Time Evolution Of Temperature Research Articles

Thermodynamic and Kinetic Studies on the Pyrophoricity of Uranium Flakes

The objective of this work was to arrive at quantitative estimates of pyrophoricity of uranium in different geometries. The major source of heat generation was identified to be exothermic chemical reactions of uranium with moist air. Time evolution of temperature was studied for uranium considering 3D conduction and convection heat loss routes using Finite Element Analysis. Auto ignition temperature for uranium flakes was quantified using heat balance equation and was found to be around 500 K. Excess heat generation rates needed to cause auto ignition of uranium flakes at room temperature were also estimated. The major sources of excess heat leading to its ambient ignition could be attributed to friction and other exothermic chemical reactions of process impurities in uranium.

Decoupling Analysis of Ignition Processes of Ammonia/N-Heptane Mixtures

Abstract: To further understand the influence of n-heptane on the ignition process of ammonia, an isotope labeling method was applied in the current investigation to decouple the influence of the chemical effect, the thermal effect, and the effect of O radical from the oxidation of n-heptane on the ignition delay times (IDTs) of ammonia. An analysis of the time evolution of fuel, analysis of the time evolution of temperature, rate of consumption and production (ROP) analysis, and sensitivity analysis were conducted to gain a further understanding of the mechanism of the influence of the chemical effect, the thermal effect, and the effect of O radical on the ignition of ammonia. The results showed that the negative temperature coefficient (NTC) behavior of n-heptane is mitigated by the blending of ammonia, and this mitigated effect of ammonia is mainly due to the chemical effect. The IDTs of ammonia under low and medium temperatures are significantly shortened by the chemical effect at a n-heptane mass fraction of 10%. The promoting effect of the chemical effect decreases when the n-heptane mass fraction increases. The time evolution of n-heptane for NC7H16/ND3-G can be classified into three stages at 800 K, and the rapid consumption stage is mitigated by an increase in temperature. The rapid consumption stage is suppressed by the chemical effect of ammonia, while O radical has a promoting effect on the rapid consumption stage. The chemical effect will enhance the sensitivities of reactions associated with ammonia. As the n-heptane mass fraction increases, the sensitivities of reactions associated with n-heptane are enhanced. Correspondingly, the effect of reactions associated with ammonia is weakened. When the n-heptane mass fraction is 30%, only reactions related to n-heptane have a great influence on the ignition of ammonia/n-heptane fuel blends under the thermal effect + the effect of O radical or only the thermal effect.

Comparison between conduction models and models including the energy balance along the flow, for the simulation of U-tube borehole heat exchangers

Most ground-coupled heat pumps exchange heat with the ground by means of a borehole-heat-exchanger (BHE) field. The time evolution of the fluid temperature at the outlet of the BHE field, employed for the design of the heat pump, is often determined starting from that of the mean temperature of the surface between the BHEs and the ground, evaluated by means of a dimensionless function called g-function. In order to obtain an accurate thermal response to peak loads, this method must be coupled with a short-term simulation tool. Simulation models that yield accurately the time evolution of either the outlet fluid temperature or the mean fluid temperature both in the short and in the long term are also available. The simplest of these models, called here conduction models, represent the fluid by a solid that receives or generates heat. Models that include the energy balance for the flow along the pipes, called here complete models, have also been proposed. Complete models are the most accurate, but can hardly be applied for long-term simulations. In this paper, the results of finite-element simulations of U-tube BHES performed by conduction models are compared with those obtained by complete models, implemented through the COMSOL Pipe Flow Module. It is shown that there is an excellent agreement between the models in the short term, while complete models yield slightly higher values of the mean fluid temperature in the medium and long term. It is also shown that one can obtain by a conduction model the same time evolution of the mean fluid temperature that would be yielded by a complete model, replacing the real 2D BHE thermal resistance, Rb2D, with a virtual one, equal to the asymptotic value of the 3D thermal resistance yielded by the complete model, RbPF. For BHEs with length 100 m, diameter 152 mm, grout thermal conductivity 1.6 W/(m K), ground thermal conductivity 1.8 W/(m K) and flow rate 14 L per minute, the ratio RbPF/Rb2D is, for instance, 1.032 for a single U-tube BHE with shank spacing s = 94 mm, and 1.090 for a double U-tube BHE with s = 85 mm. Dimensionless correlations yielding the value of RbPF/Rb2D for any U-tube BHE will be provided in a future paper.

