The P-SV wave reflection coefficients in VTI and HTI media were obtained by approximation of the Jilek(2002a and b)equation in orthotropic anisotropic media.An approximate equation for P-SV wave elastic impedance ca...The P-SV wave reflection coefficients in VTI and HTI media were obtained by approximation of the Jilek(2002a and b)equation in orthotropic anisotropic media.An approximate equation for P-SV wave elastic impedance can be derived from the combination of the new coefficients with S-wave elastic impedance(Duffaut et al.,2000).On this basis, the fluid identification factor in weakly anisotropic media was constructed and used to identify the Castagna and Smith(1994)lithologic combination and achieved good results. Finally,we specifically analyzed the anisotropic parameter impacts P-SV wave elastic impedance and fluid factor trends.展开更多
Cluster warhead has become the main ammunition of gun,rocket projectile and missile and it has been widely equipped in almost every country.More and more attention is paid to the damage effect of cluster warhead.The s...Cluster warhead has become the main ammunition of gun,rocket projectile and missile and it has been widely equipped in almost every country.More and more attention is paid to the damage effect of cluster warhead.The size of the dispersion area of cluster warhead is the main standard by which the damage effect of cluster warhead is estimated.The practical method of measuring the dispersion area was developed based on binocular stereo vision measurement theory.The calibration principle of the binocular stereo vision cameras was studied.The matching algorithm that relies on the gradient fields of the neighborhood of a pixel has been used to obtain the spatial information of matched points by acquiring apair of corresponding points in the left and right images of binocular cameras.The 3Dpositions of the flying path of cluster warhead were calculated.The umbrella that is similar to the dispersion track of static explosive cluster warhead was applied in the experiment to get the projection area of the umbrella on the ground.Experiment results verify the feasibility of the proposed method.展开更多
Magnetorheological elastomer (MRE) is a new kind of smart materials, the rheological properties can be controlled rapidly by the external magnetic field. It is mainly composed of rubber and micron-sized ferromagneti...Magnetorheological elastomer (MRE) is a new kind of smart materials, the rheological properties can be controlled rapidly by the external magnetic field. It is mainly composed of rubber and micron-sized ferromagnetic particles, which forms a chain-like structure. Therefore its mechanical, electric, and magnetic properties can be changed by the applied magnetic field, which is called as the magneto-induced effect. But this effect is not remarkable enough currently for the engineering application. So it is important for material preparation to optimize parameters to enhance the magneto-induced effect. In this work, based on chain-like model, some factors influencing the magneto-induced effect of MRE were analyzed theoretically by using dipole method with the normal distribution of chain's angle introduced. The factors included the oblique angle of particles chains, magnetic field intensity, and shear strain, etc. Some experiments were also carried out.展开更多
The influence of pseudogap on the inelastic neutron scattering spectra of the underdoped lanthanum cuprate is studied on the basis of the model which incorporates both the superconducting state and pseudogap state. It...The influence of pseudogap on the inelastic neutron scattering spectra of the underdoped lanthanum cuprate is studied on the basis of the model which incorporates both the superconducting state and pseudogap state. It is found that the striking effects of the influence of the pseudogap on the incommensurability of the spin excitation spectrum are that in the superconducting state the pseudogap makes the intensity of the incommensurate peak increase, in the normal state the pseudogap not only makes the intensity of the incommensurate peak increase, but also sharpens the incommensurate peak and increases incommensurability.展开更多
Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type vi...Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.展开更多
The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperat...The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.展开更多
