Zone Center Research Articles

Prospects for the Development of Data Centers in the Arctic

This paper examines the experience and prospects of placing data centers in the Arctic zone of circumpolar states, including Russia. The authors consider the phenomenon of commercial data centers providing services to IT-companies and the idea of building such centers in the Arctic to reduce costs. The authors analyze the advantages of the Arctic territories, including the possibility of natural cooling of installations, the use of renewable energy sources and the prospects for contribution to digitalization and development of the northern regions of the Arctic countries. Further, the authors describe the existing projects for the placement of data centers in the Arctic zone of Sweden, Finland, Norway, Denmark, Iceland and similar Russian experience. In this paper, the authors dwell in detail on projects in Karelia, Murmansk, and Norilsk. In conclusion, the authors come to the conclusion that functioning data centers are isolated projects both in Russia and in other countries. The authors analyze in detail what features of the Arctic regions determine this state of affairs, both highlighting common features and distinguishing between the Russian and foreign Arctic.

First-principles investigation on structural and optoelectronic properties of buckled SnO monolayer for effective solar energy scavenging

Two-dimensional (2D) materials have gathered considerable attention for next-generation optoelectronic devices owing to their intriguing optical and electronic properties. The semiconductor SnO has shown potential for flexible electronics, optoelectronics, gas sensing, and Li-ion battery applications due to its indirect bandgap, and high carrier mobility. In the present work, we investigate the physical properties of a buckled tin oxide (SnO) monolayer using density functional theory (DFT) calculations. The structural analysis reveals that buckled SnO monolayer is energetically stable and exhibits the hexagonal crystal structure. Phonon dispersion analysis depicts the dynamical stability of the buckled SnO monolayer and obtained the quadratic behavior of flexural acoustic modes (ZA) near the zone center. Further, the electronic property calculation shows that the buckled SnO is an indirect semiconductor with a bandgap of 1.71 eV and the transparent behavior of the material is disclosed by analyzing the optical parameters. Moreover, the computed solar power conversion efficiency of 16.76% for buckled SnO monolayer demonstrates the potential as a light absorber in the field of solar energy scavenging.

Центральные места как концептуальный конструкт: построение структуры пространственных рынков в масштабах национальной экономики

The article is devoted to determining the possibilities of building the structure of spatial markets on the scale of the national economy. An overview of the works is given, thanks to which the idea of the interregional input-output model was gradually formed as an objective calculation basis for analyzing the functional base of the regions and building a network model of economic interactions within the framework of the concept of central places. The main attention is paid to instrumental developments that can be useful for creating a universal method for recognizing the structure of economic interactions in space based on interregional balances. Three approaches to the distribution of regions by levels of the functional hierarchy have been identified. The first approach is based on estimates of the nodal structure of space, the second is based on the ordinal function of the network of interregional interactions, and the third is based on feedback loops. It has been established that the number of hierarchy levels allocated using the first approach is minimal, and using the second approach – maximum. It is determined that the central place measure can be used to test the assumptions formed on the basis of alternative approaches regarding the hierarchical structure of economic interactions. With the help of the considered instrumental developments, the hierarchical structure of economic interactions of the regions of Japan is determined based on the interregional input-output tables for 2005. It is shown that the analysis of the functional base of the regions, integrating alternative approaches to the hierarchization of flows of the interregional balance, allows us to determine the structure of spatial markets on the scale of the national economy based on the following aspects of economic interactions: the difference in the masses of the central places entering into interaction; maintaining a balance of centripetal and centrifugal forces; maximizing the «gravity» of the centers of market zones

Обоснование зон с повышенной продуктивностью нефтяных залежей в карбонатных коллекторах (на примере Зимне-Ставкинско-Правобережного месторождения)

