AN INVESTIGATION OF HIGH-TEMPERATURE DEFORMATION STRENGTHENING AND TOUGHENING MECHANISM OF TITANIUM ALLOY

The high-temperature deformation strengthening and toughening mechanisms of titanium alloys have been investigated in this paper. The materials processed by this method produce a new tri-modal microstrvcture, which consists of 10-20% equiaxed alpha, streaky alpha and transformed beta matrix. It is found that the higher ductility of tri-modal microstructure is attributed to the equiaxed alpha's coopemtive slip and coordinated deformation with the transformed beta matrix. The streaky alpha phases not only increase the strength and creep properties, but also increase the fracture toughness. Propagating along grain boundaries between two neighboring streaky alpha phases, cracks in tri-modal microstructure make a more tortuous way, and then the materials show a higher fracture toughness. This new method is applicable to α, near α,α+β and near β titanium alloys.

High-Temperature Deformation and Low-Temperature Fracture Behavior of Steel Slag Rubber Asphalt Mixture Surface Layer

Steel slag is regarded as one of the most widespread solid by-products of steel smelting with little commercial value.It can play a vital role in the construction industry especially in the field of transportation infrastructure construction.However,there are few evaluation systems established on the high-temperature deformation and low-temperature fracture behavior of steel slag rubber asphalt mixture(SSRAM).This study explores the perfor-mance of SSRAM by uniaxial penetration test,Semi-Circular Bending(SCB)test and evaluates test data through regression analysis.The uniaxial penetration test results shows that the failure deformation of SSRAM increases with the increase of steel slag content.According to the minimum allowable permanent deformation(R TS-min),the deformation of SSRAM should be controlled within 3 mm.Meanwhile,the cracking index of the SSRAM surface layer calculated at low temperature can meet the design requirements.The SCB test results show that the stress peak degradation rate(specimens with 10 mm notch are compared with 0 mm)of SSRAM with 40%steel slag content is 20.04%.That means proper steel slag content makes the stress peak degradation rate of SSRAM reaches the lowest value.The calculation results of fracture energy density(J_(1C))show that the steel slag additive reduced the fracture energy density of SSRAM.However,it is still proved that SSRAM with 40%steel slag has the best low-temperature fracture performance based on critical fracture toughness(K_(1C))and fracture stress peak.Further-more,the crack propagation velocity parametric equation of SSRAM is proposed through fracture mechanics theory and the increase of velocity is exponential.Considering the high-temperature deformation resistance and low-temperature fracture property,the SSRAM surface layer with 40%steel slag content showed a batter application potential.

Study on the effect of thermal deformation on the liquid seal of high-temperature molten salt pump in molten salt reactor

The high-temperature molten salt pump is the core equipment in a molten salt reactor that drives the flow of the molten salt coolant.Rotor stability is key to the continuous and reliable operation of the molten salt pump,and the liquid seal at the wear ring can affect the dynamic characteristics of the rotor system.When the molten salt pump is operated in the hightemperature molten salt medium,thermal deformation of the submerged parts inevitably occurs,changing clearance between the stator and rotor,affecting the leakage and dynamic characteristics of the seal.In this study,the seal leakage,seal dynamic characteristics,and rotor system dynamic characteristics are simulated and analyzed using finite element simulation software based on two cases of considering the effect of seal thermal deformation effect or not.The results show a significant difference in the leakage characteristics and dynamic characteristics of the seal obtained by considering the effect of seal thermal deformation and neglecting the effect of thermal deformation.The leakage flow rate decreases,and the first-order critical speed of the seal-bearing-rotor system decrease after considering the seal’s thermal deformation.

