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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 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Interactions between zirconia–yttria–tantala thermal barrier oxides and silicate melts

The effects of TaO 2.5 additions to Y 4 Zr 3 O 12 (YZO) on its interactions with calcium-magnesium alumino-silicate (CMAS) melts are investigated herein. YZO is a candidate material for the protection of novel ZrO 2 -YO 1.5 -TaO 2.5 based thermal barrier coatings (TBCs) against CMAS attack, but thermochemical considerations dictate that YZO contain TaO 2.5 for interfacial compatibility. Oxides based on Y 4 Zr 3-x Ta x O 12+0.5x ( x = =0, 0.7, 1.4) were mixed with various ternary and quinary silicate compositions ranging in Ca:Si ratio from 0.35 to 1.13 and equilibrated at 1300 °C. The results show that all combinations form the desired apatite phase except for the mixture of the higher Ta 5+ content with the lowest Ca:Si melt. It is found that the addition of Ta 5+ increases the capture of Y 3+ by the reprecipitated fluorite, decreasing the amount available to form apatite and eventually suppressing it at low Ca:Si. The effect is ascribed to the attractive interactions between Y 3+ and Ta 5+ in solid solution, similar to that found in tetragonal zirconia, but with concurrent incorporation of anion vacancies associated with excess Y 3+ that stabilize the cubic form. As the Ca 2+ content of the melt increases, so does the amount of Ca 2+ incorporated in fluorite. The latter also interacts attractively with Ta 5+ and leads to a reduction of captured Y 3+ in fluorite as the Ca content in the reacting deposit increases. This serves to increase the amount of Y 3+ available in the melt to form apatite in TBC-CMAS interactions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Domain patterns and super-elasticity of freestanding BiFeO 3 membranes via phase-field simulations

Super-elasticity of functional ferroelectric oxides offers promises for integrating ferroelectric films into flexible electronics. However, super-elastic deformation is a complex phenomenon related to possibly multiple concurrent mechanisms. Fundamentally understanding how multiple mechanisms contribute to the super-elasticity of ferroelectric oxides is crucial to realizing their potential flexible electronic applications. In this study, we employ phase-field simulations to model the dynamics of ferroelectric domain patterns of freestanding BiFeO 3 membranes to understand the origin of their super-elasticity under substantial bending deformation (5% strain). It is demonstrated that both a reversible Rhombohedral-Tetragonal (R-T) phase transition and a nearly reversible domain evolution of BiFeO 3 membranes contribute to accommodating the large deformation and thus their super-elasticity. The dynamics of domain evolution also reveal the formation of an exotic ferroelectric vortex and polarization rotation before the phase transition. We constructed a diagram of phases and domain patterns as a function of the membrane thickness and bending angle, which allows one to readily predict the emergence of T phase and ferroelectric vortex in bent BFO membranes. These results not only provide fundamental understanding of mesoscale super-elastic mechanisms but also reveal exotic domain states of ferroelectric membranes.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Resonant interaction between phonons and PbTe/PbSe (001) misfit dislocation networks

Here this work aims at a quantitative and mechanistic understanding of the dynamic process of the phonon-dislocation interaction in PbTe/PbSe (001) heterostructures using the Concurrent Atomistic-Continuum (CAC) method as the simulation tool. The misfit dislocation network and the atomic-scale dislocation core structure obtained in the simulations are found to agree reasonably well with the experimental observations of the PbTe/PbSe (001) interface. Through visualizing the dynamic interaction between phonons and dislocations, as well as quantifying the dislocation vibration amplitude, the phonon energy transmission, and the thermal resistance of the misfit interfaces, this work has illustrated and quantified two mechanisms for phonon-dislocation interaction: (1) phonon scattering by the strain field of dislocations, and (2) phonon scattering by dislocations that vibrate via the local modes of a dislocation network; the latter, leads to resonant phonon-dislocation interaction, which is manifested as local maxima of out-of-phase vibration of the atoms on the two sides of the slip plane, leading to local minima of the energy transmission in the heterostructure that contains one interface. The local vibrational modes are found to be excited only by shear stress induced by transverse phonons. Among various resonant modes, the one with the lowest frequency has the strongest effect. This work has also demonstrated the collective motion of dislocations under ultrafast phonon pulses. In addition, the dynamic properties of the misfit dislocation network localized within one interface are found to be significantly altered by the presence of misfit dislocations at other interfaces, thus further confirming the cooperative dynamic nature of the motion of dislocations and phonons.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Dynamic fracture processes in hydrogen embrittled iron