An infrared-optical image registration method for industrial blower monitoring based on contour-shape descriptors

Industrial blowers are energy-efficient and widely used, but fault monitoring is challenging. Infrared and visible light sensors monitor their status, capturing temperature distribution and time evolution in images and videos. Due to the complexity of the industrial scene and the large difference between the characteristics of infrared and visible images, the existing registration methods are unable to accurately align the infrared and visible images. This paper proposes a Neural Network (NN) based registration method of infrared and visible images for industrial blowers using contours and Weight Global Shape Context Descriptor (W-GSCD), by considering the distance between different feature points as weights in our feature registration method which improves the accuracy of the registration of IR and visible images compared to classical image registration methods. Experiments on real data show that the proposed method effectively addresses registration challenges from complex shapes and heterogeneous backgrounds, achieving promising results on the blower dataset.

The Age of Granulite-Facies Metamorphism in the Ivrea–Verbano Zone (NW Italy) Determined Through In Situ U–Pb Dating of Garnet

Abstract Rates of melt production, extraction and crystallization, as well as scales of melt transfer and interaction with their residuum change continuously in migmatite and granulite, affecting the behavior of monazite and zircon as time capsules. Therefore, accessory mineral chronometers may be ambiguous and incomplete in providing an overview of the temperature–time evolution of high-grade metamorphic rocks. In this study, we applied the novel technique of in situ U–Pb dating of garnet to the archetypal lower continental crust of the Ivrea–Verbano Zone (IVZ), NW Italy. In the IVZ, the temporal relationship between granulite-facies metamorphism and mafic underplating has long been debated, because of the interplay between tectonic, magmatic, metamorphic and metasomatic processes over a period of more than a hundred million years. Garnet from mafic and pelitic granulites yielded U–Pb ages between 287.4 ± 4.9 Ma and 280.1 ± 12.4 Ma, overlapping within uncertainty the time proposed for the emplacement of the Mafic Complex (286–282 Ma). These results indicate that the thermal climax in granulitic rocks was caused by mafic underplating and concomitant asthenospheric upwelling, rather than being inherited from the post-Variscan Carboniferous evolution. Providing robust dating of garnet with as low as 4 ng/g U, this study demonstrates the strength of garnet petrochronology in resolving complex tectono-metamorphic histories of high-grade terranes. It also represents a further step forward towards establishing garnet as part of the in situ U–Pb geochronology repertoire.

X-ray study on the core collapse supernova 2008ax using XMM-Newton and Swift/XRT

We studied the x-ray evolution of the core collapse, Type IIb, supernova SN 2008ax. In addition to the four Swift/XRT observations previously published, we included, for the first time, two observations from XMM-NEWTON to our analysis that have not been published before. By focusing on the early observations of the SN 2008ax, we were able to explore the time evolution of both x-ray luminosity (Lx) and temperature (Tx) during the radiative phase. The analysis showed that the evolution of Lx and Tx can be expressed as a power law as Lx ∝ t −0.87 and Tx ∝ t −0.46, respectively. Based on the observed x-ray luminosity, we estimated the mass-loss rate ( Ṁ ) for the progenitor star to be approximately 0.64 ± 0.15 × 10−5 M⊙ yr −1, for a wind velocity of 10 km s−1. This finding is in good agreement with the previous studies.

