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NASA NTRS2004

The Role of Integrated Modeling in the Design and Verification of the James Webb Space Telescope

The James Web Space Telescope (JWST) is a large, infrared-optimized space telescope scheduled for launch in 2011. System-level verification of critical optical performance requirements will rely on integrated modeling to a considerable degree. In turn, requirements for accuracy of the models are significant. The size of the lightweight observatory structure, coupled with the need to test at cryogenic temperatures, effectively precludes validation of the models and verification of optical performance with a single test in 1-g. Rather, a complex series of steps are planned by which the components of the end-to-end models are validated at various levels of subassembly, and the ultimate verification of optical performance is by analysis using the assembled models. This paper describes the critical optical performance requirements driving the integrated modeling activity, shows how the error budget is used to allocate and track contributions to total performance, and presents examples of integrated modeling methods and results that support the preliminary observatory design. Finally, the concepts for model validation and the role of integrated modeling in the ultimate verification of observatory are described.

Mosier, Gary E.↗

DOE OSTI2024

Efficient sensitivity analysis of the thermal profile in powder bed fusion of metals using hypercomplex automatic differentiation finite element method

Rapid cyclic temperature fluctuation occurring in powder bed fusion of metals using a laser beam (PBF-LB/M) influences the formation of flaws in printed parts. Consequently, there is a pressing need to enhance the quality of printed parts by developing innovative methodologies that can predict thermal histories and help uncover the intricate relationships between process parameters and thermal profiles. Sensitivity Analysis (SA) emerges as an essential tool for this, offering the potential for process optimization and enhanced quality control. Nonetheless, conventional SA methodologies often incur in excessive computational costs and potential numerical approximation errors. Here, to address this technical challenge, we present a novel method for SA that integrates the HYPercomplex-based Automatic Differentiation (HYPAD) technique with transient thermal simulations conducted via the finite element method (FEM). Leveraging this methodology, we efficiently and accurately perform SA for PBF-LB/M processes in a post-processing step. Compared to traditional methods like Finite Differences (FD), HYPAD-FEM required 96 % less computational time for obtaining sensitivities for 22 process parameters, under a comparative study conducted within the context of the 2018–02 AM benchmark of the National Institute of Standards and Technology. In summary, HYPAD-FEM offers superior efficiency and accuracy in SA over conventional methods, delivering the best sensitivity of a model without the need for step-size selection and problem or parameter-based implementations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

An analytical method for identifying synergies between behind-the-meter battery and thermal energy storage

Electric utilities build generation capacity to meet the highest demand period, and they often pass on the costs associated with these peaking generators to building owners through demand charges. Building owners can minimize these demand charges by shifting energy use away from peak periods with behind-the-meter storage. This storage can include batteries, which can directly shift the metered load, or thermal energy storage, which can shift thermal-driven electric loads like air conditioning. However, there is a lack of research on how best to combine battery and thermal energy storage. In this study, we develop an analytical sizing method to calculate the potential demand reduction and annualized cost savings for different combinations of thermal and battery energy storage sizes. We show that adding batteries to a thermal energy storage system can increase the total system's load shaving potential. This is particularly true when the building has onsite photovoltaic generation or electric vehicle charging, which add significant variability to the load shape. We also show that for a given total storage size, selecting a higher fraction of thermal energy storage can significantly lower the cycling of the battery, and therefore extend the battery life. This, combined with the expected lower first cost of thermal energy storage materials compared to batteries, shows that hybrid energy storage systems can outperform a standalone battery or standalone thermal storage system. Assuming the thermal storage has a capital cost 6x lower than the battery, our analysis shows that the optimal system is 71% thermal energy storage and 29% battery energy storage for a scenario with electric vehicle charging. The annualized cost savings for this system are $48.6 k/yr, whereas an equivalently sized standalone thermal energy storage system would provide annualized cost savings of $28.5 k/yr and a standalone battery would lead to savings of $8.72 k/yr. The hybrid system also reduces battery cycling by 52% compared to a standalone battery, extending battery lifetime.

