The influences of slight amount of B element on the microstructure and properties of AlCoCrFeNiBx high entropy alloys(x = 0,0.01,…,0.09 and 0.1,mole fraction) were investigated.The AlCoCrFeNi high entropy alloy exh...The influences of slight amount of B element on the microstructure and properties of AlCoCrFeNiBx high entropy alloys(x = 0,0.01,…,0.09 and 0.1,mole fraction) were investigated.The AlCoCrFeNi high entropy alloy exhibits equiaxed grain structures with obvious composition segregation.However,with the addition of B element,the alloys exhibit dendrite structures.Inside the dendrites,spinodal decomposition structure can be clearly observed.With the addition of B element,the crystal structures change from(B2 + BCC) to(B2 + BCC + FCC) structures,and the hardness firstly increases from HV 486.7 to HV 502.4,then declines to HV 460.7(x ≥ 0.02).The compressive fracture strength firstly shows a trend of increasing,and then declining(x ≥ 0.08).The coercive forces and the specific saturation magnetizations of the alloys decrease as B addition contents increase,the decreasing coercive forces show a better soft magnetic behavior.展开更多
Compressive anisotropy of extruded Mg-2Dy-0.5Zn (mole fraction, %) alloy sheet was investigated. The alloy sheet was mainly composed ofα-Mg, (Mg, Zn)xDy phase and a large number of long period stacking ordered (...Compressive anisotropy of extruded Mg-2Dy-0.5Zn (mole fraction, %) alloy sheet was investigated. The alloy sheet was mainly composed ofα-Mg, (Mg, Zn)xDy phase and a large number of long period stacking ordered (LPSO) phases distributed along the extrusion direction. The compressive experimental results show that the alloy sheet exhibits an obvious compressive anisotropy. The compressive strength of the specimen in the extrusion direction (ED) is higher than those of the specimens in the transverse direction (TD) and 45° inclined to the extrusion direction. The compressive yield strength (CYS), ultimate compressive strength (UCS) and compressive strain of the specimen in the ED are 274.65 MPa, 518.94 MPa and 12.93%, respectively. The compressive anisotropy is mainly attributed to the distribution of LPSO phase and formation of〈10 10〉//ED fiber texture in the deformed grains.展开更多
Semi open-cell aluminum foams having channels between individual cells were produced using low cost CaCO3foamingagent and applying the powder compact melting process.To this end,the aluminum and CaCO3powder mixtures w...Semi open-cell aluminum foams having channels between individual cells were produced using low cost CaCO3foamingagent and applying the powder compact melting process.To this end,the aluminum and CaCO3powder mixtures were coldcompacted into dense cylindrical precursors for foaming at specific temperatures under air atmosphere.The effects of severalparameters including precursor compaction pressure,foaming agent content as well as temperature and time of the foaming processon the cell microstructure,linear expansion,relative density and compressive properties were investigated.A uniform distribution ofcells with sizes less than100μm,which form semi open-cell structures with relative densities in the range of55.4%-84.4%,wasobtained.The elevation of compaction pressure between127-318MPa and blowing agent up to15%(mass fraction)led to anincrease in the linear expansion,compressive strength and densification strain.By varying the foaming temperature from800to1000°C,all of the investigated parameters increased except compressive strength and relative density.The results indicated theoptimal foaming temperature and time as900°C and10-25min,respectively.展开更多
Novel AZ91D Mg alloy/fly-ash cenospheres(AZ91D/FACs)composites were fabricated by melt stir technique.Fly-ash cenosphere particles with 4%,6%,8%,10%in mass fraction and 100μm in size were used.Hardness and compressiv...Novel AZ91D Mg alloy/fly-ash cenospheres(AZ91D/FACs)composites were fabricated by melt stir technique.Fly-ash cenosphere particles with 4%,6%,8%,10%in mass fraction and 100μm in size were used.Hardness and compressive strength of the composites were measured.The effects of mass fraction of cenospheres on the microstructure and compressive properties were characterized.The results show that the cenospheres are uniformly distributed in the matrix and there is no sign of cenosphere cluster or residual pore.The densities of the composites are 1.85-1.92 g/cm 3 .By comparing with matrix,the compressive yield strength of the composites is improved,and the cenospheres is filled with Mg matrix alloy.SEM,XRD and EDX results of the composites show clear evidence of reaction product at cenosphere/matrix interface.On the basis of XRD and EDX,composition, structure and thermodynamic analysis,the main interfacial phase between the cenosphere and AZ91D Mg alloy was identified to be MgAl2O4.展开更多
