Large-scale Instability Research Articles

Enhanced preconditioner for JOREK MHD solver

The JOREK extended magneto-hydrodynamic (MHD) code is a widely used simulation tool for studying the non-linear dynamics of large-scale instabilities in divertor tokamak plasmas. The code is usually run with a fully implicit time integration allowing to use large time steps independent of a CFL criterion. This is particularly important due to the strong scale separation between transport processes and slowly growing resistive modes in contrast to fast time scales associated with MHD waves and fast parallel heat transport. For solving the resulting large sparse-matrix system iteratively in each time step, a preconditioner based on the assumption of weak coupling between the toroidal harmonics is applied. The solution for each harmonic matrix is determined independently in this preconditioner using a direct solver. In this article, a set of developments regarding the JOREK solver and preconditioner is described, which lead to overall significant benefits for large production simulations. The developments include the implementation of a complex solver interface for the preconditioner leading to the general reduction of memory consumption. The most significant development presented consists in a generalization of the physics based preconditioner to ‘mode groups’, which allows to account for the dominant interactions between toroidal Fourier modes in highly non-linear simulations. At the cost of a moderate increase of memory consumption, the technique can strongly enhance convergence in suitable cases allowing to use significantly larger time steps, and thus improving the overall time performance by more than a factor of 3.

Hydrodynamic α-effect in a rotating stratified moist atmosphere driven by small-scale non-helical force

In this paper we have studied the large-scale instability in a rotating stratified moist atmosphere with a small-scale turbulence. The axis of rotation of the medium is deviated from the vertical direction. The turbulence is excited by an external small-scale force with zero helicity and a low Reynolds number. The nonlinear equations of a vortex dynamo were obtained on the basis of the method of multiscale asymptotic expansions. The linear instability and stationary nonlinear modes were studied. The solutions in a form of localized vortex structures were obtained.

Geometric and kinematic analysis of normal faults bordering continental shelves: A 3D seismic case study from the northwest South China Sea

Normal faults border many a continental shelf, but have only been considered to play a subordinate role to basin-controlling faults in previous studies. Their detailed geometries and kinematic histories are still poorly known. In this study, high-quality three dimensional (3D) seismic data are used to investigate distinct families of normal faults bordering the continental shelf of the Qiongdongnan Basin, northwest South China Sea. Sixty-six (66) normal faults are interpreted and found to mostly tip out in the Upper Miocene. Three large-scale faults offsetting Horizon T30 (the base of Pliocene strata), and three other faults terminating beneath this same horizon, were selected and studied in detail. We discriminate between growth and blind faults by analysing upper tip folding geometry and fault displacement distribution using throw-depth (T-z) plots. The dips of the upper parts of faults are almost twice that of their lower parts. A new three-stage model for fault reactivation in Qiongdongnan Basin is therefore proposed based on our results. In the northwest South China Sea, the propagation of normal faults on the continental shelf can be attributed to: (1) the rotation of the South China block and a reversal in the movement of the Ailao Shan-Red River Fault Zone from left-to right-lateral slip, and (2) large-scale slope instability in the Qiongdongnan Basin at ~5.5 Ma. The results presented here outline the structural evolution of the continental shelf of the northwest South China Sea after 5.5 Ma, and how regional-scale structures such as the Ailao Shan-Red River Fault Zone controlled the evolution of normal faults on continental shelves.

Localized states in coupled Cahn–Hilliard equations

Abstract The classical Cahn–Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale instability into drop, hole or labyrinthine concentration patterns of a typical structure length followed by a continuously ongoing coarsening process. Here, we consider the coupled CH dynamics of two concentration fields and show that non-reciprocal (or active or non-variational) coupling may induce a small-scale (Turing) instability. At the corresponding primary bifurcation, a branch of periodically patterned steady states emerges. Furthermore, there exist localized states that consist of patterned patches coexisting with a homogeneous background. The branches of steady parity-symmetric and parity-asymmetric localized states form a slanted homoclinic snaking structure typical for systems with a conservation law. In contrast to snaking structures in systems with gradient dynamics, here, Hopf instabilities occur at a sufficiently large activity, which results in oscillating and travelling localized patterns.

