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At least 199 records · Page 11

Titanium isotope systematics of refractory inclusions: Echoes of molecular cloud heterogeneity

Calcium-aluminum-rich inclusions (CAIs) are highly refractory objects found in different chondrite groups and represent some of the oldest known solids of the Solar System. As such, CAIs provide key information regarding the conditions prevailing in the solar protoplanetary disk as well as subsequent mixing and transport processes. Many studies have investigated CAIs for their isotopic compositions and reported nucleosynthetic isotope anomalies in numerous elements, which are typically explained by the variable incorporation of isotopically highly anomalous presolar phases. However, with the exception of 54 Cr-enriched nanospinels, the exact presolar phases responsible for the isotopic heterogeneities are yet to be identified. To address this issue, we here present in-situ Ti isotopic analyses obtained on a diverse set of CAIs from various CV3 chondrites. In this work, the in-situ measurements were performed by targeting individual mineral phases of 15 CAIs with laser-ablation mass spectrometry and indicate significant inter- and intra-CAI isotopic heterogeneity in the neutron-rich isotope 50 Ti. This is particularly pronounced for primitive fine-grained CAIs, whereas coarse-grained CAIs, which have been subject to melting, exhibit smaller degrees of Ti isotopic heterogeneity. To further investigate this Ti isotopic heterogeneity, we additionally obtained Ti isotopic compositions of sequential acid leachates from two fine-grained and two coarse-grained CAIs derived from CV3 chondrites. In contrast to potential expectations from the first part of the study, we do not observe any significant intra-CAI Ti isotopic heterogeneity between the different leaching steps. The lack of intra-CAI Ti isotopic heterogeneity in the acid leachate samples of this study likely reflects that the leaching procedure is unable to efficiently separate the carriers of isotopically anomalous Ti in CAIs. By comparing the bulk CAI Ti isotope compositions with Ti isotope data for hibonite-rich objects from the literature, we find that the range of Ti isotope compositions recorded by CAIs from various chondrite groups can be accounted for by the averaging of hibonite grains. In turn, the variable Ti isotope compositions of hibonite grains can be explained by the averaging of isotopically diverse presolar grains present in the Sun’s parental molecular cloud. This effect of averaging is statistically supported by the central limit theorem, and the concept has the potential to be useful for other isotopic systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Lubrication by Diamond and Diamondlike Carbon Coatings

Regardless of environment (ultrahigh vacuum, humid air, dry nitrogen, or water), ion-beam-deposited diamondlike carbon (DLC) and nitrogen-ion-implanted, chemical-vapor-deposited (CVD) diamond films had low steady-state coefficients of friction (less than 0.1) and low wear rates (less than or equal to 10(exp -6)cu mm/N(dot)m). These films can be used as effective wear-resistant, self-lubricating coatings regardless of environment. On the other hand, as-deposited, fine-grain CVD diamond films; polished, coarse-grain CVD diamond films; and polished and then fluorinated, coarse-grain CVD diamond films can be used as effective wear-resistant, self-lubricating coatings in humid air, in dry nitrogen, and in water, but they had a high coefficient of friction and a high wear rate in ultrahigh vacuum. The polished, coarse-grain CVD diamond film revealed an extremely low wear rate, far less than 10(exp 10) cu mm/N(dot)m, in water.

Miyoshi, Kazuhisa↗

Efficient Multiscale Optoelectronic Prediction for Conjugated Polymers

Conjugated polymers represent a high-potential material class due to the tunability of their optoelectronic properties via straightforward processing protocols. However, to in silico tailor these optoelectronic properties, one must compute the conformationally dependent electronic structure over mesoscopic length and time scales. This task represents a challenging multiscale computational problem in which quantum chemistry and atomistic or coarse-grained molecular dynamics must be integrated. Recently, we introduced a methodology, called electronic coarse graining (ECG), that utilizes artificial neural networks to compute ab initio quality electronic structures using only the reduced degrees of freedom of coarse-grained models. Here, we adapt ECG to variable-molecular weight conjugated oligomers by casting the problem in the framework of sequence detection. A machine-learning (ML) architecture employing one-dimensional convolutional neural networks and long short-term memory networks is utilized to compute ground-state orbital energies, charge density distributions, and optical spectra solely from the coarse-grained model's configurational degrees of freedom. Robust molecular weight transferability for ECG is established via a A-ML approach that leverages model electronic Hamiltonians for ground and excited-state property determination. The accuracy and transferability of the ECG methodology opens the door for scalable optoelectronic property prediction in conjugated polymers directly from coarse-grained degrees of freedom.

