (77%). The median IOERT dose delivered was 1,250 cGy (range, 1,000-2,000). Overall survival (OS) and disease-free survival (DFS) and relapse patterns were estimated using the Kaplan-Meier method. Results: The median follow-up for surviving patients was 9.9 years (range, 3.6-20 years). The OS and DFS at 1, 5, and 10 years were 91%, 40%, and 35% and 64%, 31%, and 31%, respectively. Central recurrence (within the IOERT field), LR relapse (tumor bed or regional lymph nodes), and distant metastases at 5 years were 9%, 27%, and 64%, respectively. Mortality within 30 days of surgery and IOERT was 0%. Five patients (23%) experienced acute or late National Cancer Institute Common Toxicity Criteria (NCI-CTCAE) Version 4 Grade 3 to 5 toxicities. Conclusions: In patients with LR recurrent or LR advanced primary RCC, a multimodality approach of perioperative EBRT, maximal surgical resection, and IOERT yielded encouraging results. This regimen warrants further investigation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2013

Synthesis of MOF having hydroxyl functional side groups and optimization of activation process for the maximization of its BET surface area

To accomplish the postsynthetic modification of MOF with organic-metal precursors (OMPs) described in our previous researches more efficiently, synthesis of MOF (HCC-2) possessing relatively larger pore size as well as higher number of hydroxyl functional side groups per its base unit than those of HCC-1 has been successfully conducted via adopting 1,4-di-(4-carboxy-2,6-dihydroxyphenyl)benzene as an organic ligand and Zn(NO{sub 3}){sub 2}{center_dot}6H{sub 2}O as a metal source, respectively. Also, optimization about the Activation process of HCC-2 was performed to maximize its BET (Brunauer-Emmett-Teller) surface area which was proved to be proportional to the number of exposed active sites on which its postsynthetic modification occurred. However, Activation process having been validated to be so effective with the acquirement of highly-purified HCC-1 (CO{sub 2} supercritical drying step followed by vacuum drying step) was less satisfactory with the case of HCC-2. This might be attributed to relatively higher hydrophilicity and bulkier molecular structure of organic ligand of HCC-2. However, it was readily settled by simple modification of above Activation process. Moreover, indispensable residues composed of both DMF and its thermally degraded derivatives which were chemically attached via coordination bond with hydroxyl functionalities even after Activation process III might enable their H{sub 2} adsorption properties to be seriously debased compared to that of IRMOF-16 having no hydroxyl functionalities. - Graphical abstract: Synthesis of new-structured MOF (HCC-2) simultaneously possessing relatively larger pore size as well as higher number of hydroxyl functional side groups per its base unit at the same time than those of HCC-1 has been performed via adopting 1,4-di-(4-carboxy-2,6-dihydroxyphenyl)benzene as an organic ligand and Zn(NO{sub 3}){sub 2}{center_dot}6H{sub 2}O as a metal source, respectively. Also, the optimization of activation process for HCC-2 was conducted to maximize its BET surface area while the suitability of this activation process was proved via SEM, TGA, EA, XRF, and PSD. Being compared with the crystal structures of IRMOF-16 and HCC-1 via XRD and FT-IR analysis, the crystal structure of HCC-2 having an identical chemical structure except the introduction of four hydroxyl functional side groups on the backbone of its organic ligand showed no noticeable change. Specifically, HCC-2 was established as a cubic structure with each axis of about 21.5 A. Moreover, H{sub 2} adsorption isotherms for these HCCs were attained to ultimately examine that hydroxyl functionalities inside their pores have any influence on their H{sub 2} adsorption properties. Highlights: Black-Right-Pointing-Pointer HCC-2 having higher number of hydroxyl groups than that of HCC-1 was prepared. Black-Right-Pointing-Pointer The optimization of activation process for HCC-2 was studied. Black-Right-Pointing-Pointer The crystal structure of HCC-2 was a cubic-shaped structure with each axis of 21.5 A. Black-Right-Pointing-Pointer -OH functionalities on HCCs had negative influence on their H{sub 2} adsorption abilities. Black-Right-Pointing-Pointer This might be due to impurities rigidly attached to their functional side groups.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Maximizing Diversity from a Kinase Screen: Identification of Novel and Selective pan-Trk Inhibitors for Chronic Pain