A modified two temperature molecular dynamics (2T-MD) model for cascades

Two-Temperature molecular dynamics (2T-MD) is a common approach for describing how electrons contribute to the evolution of a damage cascade by addressing their role in the redistribution of energy in the system. However, inaccuracies in 2T-MD’s treatment of the high-energy particles have limited its utilisation. Here, we propose a reformulation of the traditional 2T-MD scheme to overcome this limitation by addressing the spurious double-interaction of high-energy atoms with electrons. We conduct a series of radiation damage cascades for 30, 50, and 100 keV primary knock-on atoms in increasingly large cubic W cells. In the simulations, we employ our modified 2T-MD scheme along with other treatments of electron–phonon coupling to explore their impact on the cascade evolution and the number of remnant defects. The results suggest that with the proposed modification, 2T-MD simulations account for the temperature time evolution during the ballistic phase and remove arbitrary choices, thus providing a better description of the underlying physics of the damage process.

Time-resolved measurement of optical emission line profiles from electron cyclotron resonance ion source plasma

Optical emission spectroscopy provides a non-invasive method to probe the properties of hot and highly charged magnetically confined plasmas. The optical emission line profiles enable, for example, to identify the different species and characterize the relative population densities and temperatures of the ions and neutrals forming the plasma. The feasibility of this approach has been demonstrated at the University of Jyväskylä accelerator laboratory by measuring the light emitted by Electron Cyclotron Resonance Ion Source (ECRIS) plasma with a high-resolution spectrometer setup POSSU (Plasma Optical SpectroScopy Unit). In these previous studies, the emission line profiles were measured by scanning the desired wavelength range by rotating the diffraction grating of the spectrometer. This process is slow compared to many interesting plasma phenomena, thus limiting the applicability of the setup. Recently, POSSU has been upgraded by changing the light sensor from a photomultiplier tube to a position-sensitive imaging sensor. As a result, it is possible to measure simultaneously a 1 - 2 nm wavelength range, with a spectral resolution in the order of picometers, without moving the grating. This enables a time-resolved study of the optical emission line profiles. By turning the grating, the measured wavelength region can be chosen between 370 nm and 870 nm, which covers the visible light spectrum. The time-evolution of optical emission line profiles emitted from the JYFL 14 GHz ECRIS plasma, during shifting plasma conditions induced by changing the gas balance, has been measured to demonstrate this new capability. The time-evolution of temperatures and emission intensities of selected ion species, correlated with extracted ion beam currents, are presented.

Prediction of pellet mass thresholds for ELM triggering in low-collisionality, ITER-like discharges

In ITER, pellets are calculated to require more than 8 times the mass than currently planned to reliably trigger edge-localized modes (ELMs). Unmitigated heat flux impulses from ELMs are intolerable in ITER at full power and current. Therefore, ITER operation relies on multiple approaches to control ELM heat fluxes. One method is pellet ELM pacing to instigate small rapid ELMs with low heat flux. Predicting the performance of pellet pacing is critical for ITER, which is expected to operate in a regime with a low-collisionality, peeling-limited pedestal. However, to trigger ELMs the local pressure increase in the expanding pellet cloud pushes the equilibrium over the ballooning stability limit. In this work, linear and nonlinear M3D-C1 simulations are used to predict pellet mass thresholds in DIII-D discharges and ITER scenarios with peeling-limited pedestals. It is found that the distance of the equilibrium’s operational point from the ballooning branch of the pedestal stability boundary strongly changes thresholds. Linear M3D-C1 simulations find a strong dependence of the pellet mass threshold on the poloidal injection location for ITER’s 15 MA, Q = 10 scenario. The required pellet mass at the planned injection locations is 8 to 17 times larger than currently considered. However, such linear simulations do not include pellet ablation physics or time evolution of density and temperature. A new scheme of 2D nonlinear simulations, coupled with linear stability analysis at various steps throughout the nonlinear time evolution, was developed to include such physics and improve on the linear results. These new nonlinear-to-linear simulations confirm previous findings. This result suggests that pellet ELM triggering in ITER could require pellets much larger than those currently planned, which makes ELM-pacing operationally challenging. On the other hand, fueling pellets injected from the high-field side will likely not unintentionally trigger ELMs in an otherwise ELM-stable plasma.