Introduction. The object of the study is the carbonate deposit of the Lower Triassic Neftekumsk Formation (Zimnyaya-Stavka field and Pushkarskoye field) in the Eastern Stavropol Territory. The purpose of the study is to increase the efficiency of oil field development based on the analysis of field and geological data, deciphering of satellite images and interpretation of structures of central type (SCT). Materials and methods of research. Regional studies of the fields of the Eastern Ciscaucasia, data on oil deposits and satellite images of various levels of generalization were used. New, non-traditional methods were employed, among which a field-lineament approach and a new method for selecting objects for the additional development of oil fields, based on deciphering of satellite images and interpretation of the structures of central type, taking into account data on the location of zones of increased productivity. Results and discussion. Research results and their discussion. As a result of the analysis and mapping of wells with the largest accumulated oil recovery from the main productive formations of the studied field, local centers of high-yield zones were identified. A scheme of oil and gas geological zoning of the central type structures and lineament nodes at the studied oil field was built, promising targets for infill drilling and geological and technical operations were identified to increase the degree of development of residual reserves, indicating specific areas for further development of this field. Conclusion. Based on the analysis of the geotectonic activity of the studied region, the influence of the geodynamic factor on the productivity of wells was established. The use of these approaches will improve the efficiency of forecasting carbonate reservoirs in order to identify promising and developed objects of additional exploration and development for infill drilling, geological and technical operations, and increase the degree of reserves development.

Visualization and Characterization of Cumulative Arc Erosion Behavior Using 2-D Microscopic Images

The electrical arc erosion behavior extremely limits the lifespan of electromechanical switching devices. Observation of the gradual evolution of arc erosion is highly beneficial for to understand the arc ignition and the contact degradation. In this article, the erosion of contact materials is simulated and visualized in situ with the recorded 2-D microscopic images. A novel method for erosion area identification is proposed with the combination of difference image method and mathematical morphology operations. The variation in erosion area as a function of switching current cycles is demonstrated, and the center of erosion zone that migrates continuously during the endurance experiment is determined. Finally, not only three types of arc erosion regimes (centralized arc erosion, separated arc erosion, and commutated arc erosion) are revealed, but also the associated occurrence probabilities during 1000 cycles are provided.

Fear of COVID-19 and poor accessibility of comprehensive care has caused delay in initiation of antenatal care among pregnant women in Southwest Ethiopia: the need for disaster resilient and accessible maternal health care.

Antenatal care (ANC) is care provided to pregnant women in order to ensure positive health outcomes for both mother and baby. Late ANC contact lacks the opportunity to provide interventions that are effective early in the pregnancy. A huge proportion of pregnant women present late. The aim of this study was to identify determinants of late enrollment in the ANC among pregnant women in public health centers in Ilu Ababor Zone, South-West Ethiopia. A facility-based case-control study was conducted on 270 randomly selected pregnant women (135 cases and 135 controls). A pretested interviewer-administered questionnaire was used to collect data. Multi-variable logistic regression was run to identify the determinants of late ANC initiation. The adjusted odds ratio (AOR) and its 95% confidence interval (CI) were used to determine statistical significance at a P-value of 0.05. A total of 270 pregnant women were interviewed, making a response rate of 97%. Unplanned pregnancy [AOR: 2.8; 95% CI: (1.3, 6.0)], lack of information on time of ANC initiation [AOR: 2.7; 95% CI:(1.02, 5.0)], older age [AOR: 2.2; 95% CI:(1.01, 4.7)], not attending ANC in the previous pregnancy [AOR: 4.07; 95% CI: (1.8, 9.5)], and fear of COVID-19 were determinants of late initiation of ANC in the study area. Age, pregnancy and care-related factors, and fear of COVID-19 were determinants of late initiation of ANC. Community-based provision of comprehensive information on planned pregnancy and the ANC is important. A resilient system has to be built to deliver essential health services during emergencies like COVID-19.

Особенности формирования микроструктуры алюминиевых сплавов АК4-1 и АК12Д после их совместной обработки трением с перемешиванием

Friction stir processing is one of the modern methods of local modification of the surface of aluminum alloys in the solid-phase state, which provides the dispersion of structural components. In heat-hardened aluminum alloys with a matrix type structure, heat treatment following after friction stir processing can lead to abnormal grain growth in the stir zone. However, in alloys with the structure close to microduplex type, a fine-grained structure can be formed after friction stir processing and heat treatment. This work is aimed at evaluating the possibility of increasing the microstructure thermal stability of the AK4-1 (Al–Cu–Mg–Fe–Si–Ni) matrix-type aluminum alloy. For this purpose, AK12D (Al–Si–Cu–Ni–Mg) aluminum alloy with the structure close to microduplex type was locally mixed into the studied alloy by friction stir processing. Subsequent Т6 heat treatment was carried out according to the standard mode for the AK4-1 alloy. Studies showed that the stir zone had an elliptical shape with an onion-ring structure. This structure comprised alternating rings with different amounts and sizes of excess phases. At the same time, in the stir zone center, the width of rings and the average area of excess phases were larger compared to the stir zone periphery, where the width of rings and the average area of particles were smaller. The average area of excess phases in the rings with their higher content was smaller than in the rings with their lower content. This distribution of excess phases leads to the formation of a fine-grained microstructure, where the average size of grains depends on the interparticle distance in the α-Al solid solution.