25 ENERGY STORAGE↗

DOE OSTI2020

Performance of Photovoltaic Systems Recorded by Open Solar Performance and Reliability Clearinghouse (oSPARC)

This article analyzes data from 2,200 photovoltaic systems collected through the Open Solar Performance and Reliability Clearinghouse (oSPARC, 2018) to draw conclusions about the measured performance of the systems, how it compares to expectations, and how wide the variation is. The systems range in size from 2 kW to 1,200 kW, with an average size of 229 kW, and were activated in oSPARC between March 13, 2007 and Dec. 16, 2016. Data regarding co-incident insolation and ambient temperature are provided through the oSPARC platform for the population of systems and summarized here. Results indicate that - after correcting for measured insolation, derating for temperature, and correcting for balance-of-system efficiency and degradation as a result of system age - the performance ratio of these 2,200 systems averages 91.7%. Adjusting for known parameters such as age and efficiency, the ratio would ideally be 100%. Thus, the 'underperformance' of this system sample is measured at 9.3% and suggests that as much as 9.3% could be recovered if the systems were caused to perform as expected through optimal operation and maintenance. Efforts to correlate the performance ratio with environmental conditions resulted in very low coefficients of regression, but the method already normalizes for actual site insolation and temperature, which are responsible for much of the site-specific variation. An exemption is air-quality nonattainment areas, where the measured performance of plants averages 86.9% and is consistently lower than the average of 95.9% in areas that are in compliance with air quality standards, likely because of particulate matter such as diesel soot exacerbating the soiling rate.

14 SOLAR ENERGY↗

NASA NTRS2016

Micropulsed Plasma Thrusters for Attitude Control of a Low-Earth-Orbiting CubeSat

This study presents a 3-Unit CubeSat design with commercial-off-the-shelf hardware, Teflon-fueled micropulsed plasma thrusters, and an attitude determination and control approach. The micropulsed plasma thruster is sized by the impulse bit and pulse frequency required for continuous compensation of expected maximum disturbance torques at altitudes between 400 and 1000 km, as well as to perform stabilization of up to 20 deg /s and slew maneuvers of up to 180 deg. The study involves realistic power constraints anticipated on the 3-Unit CubeSat. Attitude estimation is implemented using the q method for static attitude determination of the quaternion using pairs of the spacecraft-sun and magnetic-field vectors. The quaternion estimate and the gyroscope measurements are used with an extended Kalman filter to obtain the attitude estimates. Proportional-derivative control algorithms use the static attitude estimates in order to calculate the torque required to compensate for the disturbance torques and to achieve specified stabilization and slewing maneuvers or combinations. The controller includes a thruster-allocation method, which determines the optimal utilization of the available thrusters and introduces redundancy in case of failure. Simulation results are presented for a 3-Unit CubeSat under detumbling, pointing, and pointing and spinning scenarios, as well as comparisons between the thruster-allocation and the paired-firing methods under thruster failure.

Gatsonis, Nikolaos A.↗

DOE OSTI2025

Develop an efficient and cost-effective novel anaerobic digestion system producing high purity of methane from diverse waste biomass

This project focuses on developing an advanced, intensified anaerobic digestion system aimed at transforming the treatment and conversion of organic wastes into valuable products, specifically renewable natural gas. The motivation for this research stems from the limitations of conventional anaerobic digestion technologies, which often face challenges such as long retention times, high operational costs, and incomplete organic material degradation. The new technology called Intensified Versatile Anaerobic Digestion (IVAD), is developed to address these challenges by incorporating innovative reactors and processes that enhance the overall efficiency and output of anaerobic digestion. The significance of this project lies in its potential to revolutionize waste management practices and waste biomass utilization. The IVAD system integrates a hyperthermophilic anaerobic acidification reactor, a hydrothermal treatment (HTT) unit, and both thermophilic and mesophilic methanogenic reactors. This combination enables a higher rate of organic breakdown and energy recovery, resulting in faster processing times, reduced reactor sizes, and lower operational costs compared to traditional systems. Key data include an increase in methane productivity to 1.18 m 3 /m 3 /day, a significant improvement compared to the baseline technology’s 0.64 m 3 /m 3 /day. Additionally, the IVAD system achieves a 45% reduction in levelized cost of energy (LCOE), down to $\$$10.04/MMBTU, and an energy return on investment (EROI) of 3.19, representing an 87% increase over baseline levels. Technical and economic analyses highlight that the IVAD system significantly reduces hydraulic retention time (HRT) and solid retention time (SRT). The HRT for the HTT reactor can be reduced from 1 hour to 0.5 hours, while decoupling SRT from HRT in the anaerobic acidification reactor (AAR) allows for further reductions. These design optimizations lead to smaller reactor volumes, cutting down equipment and construction costs. Despite these advancements, energy consumption remains comparable to conventional methods due to a novel heat recovery strategy, enhancing overall process productivity. The system also achieves in-situ CO 2 removal and ammonia stripping features, resulting in biogas with a methane purity level of 75%, and produces high-quality nitrogen fertilizer as an additional by-product. Public benefits of the IVAD system are substantial, contributing to sustainable waste management and renewable energy production. By providing a scalable solution that can be adopted by dairy farms and similar agricultural operations, the IVAD system helps reduce waste, produce renewable natural gas (RNG) suitable for transportation fuel, and generate fertilizer, supporting a circular economy. This project plays a role in achieving broader environmental objectives by mitigating greenhouse gas emissions and promoting energy independence. Additionally, it offers a pathway for farmers to lower operational costs while adopting practices that are both environmentally sustainable and economically advantageous.