Nonlinear Vortex Structures Driven by Small-Scale Non-helical Forces in Obliquely Rotating Stratified Fluids

We study a new type of large-scale instability in obliquely rotating stratifi ed fl uids with small-scale nonhelical turbulence. The small-scale turbulence is generated by the external force with zero helicity and low Reynolds number. The theory uses the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motions are obtained in the third order of perturbation theory. We consider a linear instability and stationary nonlinear modes. Solutions in the form of nonlinear Beltrami waves and localized vortex structures such as kinks of a new type are obtained.

Abstract 2050: Comprehensive genomic instability characteristics analysis in Chinese patients with osteosarcoma

Abstract Background: Previous study indicated that >80% of osteosarcomas (OSs) have genomic instability characteristics similar to BRCA1/2-deficient cancers. Such BRCA-like traits could manifest a deficiency in the DNA damage repair (DDR) pathway. Patients with alterations in DDR pathway was reported sensitive to platinum-based chemotherapy and PARP inhibitors. In order to seek more precision therapeutic opportunities, we explored the molecular profile of Chinese OS patients to identify whether the analogous phenomena exists as reported. Material and Methods: 44 archival Chinese OS patients from 3D Medicines and a public dataset including 35 OS patients (download from cBioPortal), were collected and analyzed next-generation sequencing (NGS) results on tumor tissues for gene mutations, copy number alterations (CNAs) and fusions in 33 cancer-associated DDR genes. Simultaneously, 44 Chinese OS patients' tumor analysis generated homologous recombination deficiency (HRD) scores (defined as the unweighted sum of LOH, TAI and LST scores) through the 733 gene panel sequencing. Results: Among 44 Chinese OS patients, 18 (40.9%) of OS had DDR pathway gene somatic alterations, and TP53 (31.8%) were the most frequently mapped gene. Other DDR somatic alterations were identified in BRCA2 (6.8%), BARD1 (4.5%), BRCA1 (2.3%), PMS2 (2.3%), FANCA (2.3%) and CHEK1 (2.3%). It was worth mention that all gene alterations were copy number reduction except TP53. Collectively, the frequencies of HRR and mismatch repair (MMR) alterations were 15.9% and 2.3%, respectively. HRD score were available in 18 patients, the median was 40.5 (range, 0-81). As to public dataset, 6 (17.1%) patients harbored somatic alterations in DDR genes. The variations were BRCA2 (5.7%), ATR (2.9%), BARD1 (2.9%), FANCC (2.9%), MLH1 (2.9%), MSH6 (2.9%) and PMS2 (2.9%). The HRR mutations frequency was 11% and MMR was 8.6%. Conclusions: This is the first large-scale comprehensive genomic instability characteristics analysis for Chinese patients with OS. Chinese patients and public dataset patients covers many common features. The DDR gene alteration frequency and HRD score are higher in OS patients, the association of variations in DDR genes and HRD score could be considered substitutable in predicting platinum-based therapy and PARP inhibitor response in clinical practice. Citation Format: Yonggang Wang, Hongtao Li, Jing Xia, Shiqing Chen, Yuezong Bai. Comprehensive genomic instability characteristics analysis in Chinese patients with osteosarcoma [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2021; 2021 Apr 10-15 and May 17-21. Philadelphia (PA): AACR; Cancer Res 2021;81(13_Suppl):Abstract nr 2050.

Arbitrariness Review (With Special Reference to the Social Cost of Carbon)

