Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This...Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This review explores multi-scale modeling as a tool to visualize multi-phase flow and improve mass transport in water electrolyzers.At the nanoscale,molecular dynamics(MD)simulations reveal how electrode surface features and wettability influence nanobubble nucleation and stability.Moving to the mesoscale,models such as volume of fluid(VOF)and lattice Boltzmann method(LBM)shed light on bubble transport in porous transport layers(PTLs).These insights inform innovative designs,including gradient porosity and hydrophilic-hydrophobic patterning,aimed at minimizing gas saturation.At the macroscale,VOF simulations elucidate two-phase flow regimes within channels,showing how flow field geometry and wettability affect bubble discharging.Moreover,artificial intelligence(AI)-driven surrogate models expedite the optimization process,allowing for rapid exploration of structural parameters in channel-rib flow fields and porous flow field designs.By integrating these approaches,we can bridge theoretical insights with experimental validation,ultimately enhancing water electrolyzer performance,reducing costs,and advancing affordable,high-efficiency hydrogen production.展开更多
A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz ...A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented,where the cold component models both compression and expansion states,the thermal ion component introduces the Debye approximation and melting entropy,and the thermal electron component employs the Thomas-Fermi-Kirzhnits(TFK)model.The porosity of materials is considered by introducing the dynamic porosity coefficientαand the constitutive P-αrelation,connecting the thermodynamic properties between dense and porous systems,allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones.These models enable the EOS applicable and robust at wide ranges of temperature,pressure and porosity.A systematic evaluation of the new EOS is conducted with aluminum(Al)as an example.300 K isotherm,shock Hugoniot,as well as melting curves of both dense and porous Al are calculated,which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations.Notably,it is for the first time Hugoniot P-σcurves up to 10~6 GPa and shock melting behaviors of porous Al are derived from analytical EOS models,which predict much lower compression limit and shock melting temperatures than those of dense Al.展开更多
Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative cont...Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative contributions to the overall evolution of rifting margins and possible roles in the formation of microcontinent are still elusive.Here,we use coupled geodynamic and surface processes numerical modeling to assess the extent to which surface processes may determine the formation of microcontinent during lithospheric stretching in presence or absence of a mantle plume underneath.Our modeling results indicate that fast extension rates and hillslope(i.e.,diffusion)erosion promote ridge jump events and therefore the formation of microcontinents.On the contrary,efficient fluvial erosion and far-reaching sediment transport(i.e.,stream power erosion)inhibits ridge jump events and the formation of microcontinents.The ridge jump event and overall evolution in our numerical models is consistent with the shift from the Mascarene Ridge to the Carlsberg Ridge that determined the formation of the Seychelles microcontinent.We therefore speculate that hillslope erosion,rather than fluvial erosion,was predominant during the formation of the Seychelles,a possible indication of overall dry local climate conditions.展开更多
A wide northeast-trending belt of intraplate alkaline volcanism,exhibiting similar geochemical characteristics,stretches from the Eastern Atlantic Ocean to the Cenozoic rift system in Europe.Its formation is associate...A wide northeast-trending belt of intraplate alkaline volcanism,exhibiting similar geochemical characteristics,stretches from the Eastern Atlantic Ocean to the Cenozoic rift system in Europe.Its formation is associated with both passive and active mechanisms,but it remains a source of ongoing debate among geoscientists.Here,we show that seismic whole-mantle tomography models consistently identify two extensive low-velocity anomalies beneath the Canary Islands(CEAA)and Western-Central Europe(ECRA)at mid-mantle depths,merging near the core-mantle boundary.These low-velocity features are interpreted as two connected broad plumes originating from the top of the African LLSVP,likely feeding diapir-like upwellings in the upper mantle.The CEAA rises vertically,whereas the ECRA is tilted and dissipates at mantle transition zone depths,possibly due to the interaction with the cold Alpine subducted slab,which hinders its continuity at shallower depths.While plate-boundary forces are considered the primary drivers of rifting,the hypothesis that deep mantle plumes play a role in generating volcanic activity provides a compelling explanation for the European rift-related alkaline volcanism,supported by geological,geophysical,and geochemical evidence.展开更多
The existing deep-sea sediment plume tests are mostly under small-scale static water and rarely under large-scale flowing water conditions.In this study,large-scale tank experiments of flowing water were designed and ...The existing deep-sea sediment plume tests are mostly under small-scale static water and rarely under large-scale flowing water conditions.In this study,large-scale tank experiments of flowing water were designed and conducted to investigate the morphological characteristics and concentration evolution of the sediment plumes under different discharge rates(Q)and initial sediment concentrations(c).Viscosity tests,resuspension tests and free settling tests of the sediment solution with different c values were performed to reveal the settling mechanism of the plume diffusion process.The results show that the plume diffusion morphology variation in flowing water has four stages and the plume concentration evolution has three stages.The larger the Q,the smaller the initial incidence angle at the discharge outlet,the larger the diffusion range,the poorer the stability and the more complicated the diffusion morphology.The larger the c,the larger the settling velocity,the faster the formation of high-concentration accumulation zone,the better the stability and the clearer the diffusion boundary.The research results could provide experimental data for assessing the impact of deep-sea mining on the ocean environment.展开更多
The nitrate reduction via electrochemical catalysis offers an environmentally friendly method for sustainable ammonia production and wastewater remediation.However,conventional Co-based catalysts suffer from a major l...The nitrate reduction via electrochemical catalysis offers an environmentally friendly method for sustainable ammonia production and wastewater remediation.However,conventional Co-based catalysts suffer from a major limitation:their nitrate(NO_(3)^(-))adsorption capacity remains weak.This drawback severely restricts their catalytic efficiency.To overcome this limitation,we synthesized a triphasic interface material(Cu/Co/CoO@C)via rapid joule heating and elucidated its performance-enhancing mechanisms.The exceptional catalytic performance originates from the phase interface-induced multiscale structural regulation.At the microscopic scale,electronic structure modulation through interfacial charge redistribution between Cu and Co/CoO significantly reduces intermediate adsorption energies.Co 3d and O 2p orbitals coupling generates a localized polarized electric field,enhancing NO_(3)^(-)activation.At the macroscopic scale,defect-rich structures improve mass transfer and expose abundant active sites.With the Cu/Co/CoO@C,the yield of NH_(3) is achieved to 2.03 mmol h^(-1)cm^(-2)(-0.4 V vs.RHE,Faradaic efficiency(FE)98.4%).The assembled Zn-NO_(3)^(-)battery delivered a maximum power density of 52.09 mW cm^(-2)and a NH_(3) production rate of 297.5μmol h^(-1)cm^(-2)(FE 95.4%).Based on these results,this work offers new insights into multiphase interface design.展开更多
Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to in...Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to inherent fluctuations,limited data and imperfect measurements resulting in aleatory,epistemic and measurement uncertainties of the degradation process.This paper proposes a degradation model and remaining useful life(RUL)prediction method under triple uncertainties for a category of complex equipment with multi-phase degradation and jumps.First,a multi-phase degradation model with random jumps and measurement errors is constructed based on uncertain random processes.Afterward,the analytic expression of RUL prediction considering the heterogeneity is derived by modeling the uncertainty of degradation states at change points under the concept of first hitting time.A stochastic uncertain approach is utilized for the proposed multi-phase degradation model to identify model parameters based on historical data.Furthermore,the implied degradation features are adaptively updated in online stage using similarity-based weighted stochastic uncertain maximum likelihood estimation and Kalman filtering.Finally,the effectiveness of the method is verified by simulation example and practical case.展开更多
A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting backg...A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.展开更多
A capacity model of multi-phase signalized intersections is derived by a stopping-line method. It is simplified with two normal situations： one situation involves one straight lane and one left-turn lane; the other s...A capacity model of multi-phase signalized intersections is derived by a stopping-line method. It is simplified with two normal situations： one situation involves one straight lane and one left-turn lane; the other situation involves two straight lanes and one left-turn lane. The results show that the capacity is mainly relative to signal cycle length, phase length, intersection layout and following time. With regard to the vehicles arrival rates, the optimal model is derived based on each phase＇s remaining time balance, and it is solved by Lagrange multipliers. Therefore, the calculation models of the optimal signal cycle length and phase lengths are derived and simplified. Compared to the existing models, the proposed model is more convenient and practical. Finally, a practical intersection is chosen and its signal cycles and phase lengths are calculated by the proposed model.展开更多
Mineral deposits are unevenly distributed in the Earth's crust, which is closely related to the formation and evolution of the Earth. In the early history of the Earth, controlled by the gravitational contraction ...Mineral deposits are unevenly distributed in the Earth's crust, which is closely related to the formation and evolution of the Earth. In the early history of the Earth, controlled by the gravitational contraction and thermal expansion, lighter elements, such as radioactive, halogen-family, rare and rare earth elements and alkali metals, migrated upwards; whereas heavier elements, such as iron-family and platinum-family elements, base metals and noble metals, had a tendency of sinking to the Earth's core, so that the elements iron, nickel, gold and silver are mainly concentrated in the Earth's core. However, during the formation of the stratified structure of the Earth, the existence of temperature, pressure and viscosity differences inside and outside the Earth resulted in vertical material movement manifested mainly by cascaded evolution of mantle plumes in the Earth. The stratifications and vertical movement of the Earth were interdependent and constituted the motive force of the mantle-core movement. The cascaded evolution of mantle plumes opens the passageways for the migration of deep-seated ore-forming material, and thus elements such as gold and silver concentrated in the core and on the core-mantle boundary migrate as the gaseous state together with the hot material flow of mantle plumes against the gravitational force through the passageways to the lithosphere, then migrate as the mixed gas-liquid state to the near-surface level and finally are concentrated in favorable structural expansion zones, forming mineral deposits. This is possibly the important metallogenic mechanism for gold, silver, lead, zinc, copper and other many elements. Take for example the NE-plunging crown of the Fuping mantle-branch structure, the paper analyzes ductile-brittle shear zone-type gold fields (Weijiayu) at the core of the magmatic-metamorphic complex, principal detachment-type gold fields (Shangmingyu) and hanging-wall cover fissure-vein-type lead-zinc polymetallic ore fields (Lianbaling) and further briefly analyzes the source of ore-forming material and constructs an ore-forming and -controlling model.展开更多
Using the occurrence characteristics of bubble plumes in the South China Sea as a reference, this paper continues to study the seismic responses produced by bubble plumes in the cold seepage active region. To make the...Using the occurrence characteristics of bubble plumes in the South China Sea as a reference, this paper continues to study the seismic responses produced by bubble plumes in the cold seepage active region. To make the plume modelling scheme more reasonable, we modified the original modelling scheme and reconstructed a plume water body model based on the variation of its radius as bubbles rise in seawater. The plume seismic records of shot gathers were obtained by forward simulation. The seismic records of single shot show obvious characteristics of a scattering wave field and the periodic characteristics of the model. Seismic records of shot gathers were processed using prestack depth migration. The boundary of its imaging section has a good convergence effect. The migration sections can be imaged distinctly with higher accuracy. The aforementioned studies once again laid a foundation for the further study of the seismic responses produced by plumes. They also gradually probed a more suitable seismic data processing method for plumes and provided a theoretical guidance for the identification of plumes.展开更多
To study the bubble plume's seismic response characteristics,the model of a plume water body has been built in this article using the bubble-contained medium acoustic velocity model and the stochastic medium theor...To study the bubble plume's seismic response characteristics,the model of a plume water body has been built in this article using the bubble-contained medium acoustic velocity model and the stochastic medium theory based on an analysis of both the acoustic characteristics of a bubble-contained water body and the actual features of a plume.The finite difference method is used for forward modelling,and the single-shot seismic record exhibits the characteristics of a scattered wave field generated by a plume.A meaningful conclusion is obtained by extracting seismic attributes from the pre-stack shot gather record of a plume.The values of the amplitude-related seismic attributes increase greatly as the bubble content goes up,and changes in bubble radius will not cause seismic attributes to change,which is primarily observed because the bubble content has a strong impact on the plume's acoustic velocity,while the bubble radius has a weak impact on the acoustic velocity.The above conclusion provides a theoretical reference for identifying hydrate plumes using seismic methods and contributes to further study on hydrate decomposition and migration,as well as on distribution of the methane bubble in seawater.展开更多