(CrFeCoNi)high-entropy alloy(HEA)was reinforced with various contents of WC particles from 5 wt%to 20 wt%,and prepared by powder metallurgy.The mixed powders were compacted under 700 MPa and then sintered at 1200℃in ...(CrFeCoNi)high-entropy alloy(HEA)was reinforced with various contents of WC particles from 5 wt%to 20 wt%,and prepared by powder metallurgy.The mixed powders were compacted under 700 MPa and then sintered at 1200℃in a vacuum furnace for 90 min.Density,phase composition,and microstructure of sintered samples were investigated.Hardness,compressive strength,wear resistance and coefficient of thermal expansion(CTE)were estimated.The results revealed the improvement of the density with the addition of WC.XRD results revealed the formation of new FCC chromium carbide phases.Scanning electron microscopy(SEM)results show a good distribution of the carbide phases over the alloy matrix.The CTE was decreased gradually by increasing the WC content.Compressive strength was improved by WC addition.A mathematical model was established to predict the behavior of the strength of the HEA samples.The hardness of the investigated HEAs was increased gradually with the increasing of WC content about 20.35%.Also,the wear rate of HEA without WC is 1.70×10^(−4)mm^(3)/(N·m),which is approximately 4.5 times the wear rate of 20 wt%WC HEA(3.81×10^(−5)mm^(3)/(N·m)),which means that wear resistance was significantly improved with the increase of WC content.展开更多
Ti43Al and Ti47Al alloys with different contents of zirconium were prepared by non-consumable vacuum arc melting furnace.The microstructure and mechanical properties were investigated.The results showed that Zr had no...Ti43Al and Ti47Al alloys with different contents of zirconium were prepared by non-consumable vacuum arc melting furnace.The microstructure and mechanical properties were investigated.The results showed that Zr had no obvious effect on microstructure morphology of Ti43Al,while that of Ti47Al was modified from dendrites into equiaxed grains.The addition of Zr could refine the grains.Zr promoted the formation ofγphase significantly and the solubility values of Zr inγphase were 12.0%and 5.0%(molar fraction)in Ti43Al and Ti47Al,respectively.Zr-richγphase mainly formed throughβ→γin Ti43Al-xZr(molar fraction,%)andβ→α→γin Ti47Al-xZr(molar fraction,%).Fine-grain strengthening and solution strengthening were beneficial to improving the compressive strength while severe micro-segregation was detrimental to compressive properties.Large solubility of Zr was bad for ductility of alloys as well.The maximum compressive strengths of Ti43Al-xZr and Ti47Al-xZr were 1684.82 MPa(x=5.0%)and 2158.03 MPa(x=0.5%),respectively.The compressive strain fluctuated slightly in Ti43Al-xZr and reached the maximum value of 35.24%(x=0.5%)in Ti47Al-xZr.Both alloys showed brittle fracture.展开更多
The effects of Mo addition on microstructures,phase relationships,order–disorder phase-transition temperatures and room-temperature mechanical properties of Fe50Al50-nMon alloys(n=1,3,5,7,and 9,mole fraction,%)were i...The effects of Mo addition on microstructures,phase relationships,order–disorder phase-transition temperatures and room-temperature mechanical properties of Fe50Al50-nMon alloys(n=1,3,5,7,and 9,mole fraction,%)were investigated after solidification and heat treatment.Structural characterization of the samples was performed via X-ray diffraction(XRD),scanning electron microscopy(SEM)and differential scanning calorimetry.Room-temperature mechanical properties were investigated by conducting compression and microhardness tests.Mo3Al particles precipitated in all alloys because of the limited solid solubility of Mo in the Fe-Al-based phases.The as-cast Fe50Al50-nMon alloys exhibited brittle behavior with high yield strength and limited fracture strain at room temperature.Compared with the as-cast alloys,all the heat-treated alloys except for the Fe50Al41Mo9 alloy exhibited enhanced mechanical properties at room temperature.The heat-treated Fe50Al43Mo7 alloy exhibited the highest fracture strain and compressive strength of 25.4%and 2.3 GPa,respectively.展开更多
The dynamic mechanical properties of basalt affected by microwave were investigated by performing dynamic compressive tests using the SHPB system.Meanwhile,the thermal damage of the treated basalt was characterized by...The dynamic mechanical properties of basalt affected by microwave were investigated by performing dynamic compressive tests using the SHPB system.Meanwhile,the thermal damage of the treated basalt was characterized by ultrasonic non-destructive testing and nuclear magnetic resonance technology.The results show that with the increase of microwave power and exposure time,the P-wave velocity,dynamic compressive strength and elastic modulus decrease continuously,and the dynamic failure mode tends to be a more complex fracturing.The increase in microwave power and exposure time can enhance the temperature difference and transfer coefficient among minerals,hence intensifying the rock damage induced by thermal shock.展开更多