We have identified several series of small molecule inhibitors of TrkA with unique binding modes. The starting leads were chosen to maximize the structural and binding mode diversity derived from a high throughput screen of our internal compound collection. These leads were optimized for potency and selectivity employing a structure based drug design approach adhering to the principles of ligand efficiency to maximize binding affinity without overly relying on lipophilic interactions. This endeavor resulted in the identification of several small molecule pan-Trk inhibitor series that exhibit high selectivity for TrkA/B/C versus a diverse panel of kinases. We have also demonstrated efficacy in both inflammatory and neuropathic pain models upon oral dosing. Herein we describe the identification process, hit-to-lead progression, and binding profiles of these selective pan-Trk kinase inhibitors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Epidermal growth factor receptor cascade prioritizes the maximization of signal transduction

Many studies have been performed to quantify cell signaling. Cell signaling molecules are phosphorylated in response to extracellular stimuli, with the phosphorylation sequence forming a signal cascade. The information gain during a signal event is given by the logarithm of the phosphorylation molecule ratio. The average information gain can be regarded as the signal transduction quantity (ST), which is identical to the Kullback–Leibler divergence (KLD), a relative entropy. We previously reported that if the total ST value in a given signal cascade is maximized, the ST rate (STR) of each signaling molecule per signal duration (min) approaches a constant value. To experimentally verify this theoretical conclusion, we measured the STR of the epidermal growth factor (EGF)-related cascade in A431 skin cancer cells following stimulation with EGF using antibody microarrays against phosphorylated signal molecules. The results were consistent with those from the theoretical analysis. Thus, signaling transduction systems may adopt a strategy that prioritizes the maximization of ST. Furthermore, signal molecules with similar STRs may form a signal cascade. In conclusion, ST and STR are promising properties for quantitative analysis of signal transduction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Metal oxide supported Ni-impregnated bifunctional catalysts for controlling char formation and maximizing energy recovery during catalytic hydrothermal liquefaction of food waste

Nickel (Ni)-impregnated metal oxide catalysts, Ni/CeZrO x , Ni/ZrO 2 , and Ni/CeO 2 , were investigated to maximize energy recovery and reduce char yield during catalytic hydrothermal liquefaction (CHTL) of food waste. Yields of char, biocrude, water soluble products, and gas were measured at 300 °C and 1 hour for both the parent oxides (CeZrO x , ZrO 2 , and CeO 2 ) and the Ni-impregnated versions. Using Ni-based catalysts reduced the carbon-weighted char yield from 16–24% to <10% and decreased the energy recovery of char from 39–47% to <21%, as compared with control tests. In particular, using Ni/ZrO 2 resulted in the greatest biocrude yield, greatest reduction of char yield, and greatest energy recovered as biocrude (39.2%). After factoring in all forms of usable energy produced from food waste, the total energy recovery obtained for the catalysts studied here was >60%. Ni/ZrO 2 and Ni/CeO 2 show the greatest potential for controlling char growth and maximizing energy recovered from food waste. The crystalline structures of all three oxides were hydrothermally stable. Catalyst reuse tests indicate that the biocrude and char yields remained the same for the first and second use (within uncertainty) and that the catalyst retains its initial crystallinity and 93% of its initial Ni content. Molecular composition of biocrudes analyzed by the state-of-the-art analytical platforms (including GC-MS, GC × GC, FT-ICR MS, and 1H NMR) revealed minor differences in the chemical constituents of biocrudes obtained using different catalysts and provided some insight regarding reaction mechanism.

09 BIOMASS FUELS↗
DOE OSTI2022

Variational approach to quantum state tomography based on maximal entropy formalism

Quantum state tomography is an integral part of quantum computation and offers the starting point for the validation of various quantum devices. One of the central tasks in the field of state tomography is to reconstruct, with high fidelity, the quantum states of a quantum system. From an experiment on a real quantum device, one can obtain the mean measurement values of different operators. With such data as input, in this report we employ the maximal entropy formalism to construct the least biased mixed quantum state that is consistent with the given set of expectation values. Even though, in principle, the reported formalism is quite general and should work for an arbitrary set of observables, in practice we shall demonstrate the efficacy of the algorithm on an informationally complete (IC) set of Hermitian operators. Such a set possesses the advantage of uniquely specifying a single quantum state from which the experimental measurements have been sampled and hence renders the rare opportunity not only to construct a least-biased quantum state but even replicate the exact state prepared experimentally within a preset tolerance. Here, the primary workhorse of the algorithm is reconstructing an energy function which we designate as the effective Hamiltonian of the system, and parameterizing it with Lagrange multipliers, according to the formalism of maximal entropy. These parameters are thereafter optimized variationally so that the reconstructed quantum state of the system converges to the true quantum state within an error threshold. To this end, we employ a parameterized quantum circuit and a hybrid quantum-classical variational algorithm to obtain such a target state, making our recipe easily implementable on a near-term quantum device.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Maximal Cherenkov γ-radiation on Fermi-surface of compact stars