High-temperature deformation behaviors of Ti-2Al-9.2Mo-2Fe alloy with boron

Hot deformation behaviors of Ti-2Al-9.2Mo-2Fe alloy with boron were investigated in a hot compression test at temperatures ranging from 850 to 1000℃and strain rates ranging from 0.01 to 10.00 s^(-1).With strain rate decreasing and deformation temperature increasing,dynamic recrystallization(DRX)was promoted in both alloys.The nucleation mechanism of DRX involved grain boundary bulging and subgrain rotation.In case of deformation at low temperatures and high strain rates,the boronfree alloy only showed dynamic recovery(DRV)phenomenon.However,due to the particle-stimulated nucleation mechanism of recrystallization by TiB particles,the boron-containing alloy shows DRX at that condition.These DRX grain nuclei are formed by lattice rotation and subgrain growth from deformation zone in the initial grains,which are close to those of TiB particle.Moreover,the flow stress of the boron-containing alloy is lower than that of the boron-free alloy due to the grain refinement during hot deformation process.

Microstructure evolution of a new near-β titanium alloy:Ti555211 during high-temperature deformation

The isothermal compression testing of Ti555211 titanium alloys was carried out at deformation temperatures from 750 to 950 ℃ in 50 ℃ intervals,with strain rate of 0.001-1.000 s-1and height reduction of 20%-60%.The effect of processing parameters（deformation temperature,strain rate and deformation degree） on the microstructure evolution and the microstructure variables was investigated.The results show that the content of primary α phase decreases with the increase in deformation temperature.The effect of strain rate on microstructure variables of isothermally compressed Ti555211 alloy is mainly dependent on the deformation temperature.The fine second α phase partly transforms to β phase due to the deformation heat effect at the high strain rate,α phase becomes globular with temperature increasing and strain rate decreasing.In contrast,α phase is refined with temperature decreasing and strain rate increasing.The deformation degree has a little influence on the grain size and the morphology of primary α phase,but the effect of deformation degree on the morphology of second α phase is significant.The larger deformation degree is in favor of the globularization of lamellar α structure.

Application of GNSS-PPP on Dynamic Deformation Monitoring of Offshore Platforms

The real-time dynamic deformation monitoring of offshore platforms under environmental excitation is crucial to their safe operation.Although Global Navigation Satellite System-Precise Point Positioning(GNSS-PPP)has been considered for this purpose,its monitoring accuracy is relatively low.Moreover,the influence of background noise on the dynamic monitoring accuracy of GNSS-PPP remains unclear.Hence,it is imperative to further validate the feasibility of GNSS-PPP for deformation monitoring of offshore platforms.To address these concerns,vibration table tests with different amplitudes and frequencies are conducted.The results demonstrate that GNSS-PPP can effectively monitor horizontal vibration displacement as low as±30 mm,which is consistent with GNSS-RTK.Furthermore,the spectral characteristic of background noise in GNSS-PPP is similar to that of GNSS-RTK(Real Time Kinematic).Building on this observation,an improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise(CEEMDAN)has been proposed to de-noise the data and enhance the dynamic monitoring accuracy of GNSS-PPP.Field monitoring application research is also undertaken,successfully extracting and analyzing the dynamic deformation of an offshore platform structure under environmental excitation using GNSS-PPP monitoring in conjunction with improved CEEMDAN de-noising.By comparing the de-noised dynamic deformation trajectories of the offshore platform during different periods,it is observed that the platform exhibits reversible alternating vibration responses under environmental excitation,with more pronounced displacement deformation in the direction of load action.The research results confirm the feasibility and potential of GNSS-PPP for dynamic deformation monitoring of offshore platforms.

Liquefaction susceptibility and deformation characteristics of saturated coral sandy soils subjected to cyclic loadings-a critical review