36 MATERIALS SCIENCE↗

Thermodynamics of optical Bloch equations

Abstract Optical Bloch equations (OBE) describe the coherent exchange of energy between a quantum bit (qubit) and a quasi-resonant driving field in the presence of a thermal bath. Despite it being an ubiquitous process in quantum technologies, a sound thermodynamic analysis is still missing. We hereby provide such an analysis, by deriving the relevant framework from first principles. We start from a complete microscopic description of the qubit-bath system where definitions of heat, work and entropy production are unambiguous. We trace out the bath and coarse-grain the resulting expressions in time, using a methodology similar to the derivation of the dynamical master equation, to derive closed expressions for the first and second law in terms of system properties. Long coarse graining times yield the Floquet Master equation and its already known thermodynamic description. Short coarse-graining times yield instead the OBE and a novel thermodynamic framework which explicitly depends on quantum coherences in the qubit’s energy basis which produce quantum signatures in the heat and entropy production flows. This allows us to characterize a genuinely quantum non-equilibrium situation, where the coherences created by the driving field are continuously erased by the bath. Our findings can be readily extended to larger open quantum systems. They carry the seeds for future thermodynamic analyses of quantum gates and the design of quantum engines in the strong coherent driving regime.

Elouard, Cyril↗

Dual Microstructure Heat Treatment of a Nickel-Base Disk Alloy Assessed

Gas turbine engines for future subsonic aircraft will require nickel-base disk alloys that can be used at temperatures in excess of 1300 F. Smaller turbine engines, with higher rotational speeds, also require disk alloys with high strength. To address these challenges, NASA funded a series of disk programs in the 1990's. Under these initiatives, Honeywell and Allison focused their attention on Alloy 10, a high-strength, nickel-base disk alloy developed by Honeywell for application in the small turbine engines used in regional jet aircraft. Since tensile, creep, and fatigue properties are strongly influenced by alloy grain size, the effect of heat treatment on grain size and the attendant properties were studied in detail. It was observed that a fine grain microstructure offered the best tensile and fatigue properties, whereas a coarse grain microstructure offered the best creep resistance at high temperatures. Therefore, a disk with a dual microstructure, consisting of a fine-grained bore and a coarse-grained rim, should have a high potential for optimal performance. Under NASA's Ultra-Safe Propulsion Project and Ultra-Efficient Engine Technology (UEET) Program, a disk program was initiated at the NASA Glenn Research Center to assess the feasibility of using Alloy 10 to produce a dual-microstructure disk. The objectives of this program were twofold. First, existing dual-microstructure heat treatment (DMHT) technology would be applied and refined as necessary for Alloy 10 to yield the desired grain structure in full-scale forgings appropriate for use in regional gas turbine engines. Second, key mechanical properties from the bore and rim of a DMHT Alloy 10 disk would be measured and compared with conventional heat treatments to assess the benefits of DMHT technology. At Wyman Gordon and Honeywell, an active-cooling DMHT process was used to convert four full-scale Alloy 10 disks to a dual-grain microstructure. The resulting microstructures are illustrated in the photomicrographs. The fine grain size in the bore can be contrasted with the coarse grain size in the rim. Testing (at NASA Glenn) of coupons machined from these disks showed that the DMHT approach did indeed produce a high-strength, fatigue resistant bore and a creep-resistant rim. This combination of properties was previously unobtainable using conventional heat treatments, which produced disks with a uniform grain size. Future plans are in place to spin test a DMHT disk under the Ultra Safe Propulsion Project to assess the viability of this technology at the component level. This testing will include measurements of disk growth at a high temperature as well as the determination of burst speed at an intermediate temperature.