The fluid of casting process is a typical kind of multi-phase flow. Actually, many casting phenomena have close relationship with the multi-phase flow, such as molten metal filling process, air entrapment, slag moveme...The fluid of casting process is a typical kind of multi-phase flow. Actually, many casting phenomena have close relationship with the multi-phase flow, such as molten metal filling process, air entrapment, slag movement, venting process of die casting, gas escaping of lost foam casting and so on. Obviously, in order to analyze these phenomena accurately, numerical simulation of the multi-phase fluid is necessary. Unfortunately, so far, most of the commercial casting simulation systems do not have the ability of multi-phase flow modeling due to the difficulty in the multi-phase flow calculation. In the paper, Finite Different Method (FDM) technique was adopt to solve the multi-phase fluid model. And a simple object of the muiti-phase fluid was analyzed to obtain the fluid rates of the liquid phase and the entrapped air phase.展开更多
The hydrocarbon detection techniques used currently are generally based on the theory of single-phase medium, but hydrocarbon reservoir mostly is multi-phase medium, therefore, multisolutions and uncertainties are exi...The hydrocarbon detection techniques used currently are generally based on the theory of single-phase medium, but hydrocarbon reservoir mostly is multi-phase medium, therefore, multisolutions and uncertainties are existed in the result of hydrocarbon detection. This paper presents a fast way to detect hydrocarbon in accordance with BOIT theory and laboratory data. The technique called DHAF technique has been applied to several survey area and obtained good result where the coincidence rate for hydrocarbon detection is higher than other similar techniques. The method shows a good prospect of the application in hydrocarbon detecting at exploration stage and in reservoir monitoring at production stage.展开更多
Polyamide/acrylonitrile-butadiene-styrene copolymer(PA/ABS) blends have drawn considerable attention from both academia and industry for their important applications in automotive and electronic areas. Due to poor mis...Polyamide/acrylonitrile-butadiene-styrene copolymer(PA/ABS) blends have drawn considerable attention from both academia and industry for their important applications in automotive and electronic areas. Due to poor miscibility of PA and ABS, developing an effective compatibilization strategy has been an urgent challenge to achieve prominent mechanical properties. In this study, we create a set of mechanically enhanced PA6/ABS blends using two multi-monomer melt-grafted compatibilizers, SEBSg-(MAH-co-St) and ABS-g-(MAH-co-St). The dispersed domain size is significantly decreased and meanwhile the unique "soft shell-encapsulating-hard core" structures form in the presence of compatibilizers. The optimum mechanical performances manifest an increase of 36% in tensile strength and an increase of 1300% in impact strength, compared with the neat PA6/ABS binary blend.展开更多
The infrared（IR） irradiance signature from rocket motor exhaust plumes is closely related to motor type,propellant composition,burn time,rocket geometry,chamber parameters and flight conditions.In this paper,an infr...The infrared（IR） irradiance signature from rocket motor exhaust plumes is closely related to motor type,propellant composition,burn time,rocket geometry,chamber parameters and flight conditions.In this paper,an infrared signature analysis tool（IRSAT） was developed to understand the spectral characteristics of exhaust plumes in detail.Through a finite volume technique,flow field properties were obtained through the solution of axisymmetric Navier-Stokes equations with the Reynolds-averaged approach.A refined 13-species,30-reaction chemistry scheme was used for combustion effects and a k-e-Rtturbulence model for entrainment effects.Using flowfield properties as input data,the spectrum was integrated with a line of sight（LOS） method based on a single line group（SLG） model with Curtis-Godson approximation.The model correctly predicted spectral distribution in the wavelengths of 1.50–5.50 lm and had good agreement for its location with imaging spectrometer data.The IRSAT was then applied to discuss the effects of three operating conditions on IR signatures：（a） afterburning;（b） chamber pressure from ignition to cutoff;and（c） minor changes in the ratio of hydroxyl-terminated polybutadiene（HTPB） binder to ammonium perchlorate（AP） oxidizer in propellant.Results show that afterburning effects can increase the size and shape of radiance images with enhancement of radiation intensity up to 40%.Also,the total IR irradiance in different bands can be characterized by a non-dimensional chamber pressure trace in which the maximum discrepancy is less than 13% during ignition and engine cutoff.An increase of chamber pressure can lead to more distinct diamonds,whose distance intervals are extended,and the position of the first diamond moving backwards.In addition,an increase in HTPB/AP causes a significant jump in spectral intensity.The incremental rates of radiance intensity integrated in each band are linear with the increase of HTPB,and the growth rates of radiance intensities in some bands reach up to 50% as HTPB weight increases by 3%.展开更多
The origin of zircon grains, and other exotic minerals of typical crustal origin, in mantle-hosted ophiolitic chromitites are hotly debated. We report a population of zircon grains with ages ranging from Cretaceous(99...The origin of zircon grains, and other exotic minerals of typical crustal origin, in mantle-hosted ophiolitic chromitites are hotly debated. We report a population of zircon grains with ages ranging from Cretaceous(99 Ma) to Neoarchean(2750 Ma), separated from massive chromitite bodies hosted in the mantle section of the supra-subduction(SSZ)-type Mayari-Baracoa Ophiolitic Belt in eastern Cuba. Most analyzed zircon grains(n = 20, 287 ± 3 Ma to 2750 ± 60 Ma) are older than the early Cretaceous age of the ophiolite body, show negativeε_(Hf)(t)(-26 to-0.6) and occasional inclusions of quartz, K-feldspar,biotite, and apatite that indicate derivation from a granitic continental crust. In contrast, 5 mainly rounded zircon grains(297±5 Ma to 2126±27 Ma) show positive εHf(t)(+0.7 to +13.5) and occasional apatite inclusions, suggesting their possible crystallization from melts derived from juvenile(mantle)sources. Interestingly, younger zircon grains are mainly euhedral to subhedral crystals, whereas older zircon grains are predominantly rounded grains. A comparison of the ages and Hf isotopic compositions of the zircon grains with those of nearby exposed crustal terranes suggest that chromitite zircon grains are similar to those reported from terranes of Mexico and northern South America. Hence, chromitite zircon grains are interpreted as sedimentary-derived xenocrystic grains that were delivered into the mantle wedge beneath the Greater Antilles intra-oceanic volcanic arc by metasomatic fluids/melts during subduction processes. Thus, continental crust recycling by subduction could explain all populations of old xenocrystic zircon in Cretaceous mantle-hosted chromitites from eastern Cuba ophiolite.We integrate the results of this study with petrological-thermomechanical modeling and existing geodynamic models to propose that ancient zircon xenocrysts, with a wide spectrum of ages and Hf isotopic compositions, can be transferred to the mantle wedge above subducting slabs by cold plumes.展开更多