The quantum magnetohydrodynamic model is employed in this paper to study the extraordinary (XO) elliptically polarized electromagnetic wave dispersion in quantum plasmas with spin-1/2 magnetization and relativistic degeneracy effects, considering also the electron-exchange and quantum diffraction of electrons. From the lower and upper calculated XO-modes, it is observed that, for electrons on the surface of the Fermi-sphere, the lower XO-mode can excite the Cherenkov radiation by crossing the Fermi-line, with some proper conditions depending on the values of independent plasma parameters, such as the relativistic-degeneracy, the atomic-number of constituent ions, and the magnetic field strength. Particularly, a lower electron number-density and Cherenkov radiation frequency limits are found to exist, for instance, for given values of the plasma ions atomic-number and the magnetic field strength below which the radiation can not be excited by the electrons on the Fermi-surface. This lower density limit increases by decrease in the atomic-number but decreases with decrease in the strength of the ambient magnetic field. It is remarkable that in this research it is discovered that the maximal Cherenkov-radiation per unit-length (the energy radiated by superluminal electrons traveling through the dielectric medium) coincides with the plasma number-densities, which is present in compact stars with the maximal radiation frequency lying in the gamma-ray spectrum. Current study can provide an important plasma diagnostic tool for a wide plasma density range, be it the solid density, the warm dense matter, the inertial confined or the astrophysical compact plasmas and may reveal an important cooling mechanism for white dwarfs. Current findings may also answer the fundamental astrophysical question on the mysterious origin of intense cosmic gamma-ray emissions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Image reconstruction of single photon emission computed tomography (SPECT) on a pebble bed reactor (PBR) using expectation maximization and exact inversion algorithms: Comparison study by means of numerical phantom

Single Photon Emission Computed Tomography (SPECT) is a well-known imaging technique used in medical application, and it is part of medical imaging modalities that made the diagnosis and treatment of disease possible. However, SPECT technique is not only limited to the medical sector. Many works are carried out to adapt the same concept by using high-energy photon emission to diagnose process malfunctions in critical industrial systems such as in chemical reaction engineering research laboratories, as well as in oil and gas, petrochemical and petrochemical refining industries. Motivated by vast applications of SPECT technique, this work attempts to study the application of SPECT on a Pebble Bed Reactor (PBR) using numerical phantom of pebbles inside the PBR core. From the cross-sectional images obtained from SPECT, the behavior of pebbles inside the core can be analyzed for further improvement of the PBR design. As the quality of the reconstructed image is largely dependent on the algorithm used, this work aims to compare two image reconstruction algorithms for SPECT, namely the Expectation Maximization Algorithm and the Exact Inversion Formula. The results obtained from the Exact Inversion Formula showed better image contrast and sharpness, and shorter computational time compared to the Expectation Maximization Algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

The maximally entangled set of 4-qubit states

Entanglement is a resource to overcome the natural restriction of operations used for state manipulation to Local Operations assisted by Classical Communication (LOCC). Hence, a bipartite maximally entangled state is a state which can be transformed deterministically into any other state via LOCC. In the multipartite setting no such state exists. There, rather a whole set, the Maximally Entangled Set of states (MES), which we recently introduced, is required. This set has on the one hand the property that any state outside of this set can be obtained via LOCC from one of the states within the set and on the other hand, no state in the set can be obtained from any other state via LOCC. Recently, we studied LOCC transformations among pure multipartite states and derived the MES for three and generic four qubit states. Here, we consider the non-generic four qubit states and analyze their properties regarding local transformations. As already the most coarse grained classification, due to Stochastic LOCC (SLOCC), of four qubit states is much richer than in case of three qubits, the investigation of possible LOCC transformations is correspondingly more difficult. We prove that most SLOCC classes show a similar behavior as the generic states, however we also identify here three classes with very distinct properties. The first consists of the GHZ and W class, where any state can be transformed into some other state non-trivially. In particular, there exists no isolation. On the other hand, there also exist classes where all states are isolated. Last but not least we identify an additional class of states, whose transformation properties differ drastically from all the other classes. Although the possibility of transforming states into local-unitary inequivalent states by LOCC turns out to be very rare, we identify those states (with exception of the latter class) which are in the MES and those, which can be obtained (transformed) non-trivially from (into) other states respectively. These investigations do not only identify the most relevant classes of states for LOCC entanglement manipulation, but also reveal new insight into the similarities and differences between separable and LOCC transformations and enable the investigation of LOCC transformations among arbitrary four qubit states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