Characteristics of Al6061-SiC-Al2O3 Surface Hybrid Composites Fabricated by Friction Stir Processing

Friction stir processing (FSP) has successfully evolved as an alternative technique of fabricating metal matrix composites. (MMC). FSP has been used positively to produce surface composite that offer good surface properties such as higher hardness and wear resistance, also help in the development of finer-grain structure during thermomechanical processing of the material. This work aims to fabricate a surface composite upon the AA6061-T6 Al alloy via FSP. The effect of SiC and/or Al2O3 particles on microstructure, microhardness, and wear behavior of the surface composite was investigated. Many drilled holes were made to incorporate the ceramic particles within the matrix at the optimal friction stir processing circumstances, The optimal parameters of (FSP) were (32 mm ̸min), (1250 rpm), and (2) passes in a similar track.. It was obtained that the maximum microhardness being in the stir zone center of FSP of the base alloy and all composites. The results of XRD and EDX mapping confirmed the incorporation of SiC and Al2O3 particles within the surface of Al alloy using FSP which will improve the surface properties. The improvement in microhardness was (89.3%) in the case of FSP composite sample reinforced with hybrid addition (SiC+Al2O3) particles in comparison to FSP unreinforced base alloy (75 HV). It was showed that the wear resistance of the FSP composite sample reinforced with hybrid addition of (Al2O3 and SiC ) particles was slightly better than that of the FSP composite sample reinforced with single Al2O3 or SiC particles and base Al alloy.

The carrier mobility and superconducting properties of monolayer oxygen-terminated functionalized MXene Ti2CO2.

In this study, the carrier mobility of monolayer Ti2CO2 was evaluated by employing the Boltzmann transport equation and superconducting transition temperature (Tc) of Ti2CO2 was determined by utilizing the Migdal and Eliashberg formalism in the first-principles framework. In contrast to previous studies, the results reveal that optical phonons in monolayer Ti2CO2 have dominant roles in scattering processes, which significantly reduce the mobility of carriers. Alongside the rigid band model, the jellium model is implemented to investigate the screening effects on electron-phonon interactions. Based on the jellium model and full-band electron-phonon calculations, the predicted maximum electron mobility at room temperature is 38 cm2 V-1 s-1 in which 80% of the total scattering rate originates from the intra-valley transitions within the M-valleys, indicating the crucial role of the long wavelength phonon wavevectors in scattering processes. On the other hand, for the p-type material, a maximum room temperature mobility of about 285 cm2 V-1 s-1 is calculated, which can be explained by a relatively small effective mass and tiny scattering phase space. Moreover, a maximum Tc of 39 (10) K is obtained for the n-type monolayer Ti2CO2 based on the rigid (jellium) model. Outcomes indicate that the important peaks of α2F(ω) are mainly caused by the optical phonons. The remarkable couplings between the electron states and phonons are related to the non-zero slope of (near the Brillouin zone center) the longitudinal optical branch denoted by Eu caused by the displacements of oxygen and carbon atoms at intermediate and high energy ranges of phonon dispersion, respectively.

Observation of electronic structure replicas in photoemission spectra of graphite upon adsorption of tin phthalocyanine

Cone-type bands near the center of the surface Brillouin zone were observed in low-energy angle-resolved photoemission spectra of tin phthalocyanine adsorbed on graphite. Simulations in comparison with the experimental data show that the spectral features represent replicas of the electronic structure of graphite near resulting from high-order momentum transfer processes up to the fourth order owing to the interaction of substrate electrons with the long-range structural order of the adsorbate overlayer. The analysis of time-resolved photoemission data from one of the replicas yields a quantitative and very good agreement with previous studies on the excited carrier dynamics in the Dirac cones of graphite and graphene.

