Supercritical Regime Research Articles

Energy relaxation of N2O in gaseous, supercritical, and liquid xenon and SF6

Rotational and vibrational energy relaxation (RER and VER) of N2O embedded in xenon and SF6 environments ranging from the gas phase to the liquid, including the supercritical regime, is studied at a molecular level. Calibrated intermolecular interactions from high-level electronic structure calculations, validated against experiments for the pure solvents, were used to carry out classical molecular dynamics simulations corresponding to experimental state points for near-critical isotherms. The computed RER rates in low-density solvents of krotXe=(3.67±0.25)×1010 s−1 M−1 and krotSF6=(1.25±0.12)×1011 s−1 M−1 compare well with the rates determined by the analysis of two-dimensional infrared experiments. Simulations find that an isolated binary collision description is successful up to solvent concentrations of ∼4 M. For higher densities, including the supercritical regime, the simulations do not correctly describe RER, probably due to the neglect of solvent–solute coupling in the analysis of the rotational motion. For VER, the near-quantitative agreement between simulations and pump–probe experiments captures the solvent density-dependent trends.

Global Well-Posedness and Refined Regularity Criterion for the Uni-Directional Euler-Alignment System

Abstract We investigate global solutions to the Euler-alignment system in $d$ dimensions with unidirectional flows and strongly singular communication protocols $\phi (x) = |x|^{-(d+\alpha )}$ for $\alpha \in (0,2)$. Our paper establishes global regularity results in both the subcritical regime $1<\alpha <2$ and the critical regime $\alpha =1$. Notably, when $\alpha =1$, the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime $0<\alpha <1$.

Effects of Reynolds number and surface modification on wake-induced vibrations of two staggered circular cylinders

This study explores the role of Reynolds numbers (Re) in wake-induced vibrations (WIVs) of two cylinders, specifically wake galloping and two-degree-of-freedom coupled flutter on the downstream cylinder. The center-to-center distances between the cylinders were 3.0D −5.0D in along-flow direction and 0.0D −2.0D in cross-flow direction (D is the diameter of the cylinders). The Re ranged from 1.4 × 104–6.7 × 104, within the subcritical Re regime of a smooth cylinder. The supercritical Re regime was realized by winding 12 spiral protuberances along the cylinders to lower the critical Re. Descriptions of wake interference of two smooth cylinders at Re = 850–6.5 × 105 were summarized from the literature. Wake interference strongly depended on Re, even within the subcritical Re regime. WIVs mostly occurred in the upper subcritical Re regime with strong wake interference. In the supercritical Re regime, the wakes of the cylinders were narrowed and vortex shedding was suppressed. Consequently, the wake interference and WIVs were weakened or completely disappeared. The cylinders fitted with 12 spiral protuberances reportedly reached the supercritical Re regime at Re = 3.1 × 104. Resultantly, they were stable against WIVs above this Re even at close spacing, and suitable for stay cable applications.

Vortex-induced vibration of a circular cylinder in the supercritical regime

Vortex-induced vibration of a circular cylinder in the supercritical regime

CFD simulations of the transition between non-aerated and aerated conditions in uncovered unbaffled stirred tanks

The transition between non-aerated and aerated regimes in uncovered unbaffled stirred tanks (UUSTs) was investigated using computational fluid dynamics (CFD). The Volume of Fluid (VOF) method was employed to model the free surface dynamics under various operational conditions. The simulations were able to predict the peculiar experimentally observed behavior of UUSTs and revealed that at velocities below a critical threshold (N_<_Ncrit), the system remains non-aerated, while exceeding this threshold (N_≥_Ncrit) induces bubble ingestion, leading to significant changes in power consumption and flow patterns. The CFD simulations accurately predicted the behaviour of the Power Number (Np) as well as the vortex shape inside the tank both in subcritical and supercritical regimes and showed good agreement with original experimental data and correlations from the literature. Additionally, the modeling of the aerated regime successfully predicted the vortex shape, the bubble dispersion within the tank, and the cavities formed behind the blades.