Generation of photoionized plasmas in the laboratory of relevance to accretion-powered x-ray sources using keV line radiation

We describe laboratory experiments to generate x-ray photoionized plasmas of relevance to accretion-powered x-ray sources such as neutron star binaries and quasars, with significant improvements over previous work. A key quantity is referenced, namely the photoionization parameter, defined as ξ=4πF/ne where F is the x-ray flux and ne the electron density. This is normally meaningful in an astrophysical steady-state context, but is also commonly used in the literature as a figure of merit for laboratory experiments that are, of necessity, time-dependent. We demonstrate emission-weighted values of ξ>50 erg-cm s−1 using laser-plasma x-ray sources, with higher results at the centre of the plasma which are in the regime of interest for several astrophysical scenarios. Comparisons of laboratory experiments with astrophysical codes are always limited, principally by the many orders of magnitude differences in time and spatial scales, but also other plasma parameters. However useful checks on performance can often be made for a limited range of parameters. For example, we show that our use of a keV line source, rather than the quasi-blackbody radiation fields normally employed in such experiments, has allowed the generation of the ratio of inner-shell to outer-shell photoionization expected from a blackbody source with ∼keV spectral temperature. We compare calculations from our in-house plasma modelling code with those from Cloudy and find moderately good agreement for the time evolution of both electron temperature and average ionisation. However, a comparison of code predictions for a K-β argon X-ray spectrum with experimental data reveals that our Cloudy simulation overestimates the intensities of more highly ionised argon species. This is not totally surprising as the Cloudy model was generated for a single set of plasma conditions, while the experimental data are spatially integrated.

Study of the surface damage threshold and mechanism of KDP crystal under ultrashort laser irradiation

Here, we investigate the mechanism of surface damage threshold anisotropy induced by ultrashort laser in potassium dihydrogen phosphate (KDP) crystal. Carrier-lattice nonequilibrium interaction is simulated based on Brillouin light-scattering (BLS) spectroscopy and a complete self-consistent model to obtain the time evolution of carrier density and temperature as well as lattice temperature. The results indicate that the trend of the lattice temperature is consistent with the experimental phenomena. Meanwhile, the electron-phonon coupling effect, in addition to the electron density traditionally considered, is an important factor affecting damage and is a major contributor to the anisotropy of the damage threshold.

Environmental evolution of western Tierra del Fuego (∼54°S) since ice-free conditions and its zonal/hemispheric implications

By virtue of its position adjacent to the Drake Passage, Tierra del Fuego in South America allows examining the vegetation and environmental history of the southernmost continental landmass outside Antarctica, and the evolution of the Southern Westerly Winds-Southern Ocean (SWW–SO) coupled system since the Last Glacial Maximum (LGM). For that purpose, we studied sediment cores from Lago Charquito, a small closed-basin lake in central-west Tierra del Fuego with a continuous lacustrine record since ∼17.3 ka. Ice-free conditions at the site imply a ∼70 km retreat of the Bahía Inútil glacier lobe from its LGM position during a ∼800-year interval, a trend that continued until its disappearance ∼100 km upstream from L. Charquito, ∼800 years later. Our palynological data show an open landscape dominated by cold-tolerant shrubs and herbs between ∼17.3–12.9 ka, with increases in precipitation of SWW origin at ∼16.3 ka, ∼14.7 ka, between ∼8.7–7.6 ka, and after ∼6.8 ka. Warming at ∼12.9 ka initiated an abrupt afforestation trend that stalled during the early Holocene (∼12–8.7 ka) owing to a precipitation decline and wildfires, and later resumed in response to invigorated SWW. We hypothesize that sparse Nothofagus tree populations inhabited the periphery of the Patagonian Ice Sheet (PIS) during the LGM and migrated toward the Andes contemporaneous with glacier recession as temperature rose during the Last Glacial Termination (T1). We posit that besides establishing topographic and climatic barriers for land biota, the PIS enabled the connectivity of cold-tolerant hygrophilous plant populations along a humid fringe adjacent to its land-based perimeter, despite the presumably dry conditions downwind from the eastern PIS margin. Our results suggest that southward shifts or expansion of the SWW toward or beyond Tierra del Fuego enhanced upwelling and ventilation of deep waters in the SO, northward shifts or weakening had the opposite effect. We observe that the time evolution of atmospheric CO2 concentrations, high-latitude air and sea-surface temperatures, and sea level during T1 fall short in explaining the timing and abruptness of the Bahía Inútil glacier lobe collapse, and quite possibly multiple other glacier lobes from the PIS.