Electronic and magnetic properties of the topological semimetal SmMg2Bi2

Dirac semimetals show nontrivial physical properties and can host exotic quantum states like Weyl semimetals and topological insulators under suitable external conditions. Here, by combining angle-resolved photoemission spectroscopy measurements (ARPES) and first-principle calculations, we demonstrate that the Zintl-phase compound ${\mathrm{SmMg}}_{2}{\mathrm{Bi}}_{2}$ is in close proximity to a topological Dirac semimetallic state. ARPES results show a Dirac-like band crossing at the zone center near the Fermi level (${E}_{\mathrm{F}}$), which is further confirmed by first-principle calculations. Theoretical studies also reveal that ${\mathrm{SmMg}}_{2}{\mathrm{Bi}}_{2}$ belongs to a ${Z}_{2}$ topological class and hosts spin-polarized states around the ${E}_{\mathrm{F}}$. Zintl's theory predicts that the valence state of Sm in this material should be ${\mathrm{Sm}}^{2+}$, however, we detect many Sm-$4f$ multiplet states (flat-bands) whose energy positions and relative intensities suggest the presence of both dominant ${\mathrm{Sm}}^{2+}$ and minor ${\mathrm{Sm}}^{3+}$. The small concentration (2.5%) of ${\mathrm{Sm}}^{3+}$ in the bulk of a crystal is inferred to arise from Sm vacancies in the crystal. It is also evident that these flat bands and other dispersive states are strongly hybridized when they cross each other. Due to the presence of ${\mathrm{Sm}}^{3+}$ ions, the temperature dependence of the magnetic susceptibility $\ensuremath{\chi}(T)$ shows a Curie-Weiss-like contribution in the low-temperature region, in addition to the Van Vleck-like behavior expected for the ${\mathrm{Sm}}^{2+}$ ions. The present study will help to better understand the electronic structure, magnetism, and transport properties of related materials.

Interspecific introgression of MHC genes in Triturus newts: Evidence from multiple contact zones.

The major histocompatibility complex (MHC) genes are central to the adaptive immune response in vertebrates. Selection generally maintains high MHC variation because the spectrum of recognized pathogens depends on MHC polymorphism. Novel alleles favoured by selection originate by interallelic recombination or de novo mutations but may also be acquired by introgression from related species. However, the extent and prevalence of MHC introgression remain an open question. In this study, we tested for MHC introgression in six hybrid zones formed by six Triturus newt species. We sequenced and genotyped the polymorphic second exons of the MHC class I and II genes and compared their interspecific similarity at various distances from the centre of the hybrid zone. We found evidence for introgression of both MHC classes in the majority of examined hybrid zones, with support for a more substantial class I introgression. Furthermore, the overall MHC allele sharing outside of hybrid zones was elevated between pairs of Triturus species with abutting ranges, regardless of the phylogenetic distance between them. No effect of past hybrid zone movement on MHC allele sharing was found. Finally, using previously published genome-wide data, we demonstrated that MHC introgression was more extensive than genome-wide introgression, supporting its adaptive potential. Our study thus provides evidence for the prevalence of MHC introgression across multiple Triturus hybrid zones, indicating that MHC introgression between divergent hybridizing species may be widespread and adaptive.

Complex electronic structure evolution of NdSb across the magnetic transition

The rare-earth monopnictide (REM) family, which hosts magnetic ground states with extreme magnetoresistance, has established itself as a fruitful playground for the discovery of interesting topological phases. Here, by using high-resolution angle-resolved photoemission spectroscopy complemented by first-principles density-functional-theory-based modeling, we examine the evolution of the electronic structure of the candidate REM Dirac semimetal NdSb across the magnetic transition. A complex angel-wing-like band structure near the zone center along with arclike features at the zone center and the zone corner are observed. This dramatic reconstruction of the itinerant bands around the zone center is shown to be driven by a magnetic transition: Specifically, the Nd $5d$ electron band backfolds at the $\overline{\mathrm{\ensuremath{\Gamma}}}$ point and hybridizes with the Sb $5p$ hole bands in the antiferromagnetic phase. Our study indicates that antiferromagnetism plays an intricate role in the electronic structure of the REM family.

Topological properties of tetratomic Su–Schrieffer–Heeger chains with hierarchical long-range hopping

We propose a new generalized Su–Schrieffer–Heeger model with hierarchical long-range hopping based on a one-dimensional tetratomic chain. The properties of the topological states and phase transition, which depend on the cointeraction of the intracell and intercell hoppings, are investigated using the phase diagram of the winding number. It is shown that topological states with large positive/negative winding numbers can readily be generated in this system. The properties of the topological states can be verified by the ring-type structures in the trajectory diagram of the complex plane. The topological phase transition is strongly related to the opening (closure) of an energy bandgap at the center (boundaries) of the Brillouin zone. Finally, the non-zero-energy edge states at the ends of the finite system are revealed and matched with the bulk–boundary correspondence.