Resonant effects of long-period ship-induced waves near shallow coasts

This work analyzes the propagation properties of long-period ship-induced waves of vessels in confined waterways that are surrounded by wide and shallow water bodies using numerical simulations. Previous measurements indicated that, in the presence of shallow water surroundings, the drawdown being part of the long-period wave system can travel in the form of depression waves over several ship lengths distance [Parnell et al., “Ship-induced solitary Riemann waves of depression in Venice Lagoon,” Phys. Lett. A 379, 555–559 (2015); Scarpa et al., “The effects of ship wakes in the Venice Lagoon and implications for the sustainability of shipping in coastal waters,” Sci. Rep. 9, 19014 (2019)]. The exact conditions leading to these unexpectedly large propagation distances could to date not be clarified [Parnell et al., “Depression Waves Generated by Large Ships in the Venice Lagoon,” J. Coastal Res. 75, 907–911 (2016)]. In this work, evidence from numerical simulations is presented, indicating that the far-field propagation properties are governed by the wave speed of the shallow water surroundings. In case the ship speed is larger than the surrounding wave speed (supercritical conditions), a free wave is continuously generated traveling over the shallow water with only minimal height decay. In the simulations, depression waves can travel over a distance of three ship-lengths with a height reduction below 10% in the supercritical regime, as compared to 80% height reduction in the sub-critical regime. In a one-dimensional environment, this agreement of free and forced wave speed is known as Proudman resonance.

Probing the energy and luminosity-dependent spectro-timing properties of RX J0440.9+4431 with AstroSat

ABSTRACT The Be/X-ray binary pulsar RX J0440.9+4431 went through a giant outburst in December 2022 with a peak flux of $\sim$2.3 Crab in 15–50 keV. We studied the broad-band timing and spectral properties of RX J0440.9+4431 using four AstroSat observations, where the source transited between subcritical and supercritical accretion regimes. Pulsations were detected significantly above 100 keV. The pulse profiles were found to be highly luminosity- and energy-dependent. A significant evolution in the pulse profile shape near the peak of the outburst indicates a possible change in the accretion mode and beaming patterns of RX J0440.9+4431. The rms pulsed fraction was luminosity- and energy-dependent, with a concave-like feature around 20–30 keV. The depth of this feature varied with luminosity, indicating changes in the accretion column height and proportion of reflected photons. The broad-band continuum spectra were best fitted with a two-component Comptonization model with a blackbody component or a two-blackbody component model with a thermal Comptonization component. A quasi-periodic oscillation (QPO) at 60 mHz was detected at a luminosity of $2.6 \times 10^{37}$ erg s$^{-1}$, which evolved into 42 mHz at $1.5 \times 10^{37}$ erg s$^{-1}$. The QPO rms were found to be energy dependent with an overall increasing trend with energy. For the first time, we found the QPO frequency varying with photon energy in an X-ray pulsar, which poses a challenge in explaining the QPO with current models such as the Keplarian and beat frequency model. Hence, more physically motivated models are required to understand the physical mechanism behind the mHz QPOs.

On the modulus of continuity of fractional Orlicz-Sobolev functions

AbstractNecessary and sufficient conditions are presented for a fractional Orlicz-Sobolev space on $${\mathbb {R}}^n$$ R n to be continuously embedded into a space of uniformly continuous functions. The optimal modulus of continuity is exhibited whenever these conditions are fulfilled. These results pertain to the supercritical Sobolev regime and complement earlier sharp embeddings into rearrangement-invariant spaces concerning the subcritical setting. Classical embeddings for fractional Sobolev spaces into Hölder spaces are recovered as special instances. Proofs require novel strategies, since customary methods fail to produce optimal conclusions.

