In-Situ Atomic-Scale Observation of Brownmillerite to Ruddlesden-Popper Phase Transition Tuned by Epitaxial Strain in Cobaltites

Phase transitions involving oxygen ion extraction within the framework of the crystallographic relevance have been widely exploited for sake of superconductivity,ferromagnetism,and ion conductivity in perovskiterelated oxides.However,atomic-scale pathways of phase transitions and ion extraction threshold are inadequately understood.Here we investigate the atomic structure evolution of LaCoO_(3) films upon oxygen extraction and subsequent Co migration,focusing on the key role of epitaxial strain.The brownmillerite to Ruddlesden-Popper phase transitions are discovered to stabilize at distinct crystal orientations in compressive-and tensile-strained cobaltites,which could be attributed to in-plane and out-of-plane Ruddlesden-Popper stacking faults,respectively.A two-stage process from exterior to interior phase transition is evidenced in compressive-strained LaCoO_(2.5),while a single-step nucleation process leaving bottom layer unchanged in tensile-strained situation.Strain analyses reveal that the former process is initiated by an expansion in Co layer at boundary,whereas the latter one is associated with an edge dislocation combined with antiphase boundary.These findings provide a chemomechanical perspective on the structure regulation of perovskite oxides and enrich insights into strain-dependent phase diagram in epitaxial oxides films.

Significantly enhanced thermal stability of HMX by phase-transition lysozyme coating

A new robust bio-inspired route by using lysozyme aqueous solution for surface modification on 1,3,5,7-tetranitro-1,3,5,7-tetrazocane(HMX)was described in this paper.HMX crystals were coated by in situ phase transition of lysozyme(PTL)molecules.The HMX decorated by PTL was characterized by SEM,XRD,FTIR and XPS,demonstrating a dense core-shell coating layer.The coverage of lysozyme on HMX crystal was calculated by the ratio of sulfur content.The surface coverage increased from 60.5% to 93.5% when the content of PTL was changed from 0.5 wt% to 2.0 wt%,indicating efficient coating.The thermal stability of HMX was investigated by in situ XRD and DSC.The thermal phase transition temperature of HMX(β to δ phase)was delayed by 42℃ with 2.0 wt% PTL coating,which prevented HMX from thermal damage and sensitivity by the effect of PTL coating.After heating at 215℃,large cracks appeared in the naked HMX crystal,while the PTL coated HMX still maintained intact,with the impact energy of HMX dropped dramatically from 5 J to 2 J.However,the impact energy of HMX with 1.0 wt% and 2.0 wt% coating content(HMX@PTL-1.0 and HMX@PTL-2.0)was unchanged(5 J).Present results potentially enable large-scale fabrication of polymorphic energetic materials with outstanding thermal stability by novel lysozyme coating.

Triple points and phase transitions of D-dimensional dyonic Ad S black holes with quasitopological electromagnetism in Einstein–Gauss–Bonnet gravity

By considering the negative cosmological constant Λ as a thermodynamic pressure, we study the thermodynamics and phase transitions of the D-dimensional dyonic Ad S black holes(BHs) with quasitopological electromagnetism in Einstein–Gauss–Bonnet(EGB) gravity. The results indicate that the small/large BH phase transition that is similar to the van der Waals(vdW) liquid/gas phase transition always exists for any spacetime dimensions. Interestingly, we then find that this BH system exhibits a more complex phase structure in 6-dimensional case that is missed in other dimensions.Specifically, it shows for D = 6 that we observed the small/intermediate/large BH phase transitions in a specific parameter region with the triple point naturally appeared. Moreover, when the magnetic charge turned off, we still observed the small/intermediate/large BH phase transitions and triple point only in 6-dimensional spacetime, which is consistent with the previous results. However, for the dyonic Ad S BHs with quasitopological electromagnetism in Einstein–Born–Infeld(EBI) gravity, the novel phase structure composed of two separate coexistence curves observed by Li et al. [Phys. Rev. D105 104048(2022)] disappeared in EGB gravity. This implies that this novel phase structure is closely related to gravity theories, and seems to have nothing to do with the effect of quasitopological electromagnetism. In addition, it is also true that the critical exponents calculated near the critical points possess identical values as mean field theory. Finally, we conclude that these findings shall provide some deep insights into the intriguing thermodynamic properties of the dyonic Ad S BHs with quasitopological electromagnetism in EGB gravity.