Laser-induced Fano asymmetry, electron-phonon coupling, and phase transition in lanthanide sesquioxide (Ln2O3; Ln = Eu, Gd, Dy) nanoparticles: A Raman spectroscopic investigation

Laser power-dependent Raman spectroscopy is deployed to probe Fano interference in asymmetrically broadened Tg modes and the associated line shift in three technologically sound, meticulously characterized rare-earth sesquioxide systems. Group theoretical analysis is accompanied to introspect the Raman-active optic modes in cubic, monoclinic, and trigonal phases and identify the laser heating-induced local phase transitions. With increasing laser intensity, a regular redshift and larger negative asymmetry in the Raman peaks are detected, which is attributed to moderations in Fano scattering by enhanced electron–phonon coupling amid the focussed photoexcited electron plasma and is illustrated using a Feynman diagram. A quantitative study is thereby performed to unveil the intrinsic nature of discrete-continuum Fano resonance in the nanoparticles of interest emphasizing the high sensitivity of Raman spectra to the excitation strength that perturbs the generic vibrational features at the Brillouin zone center by influencing the interference conditions, force constant, and length of the associated bonds compelled by tensile stress. A rising trend of the charge–phonon coupling constant (λ) with laser power validates a stronger particle–quasiparticle coupling, whereas a shorter anharmonic phonon lifetime (τanh) indicates faster interactions. Using Allen's formalism, the charge density of states [N(εF)] at the Fermi level per spin and molecule is calculated, which pertains to a negative regression dependence in the λN(εF)−τanh dynamics.

Variations of Subgrid-Scale Turbulent Fluxes in the Dry Convective Boundary Layer at Gray Zone Resolutions

Abstract In the numerical gray zone of the convective boundary layer (CBL), the horizontal resolution is comparable to the size of organized convective circulation. As turbulence becomes partially resolved, gridscale variations of the subgrid-scale (SGS) turbulent fluxes become significant compared to the mean. Previously, such variations have often been ignored in scale-adaptive planetary boundary layer (PBL) schemes developed for the gray zone. This study investigates these variations with respect to height and resolution based on large-eddy simulations. It is found that SGS fluxes exhibit maximum variability at the center of the gray zone, where the resolved and the SGS mean fluxes are approximately equal. A simple analytical model is used to associate such characteristic variations to the nonlinear interactions of the dominant energy-containing mode of CBL turbulence. Examination of the horizontal distribution of the SGS fluxes reveals their preferential location over the updraft edges surrounding the core. A priori analysis further suggests the ability of a scale-similarity closure to reproduce the unique spatial patterns of the SGS fluxes at gray zone resolutions. Four scale-adaptive PBL schemes are evaluated focusing on their representations of the modeled SGS flux variability. Their shared shortcomings as a result of their gradient diffusion–based formulation are exposed. This study suggests that a mixed model consisting of a scale-adaptive PBL scheme to represent the mean, and a scale-similarity component to account for gridscale variability to be advantageous for the gray zone. Significance Statement As Gresho and Lee’s famous quote on numerical schemes goes, “Don’t suppress the wiggles. They’re telling you something!” In the numerical gray zone, where the grid spacing is comparable to the characteristic length scale of the flow, turbulence is partially resolved. The “wiggles” (or gridscale variability) reflecting the resolved heterogeneity of turbulent fluxes is an outstanding feature of the gray zone. However, they are often overlooked as error bars to the mean. This study uncovers the significance of these error bars, and characterizes and explains their variations with height and grid spacing. A suitable model that captures such variations is investigated to help build better planetary boundary layer schemes.