03 NATURAL GAS↗

DOE OSTI2019

Review of Models to Evaluate and Guide the Development of Low-Thermal-Conductivity Materials

Developing insulation materials with low–thermal conductivity values is appealing for building envelope retrofits and new construction. Therefore, it is a priority research area for the US Department of Energy Building Technologies Office (BTO). Multiple institutions are exploring various methods to develop new insulation materials with a thermal resistivity ≥97 m·K/W (14 h·ft2·°F/Btu/inch). Current materials that provide such high thermal resistivity use micro- or nanoporous structures, as well as low–thermal conductivity gases and reduced pressure. Efforts to develop these new materials would benefit greatly from a tool that can numerically evaluate various options to optimize material design and achieve the desired thermal resistivity. The available models do not capture all modes of heat transfer through the complex structures required to achieve very high thermal resistivity. This paper presents a literature review of the existing models that have been used in the study of heat transfer mechanisms of insulation materials such as aerogels, foams, and fibrous materials. The review shows most of the models make some assumptions to simplify the analysis. Further, such models have not included important factors, such as the size effect and the interfacial effect, which could significantly affect heat transfer through insulation materials. Moreover, there is a lack of a database for the thermal accommodation coefficients of various insulation materials that are used to calculate gaseous thermal conductivity. In addition, this paper presents details regarding the development of new models. The new models will capture various factors that have been neglected in existing models (such as nanoscale heat transfer, interfacial thermal resistance). They will allow parametric studies that identify optimum design options for insulation materials and thus accelerate the achievement of BTO’s goal of developing insulation technologies with thermal resistivity greater than ≥97 m·K/W (14 h·ft2·°F/Btu/inch).

Shrestha, Som↗

DOE OSTI2017

A large scale system approach for stability analysis of multi-unit SMR plants - 248

In this paper we present a framework based on large scale system theory for analyzing the stability of coupled advanced high temperature molten salt small modular reactors. It has been suggested that small modular reactors be coupled through a common molten salt energy repository, called a salt vault. Using vector Lyapunov functions the connective stability of multiple reactors coupled through a salt vault can be guaranteed. In this theory, scalar Lyapunov functions are assigned to portions of the composite system state space. Functions are constructed for each small modular reactor (SMR), each Brayton cycle, and the salt vault. These functions are then aggregated, becoming components of a vector Lyapunov function. If this vector function possesses special properties, the composite system is stable. Bounds on the connective stability of a multi-reactor plant can be found in terms of a free parameter, in this case the mass of molten salt in the salt vault. Examining bounds on the connective stability allows one to use control theory as a tool for making performance and economic design decisions related to the size of the salt vault. This technique can produce a constraint that is used in a design optimization problem for finding the smallest-possible salt vault that ensures stability. It can also be used as an indicator of interconnection and its effect on system behavior. This, in turn, could be used to guide multi-unit control system design to ensure that highly coupled systems behave favorably. The theory for multi-unit control and operation is discussed. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2023

Quantifying the Impact of Vertical Resolution on the Representation of Marine Boundary Layer Physics for Global-Scale Models