Detecting the quantum phase transition from the perspective of quantum information in the Aubry–André model

We investigate the effectiveness of entropic uncertainty, entanglement and steering in discerning quantum phase transitions(QPTs). Specifically, we observe significant fluctuations in entropic uncertainty as the driving parameter traverses the phase transition point. It is observed that the entropic uncertainty, entanglement and quantum steering, based on the electron distribution probability, can serve as indicators for detecting QPTs. Notably, we reveal an intriguing anticorrelation relationship between entropic uncertainty and entanglement in the Aubry–André model. Moreover, we explore the feasibility of detecting a QPT when the period parameter is a rational number. These observations open up new and efficient avenues for probing QPTs.

Comparative study on phase transition behaviors of fractional molecular field theory and random-site Ising model

Fractional molecular field theory(FMFT)is a phenomenological theory that describes phase transitions in crystals with randomly distributed components,such as the relaxor-ferroelectrics and spin glasses.In order to verify the feasibility of this theory,this paper fits it to the Monte Carlo simulations of specific heat and susceptibility versus temperature of two-dimensional(2D)random-site Ising model(2D-RSIM).The results indicate that the FMFT deviates from the 2D-RSIM significantly.The main reason for the deviation is that the 2D-RSIM is a typical system of component random distribution,where the real order parameter is spatially heterogeneous and has no symmetry of space translation,but the basic assumption of FMFT means that the parameter is spatially uniform and has symmetry of space translation.

The Negative Thermal Expansion Property of NdMnO_(3) Based on Pores Effect and Phase Transition

A novel negative thermal expansion(NTE) material NdMnO_(3) was synthesized by solid-state method at 1 523 K. The crystal structure, phase transition, pores effect and negative expansion properties of NdMnO_(3) were investigated by variable temperature X-ray diffraction(XRD), scanning electron microscope(SEM) and variable temperature Raman spectra. The compound exhibits NTE properties in the orderly O' phase crystal structure. When the temperature is from 293 to 759 K, the ceramic NdMnO_(3) shows negative thermal expansion of-4.7×10^(-6)/K. As temperature increases, the ceramic NdMnO_(3) presents NTE property range from 759 to 1 007 K. The average linear expansion coefficient is-18.88×10^(-6)/K. The physical mechanism of NTE is discussed and clarified through experiments.

Inhibiting the phase transition of WO_(3)for highly stable aqueous electrochromic battery

Aqueous electrochromic battery(ECB)has shown intense potential for achieving energy storage and saving simultaneously.While tungsten oxide(WO_(3))is the most promising EC material for commercialization,the cycling stability of WO_(3)-based aqueous ECBs is currently unsatisfactory due to the repeated phase transition during the redox process and the corrosion by acidic electrolytes.Herein,we present a titanium-tungsten oxide alloy(Ti-WO_(3))with controllable morphology and crystal phase synthesized by a facile hot injection method to overcome the challenges.In contrast to conventional monoclinic WO_(3),the Ti-WO_(3)nanorods can stably maintain their cubic crystal phase during the redox reaction in an acidic electrolyte,thus leading to dramatically enhanced response speed and cycling stability,Specifically,when working in a well-matched hybrid Al^(3+)/Zn^(2+)aqueous electrolyte,our phasetransition-free cubic Ti-WO_(3)exhibits an ultra-high cycling stability(>20000 cycles),fast response speed(3,95 s/4,65 s for bleaching/coloring),as well as excellent discharge areal capacity of 214.5 mA h m^(-2),We further fabricate a fully complementa ry aqueous electrochromic device,for the first time,using a Ti-WO_(3)/Prussian blue device architecture.Remarkably,the complementary ECB shows>10000 stable operation cycles,attesting to the feasibility of our Ti-WO_(3)for practical applications.Our work validates the significance of inhibiting the phase transitions of WO_(3)during the electrochromic process for realizing highly cyclable aqueous ECB,which can possibly provide a generalized design guidance for other high-quality metallic oxides for electrochemical applications.