This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear di...This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.展开更多
Atomic force microscope (AFM), as an important instrument in micro/nano operation, has been widely used to measure sampie's height information. However, the so called compression effect, due to force aroused from t...Atomic force microscope (AFM), as an important instrument in micro/nano operation, has been widely used to measure sampie's height information. However, the so called compression effect, due to force aroused from the contact of AFM tip with a sample surface, would result in imprecision of the surface's height measurement, i.e., the measured height is lower than expected. Up to now, there is not any effective and rapid method to attenuate this kind of measurement error. Thus, in this paper, an algorithm to obtain high accurate height measurement is proposed. Firstly, the concept of force curve is used to analyze the basic principle of the compression effect. Secondly, an automatic compensation method by fusing the height signal and the deflection signal is proposed. The proposed algorithm can also be used to obtain a surface elasticity image. Finally, in order to validate the proposed method, two experiments are conducted with respect to mufti-wall nano-carbon tubes on a silicon substrate and graphemes on a mica substrate.展开更多
Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are ...Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.展开更多
With the development of the micro-electro-mechanical system (MEMS),the flow characteristics in micro-channels have drawn increasing attention.In this paper,numerical simulations are conducted to investigate the flow c...With the development of the micro-electro-mechanical system (MEMS),the flow characteristics in micro-channels have drawn increasing attention.In this paper,numerical simulations are conducted to investigate the flow characteristics of compressible flow through micro-channels and micronozzles.An improved surface roughness viscosity model is used to simulate the effect of surface roughness on micro-channels flow characteristics.Using this model,better agreements between the computational results and the experimental data are found.The result indicates that the surface roughness is one of the important factors affecting the flow characteristics of gas through micro-channels.The numerical investigation on the expansion channel shows that by using the laminar model that considers surface roughness,the computational results and experimental data are consistent when Re<450,whereas deviation increases when Re>450.Based on the synthetic model with considerations of turbulence viscosity and surface roughness,the numerical results and the experimental data are identical.展开更多
This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a sig...This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.展开更多
基金Projects(51134013,51104029,51471044)supported by the National Natural Science Foundation of ChinaProject supported by the Fundamental Research Funds for the Central Universities,China+1 种基金Project(LZ2014007)supported by the Key Laboratory of Basic Research Projects of Liaoning Province Department of Education,ChinaProject(2014028013)supported by the Natural Science Foundation of Liaoning Province,China
文摘The influences of slight amount of B element on the microstructure and properties of AlCoCrFeNiBx high entropy alloys(x = 0,0.01,…,0.09 and 0.1,mole fraction) were investigated.The AlCoCrFeNi high entropy alloy exhibits equiaxed grain structures with obvious composition segregation.However,with the addition of B element,the alloys exhibit dendrite structures.Inside the dendrites,spinodal decomposition structure can be clearly observed.With the addition of B element,the crystal structures change from(B2 + BCC) to(B2 + BCC + FCC) structures,and the hardness firstly increases from HV 486.7 to HV 502.4,then declines to HV 460.7(x ≥ 0.02).The compressive fracture strength firstly shows a trend of increasing,and then declining(x ≥ 0.08).The coercive forces and the specific saturation magnetizations of the alloys decrease as B addition contents increase,the decreasing coercive forces show a better soft magnetic behavior.