In its ideal form, arbitrariness review is an instrument for promoting “deliberative democracy” – a system that combines reason-giving with political accountability. Under arbitrariness review in its current form, courts tend to embrace the “hard look doctrine,” which has a procedural component, requiring agencies to offer detailed justifications, and also a substantive component, in which courts assess the reasonableness of the agencies’ choices on the merits. These are serious constraints on the executive branch, and they also reduce the risk of large-scale instability in government, in which scientific and economic judgments are overridden by political considerations. With respect to regulatory policy, it is not enough to say that “elections have consequences.” For climate change in particular, the “social cost of carbon,” or more broadly the “social cost of carbon,” is sometimes described as “the most important number you’ve never heard of.” A key reason is that within the executive branch, the stringency of regulation of greenhouse gases emissions often depends on that number. Another reason is that the social cost of carbon can and should play a role in determining the content of other kinds of initiatives, such as a carbon tax. In the United States, the relevant numbers were challenged in court under the administrations of Barack Obama (where they were upheld) and Donald Trump (where they were struck down). The litigation raises fundamental questions about the role of science, economics, and politics in judicial review of agency action, and about the relationship between courts and the administrative state. With respect to the social cost of carbon: (1) A decision to use the domestic number, as opposed to the global number, would be difficult to defend against an arbitrariness challenge; a decision to use the global number, as opposed to the domestic number, would be straightforward to defend against an arbitrariness challenge. (2) A decision to use a low discount rate, such as two percent, would be straightforward to defend against an arbitrariness challenge; a decision to use a high discount rate, such as seven percent, would be exceedingly difficult to defend against an arbitrariness challenge. (3) A decision to “back out” a social cost of carbon, from some specific target, would be challenging to defend against an arbitrariness challenge. (4) A wide range of decisions – involving, for example, climate sensitivity and the damage function -- raise difficult questions in science and economics; they should be straightforward to defend against an arbitrariness challenge, but only if they follow from a reasoned justification. (5) Approaches that take account of equity – including “prioritarianism” – should be defensible against an arbitrariness challenge, as should be a refusal to adopt such approaches, but here again, a reasoned justification is required. A general lesson, with broader implications, is that judicial review of the social cost of carbon should (and likely will) involve a procedural hard look, not a substantive hard look. A procedural hard look is important to defend against failures of both deliberation and democracy; a substantive hard look would strain judicial capacities.

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

The dependence of the Irregularity Parameter Characterizing the Equatorial Ionospheric Irregularities on the background Ionospheric Density

The low-latitude ionosphere is characterized by large-scale instabilities in the post-sunset hours due to the distinct geometry of the earth’s magnetic field lines at the equator. The magnetic field lines are horizontal at the equator contributing to the high vertical drift velocity of the plasma bubbles growing from the bottomside of the ionospheric F-region. The phenomenon, commonly known as equatorial spread F, is an important problem in aeronomy as it can cause radio wave scintillation effects representing the most critical impacts of space weather on man-made technologies, such as satellite communications and global navigation satellite systems (GNSS). Here, we report results on the dependence of the peak heights of the irregularities at the magnetic equator, also called as apex-altitude, on solar flux by analyzing in-situ observations made on-board the Communications/Navigations Outage Forecasting System (C/NOFS) satellite mission. Our analysis indicates the median of the peak-height distributions of the irregularities increases linearly from about 491 km at solar minimum to 737 km during solar maximum. The Physics-Based Model (PBMOD) has been used to confirm the space-based observational results and we find the field-line integrated conductivity is the key parameter which controls the peak-heights of the irregularities. In this investigation, we also seek to understand the possible dependence of the irregularity parameter characterizing the equatorial ionospheric irregularities on the background ionospheric density.

Low-frequency fluctuations and their suppression in the 5.5 m × 4 m aeroacoustic wind tunnel at CARDC

This paper experimentally investigated characteristics of low-frequency pressure fluctuations in a large-scale open jet wind tunnel using pressure transducers and far-field microphones. Two distinct low-frequency pressure fluctuations have been detected at the range of wind speeds between 50 m/s and 75 m/s. The two peak frequencies vary with the change of wind speed. Analysis results show that both the low-frequency pressure fluctuations are driven by the resonances of the large scale instability waves in the jet shear layer at two different feedback loop paths. One loop is through the entire circuit of the wind tunnel, another exists between the nozzle and the collector, which is termed as edge-tone feedback. A formula for predicting the peak frequency was derived and the prediction agrees well with the measurement. In addition, an effective control strategy to suppress the wind tunnel circuit resonance and the edge-tone feedback resonance were also presented.