Higher order rnultipole potentials and electrostatic screening effects are introduced to incorporate the dan gling bonds on the surface of a metallic nanopaticle and to modify the coulornb like potential energy terms,...Higher order rnultipole potentials and electrostatic screening effects are introduced to incorporate the dan gling bonds on the surface of a metallic nanopaticle and to modify the coulornb like potential energy terms, respectively. The total interaction energy function for any rnetallic nanoparticle is represented in terms of two- and three-body potentials. The two-body part is described by dipole-dipole interaction potential, and in the three-body part, triple-dipole (DDD) and dipole-dipole-quadrupole (DDQ) terrns are included. The size-dependent cohesive energy and bulk modulus are observed to decrease with decreasing sizes, a result which is in good agreement with the experimental values of Mo and W nanoparticles.展开更多
Although dielectric elastomer(DE)with substantial actuated strain(AS)has been reported 20 years ago,its scientific understanding remains unclear.The most accepted theory of DE,which is proposed in 2000,holds the view ...Although dielectric elastomer(DE)with substantial actuated strain(AS)has been reported 20 years ago,its scientific understanding remains unclear.The most accepted theory of DE,which is proposed in 2000,holds the view that AS of DE is induced by the Maxwell stress.According to this theory,materials have similar ratios of permittivity and Young’s modulus should have similar AS,while the experimental results are on contrary to this theory,and the experimental AS has no relationship with ideal AS.Here,a new dipole-conformation-actuated strain cross-scale model is proposed,which can be generally applied to explain the AS of DE without pre-strain.According to this model,several characteristics of an ideal DE are listed in this work and a new DE based on polyphosphazene(PPZ)is synthesized.The AS of PPZ can reach 84%without any pre-strain.At last,a PPZ-based all soft artificial heart(ASAH)is built,which works in the similar way with natural myocardium,indicating that this material has great application potential and possibility in the construction of an ASAH for heart failure(HF)patients.展开更多
In this paper, two AIE-active luminogens (Oxa-pTPE and Oxa-mTPE) constructed from tetraphenylethene and oxadiazole units were successfully synthesized and their thermal, optical and electronic properties were investig...In this paper, two AIE-active luminogens (Oxa-pTPE and Oxa-mTPE) constructed from tetraphenylethene and oxadiazole units were successfully synthesized and their thermal, optical and electronic properties were investigated. By linking TPE to the oxadiazole core through meta-or para-position, the intramolecular conjugation is effectively controlled. Thanks to the intelligent molecular design and specific AIE feature, when fabricated as emissive layers in non-doped OLEDs, they exhibit blue or deep-blue emission with CIE coordinates of (0.17, 0.23) and (0.15, 0.12), and good efficiencies with ηC, max and ηP, max up to 1.52 cd A-1 and 0.84 Im W-1 , shedding some light on the construction of deep-blue AIE fluorophores.展开更多
A square graphene single electron transistor (SET) was defined with two side gates, and its transport was studied at low temperature at T = 2 K. At zero magnetic field, Coulomb blockade oscillations were clearly obs...A square graphene single electron transistor (SET) was defined with two side gates, and its transport was studied at low temperature at T = 2 K. At zero magnetic field, Coulomb blockade oscillations were clearly observed near the Dirac point of this device. At high magnetic field, in the quantum Hall regime, we observed ballistic tunneling of the carders through the graphene SET, contrary to the Coulomb blockades observed while approaching the vicinity of the Dirac point.展开更多
In this paper, we have improved the fast ignition scheme in order to have more authority needed for highenergy-gain. Due to the more penetrability and energy deposition of the particle beams in fusion targets, we empl...In this paper, we have improved the fast ignition scheme in order to have more authority needed for highenergy-gain. Due to the more penetrability and energy deposition of the particle beams in fusion targets, we employ a laser-to-ion converter foil as a scheme for generating energetic ion beams to ignite the fusion fuel. We find the favorable intensity and wavelength of incident laser by evaluating the laser-proton conversion gain. By calculating the source-target distance, proton beam power and energy are estimated. Our analysis is generalized to the plasma degeneracy effects which can increase the fusion gain several orders of magnitude by decreasing the ion-electron collisions in the plasma.It is found that the wavelength of 0.53 μm and the intensity of about 1020W/cm^2, by saving about 10% conversion coefficient, are the suitable measured values for converting a laser into protons. Besides, stopping power and fusion burn calculations have been done in degenerate and non-degenerate plasma mediums. The results indicate that in the presence of degeneracy, the rate of fusion enhances.展开更多