Multi-functional photonic spin Hall effect sensor controlled by phase transition

Photonic spin Hall effect(PSHE), as a novel physical effect in light–matter interaction, provides an effective metrological method for characterizing the tiny variation in refractive index(RI). In this work, we propose a multi-functional PSHE sensor based on VO_(2), a material that can reveal the phase transition behavior. By applying thermal control, the mutual transformation into different phase states of VO_(2) can be realized, which contributes to the flexible switching between multiple RI sensing tasks. When VO_(2) is insulating, the ultrasensitive detection of glucose concentrations in human blood is achieved. When VO_(2) is in a mixed phase, the structure can be designed to distinguish between the normal cells and cancer cells through no-label and real-time monitoring. When VO_(2) is metallic, the proposed PSHE sensor can act as an RI indicator for gas analytes. Compared with other multi-functional sensing devices with the complex structures, our design consists of only one analyte and two VO_(2) layers, which is very simple and elegant. Therefore, the proposed VO_(2)-based PSHE sensor has outstanding advantages such as small size, high sensitivity, no-label, and real-time detection, providing a new approach for investigating tunable multi-functional sensors.

Crystal structure,phase transitions,and thermodynamic properties of magnesium metavanadate(MgV_(2)O_(6))

As a promising anode material for magnesium ion rechargeable batteries,magnesium metavanadate(MgV_(2)O_(6))has attracted considerable research interest in recent years.A MgV_(2)O_(6)sample was synthesized via a facile solid-state reaction by multistep-firing stoichiometric mixtures of MgO and V2O5 powder under an air atmosphere.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)occurred at 841 K and the enthalpy change was 4.37±0.04 kJ/mol.The endothermic effect at 1014 K and the enthalpy change was 26.54±0.26 kJ/mol,which is related to the incongruent melting ofβ-MgV_(2)O_(6).In situ XRD was performed to investigate phase transition of the as-prepared MgV_(2)O_(6)at high temperatures.The cell parameters obtained by Rietveld refinement indicated that it crystallizes in a monoclinic system with the C2/m space group,and the lattice parameters of a=9.280 A°,b=3.501 A°,c=6.731 A°,β=111.76°.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)was further studied by thermal kinetics,indicating that this process is controlled first by a fibril-like mechanism and then by a spherulitic-type mechanism with an increasing heating rate.Additionally,the enthalpy change of MgV_(2)O_(6)at high temperatures was measured utilizing the drop calorimetry,heat capacity was calculated and given as:Cp=208.3+0.03583T-4809000T^(−2)(298-923 K)(J mol^(−1)K^(−1)),the high-temperature heat capacity can be used to calculate Gibbs free energy of MgV_(2)O_(6)at high temperatures.

Ascending phase of solar cycle 25 tilts the current El Nino-Southern oscillation transition

自2020年初夏,赤道太平洋地区出现拉尼娜现象并持续两年半多(以下简称2020拉尼娜),对其未来演变的预测引起了很多关注,考虑到11年太阳周期活动对热带太平洋SST异常可能存在锁相影响,本研究分析了当前太阳活动周(即第25太阳周(SC25))对目前热带太平洋ENSO现象未来演变的调节作用,基于历史太阳周的统计特征,作者对第25太阳周达到其最大值的时间提出三种可能的情景,并讨论了不同情景下的太阳活动对未来两年ENSO演变的可能影响,第25太阳周的持续上升阶段在一定程度上抑制了当前2023厄尔尼诺现象发展为超级事件.

Unexpected Twinning and Phase-Transition of the Indentation Standards, Their Transition Energies, and Scientific Dichotomy