Simulation of a liquid jet in supersonic crossflow by a hybrid CLSVOF-LPT method

This study investigates the atomization process of a liquid jet in supersonic crossflow at a Mach number of 2.1 by using a multi-scale simulation method. This hybrid numerical method can realize accurate simulation of the primary and secondary breakup of the liquid jet with large scale instabilities and small droplet dynamics under compressible supersonic crossflow. The Eulerian framework is applied for capturing the gas-liquid interface by a coupled Level set and Volume-of-fluid (CLSVOF) method. Based on the Delayed Detached Eddy Simulation (DDES), the adaptive mesh refinement (AMR) method is introduced to predict the breakup of liquid column, blocks and filaments. The Lagrangian framework is applied for the dispersed droplets generated under the conversion criteria during the atomization process. The hybrid CLSVOF-LPT method can greatly reduce the loss of liquid phase mass and save computing resources. The distribution morphology of droplets in a cross-sectional plane from the simulation agreed well with the experimental data. Besides, the trends of the jet trajectory and primary breakup behavior of liquid column are well captured.

A physical modeling-based study on the control mechanisms of Negative Poisson's ratio anchor cable on the stratified toppling deformation of anti-inclined slopes

With ongoing increases in excavation depth, the large-scale toppling instability failure of stratified anti-inclined slopes is gaining wide attention. To address the problem of controlling toppling deformation failure of anti-inclined slopes with traditional small-deformation materials, this paper takes the results of existing studies on the extraordinary mechanical properties of engineering-scale Negative Poisson's ratio (NPR) anchor cable as a theoretical basis, and develops a model-scale NPR anchor cable according to similarity theory. Relying on a self-developed “engineering disaster model experimental system”, a physical modeling-based experiment to explore the reinforcement mechanism of stratified anti-inclined slope using model-scale NPR and ordinary anchor cables is performed. The physical model is monitored using static strain data acquisition equipment, an infrared thermal imager, tension sensors, and digital speckle correlation method (DSCM) displacement field measurement equipment. The evolution of the displacement field, strain field, temperature field, and anchor cable force are obtained during excavation on the physical model. By comparing the evolution of these parameters with images from both the anti-inclined slope model instability failure test and the deformation characteristics on the two sides of the slope, which were reinforced using different types of anchor cables, this paper determines the mechanisms governing instability failure of anti-inclined slopes reinforced with NPR anchor cable. In addition, this paper also proves that NPR anchor cable can be used to monitor the sliding force of anti-inclined slopes throughout excavation, and lays a foundation for the application of NPR anchor cable monitoring technology to the advanced anti-inclined slope failure warning.

Experimental and numerical investigation of high-pressure nitromethane combustion

The burning rate of liquid nitromethane as a function of pressure is known to exhibit slope breaks, following Saint-Robert's law only in limited regions of pressure. The present paper presents experimental and modeling results with the objective to better understand this behavior. A new experimental facility is used to visually observe the combustion process from 3 to 101 MPa allowing for measurement of burning rates in tubes of various diameters with high-speed cinematography. A series of modeling calculations are performed increasing in complexity first studying vapor phase flame propagation with the ideal gas equation of state and then a real gas equation of state. These results are compared with previously published predictions of the liquid regression rate using the same kinetic model and ideal gas equation of state. Theory indicates that, at high pressures, the freely propagating vapor-phase flame speed should agree with liquid regression rates. Combined, these results enable further insight into the mechanisms for the slope breaks and complex burning behavior. Three regimes were identified in the burning rate as a function of pressure. A low-pressure regime with pressure exponent of 1.16 exists where burning occurs with a distinct interface between liquid and gas. At approximately 18 MPa, an abrupt increase in burning rate occurs that is associated with the critical point of the mixture of nitromethane and near-surface species producing pressure exponents ranging from 2–10. Above this pressure, the loss of surface tension induces surface waves and large-scale hydrodynamic instabilities. With increasing pressure, burning rates continue to increase with pressure but with a gradual decrease in pressure exponent towards a value of ∼0.75. At the highest pressure the large-scale instabilities disappear, and the flame propagates with a turbulent cellular front, the speed of which depends upon the tube diameter.