The structural,electronic and elastic properties of solid nitromethane are investigated under pressure by performing first-principles density functional theory(DFT)calculations within the generalized gradient approxim...The structural,electronic and elastic properties of solid nitromethane are investigated under pressure by performing first-principles density functional theory(DFT)calculations within the generalized gradient approximation(GGA)and the local density approximation(LDA).The obtained ground state structure properties are found to be consistent with existing experimental and theoretical results.The pressure-induced variations of structure parameters(a,b,c and V)indicate that the solid nitromethane has an anisotropic compressibility,and the compression along the c direction is more difficult than along a and b directions.From the vibration curves of intermolecular bond length and bond angle,we find that the C—N bond is the most sensitive among these bonds under pressure,suggesting that the C—N bonds may be broken first under external loading.The influence of pressure on the electronic properties of solid NM has been studied,indicating that solid NM is an insulating compound with a large indirect band gap and tends to be a semiconductor with increasing pressure.Finally,we predict the elastic constants and their pressure dependence for the solid NM with the bulk modulus,Young’s modulus,shear modulus and the Poisson’s ratio derived.展开更多
Dynamically crosslinked materials generally lose their self-healing ability and mechanical robustness in aqueous,acidic,and basic environments due to disruption of their dynamic interactions and bonds.Herein,a micelle...Dynamically crosslinked materials generally lose their self-healing ability and mechanical robustness in aqueous,acidic,and basic environments due to disruption of their dynamic interactions and bonds.Herein,a micelle-like structure with a hydrophobic outer layer is used to protect ionic interactions.This structure ensures the self-healing and long-term stability of the ionically crosslinked elastomers in aqueous,acidic,and basic environments.The elastomer possesses a tensile strength of 6.7 MPa and a strain at break of 1400%,which is superior to the existing waterproof selfhealing elastomers.The strain sensors and dielectric actuators based on the elastomer are highly stable and self-healable,even in extremely harsh environments.This design strategy of hydrophobic protection for dynamic interactions is quite general,allowing it to be extended to other self-healing materials.展开更多
This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semi...This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.展开更多
基金sponsored by the National 973 Program(Grant No.2007CB209603)
文摘The P-SV wave reflection coefficients in VTI and HTI media were obtained by approximation of the Jilek(2002a and b)equation in orthotropic anisotropic media.An approximate equation for P-SV wave elastic impedance can be derived from the combination of the new coefficients with S-wave elastic impedance(Duffaut et al.,2000).On this basis, the fluid identification factor in weakly anisotropic media was constructed and used to identify the Castagna and Smith(1994)lithologic combination and achieved good results. Finally,we specifically analyzed the anisotropic parameter impacts P-SV wave elastic impedance and fluid factor trends.
基金National Major Scientific Equipment Development Projects of China(No.2013YQ240803)Natural Science Foundation for Young Scientists of Shanxi Province(No.2012021011-1)Scientific and Technological Project in Shanxi Province(No.20140321010-02)
文摘Cluster warhead has become the main ammunition of gun,rocket projectile and missile and it has been widely equipped in almost every country.More and more attention is paid to the damage effect of cluster warhead.The size of the dispersion area of cluster warhead is the main standard by which the damage effect of cluster warhead is estimated.The practical method of measuring the dispersion area was developed based on binocular stereo vision measurement theory.The calibration principle of the binocular stereo vision cameras was studied.The matching algorithm that relies on the gradient fields of the neighborhood of a pixel has been used to obtain the spatial information of matched points by acquiring apair of corresponding points in the left and right images of binocular cameras.The 3Dpositions of the flying path of cluster warhead were calculated.The umbrella that is similar to the dispersion track of static explosive cluster warhead was applied in the experiment to get the projection area of the umbrella on the ground.Experiment results verify the feasibility of the proposed method.
基金This work was supported by the National Natural Science Foundation of China (No.50830202 and No.60804018) and the Plan of the Excellent Talent for the New Century (NCET-07-0910). The authors also appreciate the help in the experimental instruments of Professor Xing-long Gong of University of Science and Technology of China deeply.