Mechanistic understanding of hydrogen embrittlement is critical to the transport and storage of hydrogen as a sustainable fuel. Experimental observation of dynamic fracture processes in hydrogen environments has been challenging. Here, in-situ transmission X-ray microscopy is used to image polycrystalline iron foils that are concurrently strained and electrochemically charged with hydrogen. Using this technique, voids and microcracks down to ∼30 nm in size are identified at or near the crack tip and tracked as strain is increased. We observe both hydrogen-induced transgranular failure and hydrogen-induced intergranular failure with distinct fracture processes. We find that transgranular fracture occurs through the formation of sharp branched structures at the main crack tip that are reminiscent of slip band formation. This is followed by void growth and coalescence, and interaction with secondary cracks that lead to propagation of the main crack. Intergranular fracture is found to occur through void coalescence along grain boundaries, along with significant secondary cracking near the crack tip. The crack growth rate is greater for void-mediated intergranular failure than for slip-mediated transgranular failure. Additionally, the removal of hydrogen results in recovered ductility for a crack initially propagated under hydrogen charging.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Strong interfaces: the key to high strength in nano metallic laminates

Excellent mechanical properties of nanomaterials are usually attributed to their nanoscale feature size and high-density interfaces. This work explores the effects of intrinsic interface properties on mechanical properties of nano metallic laminates (NMLs). We show that the interface strength significantly affects the mechanical properties of NMLs. Via in situ mechanical testing and characterization, we investigate the deformation behavior and concurrent microstructure evolution in NMLs with four types of dissimilar interfaces. Our results show that the strength and deformation behaviors of NMLs are largely determined by interface strength. Strong interfaces can simultaneously increase the strength, work hardening capability, and deformability of NMLs. In conclusion, this work brings new insight into the design of advanced metallic materials through tuning of interface properties.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Initiation of dusting corrosion in high-temperature alloys under CO exposure

Carbon monoxide is commonly encountered in energy systems, yet its reactivity with structural alloys—critical heat-resistant components in these systems—has been largely overlooked compared to the well-documented effects of oxidizing gases. In contrast, we demonstrate the high-temperature reaction of CO with NiAl using in-situ low-energy electron microscopy and X-ray photoemission electron microscopy. Our results show that CO dissociates into atomic oxygen and carbon, resulting in two concurrent reactions: selective oxidation of aluminum to form Al 2 O 3 and the initiation of dusting corrosion through carbon dissolution into the alloy and subsequent carbon deposition on the surface. These reactions produce spatially distinct surface products, preventing the formation of a continuous protective Al oxide layer. These results reveal a preference for the dissociative pathway of CO over the classic Boudouard disproportionation reaction that forms CO 2 . These insights not only advance our understanding of CO-induced alloy degradation but also highlight the practical implications for managing alloy stability and optimizing catalysis in carbon-rich environments, such as those in petrochemical processing and hydrocarbon combustion.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Surveillance of Aedes aegypti indoors and outdoors using Autocidal Gravid Ovitraps in South Texas during local transmission of Zika virus, 2016 to 2018