Гравитационная неустойчивость и образование планетных систем звезд солнечного типа

The fundamental principles of the protoplanetary ring model – the model of formation of planetary systems of stars, which is based on the origin and development of large-scale gravitational instabilities (protoplanetary rings) – are extended to the formation of regular planetary satellites. Based on these principles, a complete model of the formation of planetary systems, including their satellites, (model of gas and dust rings) for solar-type stars is proposed.

The Arithmetic of Climate Change

In its ideal form, arbitrariness review is an instrument for promoting “deliberative democracy” – a system that combines reason-giving with political accountability. Under arbitrariness review in its current form, courts tend to embrace the “hard look doctrine,” which has a procedural component, requiring agencies to offer detailed justifications, and also a substantive component, in which courts assess the reasonableness of the agencies’ choices on the merits. These are serious constraints on the executive branch, and they also reduce the risk of large-scale instability in government, in which scientific and economic judgments are overridden by political considerations. With respect to regulatory policy, it is not enough to say that “elections have consequences.” For climate change in particular, the “social cost of carbon,” or more broadly the “social cost of greenhouse gases,” is sometimes described as “the most important number you’ve never heard of.” A key reason is that within the executive branch, the stringency of regulation of greenhouse gases emissions often depends on that number. Another reason is that the social cost of carbon can and should play a role in determining the content of other kinds of initiatives, such as a carbon tax. In the United States, the relevant numbers were challenged in court under the administrations of Barack Obama (where they were upheld) and Donald Trump (where they were struck down). The litigation raises fundamental questions about the role of science, economics, and politics in judicial review of agency action, and about the relationship between courts and the administrative state. With respect to the social cost of carbon: (1) A decision to use the global number, as opposed to the domestic number, would be straightforward to defend against an arbitrariness challenge; a decision to use the domestic number, as opposed to the global number, would be difficult to defend against an arbitrariness challenge. (2) A decision to use a low discount rate, such as two percent, would be straightforward to defend against an arbitrariness challenge; a decision to use a high discount rate, such as seven percent, would be exceedingly difficult to defend against an arbitrariness challenge. (3) A wide range of decisions – involving, for example, climate sensitivity and the damage function -- raise difficult questions in science and economics; they should be straightforward to defend against an arbitrariness challenge, but only if they follow from a reasoned justification. (4) Approaches that take account of equity – including “prioritarianism” – should be defensible against an arbitrariness challenge, as should be a refusal to adopt such approaches, but here again, a reasoned justification is required. (5) A decision to “back out” a social cost of carbon, from some specific target, would be challenging to defend against an arbitrariness challenge. A general lesson, with broader implications, is that judicial review of the social cost of carbon should (and likely will) involve a procedural hard look, not a substantive hard look. A procedural hard look is important to defend against failures of both deliberation and democracy; a substantive hard look would strain judicial capacities.

Vortex Dynamo in an Obliquely Rotating Stratified Nanofluid by Small-Scale Non-Helical Forces

In this work, a large-scale instability of the hydrodynamic -effect in an obliquely rotating stratified nanofluid taking into account the effects of Brownian diffusion and particle flux under the influence of a temperature gradient (thermophoresis) is obtained. The instability is caused by the action of an external small-scale non-spiral force, which excites small-scale velocity oscillations with zero helicity and a low Reynolds number. Nonlinear equations for large-scale motions are obtained using the method of multiscale asymptotic expansions by a small parameter (Reynolds number). A linear large-scale instability of hydrodynamic -effect is investigated depending on the parameters of rotation , temperature stratification , and concentration of nanoparticles . A new effect of the generation of large-scale vortex structures in nanofluid at is associated with an increase in the concentration of nanoparticles is obtained. The maximum instability increment is reached at inclination angles for the Prandtl numbers , and for the Prandtl numbers at inclination angles . It has been found that the frequency changing of the parametric impact will make it possible to control and track the generation of large-scale vortex structures. It is shown that circularly polarized Beltrami vortices appear in nanofluid as the result of new large-scale instability development. In this paper, the saturation regime of large-scale instability in an obliquely rotating stratified nanofluid with an external small-scale non-spiral force is investigated. In the stationary regime was obtained a dynamic system of equations for large-scale perturbations of the velocity field. Numerical solutions of this system of equations are obtained, which show the existence of localized vortex structures in the form of nonlinear Beltrami waves and kinks. The velocity profile of kink tends to be constant at large Z values.