A quantitative explanation of the cyclotron-line variation in accreting magnetic neutron stars of super-critical luminosity

Context. Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Cyclotron lines are believed to be generated in the radiative shock in the accretion column. High-luminosity NSs show a smooth anti-correlation between the cyclotron-line centroid (ECRSF) and X-ray luminosity (LX). Aims. It has been pointed out that the observed ECRSF − LX smooth anti-correlation in high-luminosity NSs is in tension with the theoretically predicted one, if the radiative shock is the site of cyclotron-line formation. The shock height increases approximately linearly with luminosity, while the dipolar magnetic field drops as the cubic power of distance, thereby implying that the cyclotron-line energy ought to decrease significantly when the luminosity increases by, say, an order of magnitude, which is contrary to observations. Since there is no other candidate site for the cyclotron-line formation, we re-examine the predicted rate of change of the cyclotron-line energy with luminosity at the radiative shock, taking a closer look at the Physics involved. Methods. We developed a purely analytical model describing the overall dependence of the observed cyclotron energy centroid on the shock front’s height, including both the relativistic boosting and the gravitational redshift effects in our considerations. The relativistic boosting effect is due to the mildly relativistic motion of the accreting plasma upstream with respect to the shock’s reference frame. Reults. We find that the cyclotron-line energy varies with (a) the shock height due to the dipolar magnetic field, (b) the Doppler boosting between the shock and bulk-motion frames, and (c) the gravitational redshift. We show that the relativistic effects noticeably weaken the predicted ECRSF − LX anti-correlation. We use our model to fit the data of the X-ray source V0332+53 that exhibits a weak negative correlation and demonstrate that the model fits the data impressively well, thereby alleviating the tension between observations and theory. Conclusions. The reported weak anti-correlation between cyclotron-line centroid and X-ray luminosity in the supercritical accretion regime may be explained by the combination of the variation of the magnetic-field strength along the accretion column, the effect of Doppler boosting, and the gravitational redshift. As a result of these effects, the actual magnetic field on the surface of the neutron star may be a factor of ∼2 larger than the naively inferred value from the observed CRSF.

Resurgent dome and super-hot enhanced geothermal system: The Sahinkalesi Massif within the Hasandag Stratovolcanic Province, Central Anatolia, Turkey

The Sahinkalesi, a volcanic dome located NNE of Hasandağ, Türkiye exhibits anomalous heat flow value, geothermal gradient and the Curie point depth is located at very shallow depth in this region. Our investigation indicates presence of super-critical thermal regime (378°C) at about 4 km depth and the MT analysis indicate shallow magma chamber at about 5 km depth. The crust is relatively thin below this region with the low-velocity region located at depth of about 36 km. Thermo-Hydro-mechanical model investigation has been carried out using finite element discretization technique. For faulted zone reservoir models, 30 years of geothermal energy exploitation does not cause thermal breakthrough for mass flow rates up to 500 kg/s, however, the mean stress developed in the reservoir becomes much larger and may be unsustainable for the reservoir stability. To ensure the success of a fractured reservoir model, the use of multiple wellbores is recommended. In the case of a closed-loop geothermal system, the primary concern is the control of thermoelastic stress. This can be achieved either by increasing the wellbore depth while reducing the injection mass flow rate, or by extending the wellbore's horizontal component. The outlet temperature in both the cases maintained at 275°C. This is the first time a superhot EGS site has been identified in Türkiye.

Motion of Submerged Body in a Frozen Channel with Compressed Porous Ice

The problem of submerged body motion in a frozen channel is considered. The fluid in the channel is assumed to be inviscid and incompressible. Fluid flow is the potential. The ice cover has non-uniform compression along the principal coordinates. The damping of hydroelastic waves generated by the motion of submerged body is modeled by taking into account porosity of ice. The submerged body is modeled as a dipole, the potential of which is determined using mirror images from the channel walls. The main problem of the submerged body motion at constant speed along the central line of the channel is considered. Two subproblems are addressed: comparison of damping effects of the porosity and viscosity of ice and investigation of effects of symmetrically variable ice thickness relative to the central line of the channel. It was found that the most important compressive stress is the stress in the direction of the motion of the submerged body. The speed of the body, which was subcritical for uncompressed ice, may become critical or supercritical. Compressive stresses perpendicular to the direction of motion do not qualitatively change the character of the ice response. These stresses, in combination with compressive stresses along the direction of motion, strengthen the effect of the latter, making the transition from subcritical to supercritical regime faster.