The yellow fever mosquito, Aedes aegypti, has facilitated the re-emergence of dengue virus (DENV) and emergence of chikungunya virus (CHIKV) and Zika virus (ZIKV) in the Americas and the Caribbean. The recent transmission of these arboviruses in the continental United States has been limited, to date, to South Florida and South Texas despite Ae. aegypti occurring over a much larger geographical region within the country. The main goal of our study was to provide the first long term longitudinal study of Ae. aegypti and enhance the knowledge about the indoor and outdoor relative abundance of Ae. aegypti as a proxy for mosquito-human contact in South Texas, a region of the United States that is at high risk for mosquito-borne virus transmission. Here, the relative abundance of indoors and outdoors mosquitoes of households in eight different communities was described. Surveillance was done weekly from September 2016 to April 2018 using the CDC Autocidal Gravid Ovitraps in low- and middle-income communities. A total of 69 houses were included in this survey among which 36 were in the low-income communities (n = 11 for Donna, n = 15 for Progresso, n = 5 for Mesquite, n = 5 for Chapa) and 33 in middle-income communities (n = 9 for La Feria, n = 8 for Weslaco, n = 11 for McAllen, and n = 5 for Rio Rico). Overall, Ae. aegypti was the dominant species (59.2% of collections, n = 7255) followed by Culex spp. mosquitoes (27.3% of collections, n = 3350). Furthermore, we demonstrated for Ae. aegypti that 1) outdoor relative abundance was higher compared to indoor relative abundance, 2) low-income communities were associated with an increase in mosquito relative abundance indoors when compared to middle-income communities, 3) no difference was observed in the number of mosquitoes collected outdoors between low-income and middle-income communities, and 4) warmer months were positively correlated with outdoor relative abundance whereas no seasonality was observed in the relative abundance of mosquitoes indoors. Additionally, Ae. aegypti mosquitoes collected in South Texas were tested using a specific ZIKV/CHIKV multiplex real-time PCR assay, however, none of the mosquitoes tested positive. Our data highlights the occurrence of mosquitoes indoors in the continental United States and that adults are collected nearly every week of the calendar year. These mosquito data, obtained concurrently with local ZIKV transmission of 10 locally acquired cases in nearby communities, represent a baseline for future studies in the Lower Rio Grande Valley (LRGV) including vector control interventions relying on the oviposition behavior to reduce mosquito populations and pathogen transmission.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Disorder-order transformation in Fe-50%Co fabricated via laser powder bed fusion

Fe-Co alloys are an important class of soft magnetic materials that often pose challenges in their fabrication because of the brittle B2-ordered phase. We show that laser beam powder bed fusion (PBF-LB), owing to its rapid cooling rates, offers an avenue for the fabrication of these alloys by suppressing the disorder →order phase transformation at room temperature. We use neutron diffraction to understand the phase transformations in a Fe-50%Co alloy fabricated via PBF-LB. We report that the disorder→order phase transformation in this alloy occurs concurrently via homogeneous ordering and classical nucleation and growth.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Geometry-independent microstructure optimization for electron beam powder bed fusion additive manufacturing

The ability to manipulate the formation of microstructure is one of the potential advantages of additive manufacturing. Yet, the additive manufacturing process is riddled with complex interactions between processing parameters, geometry, and spot melting sequence which makes the task of controlling microstructure challenging. This paper proposes a method to solve the microstructure texture optimization problem by leveraging established optimization techniques and increasingly fast and accurate analytical heat transfer models. Respectively, we apply two different optimization algorithms, genetic algorithm and concurrent greedy line search, in order to induce arbitrarily shaped microstructure regions and we use a heat transfer model to evaluate the fitness of solutions in an iterative approach that is far more efficient than pure trial and error. The objective of the optimization algorithm is to control local thermal conditions – hence microstructure formation – during the melting process by manipulating the order and the dwell time of all the points of the infill pattern sequence. We then analyze the optimized sequence to determine important path characteristics that affect the microstructure formation. Through examples, we show that relative order and frequency, as measured by weighted average and variance of spot order, are important factors that influence the final characteristics.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Localized keyhole pore prediction during laser powder bed fusion via multimodal process monitoring and X-ray radiography