Abstract While GCM horizontal resolution has received the majority of scale improvements in recent years, ample evidence suggests that a model’s vertical resolution exerts a strong control on its ability to accurately simulate the physics of the marine boundary layer. Here we show that, regardless of parameter tuning, the ability of a single-column model (SCM) to simulate the subtropical marine boundary layer improves when its vertical resolution is improved. We introduce a novel objective tuning technique to optimize the parameters of an SCM against profiles of temperature and moisture and their turbulent fluxes, horizontal winds, cloud water, and rainwater from large-eddy simulations (LES). We use this method to identify optimal parameters for simulating marine stratocumulus and shallow cumulus. The novel tuning method utilizes an objective performance metric that accounts for the uncertainty in the LES output, including the covariability between model variables. Optimization is performed independently for different vertical grid spacings and value of time step, ranging from coarse scales often used in current global models (120 m, 180 s) to fine scales often used in parameterization development and large-eddy simulations (10 m, 15 s). Uncertainty-weighted disagreement between the SCM and LES decreases by a factor of ∼5 when vertical grid spacing is improved from 120 to 10 m, with time step reductions being of secondary importance. Model performance is shown to converge at a vertical grid spacing of 20 m, with further refinements to 10 m leading to little further improvement. Significance Statement In successive generations of computer models that simulate Earth’s atmosphere, improvements have been mainly accomplished by reducing the horizontal sizes of discretized grid boxes, while the vertical grid spacing has seen comparatively lesser refinements. Here we advocate for additional attention to be paid to the number of vertical layers in these models, especially in the model layers closest to Earth’s surface where climatologically important marine stratocumulus and shallow cumulus clouds reside. Our experiments show that the ability of a one-dimensional model to represent physical processes important to these clouds is strongly dependent on the model’s vertical grid spacing.

Meteorology & Atmospheric Sciences↗

DOE OSTI2019

Data from Highly Efficient Single-Pot Scarless Golden Gate Assembly

Golden Gate assembly is one of the most widely used DNA assembly methods due to its robustness and modularity. However, despite its popularity, the need for BsaI-free parts, the introduction of scars between junctions, as well as the lack of a comprehensive study on the linkers hinders its more widespread use. Here, we first developed a novel sequencing scheme to test the efficiency and specificity of 96 linkers of 4-bp length and experimentally verified these linkers and their effects on Golden Gate assembly efficiency and specificity. We then used this sequencing data to generate 200 distinct linker sets that can be used by the community to perform efficient Golden Gate assemblies of different sizes and complexity. We also present a single-pot scarless Golden Gate assembly and BsaI removal scheme and its accompanying assembly design software to perform point mutations and Golden Gate assembly. This assembly scheme enables scarless assembly without compromising efficiency by choosing optimized linkers near assembly junctions.

Conversion↗

NASA NTRS1975

Statistical estimation of service cracks and maintenance cost for aircraft structures

A method is developed for the statistical estimation of the number of cracks to be repaired in service as well as the repair and the maintenance costs. The present approach accounts for the statistical distribution of the initial crack size, the statistical nature of the NDI technique used for detecting the crack, and the renewal process for the crack propagation of repaired cracks. The mean and the standard deviation of the cumulative number of cracks to be repaired are computed as a function of service time. The statistics of the costs of repair and maintenance, expressed in terms of the percentage of the cost of replacement, are estimated as a function of service time. The results of the present study provide relevant information for the decision of fleet management, the estimation of life cycle cost, and procurement specifications. The present study is essential to the design and cost optimization of aircraft structures.

Yang, J.-N.↗

NASA NTRS2004

Mission Concept for the Single Aperture Far-Infrared (SAFIR) Observatory

We have developed a preliminary but comprehensive mission concept for SAFIR, as a 10 m-class far-infrared and submillimeter observatory that would begin development later in this decade to meet the needs outlined above. Its operating temperature (< or = 4K) and instrument complement would be optimized to reach the natural sky confusion limit in the far-infrared with diffraction-limited performance down to at least the atmospheric cutoff, lambda > or approx. 40 microns. This would provide a point source sensitivity improvement of several orders of magnitude over that of the Spitzer Space Telescope (previously SIRTF) or the Herschel Space Observatory. Additionally, it would have an angular resolution 12 times finer than that of Spitzer and three times finer than Herschel. This sensitivity and angular resolution are necessary to perform imaging and spectroscopic studies of individual galaxies in the early universe. We have considered many aspects of the SAFIR mission, including the telescope technology (optical design, materials, and packaging), detector needs and technologies, cooling method and required technology developments, attitude and pointing, power systems, launch vehicle, and mission operations. The most challenging requirements for this mission are operating temperature and aperture size of the telescope, and the development of detector arrays. SAFIR can take advantage of much of the technology under development for JWST, but with much less stringent requirements on optical accuracy.