Coral sandy soils widely exist in coral island reefs and seashores in tropical and subtropical regions.Due to the unique marine depositional environment of coral sandy soils,the engineering characteristics and responses of these soils subjected to monotonic and cyclic loadings have been a subject of intense interest among the geotechnical and earthquake engineering communities.This paper critically reviews the progress of experimental investigations on the undrained behavior of coral sandy soils under monotonic and cyclic loadings over the last three decades.The focus of coverage includes the contractive-dilative behavior,the pattern of excess pore-water pressure(EPWP)generation and the liquefaction mechanism and liquefaction resistance,the small-strain shear modulus and strain-dependent shear modulus and damping,the cyclic softening feature,and the anisotropic characteristics of undrained responses of saturated coral sandy soils.In particular,the advances made in the past decades are reviewed from the following aspects:(1)the characterization of factors that impact the mechanism and patterns of EPWP build-up;(2)the identification of liquefaction triggering in terms of the apparent viscosity and the average flow coefficient;(3)the establishment of the invariable form of strain-based,stress-based,or energy-based EPWP ratio formulas and the unique relationship between the new proxy of liquefaction resistance and the number of cycles required to reach liquefaction;(4)the establishment of the invariable form of the predictive formulas of small strain modulus and strain-dependent shear modulus;and(5)the investigation on the effects of stress-induced anisotropy on liquefaction susceptibility and dynamic deformation characteristics.Insights gained through the critical review of these advances in the past decades offer a perspective for future research to further resolve the fundamental issues concerning the liquefaction mechanism and responses of coral sandy sites subjected to cyclic loadings associated with seismic events in marine environments.

Harness High-Temperature Thermal Energy via Elastic Thermoelectric Aerogels

Despite notable progress in thermoelectric(TE)materials and devices,developing TE aerogels with high-temperature resistance,superior TE performance and excellent elasticity to enable self-powered high-temperature monitoring/warning in industrial and wearable applications remains a great challenge.Herein,a highly elastic,flame-retardant and high-temperature-resistant TE aerogel,made of poly(3,4-ethylene dioxythiophene):poly(styrenesulfonate)/single-walled carbon nanotube(PEDOT:PSS/SWCNT)composites,has been fabricated,displaying attractive compression-induced power factor enhancement.The as-fabricated sensors with the aerogel can achieve accurately pressure stimuli detection and wide temperature range monitoring.Subsequently,a flexible TE generator is assembled,consisting of 25 aerogels connected in series,capable of delivering a maximum output power of 400μW when subjected to a temperature difference of 300 K.This demonstrates its outstanding high-temperature heat harvesting capability and promising application prospects for real-time temperature monitoring on industrial high-temperature pipelines.Moreover,the designed self-powered wearable sensing glove can realize precise wide-range temperature detection,high-temperature warning and accurate recognition of human hand gestures.The aerogel-based intelligent wearable sensing system developed for firefighters demonstrates the desired self-powered and highly sensitive high-temperature fire warning capability.Benefitting from these desirable properties,the elastic and high-temperature-resistant aerogels present various promising applications including self-powered high-temperature monitoring,industrial overheat warning,waste heat energy recycling and even wearable healthcare.

High-temperature deformation behaviour of duplex stainless steel with hard boronised layer

In order to understand the high-temperature deformation behaviour of alloy having hard surface layer,thermo-mechanically treated duplex stainless steel(DSS)is boronised for 0.75-6 h at 1223 K and subsequently deformed under compression mode at the same temperature under strain rate condition of 1×10^(-3),2×10^(-4) and 6×10^(-5) s^(-1) until strain of 0.4.The substrate microstructure is almost isotropic with grain size after boronising with layer thickness between 1.61 and 2.74μm.X-ray diffraction results confirm the formation of boride on DSS surface.The surface hardness of DSS increases from 387 to 1000-2400 HV after boronising.Uniform boronised layer with thickness of 20-40μm is formed at DSS surface.Compression results show that the flow stress of the deformation increases with the strain rate and boronising time.For the boronised samples,the flow stress range is between 5 and 89 MPa.To determine the actual effect of the boronised layer on the flow stress,the results are also compared with those from un-boronised samples having similar microstructure.The results suggest that at a constant grain size,even with the hardest layer,the effect of hard surface layer on the flow stress almost could be negligible when the deformation rate is slow,but at faster deformation rate,even in the layer with the least hardness,the flow stress shows a significant increase.It is also observed that the hard boride surface disintegration could be avoided at a sufficiently low deformation flow stress that could be attributed to superplasticity.