Systematic fault detection and control during laser powder bed fusion (L-PBF) has been a long-standing objective for system manufacturers and researchers in the additive manufacturing (AM) industry. This manuscript investigates a data fusion approach for detection of keyhole porosity formation during laser irradiation of Ti-6Al-4V substrates by concurrent recording of thermally induced optical emission measured using both off-axis and coaxial photodiode sensors, and acoustic emission. Subsurface defect formation was monitored via high-speed synchrotron X-ray imaging at 20,000 frames per second, enabling temporal registration of keyhole pore formation events to the monitoring signals at a resolution of 50 µs. We developed data fusion machine learning (ML) models for localized prediction of keyhole pore formation at various time scales ranging from 0.5 ms to 2 ms. The signal segments were featurized using two independent approaches: (1) power spectral density (PSD) and (2) highly comparative time series analysis (HCTSA) framework. The extracted features from different sensor modalities were fused together to construct a multimodal feature space and sequential feature selection was used to determine the most informative features for training the ML models. The predictive performance was evaluated for three classifying algorithms: Support Vector Machine (SVM), K-Nearest Neighbor (KNN), and Gaussian Naive Bayes (GNB). As a result, pore formation events were predicted with up to 0.95 F1-score, 1.0 recall and 0.94 accuracy. The most heavily weighted features indicate that model performance is chiefly governed by the acoustic monitoring signal, with a secondary contribution from the optical emission sensors.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A probabilistic economic and environmental impact assessment of a cyanobacteria-based biorefinery

Microbial based biofuels represent a potential promising solution as an environmentally favorable transportation fuel. Cyanobacteria have many of the same advantages as microalgae: ability for rapid growth in otherwise non-arable regions, suitability for genetic engineering, and simple nutritional needs. Additionally, cyanobacteria can be engineered to secrete valuable co-products that can be harvested independent from the produced biomass. However, little work has been done to identify the processes and the economic and environmental impacts associated with a large-scale cyanobacteria-to-fuels facility. The present study is a concurrent techno-economic and life cycle assessment of a facility that generates fuels and methyl laurate, an oleochemical, from the cyanobacterial species Synechocystis sp. PCC 6803. Here, the biorefinery model includes all aspects of cultivation, separation of the secreted methyl laurate, biomass harvesting and fuel processing via hydrothermal liquefaction (HTL) of the dewatered biomass. The assessments leverage Monte Carlo analysis (MCA) to address uncertainty and variability inherent in the most significant input parameters, replacing them with probabilistic functions. For the facility configuration producing both fuels and the oleochemical co-product, the MCA average minimum fuel selling price (MFSP) is $\$2.47$ per decimeter (dm 3 ) or $\$9.34$ per gallon of gasoline equivalent (gge) with the corresponding average global warming potential determined to be 118 g CO 2 -eq-MJ -1 . The case producing only fuels results in an MCA average MFSP of $\$2.01$-(dm 3 ) -1 ($\$7.60$-gge -1 ) and an average environmental impact of 100 g CO 2 -eq-MJ -1 . These results are compared to static optimistic and conservative scenario analysis estimates, illustrating the over- and under-estimation of outcomes associated with non-stochastic methods. Suggested facility improvements include increases in pond productivity of both the biomass and methyl laurate oil production, as well as improvements to carbon utilization and bio-crude yield from HTL processing.

09 BIOMASS FUELS↗
DOE OSTI2022

Development of integrated screening, cultivar optimization, and verification research (DISCOVR): A coordinated research-driven approach to improve microalgal productivity, composition, and culture stability for commercially viable biofuels production

To address major knowledge gaps and barriers to the commercial development of algal biomass for biofuels and co-products, a collaborative consortium, Development of Integrated Screening, Cultivar Optimization, and Verification Research (DISCOVR), was established in 2016. Funded by the U.S. Department of Energy (DOE) Bioenergy Technologies Office (BETO), this consortium constitutes a partnership between four DOE national laboratories - Pacific Northwest National Laboratory (PNNL), Los Alamos National Laboratory (LANL), the National Renewable Energy Laboratory (NREL), and Sandia National Laboratories (SNL) - and the Arizona Center for Algae Technology and Innovation (AzCATI) at Arizona State University. To address the barriers of strain selection for achieving high seasonal productivities with a suitable composition and culture resilience, a tiered strain down-selection pipeline is implemented. At Tier I, the temperature and salinity tolerance of strains is determined in flask cultures; at Tier II, the areal biomass productivity and composition is determined in climate-simulation photobioreactors; at Tier III, the productivity and culture stability are determined in outdoor raceways. The top performing strains move forward to long-term testing at the algae testbed site at AzCATI to generate annual biomass productivity data. Concurrent to the strain down-selection in the DISCOVR pipeline, hypotheses for increasing biomass productivity, shifting biomass composition to enhance intrinsic value, and improving culture stability and resistance to pests are also tested. Techno-economic analyses are carried out to determine whether promising findings from laboratory studies or proposed modifications in outdoor pond cultivation conditions translate into reductions in the minimum biomass selling price (MBSP). Notably, in the three years following the launch of DISCOVR, annual biomass productivity has increased from 11.7 to 17.6 g m -2 day -1 , resulting in an MBSP decrease from 824 to 611 $ ton -1 .