The general use of aluminium as an indentation standard for the iteration of contact heights for the determination of ISO-14577 hardness and elastic modulus is challenged because of as yet not appreciated phase-changes in the physical force-depth standard curve that seemed to be secured by claims from 1992. The physical and mathematical analyses with closed formulas avoid the still world-wide standardized energy-law violation by not reserving 33.33% (h2 belief) (or 20% h3/2 physical law) of the loading force and thus energy for all not depth producing events but using 100% for the depth formation is a severe violation of the energy law. The not depth producing part of the indentation work cannot be done with zero energy! Both twinning and structural phase-transition onsets and normalized phase-transition energies are now calculated without iterations but with physically correct closed arithmetic equations. These are reported for Berkovich and cubecorner indentations, including their comparison on geometric grounds and an indentation standard without mechanical twinning is proposed. Characteristic data are reported. This is the first detection of the indentation twinning of aluminium at room temperature and the mechanical twinning of fused quartz is also new. Their disqualification as indentation standards is established. Also, the again found higher load phase-transitions disqualify aluminium and fused quartz as ISO-ASTM 14577 (International Standardization Organization and American Society for Testing and Materials) standards for the contact depth “hc” iterations. The incorrect and still world-wide used black-box values for H- and Er-values (the latter are still falsely called “Young’s moduli” even though they are not directional) and all mechanical properties that depend on them. They lack relation to bulk moduli from compression experiments. Experimentally obtained and so published force vs depth parabolas always follow the linear FN = kh3/2 + Fa equation, where Fa is the axis-cut before and after the phase-transition branches (never “h2” as falsely enforced and used for H, Er and giving incorrectly calculated parameters). The regression slopes k are the precise physical hardness values, which for the first time allow for precise calculation of the mechanical qualities by indentation in relation to the geometry of the indenter tip. Exactly 20% of the applied force and thus energy is not available for the indentation depth. Only these scientific k-values must be used for AI-advises at the expense of falsely iterated indentation hardness H-values. Any incorrect H-ISO-ASTM and also the iterated Er-ISO-ASTM modulus values of technical materials in artificial intelligence will be a disaster for the daily safety. The AI must be told that these are unscientific and must therefore be replaced by physical data. Iterated data (3 and 8 free parameters!) cannot be transformed into physical data. One has to start with real experimental loading curves and an absolute ZerodurR standard that must be calibrated with standard force and standard length to create absolute indentation results. .

基于CTA颅内动脉瘤形态联合PHASES评分对破裂出血预测研究

目的:分析头颈部计算机断层扫描血管成像(CTA)联合PHASES评分对颅内动脉瘤(IA)破裂出血的预测价值。方法:回顾性分析2021年10月—2023年9月东莞市长安医院诊治的IA患者临床资料,根据IA破裂出血与否分为IA破裂组(n=46)和IA未破裂组(n=44),收集两组临床资料,对比两组患者CTA影像瘤体特征参数和PHASES评分结果。采用受试者工作特征(ROC)曲线分析两者联合预测动脉瘤破裂的效能。结果:IA破裂组高血压、糖尿病发生率及PHASES评分均高于IA未破裂组,差异有统计学意义(P <0.05)。两组病灶位置以颈内动脉(ICA)和大脑中动脉(MCA)为主,但IA破裂组病灶位置在MCA的占比为41.30%,高于IA未破裂组的20.45%,瘤体>7 mm的最多(瘤体7~9.9 mm占65.22%),瘤体形态不规则占58.7%,未破裂组病灶位置在ICA最多(68.18%),瘤体<7 mm的居多(75.00%),瘤体形态规则囊状动脉瘤占93.18%,差异有统计学意义(P <0.05)。CTA瘤体特征参数比较,IA破裂组患者瘤颈宽度、瘤体高度、瘤体长度、动脉瘤最大直径、入射夹角、动脉瘤体颈比等参数均高于IA未破裂组,差异有统计学意义(P <0.05)。CTA瘤体特征参数+PHASES评分联合预测曲线下面积为0.916,高于CTA瘤体特征参数(0.901)和PHASES评分(0.731)。结论:CTA瘤体特征参数+PHASES评分联合预测IA患者破裂出血效能最佳。

Molecular dynamics study on the effect of temperature on HCP→FCC phase transition of magnesium alloy

To explore the effect of temperature on the phase transformation of HCP→FCC during compression, the uniaxial compression process of AZ31 magnesium alloy was simulated by the molecular dynamics method, and the changes of crystal structure and dislocation evolution were observed. The effects of temperature on mechanical properties, crystal structure, and dislocation evolution of magnesium alloy during compression were analyzed. It is concluded that some of the Shockley partial dislocation is related to FCC stacking faults. With the help of TEM characterization, the correctness of the correlation between some of the dislocations and FCC stacking faults is verified. Through the combination of simulation and experiment, this paper provides an idea for the in-depth study of the solid-phase transformation of magnesium alloys and provides reference and guidance for the design of magnesium alloys with good plasticity and formability at room temperature.