In the petroleum industry,detection of multi-phase fluid flow is very important in both surface and down-hole measurements.Accurate measurement of high rate of water or gas multi-phase flow has always been an academic...In the petroleum industry,detection of multi-phase fluid flow is very important in both surface and down-hole measurements.Accurate measurement of high rate of water or gas multi-phase flow has always been an academic and industrial focus.NMR is an efficient and accurate technique for the detection of fluids;it is widely used in the determination of fluid compositions and properties.This paper is aimed to quantitatively detect multi-phase flow in oil and gas wells and pipelines and to propose an innovative method for online nuclear magnetic resonance(NMR)detection.The online NMR data acquisition,processing and interpretation methods are proposed to fill the blank of traditional methods.A full-bore straight tube design without pressure drop,a Halbach magnet structure design with zero magnetic leakage outside the probe,a separate antenna structure design without flowing effects on NMR measurement and automatic control technology will achieve unattended operation.Through the innovation of this work,the application of NMR for the real-time and quantitative detection of multi-phase flow in oil and gas wells and pipelines can be implemented.展开更多
The rapid construction of artificial reservoirs in metropolises has promoted the emergence of city-river-reservoir systems worldwide.This study investigated the environmental behaviors and risks of heavy metals in the...The rapid construction of artificial reservoirs in metropolises has promoted the emergence of city-river-reservoir systems worldwide.This study investigated the environmental behaviors and risks of heavy metals in the aquatic environment of a typical system composed of main watersheds in Suzhou and Jinze Reservoir in Shanghai.Results shown that Mn,Zn and Cu were the dominant metals detected in multiple phases.Cd,Mn and Zn were mainly presented in exchangeable fraction and exhibited high bioavailability.Great proportion and high mobility of metals were found in suspended particulate matter(SPM),suggesting that SPM can greatly affect metal multi-phase distribution process.Spatially,city system(Ci S)exhibited more serious metal pollution and higher ecological risk than river system(Ri S)and reservoir system(Re S)owing to the diverse emission sources.Ci S and Re S were regarded as critical pollution source and sink,respectively,while Ri S was a vital transportation aisle.Microbial community in sediments exhibited evident spatial variation and obviously modified by exchangeable metals and nutrients.In particular,Bacteroidetes and Firmicutes presented significant positive correlations with most exchangeable metals.Risk assessment implied that As,Sb and Ni in water may pose potential carcinogenic risk to human health.Nevertheless,Re S was in a fairly safe state.Hg was the main risk contributor in SPM,while Cu,Zn,Ni and Sb showed moderate risk in sediments.Overall,Hg,Sb and Ci S were screened out as priority metals and system,respectively.More attention should be paid to these priority issues to promote the sustainable development of the watershed.展开更多
Based on the fundamental equations of the mechanics of solid continuum,the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed...Based on the fundamental equations of the mechanics of solid continuum,the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix,imaginarily divided into identical cells with dimensions equal to inter-particle distances,containing a central spherical particle with or without a spherical envelope on the particle surface.Consequently,the multi-particle-(envelope)-matrix system,as a model system regarding the analytical modelling,is applicable to four types of multi-phase materials.As functions of the particle volume fraction v,the inter-particle distances dl,d2,d3 along three mutually per-pendicular axes,and the particle and envelope radii,R1 and R2,respectively,the thermal stresses within the cell,are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep-resented by the matrix,envelope and particle.Analytical-(experimental)-computational lifetime prediction methods for multi-phase materials are proposed,which can be used in engineering with appropriate values of parameters of real multi-phase materials.展开更多
基金supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region,China(Project No.15308024)a grant from Research Centre for Carbon-Strategic Catalysis,The Hong Kong Polytechnic University(CE2X).
文摘Water electrolyzers play a crucial role in green hydrogen production.However,their efficiency and scalability are often compromised by bubble dynamics across various scales,from nanoscale to macroscale components.This review explores multi-scale modeling as a tool to visualize multi-phase flow and improve mass transport in water electrolyzers.At the nanoscale,molecular dynamics(MD)simulations reveal how electrode surface features and wettability influence nanobubble nucleation and stability.Moving to the mesoscale,models such as volume of fluid(VOF)and lattice Boltzmann method(LBM)shed light on bubble transport in porous transport layers(PTLs).These insights inform innovative designs,including gradient porosity and hydrophilic-hydrophobic patterning,aimed at minimizing gas saturation.At the macroscale,VOF simulations elucidate two-phase flow regimes within channels,showing how flow field geometry and wettability affect bubble discharging.Moreover,artificial intelligence(AI)-driven surrogate models expedite the optimization process,allowing for rapid exploration of structural parameters in channel-rib flow fields and porous flow field designs.By integrating these approaches,we can bridge theoretical insights with experimental validation,ultimately enhancing water electrolyzer performance,reducing costs,and advancing affordable,high-efficiency hydrogen production.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12205023,U2230401,12374056,U23A20537,11904027)。
文摘A thermodynamically complete multi-phase equation of state(EOS)applicable to both dense and porous metals at wide ranges of temperature and pressure is constructed.A standard three-term decomposition of the Helmholtz free energy as a function of specific volume and temperature is presented,where the cold component models both compression and expansion states,the thermal ion component introduces the Debye approximation and melting entropy,and the thermal electron component employs the Thomas-Fermi-Kirzhnits(TFK)model.The porosity of materials is considered by introducing the dynamic porosity coefficientαand the constitutive P-αrelation,connecting the thermodynamic properties between dense and porous systems,allowing for an accurate description of the volume decrease caused by void collapse while maintaining the quasi-static thermodynamic properties of porous systems identical to the dense ones.These models enable the EOS applicable and robust at wide ranges of temperature,pressure and porosity.A systematic evaluation of the new EOS is conducted with aluminum(Al)as an example.300 K isotherm,shock Hugoniot,as well as melting curves of both dense and porous Al are calculated,which shows great agreements with experimental data and validates the effectiveness of the models and the accuracy of parameterizations.Notably,it is for the first time Hugoniot P-σcurves up to 10~6 GPa and shock melting behaviors of porous Al are derived from analytical EOS models,which predict much lower compression limit and shock melting temperatures than those of dense Al.