Estimations of Elemental Abundances during Solar Flares Observed in Soft X-Rays by the MinXSS-1 CubeSat Mission

Solar flares are complex phenomena emitting all types of electromagnetic radiation and accelerating particles on timescales of minutes, converting magnetic energy to thermal, radiative, and kinetic energy through magnetic reconnections. As a result, local plasma can be heated to temperatures in excess of 20 MK. During the soft X-ray (SXR) solar flare peak, the elemental abundance of low first ionization potential elements are typically observed to be depleted from coronal values. We explored the abundance variations using disk-integrated solar spectra from the Miniature X-ray Solar Spectrometer CubeSat-1 (MinXSS-1). MinXSS-1 is sensitive to the 1–12 keV energy range with an effective 0.25 keV FWHM resolution at 5.9 keV. During the year-long mission of MinXSS-1, between 2016 May and 2017 May, 21 flares with intermittent data downlinks were observed ranging from C to M class. We examine the time evolution of temperature, volume emission measure, and elemental abundances of Fe, Ca, Si, S, and Ar with CHIANTI spectral models near the peak SXR emission times observed in the MinXSS-1 data. We determined the average absolute abundance of A(Fe) = 7.81, A(Ca) = 6.84, A(S) = 7.28, A(Si) = 7.90, and A(Ar) = 6.56. These abundances are depleted from coronal values during the SXR peak compared to nonflaring times. The elemental abundance values that are depleted from their coronal values are consistent with the process of chromospheric evaporation, in which the lower atmospheric plasma fills the coronal loops.

Thermal analysis and thermography observation of stainless-steel ice cubes

Alternative products for water ice cubes have long been sought due to the spread of waterborne diseases and microplastic contamination, as they are often made from unhygienic water sources. Recently, stainless-steel ice cubes have been considered as one of the best alternatives, and they have been very popular in marketplaces, although very few studies found in the literature that have investigated their potential in replacing water ice cubes. In this study, the thermal performance of stainless-steel ice cubes will be explored experimentally using a combination of an Arduino microcontroller equipped with DS18B20 thermocouple sensors and a HIKMICRO B20 thermal camera with the aim to find out how good stainless steel ice cubes for cooling food and beverages. The time evolution of water temperature in glasses filled with stainless-steel cubes of various brands is compared with that of water ice cubes. The temperature field obtained from thermal images is used to further observe the overall temperature of water in the glass. Leeseph stainless-steel ice cubes are found to have thermal performance comparable to water ice cubes, while SSGP ice cubes can retain lower temperatures for a longer time compared with other ice cubes. The effect of the number of ice cubes (N), the volume of water (V), and the average diameter of the glass used (D) are also investigated. At 1 ≤ N ≤ 4, the larger number of ice cubes used are found to lower the minimum temperature, and to decrease the minimum time, while at 150 ml ≤ V ≤ 300 ml, the larger amount of water used are observed to increase the minimum temperature and to increase the minimum time, . At 53 mm ≤ D ≤ 66 mm, larger glass diameter used are found to increase both the minimum temperature, and the minimum time

Dimensionless fluid-to-ground thermal response of single-line bore fields with isothermal fluid