Gayda, John↗

Educational Brief: Using Space for a Better Foundation on Earth Mechanics of Granular Materials

Soils are three-phase composite materials that consist of soil, solid particles, and voids filled with water and/or air. Based on the particle-size distribution, they are generally classified as fine-grained (clays and plastic silts) and coarse-grained soils (nonplastic silts, sand, and gravel). Soil's resistance to external loadings is mainly derived from friction between particles and cohesion. Friction resistance is due to particles' surface-to-surface friction, interlocking, crushing, rearrangement, and dilation (or expansion) during shearing. Cohesion can be due to chemical cementation between particles, electrostatic and electromagnetic forces, and soil-water reaction and equilibrium. The basic factor responsible for the strength of coarse-grained soils is friction. Cohesion can be ignored. This educational brief focuses on measuring shear strength of sands (typical example of coarse-grained soils) where, for the same material, packing density is a main factor to be considered when one asks about the shear strength value. As the external load is applied, the soil's resistance is attained through shearing resistance, which causes the soil volume to increase (expand) or decrease (compress) depending on the initial packing density.

Dooling, Dave↗

Scalable parallel communications

Coarse-grain parallelism in networking (that is, the use of multiple protocol processors running replicated software sending over several physical channels) can be used to provide gigabit communications for a single application. Since parallel network performance is highly dependent on real issues such as hardware properties (e.g., memory speeds and cache hit rates), operating system overhead (e.g., interrupt handling), and protocol performance (e.g., effect of timeouts), we have performed detailed simulations studies of both a bus-based multiprocessor workstation node (based on the Sun Galaxy MP multiprocessor) and a distributed-memory parallel computer node (based on the Touchstone DELTA) to evaluate the behavior of coarse-grain parallelism. Our results indicate: (1) coarse-grain parallelism can deliver multiple 100 Mbps with currently available hardware platforms and existing networking protocols (such as Transmission Control Protocol/Internet Protocol (TCP/IP) and parallel Fiber Distributed Data Interface (FDDI) rings); (2) scale-up is near linear in n, the number of protocol processors, and channels (for small n and up to a few hundred Mbps); and (3) since these results are based on existing hardware without specialized devices (except perhaps for some simple modifications of the FDDI boards), this is a low cost solution to providing multiple 100 Mbps on current machines. In addition, from both the performance analysis and the properties of these architectures, we conclude: (1) multiple processors providing identical services and the use of space division multiplexing for the physical channels can provide better reliability than monolithic approaches (it also provides graceful degradation and low-cost load balancing); (2) coarse-grain parallelism supports running several transport protocols in parallel to provide different types of service (for example, one TCP handles small messages for many users, other TCP's running in parallel provide high bandwidth service to a single application); and (3) coarse grain parallelism will be able to incorporate many future improvements from related work (e.g., reduced data movement, fast TCP, fine-grain parallelism) also with near linear speed-ups.

Maly, K.↗

CoarsenConf: Equivariant Coarsening with Aggregated Attention for Molecular Conformer Generation

Molecular conformer generation (MCG) is an important task in cheminformatics and drug discovery. The ability to efficiently generate low-energy 3D structures can avoid expensive quantum mechanical simulations, leading to accelerated virtual screenings and enhanced structural exploration. Several generative models have been developed for MCG, but many struggle to consistently produce high-quality conformers for meaningful downstream applications. To address these issues, we introduce CoarsenConf, which coarse-grains molecular graphs based on torsional angles and integrates them into an SE(3)-equivariant hierarchical variational autoencoder. Through equivariant coarse-graining, we aggregate the fine-grained atomic coordinates of subgraphs connected via rotatable bonds, creating a variable-length coarse-grained latent representation. Our model uses a novel aggregated attention mechanism to restore fine-grained coordinates from the coarse-grained latent representation, enabling efficient generation of accurate conformers. Furthermore, we evaluate the chemical and biochemical quality of our generated conformers on multiple downstream applications, including property prediction and large-scale oracle-based protein docking. Overall, CoarsenConf generates more accurate conformer ensembles compared to prior generative models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Investigating the Effect of Water on the Mechanical Properties of Cellulose from Multiscale Molecular Dynamics Simulations