基金financially supported by the National Science Foundation of China(No.41920104010)the China Postdoctoral Science Foundation(No.2024M762767)+3 种基金the Fundamental Research Funds for the Central University,CHD(No.300102264104)by the Postdoctoral Fellowship Program of CPSF(No.GZC20241444)supported by Fondazione Cariplo and Fondazione CDP(No.2022-1546_001)by the Italian Ministry of Education,MUR(Project Dipartimenti di Eccellenza,TECLA,Department of Earth and Environmental Sciences,University of Milano-Bicocca)。
文摘Mantle plumes and surface erosion and sediment deposition affect the modes of continental lithospheric rupturing in extensional tectonic settings,modulating the evolution of rifting margins.However,their relative contributions to the overall evolution of rifting margins and possible roles in the formation of microcontinent are still elusive.Here,we use coupled geodynamic and surface processes numerical modeling to assess the extent to which surface processes may determine the formation of microcontinent during lithospheric stretching in presence or absence of a mantle plume underneath.Our modeling results indicate that fast extension rates and hillslope(i.e.,diffusion)erosion promote ridge jump events and therefore the formation of microcontinents.On the contrary,efficient fluvial erosion and far-reaching sediment transport(i.e.,stream power erosion)inhibits ridge jump events and the formation of microcontinents.The ridge jump event and overall evolution in our numerical models is consistent with the shift from the Mascarene Ridge to the Carlsberg Ridge that determined the formation of the Seychelles microcontinent.We therefore speculate that hillslope erosion,rather than fluvial erosion,was predominant during the formation of the Seychelles,a possible indication of overall dry local climate conditions.
基金supported by grant D86-RALMI23CIVIE_01 awarded by the Italian Ministry of University and Research under the Program for Young Researchers“Rita Levi Montalcini”.
文摘A wide northeast-trending belt of intraplate alkaline volcanism,exhibiting similar geochemical characteristics,stretches from the Eastern Atlantic Ocean to the Cenozoic rift system in Europe.Its formation is associated with both passive and active mechanisms,but it remains a source of ongoing debate among geoscientists.Here,we show that seismic whole-mantle tomography models consistently identify two extensive low-velocity anomalies beneath the Canary Islands(CEAA)and Western-Central Europe(ECRA)at mid-mantle depths,merging near the core-mantle boundary.These low-velocity features are interpreted as two connected broad plumes originating from the top of the African LLSVP,likely feeding diapir-like upwellings in the upper mantle.The CEAA rises vertically,whereas the ECRA is tilted and dissipates at mantle transition zone depths,possibly due to the interaction with the cold Alpine subducted slab,which hinders its continuity at shallower depths.While plate-boundary forces are considered the primary drivers of rifting,the hypothesis that deep mantle plumes play a role in generating volcanic activity provides a compelling explanation for the European rift-related alkaline volcanism,supported by geological,geophysical,and geochemical evidence.
基金supported by the Major Project of Hunan Natural Science Foundation,China(No.2021JC0010)the National Natural Science Foundation of China(No.51274251)。
文摘The existing deep-sea sediment plume tests are mostly under small-scale static water and rarely under large-scale flowing water conditions.In this study,large-scale tank experiments of flowing water were designed and conducted to investigate the morphological characteristics and concentration evolution of the sediment plumes under different discharge rates(Q)and initial sediment concentrations(c).Viscosity tests,resuspension tests and free settling tests of the sediment solution with different c values were performed to reveal the settling mechanism of the plume diffusion process.The results show that the plume diffusion morphology variation in flowing water has four stages and the plume concentration evolution has three stages.The larger the Q,the smaller the initial incidence angle at the discharge outlet,the larger the diffusion range,the poorer the stability and the more complicated the diffusion morphology.The larger the c,the larger the settling velocity,the faster the formation of high-concentration accumulation zone,the better the stability and the clearer the diffusion boundary.The research results could provide experimental data for assessing the impact of deep-sea mining on the ocean environment.
基金financial support provided by the National Natural Science Foundation of Yunnan Province(202301AS070040,202301AU070209)the Major Science and Technology Projects of Yunnan Province(202302AB080019-3)+3 种基金the Scientific Research Fund Project of Yunnan Provincial Department of Education(2023J0033)the Laboratory of Solid-State Ions for Green Energy of Yunnan Universitythe Analysis and Measurements Center of Yunnan University for the sample testing servicethe Electron Microscope Center of Yunnan University for the support of this work。
文摘The nitrate reduction via electrochemical catalysis offers an environmentally friendly method for sustainable ammonia production and wastewater remediation.However,conventional Co-based catalysts suffer from a major limitation:their nitrate(NO_(3)^(-))adsorption capacity remains weak.This drawback severely restricts their catalytic efficiency.To overcome this limitation,we synthesized a triphasic interface material(Cu/Co/CoO@C)via rapid joule heating and elucidated its performance-enhancing mechanisms.The exceptional catalytic performance originates from the phase interface-induced multiscale structural regulation.At the microscopic scale,electronic structure modulation through interfacial charge redistribution between Cu and Co/CoO significantly reduces intermediate adsorption energies.Co 3d and O 2p orbitals coupling generates a localized polarized electric field,enhancing NO_(3)^(-)activation.At the macroscopic scale,defect-rich structures improve mass transfer and expose abundant active sites.With the Cu/Co/CoO@C,the yield of NH_(3) is achieved to 2.03 mmol h^(-1)cm^(-2)(-0.4 V vs.RHE,Faradaic efficiency(FE)98.4%).The assembled Zn-NO_(3)^(-)battery delivered a maximum power density of 52.09 mW cm^(-2)and a NH_(3) production rate of 297.5μmol h^(-1)cm^(-2)(FE 95.4%).Based on these results,this work offers new insights into multiphase interface design.