Evaporation and breakup effects in the shock-driven multiphase instability

Abstract

Damping of Climate-Scale Oceanic Variability by Mesoscale Eddy Turbulence

AbstractThe impact of mesoscale eddy turbulence on long-term, climatic variability in the ocean’s buoyancy structure is investigated using observations from a mooring deployed in the Drake Passage, Southern Ocean. By applying the temporal-residual-mean framework and characterizing the variance contributors and the buoyancy variance budget, we identify the main source and sink of long-term buoyancy variance. Long-term buoyancy variance amplitude is set by long-term vertical velocity fluctuations acting on the steady stratification. This baroclinic buoyancy flux is also the main source of the variance, indicative of the effect of large-scale baroclinic instability. This source is balanced by a sink of long-term buoyancy variance associated with the vertical advection of the steady stratification by the eddy-induced circulation. We conclude that mesoscale eddy turbulence acts as a damping mechanism for long-term, climatic variability in the region of the observations, consistent with an “eddy saturated” behavior of the Antarctic Circumpolar Current.

Efficient Passage-Spectral Method For Unsteady Flows Under Stall Conditions

AbstractThis paper presents an efficient method of approximating unsteady flows using a block-wise discrete spatial Fourier series for the modeling of three-dimensional non-axisymmetric flows without making any hypothesis about its temporal periodicity. The method aims at capturing the long-wavelength flow patterns that are present in many unsteady problems of industrial interest, such as compressor stability, with a drastic reduction in computational resources. The method is intended to be used to compute flows exhibiting large-scale instabilities and where the fundamental frequency of the problem is not known beforehand. The approach discretizes the domain using a finite number of blocks or passages, where the flow variables at the supposedly periodic boundaries are continuously updated using the spatial Fourier coefficients of a uniformly spaced set of reduced-passage domains. The NASA rotor 67 under the effect of distorted inflow conditions has been used as verification case to demonstrate the effectiveness and viability of the method. The comparison between the passage-spectral method and the full-annulus solution shows that sound solutions can be obtained with a low number of harmonics. The new method has also been applied to investigate the rotating stall inception of the NASA rotor 67 for distorted inlet flows near stall operating conditions. The method is shown to accurately reproduce the full-annulus solution with a few spatial harmonics, capturing the characteristic features of the complex flow induced by the tip leakage vortex breakdown. The computational cost in this application has been reduced by a factor of between three and seven. This number heavily depends on the ratio between the number of retained harmonics to the number of blades.

Constraints on neutrino mass in the scenario of vacuum energy interacting with cold dark matter after Planck 2018

In this work, we investigate the constraints on the total neutrino mass in the scenario of vacuum energy interacting with cold dark matter (abbreviated as IΛCDM) by using the latest cosmological observations. We consider four typical interaction forms, i.e. , , , and , in the IΛCDM scenario. To avoid the large-scale instability problem in interacting dark energy models, we employ the extended parameterized post-Friedmann method for interacting dark energy to calculate the perturbation evolution of dark energy in these models. The observational data used in this work include the cosmic microwave background (CMB) measurements from the Planck 2018 data release, the baryon acoustic oscillation (BAO) data, the type Ia supernovae (SN) observation (Pantheon compilation), and the 2019 local distance ladder measurement of the Hubble constant H 0 from the Hubble Space Telescope. We find that, compared with those in the ΛCDM+ model, the constrains on are looser in the four IΛCDM+ models. When considering the three mass hierarchies of neutrinos, the constraints on are tightest in the degenerate hierarchy case and loosest in the inverted hierarchy case. In addition, in the four IΛCDM+ models, the values of coupling parameter β are larger using the CMB+BAO+SN+H 0 data combination than that using the CMB+BAO+SN data combination, and β > 0 is favored at more than 1σ level when using CMB+BAO+SN+H 0 data combination. The issue of the H 0 tension is also discussed in this paper. We find that, compared with the ΛCDM+ model, the H 0 tension can be alleviated in the IΛCDM+ model to some extent.