Classical molecular dynamics (MD) simulations provide insight into the structure and physicochemical properties of materials with atomic resolution. However, the length and time scales accessible to atomistic MD are orders of magnitude smaller than many relevant processes such as the response of a bulk material to experimentally accessible strain rates, which presents challenges when comparing models to experimental measurements. Bottom-up coarse-graining provides a means for systematically mapping atomistic information to lower resolution models to increase the length and time scales achievable by simulation. Cellulose is an abundant carbohydrate biopolymer with applications to many fields of research, such as materials science and renewable energy, due to its desirable mechanical properties and viability for conversion into biofuel. The effect of moisture content on the Young's modulus of cellulose is of special interest due to its native environment often being in the hydrated secondary plant cell wall and the grinding energy requirements for biomass feedstock preprocessing. The current work investigates the effects of water solvent on the Young's modulus of cellulose calculated from coarse-grained MD mechanical stress simulations. The coarse-grained model was parametrized from atomistic MD calculations of cellulose-cellulose potentials of mean force using umbrella sampling techniques under vacuum and solvated conditions. The Young's moduli of the coarse-grained cellulose assemblies parametrized from cellulose in vacuum or solvated in water were computed via mechanical stress simulations to highlight the importance of capturing solvent interactions for modeling the mechanical behavior of cellulose.

BASIC BIOLOGICAL SCIENCES,RADIATION PROTECTION AND↗

Effective drift velocity from turbulent transport by vorticity

Here, we highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length scales larger than ℓ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to which exhibits excellent correlation with the exact subscale physics when the partitioning length ℓ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, v * , that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, u¯ ℓ , but by the effective velocity, u¯ ℓ + v * , the physics of which may improve commonly used LES models.

42 ENGINEERING↗

Axial and torsional fatigue behavior of Waspaloy

The cyclic flow response and crack growth behavior of Waspaloy at room temperature and 650 C under tensile loading and torsional loading was studied, for two conditions of Waspaloy: fine grain, large gamma prime size; coarse grain, small gamma prime size. The fine grain material showed 5 to 10 percent hardening after about 10 percent of life, with sequent softening to failure at both themperature levels. The coarse grain material showed either stable response or monotonic softening to failure. Early crack initiation was observed on planes of maximum shear, with eventual branching to principle planes under torsional loading; cracks were always normal to load axis under tensile loading. Also, crack paths were intergranular at 650 C, mostly transgranular at room temperature.

Zamrik, S.↗

Microstructure refinement of hot deformed Dy-free NdFeB magnets through a novel cold sintering approach by pressure-assisted spark plasma sintering

Anisotropic fine-grained Dy-free NdFeB high-performance magnets were produced using a novel cold sintering approach by pressure-assisted spark plasma sintering (SPS). The NdFeB nanocrystalline ribbon powders were subjected to cold sintering below 450 °C using pressure-assisted SPS, followed by hot deformation at 710 °C and 810 °C via SPS. Results indicate that cold sintering below 450 °C effectively restricts grain growth in the NdFeB magnets, yielding sub-100 nm scale grains across both fine-grained regions and most coarse-grained regions. The refined grain structure achieved through cold sintering allows for a lower hot deformation temperature as compared with the magnet by conventional sintering, as finer grains allow easier deformation and grain sliding/rotation. This process produces a highly fine-grained and anisotropic microstructure to achieve high magnetic performance (i.e., high intrinsic coercivity, remanence, and maximum energy product) in the magnets. The cold sintering (at 350 °C) and lower hot deformation temperatures required (e.g., 710 °C) help control grain coarsening and limit grain size that is commensurate with the size of a single magnetic domain of the Nd 2 Fe 14 B magnetic matrix phase, resulting in high intrinsic coercivity (H ci =11.4 kOe). Furthermore, the reduced hot deformation temperature mitigates the formation of coarse grain bands, leading to improved magnetic properties, specifically an increased remanence (B r = 14.3 kGs) and a high maximum energy product ((BH) max = 48 MGOe). In conclusion, cold sintered hot deformed NdFeB magnet also shows good thermal stability with reversible temperature coefficient α(B r )= -0.097 %/K and α(H ci )= -0.616 %/K at elevated temperatures up to 400 K.

