Gödel Fuzzy Argumentation Frameworks

Acknowledgements This work is supported by the Excellent Young Scholars Research Fund of Shandong Normal University. This research was sponsored by the U.S. Army Research Laboratory and the U.K. Ministry of Defence and was accomplished under Agreement Number W911NF-06-3-0001.Publisher PD

Kinetic Control on the Depth Distribution of Superdeep Diamonds

Superdeep diamonds contain unique information from the sublithospheric regions of Earth’s interior. Recent studies suggest that reaction between subducted carbonate and iron metal in the mantle plays an important role in the production of superdeep diamonds. It is unknown if this reaction is kinetically feasible in cold slabs subducted into the deep mantle. Here we present experimental data on real‐time tracking of the magnesite‐iron reaction at high pressures and high temperatures to demonstrate the production of diamond at the surface conditions of cold slabs in the transition zone and lower mantle. Our data reveal that the diamond production rate has a positive temperature dependence and a negative pressure dependence, and along a slab geotherm it decreases by a factor of three at pressures from 14.4 to 18.4 GPa. This rate reduction provides an explanation for the rarity of superdeep diamonds from the interior of the mantle transition zone.Plain Language SummarySuperdeep diamonds originate from great depths inside Earth, carrying samples from inaccessible mantle to the surface. The reaction between carbonate and iron may be an important mechanism to form diamond through interactions between subducting slabs and surrounding mantle. Interestingly, most superdeep diamonds formed in two narrow zones, at 250–450 and 600–800 km depths within the ~2,700‐km‐deep mantle. No satisfactory hypothesis explains these preferred depths of diamond formation. We measured the rate of a diamond forming reaction between magnesite and iron. Our data show that high temperature promotes the reaction, while high pressure does the opposite. Particularly, the reaction slows down drastically at about 475(±55) km depth, which may explain the rarity of diamond formation below 450 km depth. The only exception is the second zone at 600–800 km, where carbonate accumulates and warms up due to the stagnation of subducting slabs at the top of lower mantle, providing more reactants and higher temperature for diamond formation. Our study demonstrates that the depth distribution of superdeep diamonds may be controlled by reaction rates.Key PointsReal‐time tracking of diamond production from iron‐magnesite reaction at high pressures and high temperaturesThreefold reduction in the rate of iron‐magnesite reaction from 14.4 to 18.4 GPaDepth distribution of superdeep diamonds may be explained by reaction kineticsPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148362/1/grl58460_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148362/2/grl58460.pd

Exactly solvable configuration mixing scheme in the vibrational limit of the interacting boson model

An intruder configuration mixing scheme with 2n-particle and 2n-hole configurations from n=0 up to n→ in the U(5) (vibrational) limit of the interacting boson model is proposed. A simple Hamiltonian suitable to describe the intruder and normal configuration mixing is found to be exactly solvable, and its eigenstates can be expressed as the SU(1,1) coherent states built on the U(5) basis vectors of the interacting boson model. It is shown that the configuration mixing scheme keeps lower part of the vibrational spectrum unchanged and generates the intruder states due to the mixing. Some low-lying level energies and experimentally known B(E2) ratios of Cd108,110 are fitted and compared with the experimental results

Elastic fractal higher-order topological states

In this work, elastic fractal higher-order topological states are investigated. Bott index is adopted to characterize the topological property of elastic fractal structures. The topological corner and edge states of elastic waves in fractal structures are realized theoretically and experimentally. Different from traditional two-dimension (2D) high-order topological insulators based on periodic structures, the high-order topological states based on elastic fractal structures in this work intuitively reflect the fractal dimension in physics, supporting not only abundant topological outer corner states, but also rich inner corner states. The richness of corner states is much higher than that of topological insulators based on periodic structures. The strong robustness of the topological corner states in the fractal structure are verified by introducing disorders and defects. The topological phenomenon of in elastic fractal structures revealed in this work enriches the topological physics of elastic systems and breaks the limitation of that relies on periodic elastic structures. The results have important application prospects in energy harvesting, information transmissions, elastic energy acquisitions and high-sensitivity detections

Spin Transitions and Compressibility of ε‐Fe7N3 and γ′‐Fe4N: Implications for Iron Alloys in Terrestrial Planet Cores