Investigation of material flow, microstructure evolution, and texture development in dissimilar friction stir welding of Al6061 to Ti6Al4V

Aluminium -Titanium dissimilar welds are widely used in defence and aerospace industries. Welding of Al to Ti is highly challenging due to the wide difference in thermo-mechanical properties. One of the most promising techniques for producing dissimilar welds is friction stir welding. In the present study, material flow, texture, and microstructural evolution of Ti-6Al-4 V and Al6061 dissimilar friction stir welded joints are elucidated at the Ti interface and centre of the stir zone (CSZ). Material flow pattern reveals the spread of fragments of Ti particles of around 80.3% at the interface and about 23% at the CSZ. The dispersion of Ti fragments in the stir zone resulted in better strength and hardness values of around 256 MPa and 345 HV, respectively, with failure of the specimens in the heat-affected zone of Al6061 side. The interface microstructure at Ti reveals plenty of equiaxed and recrystallized grains. The strengthening mechanism at the Ti interface is due to the dynamic recovery driven by adiabatic shear bands (ASBs) and twin-induced deformation. The electron backscattered diffraction results revealed the presence of 91% and 77% of strain-free recrystallized grains at the Ti interface and CSZ, respectively. The strong texture components of S {123} < 346 > in Al and D {0001} < 112̅0 > in Ti were also observed.

Rapid astrocyte-dependent facilitation amplifies multi-vesicular release in hippocampal synapses

Synaptic facilitation is a major form of short-term plasticity typically driven by an increase in residual presynaptic calcium. Using near-total internal reflection fluorescence (near-TIRF) imaging of single vesicle release in cultured hippocampal synapses, we demonstrate a distinctive, release-dependent form of facilitation in which probability of vesicle release is higher following a successful glutamate release event than following a failure. This phenomenon has an onset of ≤500ms and lasts several seconds, resulting in clusters of successful release events. The release-dependent facilitation requires neuronal contact with astrocytes and astrocytic glutamate uptake by EAAT1. It is not observed in neurons grown alone or in the presence of astrocyte-conditioned media. This form of facilitation dynamically amplifies multi-vesicular release. Facilitation-evoked release events exhibit spatial clustering and have a preferential localization toward the active zone center. These results uncover a rapid astrocyte-dependent form of facilitation acting via modulation of multi-vesicular release and displaying distinctive spatiotemporal properties.

Experimental study on near wake shedding structure of pyramid roughness element in liquid–solid two-phase turbulent boundary layer

Particle image velocimetry (PIV) on the liquid–solid turbulent boundary layer containing solid particles with an average diameter of 355 μm is used to study the shedding structure near-field of the pyramid with varied yaw angle values (0°, 15°, 30°, and 45°). We find that the recirculation zone grows larger with increasing value by comparing the average velocity field and turbulence intensity at various angles. When closed vortex lines develop behind the pyramid at about (h, 0.8 h), the center of the recirculation zone gradually stabilizes; in the meantime, the turbulence intensity rises relative to the small α values. Power spectral density function (PSD) and proper orthogonal decomposition (POD) are used to analyze the near-field. According to the findings, various values have an impact on wake shedding structures. At the top and base of the pyramid, shearing vortices occur simultaneously on a regular basis, and their incidence is sensitive to variations in α. Similar top shedding structures are observed at various angles in the POD results. Furthermore, with increasing α, the reattachment vortex is observed at the downstream edge of the pyramid. We study the behavior and statistical properties of particles at various positions, and our findings suggest that the upper flow field's particle concentration distribution dispersion is greater than that of the wake. Some particles from the vicinity of the pyramid is attracted into the wake's recirculation zone and is carried downstream by the shedding vortex.

Thermodynamic signature of topological quantum phase transition in a two-leg Kitaev ladder

We study the topological quantum phase transitions (QPTs) and quantum criticality of a two-leg Kitaev ladder. In the absence of superconducting phase difference, the thermal Drude weight portrays well the gapped topological quantum phases (Dth=0) and gapless quantum criticality (Dth>0), which is further manifested by the critical energy spectrum with different gapless linear relation modes. The self-dual quantum criticality is demonstrated by the Grüneisen ratio (GR) Γ= constant irrelevant of temperature. Tuning the superconducting phase difference Φ=π, the system undergoes a gapped topological nontrivial phase transition into a gapless trivial one, manifested by the quadratic contact point at the center of Brillouin zone. Meanwhile, it is identified by the temperature dependent power-law divergence: Γ∼±T−1 at low temperature, which is similar to the general QPT. In particular, with the chemical potential vanishing, one can obtain full flat bands, giving rise to the discontinuous topological QPT. Furthermore, it is worth noting that the scaling of GR provides a new thermodynamic means to check the order of topological QPTs, which falls on a universal curve or not, indicating the continuous or discontinuous transition.