Cold Sintering↗

Quantum algorithms for geologic fracture networks

Abstract Solving large systems of equations is a challenge for modeling natural phenomena, such as simulating subsurface flow. To avoid systems that are intractable on current computers, it is often necessary to neglect information at small scales, an approach known as coarse-graining. For many practical applications, such as flow in porous, homogenous materials, coarse-graining offers a sufficiently-accurate approximation of the solution. Unfortunately, fractured systems cannot be accurately coarse-grained, as critical network topology exists at the smallest scales, including topology that can push the network across a percolation threshold. Therefore, new techniques are necessary to accurately model important fracture systems. Quantum algorithms for solving linear systems offer a theoretically-exponential improvement over their classical counterparts, and in this work we introduce two quantum algorithms for fractured flow. The first algorithm, designed for future quantum computers which operate without error, has enormous potential, but we demonstrate that current hardware is too noisy for adequate performance. The second algorithm, designed to be noise resilient, already performs well for problems of small to medium size (order 10–1000 nodes), which we demonstrate experimentally and explain theoretically. We expect further improvements by leveraging quantum error mitigation and preconditioning.

58 GEOSCIENCES↗

The isotopic composition of uranium and lead in Allende inclusions and meteoritic phosphates

The isotopic compositions of uranium and lead in Ca-Al-rich inclusions from the Allende chondrite and in whitlockite from the St. Severin chondrite and the Angra dos Reis achondrite are reported. Isoptopic analysis of acid soluble fractions of the Allende inclusions and the meteoritic whitlockite, which show isotopic anomalies in other elements, reveals U-235/U-238 ratios from 1/137.6 to 1/138.3, within 20 per mil of normal terrestrial U abundances. The Pb isotopic compositions of five coarse-grained Allende inclusions give a mean Pb-207/Pb-206 model age of 4.559 + or - 0.015 AE, in agreement with the U results. Pb isotope ratios of two fine-grained inclusions and a coarse-grained inclusion with strong mass fractionation and some nonlinear isotopic anomalies indicate that the U-Pb systems of these inclusions have evolved differently from the rest of Allende. Th/U abundance ratios in the Allende inclusions and meteoritic phosphate are found to range from 3.8 to 96, presumably indicating an optimal case for Cm/U fractionation, although the normal U concentrations do not support claims of abundant live Cm-247 or Cm-247/U-238 fractionation at the time of meteorite formation, in contrast to previous results. A limiting Cm-247/U-235 ratio of 0.004 at the time of meteorite formation is calculated which implies that the last major r process contribution at the protosolar nebula was approximately 100 million years prior to Al-26 formation and injection.

Chen, J. H.↗

Opaque-rich lithology in the Divnoe achondrite: Petrology and origin

An opaque-rich lithology (ORL) makes up to approximately 9 vol. percent of the Divnoe achondrite. It is characterized by enrichment of troilite and pyroxene, compared to the bulk Divnoe, and by the presence of tiny remnants of olivine in low-CA pyroxene and low minor element concentrations in pyroxene. The ORL was formed by local reaction between gaseous sulfur and olivine in the Divnoe. The Divnoe meteorite is an olivine-rich achondrite with subchondritic chemistry and mineralogy. It has a granoblastic coarse-grained olivine groundmass (CGL: coarse-grained lithology) with relatively large (2-10 mm) poikilitic patches (PP) of pyroxene and, rarely, plagioclase. The groundmass also contains an opaque-rich fine-grained lithology (ORL) which comprises approximately 9 vol. percent of the meteorite, displays reaction boundaries with the groundmass, and differs in mineral chemistry from it. Numerous micron- to mm-thick veins of troilite and, rarely, metal cross all the lithologies found in the meteorite. The Divnoe itself appears to represent a sample of an igneous source region.