Benford, Dominic J.↗

DOE OSTI2018

Graded Infill Structure of Wind Turbine Blade Accounting for Internal Stress in Big Area Additive Manufacturing

In additively manufactured (AM) components, infill structure significantly affects the mechanical performance of the final printed part. However, mechanical stress induced by operation loads has been so far neglected for infill patterning. Most slicers currently available in the market provide infill patterns that are uniform in shape and size regardless of the operational loading. We develop a design approach for infill patterns that accounts for the induced stress. This approach differs from topology optimization as it focuses on the porous infill, which allows the external shape of the printed part to remain intact. The proposed approach uses a computational stress analysis to control the distribution of the local density of the infill pattern. We have applied the approach to a wind turbine blade core with infill densities optimized based on the structural loads. The blade core is fabricated in our big area additive manufacturing (BAAM) system. To ensure less warpage and better inter-layer bonding, fast layer deposition is critical in BAAM system. We have optimized the tool path sequences to minimize the deposition time via the solution to the Chinese Postman Problem (CPP). For the application of wind turbine infill, the deposition from the CPP method is twice faster than the deposition from conventional slicing.

Kim, Pum↗

DOE OSTI2019

Expanded Use of ISOCS Characterization Techniques for WIPP Certification at the Idaho Clean-up Project - 19623

The Advanced Mixed Waste Treatment Project (AMWTP) has been retrieving, treating, characterizing, and shipping legacy Transuranic (TRU) waste for disposal since 2003 as part of the overall Idaho Cleanup Project (ICP) in support of the US Department of Energy. As the ICP has progressed, over 700 containers have been identified that cannot be successfully assayed using the current suite of non-destructive assay (NDA) instruments. To meet this challenge, Fluor Idaho, LLC, and Mirion Technologies (formerly Canberra Industries) have teamed to deploy the In-Situ Object Counting System (ISOCS) to supplement the current NDA capabilities. ISOCS has long been used in various radioactive waste management applications, but never has the ISOCS ability to perform intrinsic efficiency modeling of discrete waste containers been employed to characterize and certify TRU waste for disposal at the Waste Isolation Pilot Plant (WIPP), near Carlsbad, New Mexico. Since the primary disposal facility for this waste is the WIPP, the characterization processes for determining the quantity of radioactive material entrained in the waste are subject to WIPP Waste Acceptance Criteria (WAC) quality requirements and associated performance criteria. Until now, the Carlsbad Field Office (CBFO) WIPP-certified NDA equipment has utilized pre-defined efficiency calibrations for fixed geometries. However, due to the radioactive material content, activity levels, waste stream matrix, and/or the geometries of various size drums, boxes and other-odd-shaped containers or container integrity issues, it may not be suitable to characterize these containers with any of the existing WIPP-certified NDA equipment located at the AMWTP. Therefore, advanced technologies are needed to complete characterization of these problematic waste containers. The July 5, 2016 release of the WIPP WAC, DOE/WIPP-02-3122, Revision 8.0, Appendix A, 'Radioassay Requirements for Transuranic Waste,' was expanded to include several newer concepts such as American Society for Testing and Materials (ASTM) approved methods for efficiency-based calibrations and the use of mathematical computer modeling techniques for calibration. This change prompted AMWTP to pursue obtaining WIPP certification authority for expanded ISOCS techniques to deal with the remaining challenging waste containers and the development and implementation of Mirion's Figures of Merit (FOM) evaluations. These vital FOM evaluations enhance the ISOCS's modeling capabilities by optimizing the dynamic efficiency calibration for each object and reducing the assay's Total Measurement Uncertainty (TMU) budget. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Mechanics of vitrimer particle compression and fusion under heat press

The compression and fusion of vitrimer particles is a fundamental problem underlying the recycling of vitrimers. Incomplete particle compression can lead to voids in the fused vitrimer, thereby impacting its mechanical property. In this work, we present a two-dimensional finite element model to capture the interplay of multiple complex mechanisms including random particle packing, large deformation, inter-particle contact, thermally activated bulk stress relaxation, and interface healing. Specifically, we focus on understanding two key components of this problem: i) evolution of porosity during compression and fusion of randomly packed vitrimer particles, and ii) effective tensile modulus and strength of fused vitrimer. Using the finite element model, we first show that using smaller particles can reduce the porosity in the fused vitrimer, which only slightly increases the effective modulus, but the increase in tensile strength is more pronounced. In addition, under the same processing conditions, particles with mixed sizes can achieve better densification and higher tensile strength after fusion than uniformly sized particles with the same average radius. Regarding the effects of processing conditions, we discuss how the porosity and effective modulus of the fused vitrimer depend on the processing time, temperature and pressure, and find a general trend consistent with experimental observations, i.e. longer processing time, higher temperature or higher pressure can lead to lower porosity and higher modulus of the fused vitrimer. Finally, the theoretical insights towards the compression and fusion process as well as the simulation framework can be useful in optimizing the powder-based heat press process of vitrimer and its composites.