The design of a borehole-heat-exchanger (BHE) field is usually performed by means of dimensionless functions, called g-functions, that yield the time evolution of the mean temperature of the external surface of the BHEs, Tsm, produced by a time constant heat flux, which is usually considered as uniform. The mean temperature of the fluid, Tfm, is then evaluated by adding to Tsm the product of the heat flux per unit length and the BHE thermal resistance. This method overestimates the difference between Tfm and Tsm in the short term, and overestimates the g-function of the field in the long term. Methods to obtain more accurate results have been proposed, but require difficult and time-consuming numerical computations. In this paper dimensionless fluid-to-ground (ftg) functions that yield directly the time evolution of Tfm, in a time scale from a few minutes to hundreds of years, are provided for any single-line bore field subjected to a time constant heat flux, composed of up to four BHEs fed in parallel with the same inlet temperature. The ftg-functions are obtained by finite-element simulations implemented in COMSOL Multiphysics, and are reported in two Excel files that, after entering the dimensionless parameters of the BHE field under examination, instantly yield a short-term and a long-term ftg-function perfectly joined at the separation instant. The main novelties of this work are the characterization of each BHE field by a few dimensionless parameters, the improvement of the BHE model presented in Naldi and Zanchini 2020, the accuracy, speed and simplicity of use of the final results. The validations of the simulation codes for a single BHE and for fields of 3 and 4 BHEs, by comparison with analytical solutions, yielded root-mean-square deviations equal to 0.023%, 0.43%, and 0.49% of the mean value, respectively. The validation of the simulation code for two BHEs, performed with an extremely high distance between the BHEs, yielded a root-mean-square deviation equal to 0.054% of the mean value, with respect to the long-term ftg-function obtained for a single BHE.

Electron cooling in graphene enhanced by plasmon-hydron resonance.

Evidence is accumulating for the crucial role of a solid's free electrons in the dynamics of solid-liquid interfaces. Liquids induce electronic polarization and drive electric currents as they flow; electronic excitations, in turn, participate in hydrodynamic friction. Yet, the underlying solid-liquid interactions have been lacking a direct experimental probe. Here we study the energy transfer across liquid-graphene interfaces using ultrafast spectroscopy. The graphene electrons are heated up quasi-instantaneously by a visible excitation pulse, and the time evolution of the electronic temperature is then monitored with a terahertz pulse. We observe that water accelerates the cooling of the graphene electrons, whereas other polar liquids leave the cooling dynamics largely unaffected. A quantum theory of solid-liquid heat transfer accounts for the water-specific cooling enhancement through a resonance between the graphene surface plasmon mode and the so-called hydrons-water charge fluctuations-particularly the water libration modes, which allows for efficient energy transfer. Our results provide direct experimental evidence of a solid-liquid interaction mediated by collective modes and support the theoretically proposed mechanism for quantum friction. They further reveal a particularly large thermal boundary conductance for the water-graphene interface and suggest strategies for enhancing the thermal conductivity in graphene-based nanostructures.

Microstructure evolution in the self-propagating reaction in Al/Ru bilayers by phase-field simulations and experiments

The self-propagating reaction in binary Al/Ru multilayers with two different bilayer thicknesses (89 and 178 nm, respectively) forming single-phase AlRu intermetallic compound is investigated experimentally and by means of phase-field simulations. Experimentally, the time-temperature evolution in free-standing films was recorded with a high-speed pyrometer, and the resulting microstructure was determined from electron backscatter diffraction measurements. The phase-field model is constructed based on the minimization of the grand potentials for which the required thermodynamic data are taken from the Calphad database. The simulation of the reaction and subsequent AlRu grain growth starts from Al-rich and Ru-rich layer fillings. After the formation of the AlRu phase is complete, the grain growth during cooling is simulated based on the experimentally recorded time-temperature curves. Finally, the resulting grain sizes obtained from the simulation are found to be in good agreement with the experimental results. Furthermore, it is shown that the final grain sizes in both simulations and experiments depend on the initial bilayer thicknesses.

Application of imaging techniques for the characterization of lumps behaviour in gas–solid fluidized-bed reactors