The structural information filtered features (SIFF) potential: Maximizing information stored in machine-learning descriptors for materials prediction

Machine learning inspired potentials continue to improve the ability for predicting structures of materials. However, many challenges still exist, particularly when calculating structures of disordered systems. These challenges are primarily due to the rapidly increasing dimensionality of the feature-vector space which in most machine-learning algorithms is dependent on the size of the structure. In this article, we present a feature-engineered approach that establishes a set of principles for representing potentials of physical structures (crystals, molecules, and clusters) in a feature space rather than a physically motivated space. Our goal in this work is to define guiding principles that optimize information storage of the physical parameters within the feature representations. In this manner, we focus on keeping the dimensionality of the feature space independent of the number of atoms in the structure. Our Structural Information Filtered Features (SIFF) potential represents structures by utilizing a feature vector of low-correlated descriptors, which correspondingly maximizes information within the descriptor. We present results of our SIFF potential on datasets composed of disordered (carbon and carbon–oxygen) clusters, molecules with C 7 O 2 H 2 stoichiometry in the GDB9-14B dataset, and crystal structures of the form (Al x Ga y In z ) 2 O 3 as proposed in the NOMAD Kaggle competition. Our potential's performance is at least comparable, sometimes significantly more accurate, and often more efficient than other well-known machine-learning potentials for structure prediction. However, primarily, we offer a different perspective on how researchers should consider opportunities in maximizing information storage for features.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Simultaneous inference of equation of state parameters and unknown data errors with uncertainty quantification via hierarchical Bayesian posterior maximization

Equations of state (EOSs) are a key component in running hydrodynamic simulations as they relate the thermodynamic states for the material. The Davis reactants EOS is commonly used for modeling high explosives (HEs), and the EOS model parameters are calibrated using material specific data. The calibrations are often performed with uncertainty quantification via Bayesian inference to account for uncertainty in the data and generate ensembles of likely parameters. However, there are relatively few HE data sets to use for calibration and many are historical and lack error information. In this work, we simultaneously calibrate the Davis reactants EOS model parameters and unknown data error terms for the high explosive PBX 9501. To quantify the uncertainty in the models and the data, we use a Bayesian framework for the calibration and compute the hierarchical Bayesian posterior distribution with both a posteriori maximization approach and Markov Chain Monte Carlo. In general, we find that, given our assumptions, the two approaches result in similar calibrated parameters, posterior covariance matrices, and insights about the parameters but that the posterior maximization requires far less computational resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Optimal deployment of resources for maximizing impact in spreading processes

Significance Spreading processes play an increasingly important role in marketing, opinion setting, and epidemic modeling. Most existing algorithms for optimal resource allocation in spreading processes are based on topological characteristics of the underlying network and aim to maximize impact at infinite time. Clearly, realistic and efficient real-time allocation policies should consider both network properties and details of the dynamics; additionally, control may be applied only to a restricted set of accessible nodes, and impact should be maximized in a limited time window. We introduce a probabilistic targeting framework that incorporates the dynamics and encompasses previously considered optimization formulations. It is based on a scalable dynamic message-passing approach that allows for the solution of large real-world network instances.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2012

DISTRIBUTION OF MAXIMAL LUMINOSITY OF GALAXIES IN THE SLOAN DIGITAL SKY SURVEY

Extreme value statistics is applied to the distribution of galaxy luminosities in the Sloan Digital Sky Survey. We analyze the DR8 Main Galaxy Sample (MGS), as well as the luminous red galaxies (LRGs). Maximal luminosities are sampled from batches consisting of elongated pencil beams in the radial direction of sight. For the MGS, results suggest a small and positive tail index {xi}, effectively ruling out the possibility of having a finite maximum cutoff luminosity, and implying that the luminosity distribution function may decay as a power law at the high-luminosity end. Assuming, however, {xi} = 0, a non-parametric comparison of the maximal luminosities with the Fisher-Tippett-Gumbel distribution (limit distribution for variables distributed by the Schechter fit) indicates a good agreement provided that uncertainties arising from both the finite batch size and the batch-size distribution are accounted for. For a volume-limited sample of LRGs, results show that they can be described as being the extremes of a luminosity distribution with an exponentially decaying tail, provided that the uncertainties related to batch-size distribution are taken care of.

79 ASTRONOMY AND ASTROPHYSICS↗