基金supported by the National Key Research and Development Program of China(2021YFB3301200)the National Natural Science Foundation of China(NSFC)(U21A20483,62373040,62203042).
文摘Due to abrupt changes in the intrinsic degradation mechanism or shock from external environmental pressure,degradations of some equipment are characterized by multi-phase and jumps.Meanwhile,equipment is subject to inherent fluctuations,limited data and imperfect measurements resulting in aleatory,epistemic and measurement uncertainties of the degradation process.This paper proposes a degradation model and remaining useful life(RUL)prediction method under triple uncertainties for a category of complex equipment with multi-phase degradation and jumps.First,a multi-phase degradation model with random jumps and measurement errors is constructed based on uncertain random processes.Afterward,the analytic expression of RUL prediction considering the heterogeneity is derived by modeling the uncertainty of degradation states at change points under the concept of first hitting time.A stochastic uncertain approach is utilized for the proposed multi-phase degradation model to identify model parameters based on historical data.Furthermore,the implied degradation features are adaptively updated in online stage using similarity-based weighted stochastic uncertain maximum likelihood estimation and Kalman filtering.Finally,the effectiveness of the method is verified by simulation example and practical case.
文摘A new multi-phase active contour model is proposed for the image segmentation. It is a generalization of the C-V model with the following characteristics： （1） A key technique, called the technique of painting background （TPBG）, is developed to remove the information of the background, which blocks the detection of weak boundaries in the object; （2） The two-phase level set is applied multiple times for getting the multi-phase segmentation model （n-1 times for the n-phase model, n〉1）; （3） A scaling-based method is introduced to improve the basic model. Experimental results show that the proposed model is effective for detecting weak boundaries.
基金China Postdoctoral Science Foundation(No.2004035208)Jiangsu Communication Science Foundation (No.06Y36)
文摘A capacity model of multi-phase signalized intersections is derived by a stopping-line method. It is simplified with two normal situations： one situation involves one straight lane and one left-turn lane; the other situation involves two straight lanes and one left-turn lane. The results show that the capacity is mainly relative to signal cycle length, phase length, intersection layout and following time. With regard to the vehicles arrival rates, the optimal model is derived based on each phase＇s remaining time balance, and it is solved by Lagrange multipliers. Therefore, the calculation models of the optimal signal cycle length and phase lengths are derived and simplified. Compared to the existing models, the proposed model is more convenient and practical. Finally, a practical intersection is chosen and its signal cycles and phase lengths are calculated by the proposed model.
基金This research was performed as part of the project supported by the National Natural Science Foundation of China(grant 40272088)Knowledge Innovation Project of the Chinese Academy of Sciences(KZCX1-07)the Program of Financially Aiding Backbone Teachers Working in Colleges and Universities(J-00-25).
文摘Mineral deposits are unevenly distributed in the Earth's crust, which is closely related to the formation and evolution of the Earth. In the early history of the Earth, controlled by the gravitational contraction and thermal expansion, lighter elements, such as radioactive, halogen-family, rare and rare earth elements and alkali metals, migrated upwards; whereas heavier elements, such as iron-family and platinum-family elements, base metals and noble metals, had a tendency of sinking to the Earth's core, so that the elements iron, nickel, gold and silver are mainly concentrated in the Earth's core. However, during the formation of the stratified structure of the Earth, the existence of temperature, pressure and viscosity differences inside and outside the Earth resulted in vertical material movement manifested mainly by cascaded evolution of mantle plumes in the Earth. The stratifications and vertical movement of the Earth were interdependent and constituted the motive force of the mantle-core movement. The cascaded evolution of mantle plumes opens the passageways for the migration of deep-seated ore-forming material, and thus elements such as gold and silver concentrated in the core and on the core-mantle boundary migrate as the gaseous state together with the hot material flow of mantle plumes against the gravitational force through the passageways to the lithosphere, then migrate as the mixed gas-liquid state to the near-surface level and finally are concentrated in favorable structural expansion zones, forming mineral deposits. This is possibly the important metallogenic mechanism for gold, silver, lead, zinc, copper and other many elements. Take for example the NE-plunging crown of the Fuping mantle-branch structure, the paper analyzes ductile-brittle shear zone-type gold fields (Weijiayu) at the core of the magmatic-metamorphic complex, principal detachment-type gold fields (Shangmingyu) and hanging-wall cover fissure-vein-type lead-zinc polymetallic ore fields (Lianbaling) and further briefly analyzes the source of ore-forming material and constructs an ore-forming and -controlling model.
基金The National Natural Science Foundation under contract No.41306050the Science and Technology Project of Guangdong Province under contract No.2014A010103030+1 种基金the Natural Science Foundation of Guangdong Province under contract No.2015A030313617the National Marine Important Charity Special Foundation under contract No.201305019
文摘Using the occurrence characteristics of bubble plumes in the South China Sea as a reference, this paper continues to study the seismic responses produced by bubble plumes in the cold seepage active region. To make the plume modelling scheme more reasonable, we modified the original modelling scheme and reconstructed a plume water body model based on the variation of its radius as bubbles rise in seawater. The plume seismic records of shot gathers were obtained by forward simulation. The seismic records of single shot show obvious characteristics of a scattering wave field and the periodic characteristics of the model. Seismic records of shot gathers were processed using prestack depth migration. The boundary of its imaging section has a good convergence effect. The migration sections can be imaged distinctly with higher accuracy. The aforementioned studies once again laid a foundation for the further study of the seismic responses produced by plumes. They also gradually probed a more suitable seismic data processing method for plumes and provided a theoretical guidance for the identification of plumes.