Gas-solid fluidized-bed reactors are often used in waste pyrolysis and gasification processes thanks to their excellent mixing properties, which guarantee temperature uniformity. However, this latter property can fail when large objects, such as lumps, are introduced or form in the system. Understanding the motion characteristics and thermal behaviour of lumps in a high temperature fluidized-bed reactor can help determining how the presence of lumps impact reactors’ performance. This was the object of this study. In particular, this work aims to assess how process variables and physical properties impact the segregation behaviour, dispersion coefficients and heat transfer coefficients of these lumps during operation. The system used in this work is a down-scaled pseudo-2D fluidized bed operated at ambient temperature and at fluidization velocities ranging between 1 Umf and 10 Umf. Rutile sand with four different mean particle sizes (60 μm, 100 μm, 153 μm and 215 μm) was used as bed material. Fabricated lumps were introduced in the fluidized bed to reproduce realistic conditions, as when lumps form in a high-temperature fluid bed. The density ratio between the lump and the bed material particle was varied between 0.32 and 0.55 to account for different lump compositions. X-ray digital radiography and infrared thermography were used respectively to track the fabricated lumps and to obtain their temperature time evolution. The lump density was found not to have a significant effect on the lump dispersion coefficients or on the heat transfer coefficient. Optimal values of fluidization velocities that guarantee proper lump mixing and maximum heat transfer coefficient were obtained. This latter increases by up to 10 times if the optimal fluidization velocity is selected. An increase in the bed material particle size was found to cause an increase in the dispersion coefficients and a decrease in the heat transfer coefficient. The trend of the heat transfer coefficient as a function of the fluidization velocity was found to vary significantly between different bed material particle sizes. A new correlation for the Nusselt number as a function of the object Reynolds number and of the size ratio between lump and bed material was obtained. This correlation applies to cases where particle convection is the dominant mechanism of heat transfer. The results of this work provide important knowledge to minimize the impact of lumps on fluidized-bed reactors and to optimize their operation.

The late to early time behaviour of an expanding plasma: hydrodynamisation from exponential asymptotics

We use exponential asymptotics to match the late time temperature evolution of an expanding conformally invariant fluid to its early time behaviour. We show that the rich divergent transseries asymptotics at late times can be used to interpolate between the two regimes with exponential accuracy using the well-established methods of hyperasymptotics, Borel resummation and transasymptotics. This approach is generic and can be applied to any interpolation problem involving a local asymptotic transseries expansion as well as knowledge of the solution in a second region away from the expansion point. Moreover, we present global analytical properties of the solutions such as analytic approximations to the locations of the square-root branch points, exemplifying how the summed transseries contains within itself information about the observable in regions with different asymptotics.

Timescales of ultra-high temperature metamorphism and crustal differentiation: Zircon petrochronology from granulite xenoliths of the Variscan French Massif Central

Lower crustal ultra-high temperature (UHT) metamorphism and the resulting production and transfer of granitic magmas represent key processes of intracrustal differentiation. The timescales of these phenomena are debated, due to the complexity of the granulite zircon U-Pb record and because direct links between granulites and granites are difficult to establish. To address these issues, we present the results of zircon petrochronology (coupled U-Pb dating, trace element and Lu-Hf isotopic analyses) for lower crustal felsic and mafic granulite xenoliths from the Variscan eastern French Massif Central and compare them with data from well-characterized mid-/upper crustal migmatites and granites. The felsic and mafic granulites represent pre-Variscan meta-sedimentary and meta-igneous mafic rocks, respectively; which experienced Variscan UHT peak metamorphism at 940–970°C and 8 ± 2 kbar. Zircons from the felsic granulites show U-Pb dates spreading over ∼50 Myr between ∼315 and ∼265 Ma, correlated to Ti-in-zircon temperatures decreasing from 940–970°C to 800°C and REE contents consistent with growth in equilibrium with garnet at (U)HT conditions. This is best explained by continuous crystallization of zircon upon cooling from the thermal peak owing to decreasing Zr solubility of residual melt, despite significant prograde melt loss. Zircons from the mafic granulite only record the last stage of this time-temperature evolution (295–265 Ma; 800–900°C) due to later zircon saturation. Upper crustal granite emplacement started at 340 Ma and culminated at the age of the lower crustal thermal peak of 313 ± 3 Ma (defined by the highest-temperature zircons from felsic granulites), reflecting melt extraction along the ∼27 Myr prograde path of the lower crust. In turn, the crystallization ages of mid-crustal migmatites (315–300 Ma) and the lower crustal granulites (315–265 Ma) are consistent with slow cooling in the presence of melt. These results provide a direct assessment of the timescales of melt production and residence at the crustal scale; and validate the granulite-granite connection in the framework of the melt loss theory in migmatitic systems.