42 ENGINEERING↗

DOE OSTI2018

Development of microstructure and texture during single and multiple pass friction stir processing of a strain hardenable aluminium alloy

Highlights: • Development of microstructure and texture during single and multiple pass FSP of a strain hardenable aluminium alloy • Strain induced boundary migration (SIBM) is the dominant nucleation mechanism for recrystallization • Weak crystallographic texture development influenced by SIBM with the relative dominance of shear texture components • Stable microstructure and texture development after multiple pass FSP • FSP is a promising method for the secondary processing of strain hardenable aluminium alloys - Abstract: In the present study, microstructure and texture development during single and multiple pass friction stir processing (FSP) of a strain hardenable wrought AlMg alloy (AA5086) was investigated. Subtle differences were observed while comparing with heat treatable alloys in the nucleation mechanism of the recrystallized microstructure observed in the nugget zone. Strain induced boundary migration was the dominant mechanism of microstructure evolution in the alloy, which influenced the crystallographic texture development by weakening it. Micro-texture measurements reveal variations in the crystallographic texture along the thickness of the sample. Recrystallization texture components were observed in the nugget zone indicative of a pronounced static recrystallization in the alloy as compared to the heat treatable alloys. Bulk texture measurements within the nugget zone of the optimally processed sample reveal a relatively dominant C component of shear texture. Average grain size in the nugget zone remained the same and the bulk crystallographic texture components were retained during multiple-pass FSP. The lower strain energies involved and the enhanced recovery processes due to the high temperature materials processing of the alloy during FSP resulted in a stable microstructure and texture. In summary, FSP could be promoted as a competent and suitable secondary processing technique for the bulk production of ultra-fine-grained materials in strain hardenable aluminium alloys.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Highly Efficient Single-Pot Scarless Golden Gate Assembly

We report that Golden Gate assembly is one of the most widely used DNA assembly methods due to its robustness and modularity. However, despite its popularity, the need for BsaI-free parts, the introduction of scars between junctions, as well as the lack of a comprehensive study on the linkers hinders its more widespread use. Here, we first developed a novel sequencing scheme to test the efficiency and specificity of 96 linkers of 4-bp length and experimentally verified these linkers and their effects on Golden Gate assembly efficiency and specificity. We then used this sequencing data to generate 200 distinct linker sets that can be used by the community to perform efficient Golden Gate assemblies of different sizes and complexity. We also present a single-pot scarless Golden Gate assembly and BsaI removal scheme and its accompanying assembly design software to perform point mutations and Golden Gate assembly. Finally, this assembly scheme enables scarless assembly without compromising efficiency by choosing optimized linkers near assembly junctions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Uniform redundancy allocation maximizes the robustness of flow networks against cascading failures

We study the robustness of flow networks against cascading failures under a partial load redistribution model. In particular, we consider a flow network of N lines with initial loads L 1 ,...,L N and free spaces (i.e., redundant space) S 1 ,...,S N that are independent and identically distributed with joint distribution P LS (x,y) = P[L ≤ x, S ≤ y]. The capacity C i is the maximum load allowed on line i and is given by C i = L i + S i . Furthermore, when a line fails due to overloading, it is removed from the system and (1 – ε) fraction of the load it was carrying is redistributed equally among all remaining lines in the system. The rest (i.e., ε fraction) of the load is assumed to be lost or absorbed, e.g., due to advanced circuitry disconnecting overloaded power lines or an interconnected network or material absorbing a fraction of the flow from overloaded lines. We analyze the robustness of this flow network against random attacks that remove a p fraction of the lines. Our contributions include (i) deriving the final fraction of alive lines n ∞ (p,ε) for all p,εϵ(0,1) and confirming the results via extensive simulations; (ii) showing that partial redistribution might lead to (depending on the parameter 0 < ε ≤ 1) the order of transition at the critical attack size p* changing from first to second-order; and (iii) proving analytically that flow networks achieve maximum robustness [quantified by the area ∫$^{1}_{0}$ n ∞ (p,ε)dp] when all lines have the same free space regardless of their initial load. The optimality of equal free-space allocation is also confirmed on real-world data from the UK National Power Grid.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