Atomic cluster expansion potential for large scale simulations of hydrocarbons under shock compression.

We present an Atomic Cluster Expansion (ACE) machine learned potential developed for high-fidelity atomistic simulations of hydrocarbons, targeting pressures and temperatures near and above supercritical fluid regimes for molecular fluids. A diverse set of stoichiometries were covered in training, including 1:0 (pure carbon), 1:4 (methane), and 1:1 (benzene), and rich bonding environments sampled at supercritical temperatures, hydrogen rich, reactive mixtures where metastable stoichiometries arise, including 1:2 (ethylene) and 1:3 (ethane). A high-fidelity training database was constructed by performing large-scale quantum molecular dynamic simulations [density functional theory (DFT) MD] of diamond, graphite, methane, and benzene. A novel approach to selecting structures from DFT MD is also presented, which allows for the rapid selection of unique DFT MD frames from complex trajectories. Comparisons to DFT and experimental data demonstrate that the presented ACE potential accurately reproduces isotherms, carbon melting curves, radial distribution functions, and shock Hugoniots for carbon and hydrocarbon systems for pressures up to 100GPa and temperatures up to 6000K for hydrocarbon systems and up to 9000K for pure carbon systems. This work delivers a potential that can be used for accurate, large-scale simulations of shocked hydrocarbons and demonstrates a methodology for fitting and validating machine learning interatomic potentials to complex molecular environments, which can be applied to energetic materials in future works.

The dipole moment of supercritical water – local vs. mean-field polarisation contributions

Supercritical water has attracted much attention from both fundamental and technological perspectives, based largely on its ability to solvate other molecules. Predicting and controlling this requires a deeper understanding of water's polarisation behaviour. Using the computationally efficient Self-Consistent Electrostatic Embedding method, we were able to calculate the water dipole moment over an unprecedented range of thermodynamic conditions, covering gas, liquid and supercritical states, with large simulation systems and a high-level quantum mechanical method. We find a discontinuous change in the dipole moment along subcritical isotherms, corresponding to the sharp transition between the vapour and liquid states, with the latter exhibiting induced dipole moments between 0.5 and 0.9 D, depending on the temperature. In contrast, the dipole moment changes continuously from gas-like to liquid-like behaviour in the supercritical regime, allowing the degree of polarisation to be controlled through manipulating temperature and pressure. The dipole moment was found to be linearly related to the average number of hydrogen-bonded neighbours of water, emphasising the key role of local interactions to the polarisation process. Mean-field approaches based on a dielectric continuum representation of the solvent are unable to predict this behaviour due to the neglect of local interactions.

Homogeneous Equilibrium Modeling for Subcritical Flows in Liquid Rocket Engine Cooling Systems

During off-design operations of liquid rocket engines, the coolant operating conditions can easily extend from the subcritical to the supercritical regime. As a matter of fact, it is very useful to have a single software able to study the flow in this range of operating conditions, providing reliable simulations that are reasonably quick and able to accurately estimate and assess the increase in coolant temperature along the channel and the wall temperature field. This objective is pursued by extending an established approach for the study of supercritical flows to the case of subcritical heating, where a two-phase flow may occur. This is done by exploiting the so-called homogeneous equilibrium model, which has been shown to be sufficiently predictive and accurate for specific applications. With the aim of demonstrating and discussing the potential and limitations of such a single software approach, analyses are conducted on different test cases where two-phase flow is induced by cavitation or flow boiling, and results are compared with those of analytical models and experimental data. It is found that, in addition to some intrinsic limitations in the analysis of subcooled boiling flows, satisfactory agreement with experimental data is obtained in the post-critical-heat-flux regime.