Iron nitrides are possible constituents of the cores of Earth and other terrestrial planets. Pressure‐induced magnetic changes in iron nitrides and effects on compressibility remain poorly understood. Here we report synchrotron X‐ray emission spectroscopy (XES) and X‐ray diffraction (XRD) results for ε‐Fe7N3 and γ′‐Fe4N up to 60 GPa at 300 K. The XES spectra reveal completion of high‐ to low‐spin transition in ε‐Fe7N3 and γ′‐Fe4N at 43 and 34 GPa, respectively. The completion of the spin transition induces stiffening in bulk modulus of ε‐Fe7N3 by 22% at ~40 GPa, but has no resolvable effect on the compression behavior of γ′‐Fe4N. Fitting pressure‐volume data to the Birch‐Murnaghan equation of state yields V0 = 83.29 ± 0.03 (Å3), K0 = 232 ± 9 GPa, K0′ = 4.1 ± 0.5 for nonmagnetic ε‐Fe7N3 above the spin transition completion pressure, and V0 = 54.82 ± 0.02 (Å3), K0 = 152 ± 2 GPa, K0′ = 4.0 ± 0.1 for γ′‐Fe4N over the studied pressure range. By reexamining evidence for spin transition and effects on compressibility of other candidate components of terrestrial planet cores, Fe3S, Fe3P, Fe7C3, and Fe3C based on previous XES and XRD measurements, we located the completion of high‐ to low‐spin transition at ~67, 38, 50, and 30 GPa at 300 K, respectively. The completion of spin transitions of Fe3S, Fe3P, and Fe3C induces elastic stiffening, whereas that of Fe7C3 induces elastic softening. Changes in compressibility at completion of spin transitions in iron‐light element alloys may influence the properties of Earth’s and planetary cores.Key PointsSpin transition in ε‐Fe7N3 and γ′‐Fe4N at 300 K completes at 43 and 34 GPa, respectivelyThe completion of spin transition leads to stiffening in bulk modulus of ε‐Fe7N3, but not in γ′‐Fe4NEvidence for spin transitions in Fe‐light‐element alloys and their effects are reexaminedPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/163586/2/jgrb54505_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/163586/1/jgrb54505.pd

Case report: Endovascular intervention of internal carotid artery pseudoaneurysm secondary to nasopharyngeal carcinoma radiotherapy

BackgroundInternal carotid artery pseudoaneurysm (PSA) is a serious complication after radiotherapy for nasopharyngeal carcinoma, and once it ruptures and bleeds, it will seriously affect the patient's survival and prognosis. However, because of its relatively low incidence, many medical institutions lack experience in managing this type of emergency.Case informationIn this case report, we described two cases suffered ruptured internal carotid artery PSA after radiotherapy for nasopharyngeal carcinoma, including their history, diagnosis, and treatment. Both cases underwent emergency endovascular interventions, one of which with long-term healing after embolization of the PSA, and the other one with re-bleeding after embolization and was eventually stopped by embolization of the parent artery. Ultimately, both cases received timely and effective treatment.ConclusionThis case report detailed the diagnosis and treatment course of internal carotid artery PSA after radiotherapy for nasopharyngeal carcinoma, which enhanced the understanding of this emergency, and provided valuable information and experience for the treatment strategy of similar PSA on the internal carotid artery

Hidden carbon in Earth’s inner core revealed by shear softening in dense Fe₇C₃

Earth’s inner core is known to consist of crystalline iron alloyed with a small amount of nickel and lighter elements, but the shear wave (S wave) travels through the inner core at about half the speed expected for most iron-rich alloys under relevant pressures. The anomalously low S-wave velocity (v_S) has been attributed to the presence of liquid, hence questioning the solidity of the inner core. Here we report new experimental data up to core pressures on iron carbide Fe_7C_3, a candidate component of the inner core, showing that its sound velocities dropped significantly near the end of a pressure-induced spin-pairing transition, which took place gradually between 10 GPa and 53 GPa. Following the transition, the sound velocities increased with density at an exceptionally low rate. Extrapolating the data to the inner core pressure and accounting for the temperature effect, we found that low-spin Fe_7C_3 can reproduce the observed v_S of the inner core, thus eliminating the need to invoke partial melting or a postulated large temperature effect. The model of a carbon-rich inner core may be consistent with existing constraints on the Earth's carbon budget and would imply that as much as two thirds of the planet's carbon is hidden in its center sphere

Synthesis, Elasticity, and Spin State of an Intermediate MgSiO3‐FeAlO3 Bridgmanite: Implications for Iron in Earth’s Lower Mantle