Petaev, M. I.↗

The Divnoe meteorite: Petrology, chemistry, oxygen isotopes and origin

The Divnoe meteorite is an olivine-rich primitive achondrite with subchondritic chemistry and mineralogy. It has a granoblastic, coarse-grained, olivine groundmass (CGL: coarse-grained lithology) with relatively large pyroxene-plagioclase poiklitic patches (PP) and small fine-grained domains of an opaque-rich lithology (ORL). Both PP and ORL are inhomogeneously distributed and display reaction boundaries with the groundmass. Major silicates, olivine Fa(20-28) and orthopyroxyene Fs(20-28 Wo(0.5-2.5), display systematic differences in composition between CGL and ORL as well as a complicated pattern of variations within CGL. Accessory plagioclase has low K content and displays regular igneous zoning with core compositions An(40-45) and rims An(32-37). The bulk chemical composition of Divnoe is similar to that of olivine-rich primitive achondrites, except for a depletion of incompatible elements and minor enrichment of refractory siderophiles. Oxygen isotope compositions for whole-rock and separated minerals from Divnoe fall in a narrow range, with mean delta O-18 = +4.91, delta O-17 = +2.24, and Delta O-17 = -0.26 +/- 0.11. The isotopic composition is not within the range of any previously recognized group but is very close to that of the brachinites. To understand the origin of Divnoe lithologies, partial melting and crystallization were modelled using starting compositions equal to that of Divnoe and some chondritic meteorites. It was found that the Divnoe composition could be derived from a chondritic source region by approximately 20 wt% partial melting at Ta approximately 1300 C and log(fO2) = IW-1.8, followed by approximtely 60 wt% crystallization of the partial melt formed, and removal of the still-liquid portion of the partial melt. Removal of the last partial melt resulted in depletion of the Divnoe plagioclase in Na and K. In this scenario, CGL represents the residue of partial melting, and PP is a portion of the partial melt that crystallized in situ. The ORL was formed during the final stages of partial melting by reaction between gaseous sulfur and residual olivine in the source region. A prominent feature of Divnoe is fine micron-scale chemical variations within olivine grains, related to lamellar structures the olivines display. The origin of these structures is not known.

Petaev, M. I.↗

Driving force and pathway in polyelectrolyte complex coacervation

There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation–polyanion complexation and polyion pair–pair condensation. We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we show that prior to contact, two neutral polyion pairs weakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A software‐defined networks ‐based measurement method of network traffic for 6G technologies

Abstract In software‐defined networks (SDN) for 6G technologies, the controller should accurately and efficiently measure the flow traffic in switches for traffic engineering. Fine‐grained flow measurement can more accurately describe the traffic in the network, but it also consumes much more resources. To reduce the overhead incurred in the measurement process and obtain the approximate fine‐grained measurements, we propose a novel lightweight measurement scheme that runs in the controller. The novel lightweight measurement architecture consists of two parts: coarse‐grained measurement and interpolation‐optimization. In the first part, based on the SDN architecture, we use the pull‐based random sampling method to quickly obtain the coarse‐grained measurement of flow traffic through OpenFlow protocol. In the second part, we insert some discrete values into the coarse‐grained measurement with the interpolation theory, then we optimize interpolation results until finding the optimal fine‐grained flow traffic measurement by utilizing the multiconstraint method. We verified the feasibility of the proposed measurement method, and simulation results show that the measurement error of the proposed method is under 25%, but the flow measurement overhead of this method occupies only 3.3% compared with that of the fine‐grained method.

Huo, Liuwei↗