基金Projects(51301082,51464031,51201158)supported by the National Natural Science Foundation of China
文摘Compressive anisotropy of extruded Mg-2Dy-0.5Zn (mole fraction, %) alloy sheet was investigated. The alloy sheet was mainly composed ofα-Mg, (Mg, Zn)xDy phase and a large number of long period stacking ordered (LPSO) phases distributed along the extrusion direction. The compressive experimental results show that the alloy sheet exhibits an obvious compressive anisotropy. The compressive strength of the specimen in the extrusion direction (ED) is higher than those of the specimens in the transverse direction (TD) and 45° inclined to the extrusion direction. The compressive yield strength (CYS), ultimate compressive strength (UCS) and compressive strain of the specimen in the ED are 274.65 MPa, 518.94 MPa and 12.93%, respectively. The compressive anisotropy is mainly attributed to the distribution of LPSO phase and formation of〈10 10〉//ED fiber texture in the deformed grains.
文摘Semi open-cell aluminum foams having channels between individual cells were produced using low cost CaCO3foamingagent and applying the powder compact melting process.To this end,the aluminum and CaCO3powder mixtures were coldcompacted into dense cylindrical precursors for foaming at specific temperatures under air atmosphere.The effects of severalparameters including precursor compaction pressure,foaming agent content as well as temperature and time of the foaming processon the cell microstructure,linear expansion,relative density and compressive properties were investigated.A uniform distribution ofcells with sizes less than100μm,which form semi open-cell structures with relative densities in the range of55.4%-84.4%,wasobtained.The elevation of compaction pressure between127-318MPa and blowing agent up to15%(mass fraction)led to anincrease in the linear expansion,compressive strength and densification strain.By varying the foaming temperature from800to1000°C,all of the investigated parameters increased except compressive strength and relative density.The results indicated theoptimal foaming temperature and time as900°C and10-25min,respectively.
基金Project(2007KZ07)supported by Plans for Science and Technology of Changchun City,ChinaProject supported by the Program for New Century Excellent Talents in University,ChinaProject supported by the 985 Project of Jilin University,China
文摘Novel AZ91D Mg alloy/fly-ash cenospheres(AZ91D/FACs)composites were fabricated by melt stir technique.Fly-ash cenosphere particles with 4%,6%,8%,10%in mass fraction and 100μm in size were used.Hardness and compressive strength of the composites were measured.The effects of mass fraction of cenospheres on the microstructure and compressive properties were characterized.The results show that the cenospheres are uniformly distributed in the matrix and there is no sign of cenosphere cluster or residual pore.The densities of the composites are 1.85-1.92 g/cm 3 .By comparing with matrix,the compressive yield strength of the composites is improved,and the cenospheres is filled with Mg matrix alloy.SEM,XRD and EDX results of the composites show clear evidence of reaction product at cenosphere/matrix interface.On the basis of XRD and EDX,composition, structure and thermodynamic analysis,the main interfacial phase between the cenosphere and AZ91D Mg alloy was identified to be MgAl2O4.
文摘(CrFeCoNi)high-entropy alloy(HEA)was reinforced with various contents of WC particles from 5 wt%to 20 wt%,and prepared by powder metallurgy.The mixed powders were compacted under 700 MPa and then sintered at 1200℃in a vacuum furnace for 90 min.Density,phase composition,and microstructure of sintered samples were investigated.Hardness,compressive strength,wear resistance and coefficient of thermal expansion(CTE)were estimated.The results revealed the improvement of the density with the addition of WC.XRD results revealed the formation of new FCC chromium carbide phases.Scanning electron microscopy(SEM)results show a good distribution of the carbide phases over the alloy matrix.The CTE was decreased gradually by increasing the WC content.Compressive strength was improved by WC addition.A mathematical model was established to predict the behavior of the strength of the HEA samples.The hardness of the investigated HEAs was increased gradually with the increasing of WC content about 20.35%.Also,the wear rate of HEA without WC is 1.70×10^(−4)mm^(3)/(N·m),which is approximately 4.5 times the wear rate of 20 wt%WC HEA(3.81×10^(−5)mm^(3)/(N·m)),which means that wear resistance was significantly improved with the increase of WC content.