Fe‐Al‐bearing bridgmanite may be the dominant host for ferric iron in Earth’s lower mantle. Here we report the synthesis of (Mg0.5Fe3+0.5)(Al0.5Si0.5)O3 bridgmanite (FA50) with the highest Fe3+‐Al3+ coupled substitution known to date. X‐ray diffraction measurements showed that at ambient conditions, the FA50 adopted the LiNbO3 structure. Upon compression at room temperature to 18 GPa, it transformed back into the bridgmanite structure, which remained stable up to 102 GPa and 2,600 K. Fitting Birch‐Murnaghan equation of state of FA50 bridgmanite yields V0 = 172.1(4) Å3, K0 = 229(4) GPa with K0′ = 4(fixed). The calculated bulk sound velocity of the FA50 bridgmanite is ~7.7% lower than MgSiO3 bridgmanite, mainly because the presence of ferric iron increases the unit‐cell mass by 15.5%. This difference likely represents the upper limit of sound velocity anomaly introduced by Fe3+‐Al3+ substitution. X‐ray emission and synchrotron Mössbauer spectroscopy measurements showed that after laser annealing, ~6% of Fe3+ cations exchanged with Al3+ and underwent the high‐ to low‐spin transition at 59 GPa. The low‐spin proportion of Fe3+ increased gradually with pressure and reached 17–31% at 80 GPa. Since the cation exchange and spin transition in this Fe3+‐Al3+‐enriched bridgmanite do not cause resolvable unit‐cell volume reduction, and the increase of low‐spin Fe3+ fraction with pressure occurs gradually, the spin transition would not produce a distinct seismic signature in the lower mantle. However, it may influence iron partitioning and isotopic fractionation, thus introducing chemical heterogeneity in the lower mantle.Plain Language SummaryFe‐Al‐bearing bridgmanite may be the dominant mineral in the lower mantle, which occupies more than half of Earth’s volume. A subject of much debate is whether spin transition of Fe in bridgmanite produces an observable influence on the physics and chemistry of the lower mantle. In this study, we synthesized a new (Mg0.5Fe3+0.5)(Al0.5Si0.5)O3 bridgmanite with the highest Fe3+‐Al3+ coupled substitution known to date. We studied its structure, elasticity, and spin state by multiple experimental and theoretical methods. The high Fe content allowed us to better resolve a pressure‐induced spin transition of Fe3+ caused by Fe‐Al cation exchange at high temperature. Our results suggest that the spin transition is enabled by cation exchange but has a minor effect on the seismic velocity, although it may introduce chemical heterogeneity in the lower mantle. Our study helps resolve existing discrepancies on the nature of spin transition of Fe‐Al bridgmanite and its influence on the physics and chemistry of the lower mantle.Key PointsBridgmanite may contain 50% trivalent cations through Fe3+‐Al3+ coupled substitutionThe bulk sound velocity of (Mg0.5Fe3+0.5)(Al0.5Si0.5)O3 bridgmanite is 7.7% lower than MgSiO3Through Fe‐Al cation exchange, Fe3+ in (Mg0.5Fe3+0.5)(Al0.5Si0.5)O3 bridgmanite undergoes gradual spin transition at lower mantle conditionsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/156245/3/jgrb54280-sup-0001-2020JB019964-SI.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156245/2/jgrb54280.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/156245/1/jgrb54280_am.pd

Research on decision-making of water diversion supply chain considering both social welfare and water quality utility

When water diversion projects become important part of the water network around the world, the effective operation and management of the projects play important roles in giving full play to the optimal allocation of water resources. For the operation and management of water transfer, the decision-making of water supply chain under the scenario of economic benefit, producer surplus, and water quality utility should be considered simultaneously. According to the idea of supply chain, this paper regards water transfer operation management as a water supply chain composed of water transfer companies, water supply companies, and consumers. From the perspective of social welfare and water quality utility, a comprehensive optimization and coordination decision model for water transfer is proposed. Taking the South-to-North Water Diversion Project as the research object, the cost-sharing contract is designed, and the Stackelberg game method is used to optimize the decision-making and coordination of the water supply chain. The results show that when the concern coefficient and the cost-sharing ratio are evaluated within a given feasible value region, the profits of both the water transfer company and the water supply company can be improved. The feasible value interval of the concern coefficient decreases with the increase in the cost-bearing proportion. When the concern coefficient increases, the profit of the water transfer company decreases, while profit of the water supply company, water quality, consumer surplus, water quality utility, and utility of the water transfer company increase gradually. The results provide valuable references for water transfer decision-making