Deformation monitoring of long-span railway bridges based on SBAS-InSAR technology

The deformation monitoring of long-span railway bridges is significant to ensure the safety of human life and property.The interferometric synthetic aperture radar(In SAR)technology has the advantage of high accuracy in bridge deformation monitoring.This study monitored the deformation of the Ganjiang Super Bridge based on the small baseline subsets(SBAS)In SAR technology and Sentinel-1A data.We analyzed the deformation results combined with bridge structure,temperature,and riverbed sediment scouring.The results are as follows:(1)The Ganjiang Super Bridge area is stable overall,with deformation rates ranging from-15.6 mm/yr to 10.7 mm/yr(2)The settlement of the Ganjiang Super Bridge deck gradually increases from the bridge tower toward the main span,which conforms to the typical deformation pattern of a cable-stayed bridge.(3)The sediment scouring from the riverbed cause the serious settlement on the bridge’s east side compared with that on the west side.(4)The bridge deformation negatively correlates with temperature,with a faster settlement at a higher temperature and a slow rebound trend at a lower temperature.The study findings can provide scientific data support for the health monitoring of long-span railway bridges.

Synergistic effect of Zr and Mo on precipitation and high-temperature properties of Al-Si-Cu-Mg alloys

This study focuses on finding a solution to the sharp decline in mechanical properties of Al-Si-Cu-Mg alloys due to rapid coarsening of traditional intermediate phases at high temperature.A new type of modified al oy,to be used in automobile engines at high temperatures,was prepared by adding Zr and Mo into Al-Si-Cu-Mg alloy.The synergistic effects of Zr and Mo on the microstructure evolution and high-temperature mechanical properties were studied.Results show that the addition of Zr and Mo generates a series of intermetallic phases dispersed in the alloy.They can improve the strength of the alloy by hindering dislocation movement and crack propagation.In addition,some nano-strengthened phases show coherent interfaces with the matrix and improve grain refinement.The addition of Mo greatly improves the heat resistance of the alloy.The extremely low diffusivity of Mo enables it to improve the thermal stability of the intermetallic phases,inhibit precipitation during aging,reduce the size of the precipitates,and improve the heat resistance of the alloy.

HZSM-5 zeolites undergoing the high-temperature process for boosting the bimolecular reaction in n-heptane catalytic cracking

High-temperature treatment is key to the preparation of zeolite catalysts.Herein,the effects of hightemperature treatment on the property and performance of HZSM-5 zeolites were studied in this work.X-Ray diffraction,N2physisorption,27Al magic angle spinning nuclear magnetic resonance(MAS NMR),and temperature-programmed desorption of ammonia results indicated that the hightemperature treatment at 650℃ hardly affected the inherent crystal and texture of HZSM-5zeolites but facilitated the conversion of framework Al to extra-framework Al,reducing the acid site and enhancing the acid strength.Moreover,the high-temperature treatment improved the performance of HZSM-5 zeolites in n-heptane catalytic cracking,promoting the conversion and light olefins yield while inhibiting coke formation.Based on the kinetic and mechanism analysis,the improvement of HZSM-5 performance caused by high-temperature treatment has been attributed to the formation of extra-framework Al,which enhanced the acid strength,facilitated the bimolecular reaction,and promoted the entropy change to overcome a higher energy barrier in n-heptane catalytic cracking.