基金Project(51741404)supported by the National Natural Science Foundation of ChinaProject(2017YFA0403802)supported by National Key Research and Development Program of China
文摘Ti43Al and Ti47Al alloys with different contents of zirconium were prepared by non-consumable vacuum arc melting furnace.The microstructure and mechanical properties were investigated.The results showed that Zr had no obvious effect on microstructure morphology of Ti43Al,while that of Ti47Al was modified from dendrites into equiaxed grains.The addition of Zr could refine the grains.Zr promoted the formation ofγphase significantly and the solubility values of Zr inγphase were 12.0%and 5.0%(molar fraction)in Ti43Al and Ti47Al,respectively.Zr-richγphase mainly formed throughβ→γin Ti43Al-xZr(molar fraction,%)andβ→α→γin Ti47Al-xZr(molar fraction,%).Fine-grain strengthening and solution strengthening were beneficial to improving the compressive strength while severe micro-segregation was detrimental to compressive properties.Large solubility of Zr was bad for ductility of alloys as well.The maximum compressive strengths of Ti43Al-xZr and Ti47Al-xZr were 1684.82 MPa(x=5.0%)and 2158.03 MPa(x=0.5%),respectively.The compressive strain fluctuated slightly in Ti43Al-xZr and reached the maximum value of 35.24%(x=0.5%)in Ti47Al-xZr.Both alloys showed brittle fracture.
基金OYP Program at Middle East Technical University and The Scientific and Technological Research Council of Turkey,TUBITAKNational Scholarship Programme for PhD Students
文摘The effects of Mo addition on microstructures,phase relationships,order–disorder phase-transition temperatures and room-temperature mechanical properties of Fe50Al50-nMon alloys(n=1,3,5,7,and 9,mole fraction,%)were investigated after solidification and heat treatment.Structural characterization of the samples was performed via X-ray diffraction(XRD),scanning electron microscopy(SEM)and differential scanning calorimetry.Room-temperature mechanical properties were investigated by conducting compression and microhardness tests.Mo3Al particles precipitated in all alloys because of the limited solid solubility of Mo in the Fe-Al-based phases.The as-cast Fe50Al50-nMon alloys exhibited brittle behavior with high yield strength and limited fracture strain at room temperature.Compared with the as-cast alloys,all the heat-treated alloys except for the Fe50Al41Mo9 alloy exhibited enhanced mechanical properties at room temperature.The heat-treated Fe50Al43Mo7 alloy exhibited the highest fracture strain and compressive strength of 25.4%and 2.3 GPa,respectively.
基金supported by the National Natural Science Foundation of China(Nos.51774325,41972283,11972378).
文摘The dynamic mechanical properties of basalt affected by microwave were investigated by performing dynamic compressive tests using the SHPB system.Meanwhile,the thermal damage of the treated basalt was characterized by ultrasonic non-destructive testing and nuclear magnetic resonance technology.The results show that with the increase of microwave power and exposure time,the P-wave velocity,dynamic compressive strength and elastic modulus decrease continuously,and the dynamic failure mode tends to be a more complex fracturing.The increase in microwave power and exposure time can enhance the temperature difference and transfer coefficient among minerals,hence intensifying the rock damage induced by thermal shock.
文摘This article puts forward a general shape invariant potential, which includes the translational shape invariant potential and scaling shape invariant potential as two particular cases, and derives the set of linear differential equations for obtaining general solutions of the generalized shape invariance condition.