Evidence for a Cyclotron Absorption Line and Spectral Transition in EXO 2030+375 during the 2021 Giant Outburst

Based on Insight-HXMT observations of EXO 2030+375 during its 2021 giant outburst, we report the analysis of pulse variations and the broadband X-ray spectrum, and find the presence of a potential cyclotron resonant scattering feature (CRSF) with the fundamental line at ∼47 keV from both average spectra and phase-resolved spectroscopy. During the outburst, the source reached an X-ray luminosity of ∼1038 erg s−1 from 2 to 105 keV at a distance of 7.1 kpc. The X-ray pulsar at the spin period of 41.27 ± 0.61 s exhibits complex timing and spectral variations with both energy and luminosity during the outburst. The shapes of the pulse profiles show the single main peak above ∼20 keV, while appearing to exhibit multipeak patterns in low-energy bands, and the transition of the 10–20 keV pulse profiles from multipeak to single peak is observed at ∼0.8 × 1038 erg s−1, which suggests the evolution from the subcritical luminosity (pencil-beam dominated) to the supercritical luminosity (fan-beam dominated) regime. A dip structure before the energy of the CRSFs is found in the pulse fraction–energy relation of EXO 2030+375 near the peak luminosity. A detailed analysis of spectral parameters showed that the power-law photon index exhibits three distinct trends as luminosity increases, and these spectral changes also signify a spectral transition from subcritical to supercritical regimes. The critical luminosity infers a magnetic field of ∼(4.8−6.0) × 1012 G, which supports the presence of the cyclotron line at ∼47 keV. A Comptonization model applied for the broad X-ray spectra during the outburst also suggests the surface magnetic field ranging from ∼(5−9) × 1012 G.

Modeling the effects of starspots on stellar magnetic cycles

Context. Observations show that faster rotating stars tend to have stronger magnetic activity and shorter magnetic cycles. The cyclical magnetic activity of the Sun and stars is believed to be driven by the dynamo process. The success of the Babcock-Leighton (BL) dynamo in explaining the solar cycle suggests that starspots could play an important role in stellar magnetic cycles. Aims. We aim to extend the BL mechanism to solar-mass stars with various rotation rates and explore the effects of emergence properties of starspots in latitudes and tilt angles on stellar magnetic cycles. Methods. We adopt a kinematic BL-type dynamo model operating in the bulk of the convection zone. The profiles of the large-scale flow fields are from the mean-field hydrodynamical model for various rotators. The BL source term in the model is constructed based on the rotation dependence of starspot emergence; that is, faster rotators have starspots at higher latitudes with larger tilt angles. Results. Faster rotators have poloidal flux appearing closer to about ±55° latitudes, where the toroidal field generation efficiency is the strongest because of the peak in the strength of the latitudinal differential rotation there. It takes a shorter time for faster rotators to transport the surface poloidal field from their emergence latitude to the ±55° latitudes of efficient Ω-effect, which shortens their magnetic cycles. The faster rotators operate in a more supercritical regime because of a stronger BL α-effect relating to the tilt angles, which leads to stronger saturated magnetic fields and makes the coupling of the poloidal field between two hemispheres more difficult. The magnetic field parity therefore shifts from the hemispherically asymmetric mixed mode to quadrupole, and further to dipole when a star spins down. Conclusions. The emergence of starspots plays an essential role in the large-scale stellar dynamo.