Effect of deformation parameters on the austenite dynamic recrystallization behavior of a eutectoid pearlite rail steel

Understandings of the effect of hot deformation parameters close to the practical production line on grain refinement are crucial for enhancing both the strength and toughness of future rail steels.In this work,the austenite dynamic recrystallization(DRX)behaviors of a eutectoid pearlite rail steel were studied using a thermo-mechanical simulator with hot deformation parameters frequently employed in rail production lines.The single-pass hot deformation results reveal that the prior austenite grain sizes(PAGSs)for samples with different deformation reductions decrease initially with an increase in deformation temperature.However,once the deformation temperature is beyond a certain threshold,the PAGSs start to increase.It can be attributed to the rise in DRX volume fraction and the increase of DRX grain with deformation temperature,respectively.Three-pass hot deformation results show that the accumulated strain generated in the first and second deformation passes can increase the extent of DRX.In the case of complete DRX,PAGS is predominantly determined by the deformation temperature of the final pass.It suggests a strategic approach during industrial production where part of the deformation reduction in low temperature range can be shifted to the medium temperature range to release rolling mill loads.

A Novel Fracturing Fluid with High-Temperature Resistance for Ultra-Deep Reservoirs

Ultra-deep reservoirs play an important role at present in fossil energy exploitation.Due to the related high temperature,high pressure,and high formation fracture pressure,however,methods for oil well stimulation do not produce satisfactory results when conventional fracturing fluids with a low pumping rate are used.In response to the above problem,a fracturing fluid with a density of 1.2~1.4 g/cm^(3)was developed by using Potassium formatted,hydroxypropyl guanidine gum and zirconium crosslinking agents.The fracturing fluid was tested and its ability to maintain a viscosity of 100 mPa.s over more than 60 min was verified under a shear rate of 1701/s and at a temperature of 175℃.This fluid has good sand-carrying performances,a low viscosity after breaking the rubber,and the residue content is less than 200 mg/L.Compared with ordinary reconstruction fluid,it can increase the density by 30%~40%and reduce the wellhead pressure of 8000 m level reconstruction wells.Moreover,the new fracturing fluid can significantly mitigate safety risks.

Mechanical Behavior and Microstructure Evolution during Tensile Deformation of Twinning Induced Plasticity Steel Processed by Warm Forgings

The mechanical behavior and microstructural evolution of an Fe-30Mn-3Al-3Si twinninginduced plasticity(TWIP)steel processed using warm forging was investigated.It is found that steel processed via warm forging improves comprehensive mechanical properties compared to the TWIP steel processed via cold rolling,with a high tensile strength(R_(m))of 793 MPa,a yield strength(R_(P))of 682 MPa,an extremely large R_(P)/R_(m)ratio as high as 0.86 as well as an excellent elongation rate of 46.8%.The microstructure observation demonstrates that steel processed by warm forging consists of large and elongated grains together with fine,equiaxed grains.Complicated micro-defect configurations were also observed within the steel,including dense dislocation networks and a few coarse deformation twins.As the plastic deformation proceeds,the densities of dislocations and deformation twins significantly increase.Moreover,a great number of slip lines could be observed in the elongated grains.These findings reveal that a much more dramatic interaction between microstructural defect and dislocations glide takes place in the forging sample,wherein the fine and equiaxed grains propagated dislocations more rapidly,together with initial defect configurations,are responsible for enhanced strength properties.Meanwhile,larger,elongated grains with more prevalently activated deformation twins result in high plasticity.

Unraveling engineering disturbance effects on deformation in red-bed mudstone railway cuttings:incorporating crack-facilitated moisture diffusion

Red-bed mudstone, prevalent in southwest China, poses a formidable challenge due to its hydrophilic clay minerals, resulting in expansion, deformation, and cracking upon exposure to moisture. This study addresses uplift deformation disasters in high-speed railways by employing a moisture diffusion-deformation-fracture coupling model based on the finite-discrete element method(FDEM). The model integrates the influence of cracks on moisture diffusion. The investigation into various excavation depths reveals a direct correlation between depth and the formation of tensile cracks at the bottom of the railway cutting. These cracks expedite moisture migration, significantly impacting the temporal and spatial evolution of the moisture field. Additionally, crack expansion dominates hygroscopic deformation, with the lateral coordinate of the crack zone determining peak vertical displacement. Furthermore, key factors influencing deformation in railway cuttings, including the swelling factor and initial moisture content at the bottom of the cutting, are explored. The number of tensile and shear cracks increases with greater excavation depth, particularly concerning shear cracks. Higher swelling factors and initial moisture contents result in an increased total number of cracks, predominantly shear cracks. Numerical calculations provide valuable insights, offering a scientific foundation and directional guidance for the precise prevention, control, prediction, and comprehensive treatment of mudstone-related issues in high-speed railways.