09 BIOMASS FUELS↗
DOE OSTI2025

Optimized Illuminance Operation-A Light-Driven Dilution Strategy to Improve Microalgae Biomass Productivity

Periodic dilution is a necessary operation to avoid light limitation due to self-shading as the culture grows dense. However, environmental conditions are constantly changing in outdoor cultivation systems, making it difficult to determine the optimal dilution rate. To address this challenge, this study evaluated a dilution approach based on light penetration to optimize illuminance (OptiLum) in the culture. Biomass concentration was controlled via sensor-feedback directed dilution to ensure that light reaching the bottom of the culture was maintained above the compensation intensity. Under replicated outdoor pond conditions, by keeping the entire culture within a net-positive photosynthetic zone, the OptiLum operation improved the biomass productivities of two top-performing strains, Picochlorum celeri and Tetraselmis striata, by 95 % and 86 %, respectively, compared to conventional semi-continuous batch cultivation. The dilution rate varied daily and was dynamically adjusted based on the light status within the culture, which is concurrently influenced by weather, culture density, and growth rate. The techno-economic analysis showed that the OptiLum operation could reduce biomass production cost by as much as 24 % and 33 % for P. celeri and T. striata, respectively, assuming a low-cost dewatering approach with initial gravity settling of biomass can be realized for both strains. However, a more costly two-stage dewatering strategy, comprising only membranes and centrifuges, may be necessary for non-settling strains, such as P. celeri, which would alternatively increase production costs by 23 % for the OptiLum case. The results demonstrated that the proposed OptiLum operation is a promising approach to improve biomass productivity and lower production cost via weather-responsive and self-adjusting dilution.

09 BIOMASS FUELS↗
DOE OSTI2014

Gamma/neutron time-correlation for special nuclear material detection – Active stimulation of highly enriched uranium

A series of simulations and experiments were undertaken to explore and evaluate the potential for a novel new technique for fissile material detection and characterization, the timecorrelated pulse-height (TCPH) method, to be used concurrent with active stimulation of potential nuclear materials. In previous work TCPH has been established as a highly sensitive method for the detection and characterization of configurations of fissile material containing Plutonium in passive measurements. By actively stimulating fission with the introduction of an external radiation source, we have shown that TCPH is also an effective method of detecting and characterizing configurations of fissile material containing Highly Enriched Uranium (HEU). The TCPH method is shown to be robust in the presence of the proper choice of external radiation source. An evaluation of potential interrogation sources is presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Model for radiation damage-induced grain subdivision and its influence in U 3 Si 2 fuel swelling

Here, the swelling mechanisms of U 3 Si 2 from neutron irradiation under reactor conditions are not unequivocally known. The limited experimental evidence that is available suggests that the main driver of the swelling in this material would be fission gases accumulation at crystalline grain boundaries. The steps that lead to the accumulation of fission gases at these locations are multiple and complex. However, gradually, the gaseous fission products migrate by diffusion. Upon reaching a grain boundary, which acts as a trap, the gaseous fission products start to accumulate, thus leading to formation of bubbles and hence to induced swelling. Therefore, a quantitative model of swelling requires the incorporation of phenomena that increase the presence of grain boundaries and decrease grain sizes, thus creating sites for bubble formation and growth while concurrently deceasing the distance from gas species formation to gas accumulation sites. It is assumed that grain boundary formation results from the conversion of stored energy from accumulated dislocations into energy for the formation of new grain boundaries. This work attempts to develop a quantitative model for grain subdivision in U 3 Si 2 based on the above mentioned phenomena to quantitatively corroborate the presence of such a mechanism. Then the model is used in conjunction with swelling codes to evaluate the total swelling of a fuel pellet during its lifetime in the I 2 S-LWR reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2013