Enhancing the performance of coherent Ising machines in the large-noise regime with a fifth-order nonlinearity

Coherent Ising machines (CIMs), leveraging the bistable physical properties of coherent light to emulate Ising spins, exhibit great potential as hardware accelerators for tackling complex combinatorial optimization problems. Recent advances have demonstrated that the performance of CIMs can be enhanced either by incorporating large random noise or higher-order nonlinearities, yet their combined effects on CIM performance remain mainly unexplored. In this work, we develop a numerical CIM model that utilizes a tunable fifth-order polynomial nonlinear dynamic function under large noise levels, which has the potential to be implemented in all-optical platforms. We propose a normal form of a CIM model that allows for both supercritical and subcritical pitchfork bifurcation operational regimes, with fifth-order nonlinearity and tunable hyperparameters to control the Ising spin dynamics. In the benchmark studies, we simulate various sets of MaxCut problems using our fifth-order polynomial CIM model. The results show a significant performance improvement, achieving an average of 59.5% improvement in median time-to-solution (TTS) and an average of 6 times improvement in median success rate (SR) for dense Maxcut problems in the BiqMac library, compared to the commonly used third-order polynomial CIM model with low noise. The fifth-order polynomial CIM model in the large-noise regime also shows better performance trends as the problem size scales up. These findings reveal the enhancements on the computational performance of Ising machines in the large-nose regime from fifth-order nonlinearity, showing important implications for both simulation and hardware perspectives.

Barely Supercritical Percolation on Poissonian Scale-free Networks

We study the giant component problem slightly above the critical regime for percolation on Poissonian random graphs in the scale-free regime, where the vertex weights and degrees have a diverging second moment. Critical percolation on scale-free random graphs has been observed to have incredibly subtle features that are markedly different compared to those in random graphs with a converging second moment. In particular, the critical window for percolation depends sensitively on whether we consider single- or multi-edge versions of the Poissonian random graph. In this paper, and together with our companion paper [3], we build a bridge between these two cases. Our results characterize the part of the barely supercritical regime where the size of the giant components are approximately same for the single- and multi-edge settings. The methods for establishing concentration of giant for the single- and multi-edge versions are quite different. While the analysis in the multi-edge case is based on scaling limits of exploration processes, the single-edge setting requires identi fication of a core structure inside certain high-degree vertices that forms the giant component.

Thermal Density Fluctuations and Polymorphic Phase Transitions of Ethane (C2D6) in the Gas/Liquid and Supercritical States.

The phase behavior of the liquid C2D6 below and above the critical point was investigated using small-angle neutron scattering (SANS) in temperature and pressure ranges from 10 to 45 °C and 20 to 126 bar, respectively. The scattering of thermal fluctuations of the molecular density was determined and thus the gas-liquid and Widom lines. At the same time, we observed additional scattering of droplets of more densely packed C2D6 molecules above the gas-liquid line and in the supercritical fluid regime from just below the critical point for all temperatures at about ΔP = 10 bar above the Widom line. This line is interpreted as the Frenkel line. These results are consistent with our previous studies on CO2 and thus indicate a universal phase behavior for monomolecular liquids below and above the critical point. The interpretation of the Frenkel line as the lower limit of a polymorphic phase transition is in contrast to the usual interpretation as the limit of a dynamic process. The correlation lengths (ξ) of the thermal density fluctuations at the critical point and at the Widom line are determined between 20 and 35 Å and thus in the range of the droplet radius between 60 and 80 Å. These long-range fluctuations appear to suppress the formation of droplets, which can only form at about 10 bar above the critical point and the Widom line when ξ becomes smaller than 10 Å.

The multi-scale coupled model: a new framework capturing wind farm–atmosphere interaction and global blockage effects

Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially heterogeneous background velocity field obtained from a reduced-order meso-scale model. Verification of the MSC model is performed against two large-eddy simulations (LESs) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. On the other hand, in the supercritical regime their propagation speed is less than their advection velocity, and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two analyzed regimes, but also captures the interaction between the wind farm and gravity waves, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone cannot distinguish between differences in thermal stratification, even if combined with a local induction model. Specifically, they are affected by a first-row overprediction bias that leads to an overestimation of the wind farm power by 13 % to 20 % for the modeled regimes.