Kinematic deformation and intensity assessment of the 2021 Maduo M_(S)7.4 earthquake in Qinghai revealed by high-frequency GNSS

Rapid acquisition of the kinematic deformation field and seismic intensity distribution of large earthquakes is crucial for postseismic emergency rescue,disaster assessment,and future seismic risk research.The advancement of GNSS observation and data processing makes it play an important role in this field,especially the high-frequency GNSS.We used the differential positioning method to calculate the 1 HZ GNSS data from 98 sites within 1000 km of the M_(S)7.4 Maduo earthquake epicenter.The kinematic deformation field and the distribution of the seismic intensity by using the peak ground velocity derived from displacement waveforms were obtained.The results show that:1)Horizontal coseismic response deformation levels ranging from 25 mm to 301 mm can be observed within a 1000 km radius from the epicenter.Coseismic response deformation on the east and west sides shows bilateral asymmetry,which markedly differs from the symmetry presented by surface rupture.2)The seismic intensity obtained through high-frequency GNSS and field investigations exhibits good consistency of the scope and orientation in the high seismic intensity area,although the former is generally slightly smaller than the latter.3)There may exist obstacles on the eastern side of the seismogenic fault.The Maduo earthquake induced a certain tectonic stress loading effect on the western Kunlun Pass-Jiangcuo fault(KPJF)and Maqin-Maqu segment,resulting in higher seismic risk in the future.

Impact of initial fluctuations and nuclear deformations in isobar collisions

Relativistic isobar^(96)_(44)Ru+^(96)_(44)Ru and^(96)_(40)Zr+^(96)_(40)Zrcollisions have revealed intricate differences in their nuclear size and shape,inspiring unconventional studies of nuclear structure using relativistic heavy ion collisions.In this study,we investigate the relative differences in the mean multiplicityR_(<Nch>)and the secondR_(ε2)and third-order eccentricityR_(ε3)between isobar collisions using initial state Glauber models.It is found that initial fluctuations and nuclear deformations have negligible effects on R_(<Nch>)in most central collisions,while both are important for the R_(ε2)and R_(ε3),the degree of which is sensitive to the underlying nucleonic or sub-nucleonic degree of freedom.These features,compared to real data,may probe the particle production mechanism and the physics underlying nuclear structure.

Novel Method for Evaluating the Aging of Aviation Turbine Engine Oils via High-Temperature Bearing Deposit Tests

Aviation turbine engine oils require excellent thermal-oxidative stability because of their high-temperature environments.High-temperature bearing deposit testing is a mandatory method for measuring the thermal-oxidative performance of aviation lubricant oils,and the relevant apparatus was improved in the present study.Two different commercial aviation turbine engine oils were tested,one with standard performance(known as the SL oil)and the other with high thermal stability,and their thermal-oxidative stability characteristics were evaluated.After 100 h of high-temperature bearing testing,the SL oil was analyzed by using various analytical techniques to investigate its thermal-oxidative process in the bearing test,with its thermal-oxidative degradation mechanism also being discussed.The results indicate that the developed high-temperature bearing apparatus easily meets the test requirements of method 3410.1 in standard FED-STD-791D.The viscosity and total acid number(TAN)of the SL oil increased with the bearing test time,and various deposits were produced in the bearing test,with the micro-particles of the carbon deposits being sphere-like,rod-like,and sheet-like in appearance.The antioxidant additives in the oil were consumed very rapidly in the first 30 h of the bearing test,with N-phenyl-1-naphthylamine being consumed faster than dioctyldiphenylamine.Overall,the oil thermal-oxidative process involves very complex physical and chemical mechanisms.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.