Phase-engineering modulation of Mn-based oxide cathode for constructing super-stable sodium storage

The Mn-based oxide cathode with enriched crystal phase structure and component diversity can provide the excellent chemistry structure for Na-ion batteries.Nevertheless,the broad application prospect is obstructed by the sluggish Na^(+)kinetics and the phase transitions upon cycling.Herein,we establish the thermodynamically stable phase diagram of various Mn-based oxide composites precisely controlled by sodium content tailoring strategy coupling with co-doping and solid-state reaction.The chemical environment of the P2/P'3 and P2/P3 biphasic composites indicate that the charge compensation mechanism stems from the cooperative contribution of anions and cations.Benefiting from the no phase transition to scavenge the structure strain,P2/P'3 electrode can deliver long cycling stability(capacity retention of 73.8%after 1000 cycles at 10 C)and outstanding rate properties(the discharge capacity of 84.08 mA h g^(-1)at 20 C)than P2/P3 electrode.Furthermore,the DFT calculation demonstrates that the introducing novel P'3 phase can significantly regulate the Na^(+)reaction dynamics and modify the local electron configuration of Mn.The effective phase engineering can provide a reference for designing other high-performance electrode materials for Na-ion batteries.

Shikimic acid accelerates phase change and flowering in Chinese jujube

The juvenile-to-adult phase change with first flowering as the indicator plays a crucial role in the lifecycle of fruit trees. However, the molecular mechanisms underlying phase change in fruit trees remain largely unknown. Shikimic acid (ShA) pathway is a main metabolic pathway closely related to the synthesis of hormones and many important secondary metabolites participating in plant phase change. So,whether ShA regulates phase change in plants is worth clarifying. Here, the distinct morphological characteristics and the underlying mechanisms of phase change in jujube (Ziziphus jujuba Mill.), an important fruit tree native to China with nutritious fruit and outstanding tolerance abiotic stresses, were clarified. A combined transcriptome and metabolome analysis found that ShA is positively involved in jujube(Yuhong’×Xing 16’) phase change. The genes in the upstream of ShA synthesis pathway (ZjDAHPS, ZjDHQS and ZjSDH), the contents of ShA and the downstream secondary metabolites like phenols were significantly upregulated in the phase change period. Further, the treatment of spraying exogenous ShA verified that ShA at a very low concentration (60 mg·L^(-1)) can substantially speed up the phase change and flowering of jujube and other tested plants including Arabidopsis, tomato and wheat. The exogenous ShA (60 mg·L^(-1)) treatment in jujube seedlings could increase the accumulation of endogenous ShA, enhance leaf photosynthesis and the synthesis of phenols especially flavonoids and phenolic acids, and promote the expression of genes (ZjCOs, ZjNFYs and ZjPHYs) involved in flowering pathway. Basing on above results, we put forward a propose for the underlying mechanism of ShA regulating phase change, and a hypothesis that ShA could be considered a phytohormone-like substance because it is endogenous, ubiquitous, movable and highly efficient at very low concentrations. This study highlights the critical role of ShA in plant phase change and its phytohormone-like properties.

First-order quantum phase transition and entanglement in the Jaynes-Cummings model with a squeezed light

We study the quantum phase transition and entanglement in the Jaynes-Cummings model with squeezed light,utilize a special transformation method to obtain the analytical ground state of the model within the near-resonance regime,and numerically verify the validity of the analytical ground state.It is found that the ground state exhibits a first-order quantum phase transition at the critical point linearly induced by squeezed light,and the ground state entanglement reaches its maximum when the qubit-field coupling strength is large enough at the critical point.

Microstructure and damping properties of LPSO phase dominant Mg-Ni-Y and Mg-Zn-Ni-Y alloys

This work studied the microstructure,mechanical properties and damping properties of Mg_(95.34)Ni_(2)Y_(2.66) and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys systematically.The difference in the evolution of the long-period stacked ordered(LPSO)phase in the two alloys during heat treatment was the focus.The morphology of the as-cast Mg_(95.34)Ni_(2)Y_(2.66)presented a disordered network.After heat treatment at 773 K for 2 hours,the eutectic phase was integrated into the matrix,and the LPSO phase maintained the 18R structure.As Zn partially replaced Ni,the crystal grains became rounded in the cast alloy,and lamellar LPSO phases and more solid solution atoms were contained in the matrix after heat treatment of the Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloy.Both Zn and the heat treatment had a significant effect on damping.Obvious dislocation internal friction peaks and grain boundary internal friction peaks were found after temperature-dependent damping of the Mg_(95.34)Ni_(2)Y_(2.66)and Mg_(95.34)Zn_(1)Ni_(1)Y_(2.66)alloys.After heat treatment,the dislocation peak was significantly increased,especially in the alloy Mg_(95.34)Ni_(2)Y_(2).66.The annealed Mg_(95.34)Ni_(2)Y_(2.66)alloy with a rod-shaped LPSO phase exhibited a good damping performance of 0.14 atε=10^(−3),which was due to the difference between the second phase and solid solution atom content.These factors also affected the dynamic modulus of the alloy.The results of this study will help in further development of high-damping magnesium alloys.