基金financially supported by the National Natural Science Foundation of China(No.41306050)the Science and Technology Project of Guangdong Province of China(No.2014A010103030)+1 种基金the Natural Science Foundation of Guangdong Province under contract(No.2015A030313617)the National Marine Important Charity Special Foundation of China(No.201305019)
文摘To study the bubble plume's seismic response characteristics,the model of a plume water body has been built in this article using the bubble-contained medium acoustic velocity model and the stochastic medium theory based on an analysis of both the acoustic characteristics of a bubble-contained water body and the actual features of a plume.The finite difference method is used for forward modelling,and the single-shot seismic record exhibits the characteristics of a scattered wave field generated by a plume.A meaningful conclusion is obtained by extracting seismic attributes from the pre-stack shot gather record of a plume.The values of the amplitude-related seismic attributes increase greatly as the bubble content goes up,and changes in bubble radius will not cause seismic attributes to change,which is primarily observed because the bubble content has a strong impact on the plume's acoustic velocity,while the bubble radius has a weak impact on the acoustic velocity.The above conclusion provides a theoretical reference for identifying hydrate plumes using seismic methods and contributes to further study on hydrate decomposition and migration,as well as on distribution of the methane bubble in seawater.
文摘The fluid of casting process is a typical kind of multi-phase flow. Actually, many casting phenomena have close relationship with the multi-phase flow, such as molten metal filling process, air entrapment, slag movement, venting process of die casting, gas escaping of lost foam casting and so on. Obviously, in order to analyze these phenomena accurately, numerical simulation of the multi-phase fluid is necessary. Unfortunately, so far, most of the commercial casting simulation systems do not have the ability of multi-phase flow modeling due to the difficulty in the multi-phase flow calculation. In the paper, Finite Different Method (FDM) technique was adopt to solve the multi-phase fluid model. And a simple object of the muiti-phase fluid was analyzed to obtain the fluid rates of the liquid phase and the entrapped air phase.
基金The project is sponsored by the Innovation Foundation of Key Lab of Geophysical Exploration under CNPC.
文摘The hydrocarbon detection techniques used currently are generally based on the theory of single-phase medium, but hydrocarbon reservoir mostly is multi-phase medium, therefore, multisolutions and uncertainties are existed in the result of hydrocarbon detection. This paper presents a fast way to detect hydrocarbon in accordance with BOIT theory and laboratory data. The technique called DHAF technique has been applied to several survey area and obtained good result where the coincidence rate for hydrocarbon detection is higher than other similar techniques. The method shows a good prospect of the application in hydrocarbon detecting at exploration stage and in reservoir monitoring at production stage.
基金the National Natural Science Foundation of China (No. 51633003) for the financial support
文摘Polyamide/acrylonitrile-butadiene-styrene copolymer(PA/ABS) blends have drawn considerable attention from both academia and industry for their important applications in automotive and electronic areas. Due to poor miscibility of PA and ABS, developing an effective compatibilization strategy has been an urgent challenge to achieve prominent mechanical properties. In this study, we create a set of mechanically enhanced PA6/ABS blends using two multi-monomer melt-grafted compatibilizers, SEBSg-(MAH-co-St) and ABS-g-(MAH-co-St). The dispersed domain size is significantly decreased and meanwhile the unique "soft shell-encapsulating-hard core" structures form in the presence of compatibilizers. The optimum mechanical performances manifest an increase of 36% in tensile strength and an increase of 1300% in impact strength, compared with the neat PA6/ABS binary blend.
基金supported by the National Natural Science Foundation of China(No.51576054)
文摘The infrared（IR） irradiance signature from rocket motor exhaust plumes is closely related to motor type,propellant composition,burn time,rocket geometry,chamber parameters and flight conditions.In this paper,an infrared signature analysis tool（IRSAT） was developed to understand the spectral characteristics of exhaust plumes in detail.Through a finite volume technique,flow field properties were obtained through the solution of axisymmetric Navier-Stokes equations with the Reynolds-averaged approach.A refined 13-species,30-reaction chemistry scheme was used for combustion effects and a k-e-Rtturbulence model for entrainment effects.Using flowfield properties as input data,the spectrum was integrated with a line of sight（LOS） method based on a single line group（SLG） model with Curtis-Godson approximation.The model correctly predicted spectral distribution in the wavelengths of 1.50–5.50 lm and had good agreement for its location with imaging spectrometer data.The IRSAT was then applied to discuss the effects of three operating conditions on IR signatures：（a） afterburning;（b） chamber pressure from ignition to cutoff;and（c） minor changes in the ratio of hydroxyl-terminated polybutadiene（HTPB） binder to ammonium perchlorate（AP） oxidizer in propellant.Results show that afterburning effects can increase the size and shape of radiance images with enhancement of radiation intensity up to 40%.Also,the total IR irradiance in different bands can be characterized by a non-dimensional chamber pressure trace in which the maximum discrepancy is less than 13% during ignition and engine cutoff.An increase of chamber pressure can lead to more distinct diamonds,whose distance intervals are extended,and the position of the first diamond moving backwards.In addition,an increase in HTPB/AP causes a significant jump in spectral intensity.The incremental rates of radiance intensity integrated in each band are linear with the increase of HTPB,and the growth rates of radiance intensities in some bands reach up to 50% as HTPB weight increases by 3%.