Deterministic LOCC transformation of three-qubit pure states and entanglement transfer

A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences C{sub AB}, C{sub AC}, C{sub BC}, the tangle {tau}{sub ABC} and the fifth parameter J{sub 5} of Acin et al. (2000) Ref. [19], while the other new one is the entanglement charge Q{sub e}. The order of the partially ordered set is defined by the possibility of a deterministic LOCC transformation from a state to another state. In this sense, the present condition is an extension of Nielsen's work (Nielsen (1999) [14]) to three-qubit pure states. We also clarify the rules of transfer and dissipation of the entanglement which is caused by deterministic LOCC transformations. Moreover, the minimum number of times of measurements to reproduce an arbitrary deterministic LOCC transformation between three-qubit pure states is given. - Highlights: Black-Right-Pointing-Pointer We obtained a necessary and sufficient condition for deterministic LOCC of 3 qubits. Black-Right-Pointing-Pointer We clarified rules of entanglement flow caused by measurements. Black-Right-Pointing-Pointer We found a new parameter which is interpreted as 'Charge of Entanglement'. Black-Right-Pointing-Pointer We gave a set of entanglements which determines whether two states are LU-eq. or not. Black-Right-Pointing-Pointer Our approach to deterministic LOCC of 3 qubits may be applicable to N qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Nonlocality and entanglement via the Unruh effect

Modeling the qubit by a two-level semiclassical detector coupled to a massless scalar field, we investigate how the Unruh effect affects the nonlocality and entanglement of two-qubit and three-qubit states when one of the entangled qubits is accelerated. Two distinct differences with the results of free field model in non-inertial frames are (i) for the two-qubit state, the CHSH inequality cannot be violated for sufficiently large but finite acceleration, furthermore, the concurrence will experience “sudden death”; and (ii) for the three-qubit state, not only does the entanglement vanish in the infinite acceleration limit, but also the Svetlichny inequality cannot be violated in the case of large acceleration. -- Highlights: ► We compare entanglement and nonlocality of two-level detector model with that of free field model in noninertial frame. ► Two-qubit state entanglement experiences “sudden death”. ► Three-qubit state entanglement vanishes in the infinite acceleration limit. ► Bipartite nonlocal correlations vanish for finite values of the acceleration. ► Tripartite nonlocal correlations vanish for finite values of the acceleration as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Speed of disentanglement in multiqubit systems under a depolarizing channel

We investigate the speed of disentanglement in the multiqubit systems under the local depolarizing channel, in which each qubit is independently coupled to the environment. We focus on the bipartition entanglement between one qubit and the remaining qubits constituting the system, which is measured by the negativity. For the two-qubit system, the speed for the pure state completely depends on its entanglement. The upper and lower bounds of the speed for arbitrary two-qubit states, and the necessary conditions for a state achieving them, are obtained. For the three-qubit system, we study the speed for pure states, whose entanglement properties can be completely described by five local-unitary-transformation invariants. An analytical expression of the relation between the speed and the invariants is derived. The speed is enhanced by the three-tangle which is the entanglement among the three qubits, but reduced by the two-qubit correlations outside the concurrence. The decay of the negativity can be restrained by the other two negativity with the coequal sense. The unbalance between two qubits can reduce the speed of disentanglement of the remaining qubit in the system, and even can retrieve the entanglement partially. For the k-qubit systems in an arbitrary superposition of Greenberger–Horne–Zeilinger state and W state, the speed depends almost entirely on the amount of the negativity when k increases to five or six. An alternative quantitative definition for the robustness of entanglement is presented based on the speed of disentanglement, with comparison to the widely studied robustness measured by the critical amount of noise parameter where the entanglement vanishes. In the limit of large number of particles, the alternative robustness of the Greenberger–Horne–Zeilinger-type states is inversely proportional to k, and the one of the W states approaches 1/√(k)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