Pore pressure built-up in hydrate-bearing sediments during phase transition: A poromechanical approach

Due to the density contrast between the hydrate and methane gas,the pore pressure is accumulated in the sediment during the decomposition process of methane hydrate.This accumulation of pore pressure decreases the magnitude of effective stress,further triggering potential geological disasters such as landslide.This paper establishes a theoretical framework to investigate the evolution of fluid pressure in the hydrate-bearing sediments during the decomposition process.This model consists of two parts:an unsaturated thermo-poromechanical constitutive law as well as a phase equilibrium equation.Compared with the existing studies,the present work incorporates the effect of pore volume change into the pressure built-up model.In addition,the capillary effect is considered,which plays a nontrivial role in fine-grained sediments.Based on this model,the evolution of fluid pressure is investigated in undrained conditions.It is shown that four mechanisms mainly contribute to the pressure built-up:the density contrast between decomposing hydrate and producing fluid,the variation of pore volume,the compaction of hydrate due to variation of capillary pressure,and the thermal deformation of pore constituents induced by temperature change.Among these mechanisms,the density contrast dominates the pore pressure accumulation.Under the combined effect of these contributions,the evolution of fluid pressure exhibits a strong nonlinearity during the decomposition process and can reach up to dozens of mega Pascal.Nevertheless,this high-level pressure built-up results in a significant tensile strain,yielding potential fracturing of the sediment.

A new insight into LPSO phase transformation and mechanical properties uniformity of large-scale Mg-Gd-Y-Zn-Zr alloy prepared by multi-pass friction stir processing

A large-scale fine-grained Mg-Gd-Y-Zn-Zr alloy plate with high strength and ductility was successfully prepared by multi-pass friction stir processing(MFSP)technology in this work.The structure of grains and long period stacking ordered(LPSO)phase were characterized,and the mechanical properties uniformity was investigated.Moreover,a quantitative relationship between the microstructure and tensile yield strength was established.The results showed that the grains in the processed zone(PZ)and interfacial zone(IZ)were refined from 50μm to 3μm and 4μm,respectively,and numerous original LPSO phases were broken.In IZ,some block-shaped 18R LPSO phases were transformed into needle-like 14H LPSO phases due to stacking faults and the short-range diffusion of solute atoms.The severe shear deformation in the form of kinetic energy caused profuse stacking fault to be generated and move rapidly,greatly increasing the transformation rate of LPSO phase.After MFSP,the ultimate tensile strength,yield strength and elongation to failure of the large-scale plate were 367 MPa,305 MPa and 18.0% respectively.Grain refinement and LPSO phase strengthening were the major strengthening mechanisms for the MFSP sample.In particularly,the strength of IZ was comparable to that of PZ because the strength contribution of the 14H LPSO phase offsets the lack of grain refinement strengthening in IZ.This result opposes the widely accepted notion that IZ is a weak region in MFSP-prepared large-scale fine-grained plate.

Topological phase transition in network spreading

This paper investigates information spreading from the perspective of topological phase transition.Firstly,a new hybrid network is constructed based on the small-world networks and scale-free networks.Secondly,the attention mechanism of online users in information spreading is studied from four aspects:social distance,individual influence,content richness,and individual activity,and a dynamic evolution model of connecting with spreading is designed.Eventually,numerical simulations are conducted in three types of networks to verify the validity of the proposed dynamic evolution model.The simulation results show that topological structure and node influence in different networks have undergone phase transition,which is consistent with the phenomenon that followers and individual influence in real social networks experience phase transition within a short period.The infection density of networks with the dynamic evolution rule changes faster and reaches higher values than that of networks without the dynamic evolution rule.Furthermore,the simulation results are compared with the real data,which shows that the infection density curve of the hybrid networks is closer to that of the real data than that of the small-world networks and scale-free networks,verifying the validity of the model proposed in this paper.