基金supported by the CAS FEA International Partnership Program for Creative Research Teams
文摘Atomic force microscope (AFM), as an important instrument in micro/nano operation, has been widely used to measure sampie's height information. However, the so called compression effect, due to force aroused from the contact of AFM tip with a sample surface, would result in imprecision of the surface's height measurement, i.e., the measured height is lower than expected. Up to now, there is not any effective and rapid method to attenuate this kind of measurement error. Thus, in this paper, an algorithm to obtain high accurate height measurement is proposed. Firstly, the concept of force curve is used to analyze the basic principle of the compression effect. Secondly, an automatic compensation method by fusing the height signal and the deflection signal is proposed. The proposed algorithm can also be used to obtain a surface elasticity image. Finally, in order to validate the proposed method, two experiments are conducted with respect to mufti-wall nano-carbon tubes on a silicon substrate and graphemes on a mica substrate.
基金supported by the National Natural Science Foundation of China(Grant No.11032008)the Youth Fund of Taiyuan University of Technology
文摘Micropipette aspiration(MA) is widely applied in cell mechanics, however, at small deformations a common model corresponding to the MA is the half-space model wherein the finite cell size and cell compressibility are neglected. This study extends the half-space model by accounting for the influence of cell geometry and compressibility(sphere model). Using a finite element analysis of cell aspiration into a micropipette, an elastic approximation formula of the aspirated length was derived for the sphere model. The approximation formula includes the geometry parameter of the sphere model(ζ = R/a, R is the radius of the cell, and a is the inner radius of the micropipette) and the Poisson's ratio v of the cell. The results indicate that the parameter and Poisson's ratio v markedly affect the aspirated length, particularly for small and v. When ζ→∞ and v→0.5,the approximation formula tends to the analytical solution for the half-space model. In the incompressible case(v = 0.5), within the general experimental range(ζ varying from 2 to 4), the difference between the analytical solution and the approximate one is significant, and is up to 29% of the approximation solution when ζ= 2. Additionally, parametere was introduced to evaluate the error of elastic moduli between the half-space model and sphere model. Based on the approximation formula, the ζ thresholds, beyond which e becomes larger than 10% and 20%, were derived.
基金supported by the National Natural Science Foundation of China(Grant No. 10872106)
文摘With the development of the micro-electro-mechanical system (MEMS),the flow characteristics in micro-channels have drawn increasing attention.In this paper,numerical simulations are conducted to investigate the flow characteristics of compressible flow through micro-channels and micronozzles.An improved surface roughness viscosity model is used to simulate the effect of surface roughness on micro-channels flow characteristics.Using this model,better agreements between the computational results and the experimental data are found.The result indicates that the surface roughness is one of the important factors affecting the flow characteristics of gas through micro-channels.The numerical investigation on the expansion channel shows that by using the laminar model that considers surface roughness,the computational results and experimental data are consistent when Re<450,whereas deviation increases when Re>450.Based on the synthetic model with considerations of turbulence viscosity and surface roughness,the numerical results and the experimental data are identical.
基金supported by the UK EPSRC Science and Innovation Award to the Oxford Centre for Nonlinear PDE(No.EP/E035027/1)the UK EPSRC Award to the EPSRC Centre for Doctoral Training in PDEs(No.EP/L015811/1)+1 种基金the National Natural Science Foundation of China(No.10728101)the Royal Society-Wolfson Research Merit Award(UK)
文摘This paper presents several examples of fundamental problems involving weak continuity and compactness for nonlinear partial differential equations, in which compensated compactness and related ideas have played a significant role. The compactness and convergence of vanishing viscosity solutions for nonlinear hyperbolic conservation laws are first analyzed, including the inviscid limit from the Navier-Stokes equations to the Euler equations for homentropic flow, the vanishing viscosity method to construct the global spherically symmetric solutions to the multidimensional compressible Euler equations, and the sonic-subsonic limit of solutions of the full Euler equations for multi-dimensional steady compressible fluids. Then the weak continuity and rigidity of the Gauss-Codazzi-Ricci system and corresponding isometric embeddings in differential geometry are revealed. Further references are also provided for some recent developments on the weak continuity and compactness for nonlinear partial differential equations.