基金financially supported by FEDER Funds,the Spanish Project CGL2015-65824 granted by the Spanish“Ministerio de Economía y Competitividad”to JAPthe Ramón y Cajal Fellowship RYC-2015-17596 to JMGJ
文摘The origin of zircon grains, and other exotic minerals of typical crustal origin, in mantle-hosted ophiolitic chromitites are hotly debated. We report a population of zircon grains with ages ranging from Cretaceous(99 Ma) to Neoarchean(2750 Ma), separated from massive chromitite bodies hosted in the mantle section of the supra-subduction(SSZ)-type Mayari-Baracoa Ophiolitic Belt in eastern Cuba. Most analyzed zircon grains(n = 20, 287 ± 3 Ma to 2750 ± 60 Ma) are older than the early Cretaceous age of the ophiolite body, show negativeε_(Hf)(t)(-26 to-0.6) and occasional inclusions of quartz, K-feldspar,biotite, and apatite that indicate derivation from a granitic continental crust. In contrast, 5 mainly rounded zircon grains(297±5 Ma to 2126±27 Ma) show positive εHf(t)(+0.7 to +13.5) and occasional apatite inclusions, suggesting their possible crystallization from melts derived from juvenile(mantle)sources. Interestingly, younger zircon grains are mainly euhedral to subhedral crystals, whereas older zircon grains are predominantly rounded grains. A comparison of the ages and Hf isotopic compositions of the zircon grains with those of nearby exposed crustal terranes suggest that chromitite zircon grains are similar to those reported from terranes of Mexico and northern South America. Hence, chromitite zircon grains are interpreted as sedimentary-derived xenocrystic grains that were delivered into the mantle wedge beneath the Greater Antilles intra-oceanic volcanic arc by metasomatic fluids/melts during subduction processes. Thus, continental crust recycling by subduction could explain all populations of old xenocrystic zircon in Cretaceous mantle-hosted chromitites from eastern Cuba ophiolite.We integrate the results of this study with petrological-thermomechanical modeling and existing geodynamic models to propose that ancient zircon xenocrysts, with a wide spectrum of ages and Hf isotopic compositions, can be transferred to the mantle wedge above subducting slabs by cold plumes.
基金supported by the National Natural Science Foundation of China(Grant No.51704327)
文摘In the petroleum industry,detection of multi-phase fluid flow is very important in both surface and down-hole measurements.Accurate measurement of high rate of water or gas multi-phase flow has always been an academic and industrial focus.NMR is an efficient and accurate technique for the detection of fluids;it is widely used in the determination of fluid compositions and properties.This paper is aimed to quantitatively detect multi-phase flow in oil and gas wells and pipelines and to propose an innovative method for online nuclear magnetic resonance(NMR)detection.The online NMR data acquisition,processing and interpretation methods are proposed to fill the blank of traditional methods.A full-bore straight tube design without pressure drop,a Halbach magnet structure design with zero magnetic leakage outside the probe,a separate antenna structure design without flowing effects on NMR measurement and automatic control technology will achieve unattended operation.Through the innovation of this work,the application of NMR for the real-time and quantitative detection of multi-phase flow in oil and gas wells and pipelines can be implemented.
基金supported by the Scientific and Innovative Action Plan of Shanghai(CN)“One Belt One Road”International Cooperation Project(No.20260750400)the Singapore National Research Foundation(NRF)under its Campus for Research Excellence and Technological Enterprise(CREATE)program(E2S2-CREATE project ES-2:Detection,Assessment&Modelling of Emerging Contaminants in the Urban Environment)。
文摘The rapid construction of artificial reservoirs in metropolises has promoted the emergence of city-river-reservoir systems worldwide.This study investigated the environmental behaviors and risks of heavy metals in the aquatic environment of a typical system composed of main watersheds in Suzhou and Jinze Reservoir in Shanghai.Results shown that Mn,Zn and Cu were the dominant metals detected in multiple phases.Cd,Mn and Zn were mainly presented in exchangeable fraction and exhibited high bioavailability.Great proportion and high mobility of metals were found in suspended particulate matter(SPM),suggesting that SPM can greatly affect metal multi-phase distribution process.Spatially,city system(Ci S)exhibited more serious metal pollution and higher ecological risk than river system(Ri S)and reservoir system(Re S)owing to the diverse emission sources.Ci S and Re S were regarded as critical pollution source and sink,respectively,while Ri S was a vital transportation aisle.Microbial community in sediments exhibited evident spatial variation and obviously modified by exchangeable metals and nutrients.In particular,Bacteroidetes and Firmicutes presented significant positive correlations with most exchangeable metals.Risk assessment implied that As,Sb and Ni in water may pose potential carcinogenic risk to human health.Nevertheless,Re S was in a fairly safe state.Hg was the main risk contributor in SPM,while Cu,Zn,Ni and Sb showed moderate risk in sediments.Overall,Hg,Sb and Ci S were screened out as priority metals and system,respectively.More attention should be paid to these priority issues to promote the sustainable development of the watershed.
基金the Slovak Research and Development Agency under the contract No.COST-0022-06,APVV-51-061505the 6th FP EU NESPA+5 种基金the Slovak Grant Agency VEGA(2/7197/27,2/7194/27,2/7195/27)NANOSMART,Centre of Excellence(1/1/2007-31/12/2010)Slovak Academy of Sciences,by KMM-NoE 502243-2(10/2004-9/2008)NENAMAT INCO-CT-2003-510363COST Action 536 and COST Action 538János Bolyai Research Grant NSF-MTA-OTKA grant-MTA:96/OTKA:049953,OTKA 63609
文摘Based on the fundamental equations of the mechanics of solid continuum,the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix,imaginarily divided into identical cells with dimensions equal to inter-particle distances,containing a central spherical particle with or without a spherical envelope on the particle surface.Consequently,the multi-particle-(envelope)-matrix system,as a model system regarding the analytical modelling,is applicable to four types of multi-phase materials.As functions of the particle volume fraction v,the inter-particle distances dl,d2,d3 along three mutually per-pendicular axes,and the particle and envelope radii,R1 and R2,respectively,the thermal stresses within the cell,are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep-resented by the matrix,envelope and particle.Analytical-(experimental)-computational lifetime prediction methods for multi-phase materials are proposed,which can be used in engineering with appropriate values of parameters of real multi-phase materials.