文摘Magnetorheological elastomer (MRE) is a new kind of smart materials, the rheological properties can be controlled rapidly by the external magnetic field. It is mainly composed of rubber and micron-sized ferromagnetic particles, which forms a chain-like structure. Therefore its mechanical, electric, and magnetic properties can be changed by the applied magnetic field, which is called as the magneto-induced effect. But this effect is not remarkable enough currently for the engineering application. So it is important for material preparation to optimize parameters to enhance the magneto-induced effect. In this work, based on chain-like model, some factors influencing the magneto-induced effect of MRE were analyzed theoretically by using dipole method with the normal distribution of chain's angle introduced. The factors included the oblique angle of particles chains, magnetic field intensity, and shear strain, etc. Some experiments were also carried out.
文摘The influence of pseudogap on the inelastic neutron scattering spectra of the underdoped lanthanum cuprate is studied on the basis of the model which incorporates both the superconducting state and pseudogap state. It is found that the striking effects of the influence of the pseudogap on the incommensurability of the spin excitation spectrum are that in the superconducting state the pseudogap makes the intensity of the incommensurate peak increase, in the normal state the pseudogap not only makes the intensity of the incommensurate peak increase, but also sharpens the incommensurate peak and increases incommensurability.
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10475009 and 10465004, the Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy under the Associate Programm, and the Foundation for New Century Excellent Talents in University of China. Authors thank Profs. K.F. He and Z.Q. Huang for useful discussions.
文摘Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss (gain) behavior when the elasticity parameter of the medium is larger (smaller) than the critical value for Kelvin (Maxwell) viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.
基金中国科学院资助项目,Scientific Research Foundation for Returned Overseas Chinese Scholars,Ministry of Education of China
文摘The elastic constants of superconducting MgB2 are calculated using a molecular dynamics method (MD)with shell model. The lattice parameters, five independent elastic constants, equations of state (EOS), Debye temperature, and bulk modulus of MgB2 are obtained. Meanwhile, the dependence of the bulk modulus B, the lattice parameters a and c, and the unit cell volume V on the applied pressure are presented. It is demonstrated that the method introduced here can well reproduce the experimental results with a reasonable accuracy.
基金Supported by King Saud University,College of Science-Research Center,Project Number PHYS/2009/19
文摘Higher order rnultipole potentials and electrostatic screening effects are introduced to incorporate the dan gling bonds on the surface of a metallic nanopaticle and to modify the coulornb like potential energy terms, respectively. The total interaction energy function for any rnetallic nanoparticle is represented in terms of two- and three-body potentials. The two-body part is described by dipole-dipole interaction potential, and in the three-body part, triple-dipole (DDD) and dipole-dipole-quadrupole (DDQ) terrns are included. The size-dependent cohesive energy and bulk modulus are observed to decrease with decreasing sizes, a result which is in good agreement with the experimental values of Mo and W nanoparticles.
基金supported by the Basic Science Center Program of the National Natural Science Foundation of China (51988102)the National Key Research and Development Program of China (2017YFB0306903)+2 种基金the Major Program of National Natural Science Foundation of China (51790501)the Innovative Research Groups (51221002 and 51521062)the National Natural Science Foundation of China (52003024)
文摘Although dielectric elastomer(DE)with substantial actuated strain(AS)has been reported 20 years ago,its scientific understanding remains unclear.The most accepted theory of DE,which is proposed in 2000,holds the view that AS of DE is induced by the Maxwell stress.According to this theory,materials have similar ratios of permittivity and Young’s modulus should have similar AS,while the experimental results are on contrary to this theory,and the experimental AS has no relationship with ideal AS.Here,a new dipole-conformation-actuated strain cross-scale model is proposed,which can be generally applied to explain the AS of DE without pre-strain.According to this model,several characteristics of an ideal DE are listed in this work and a new DE based on polyphosphazene(PPZ)is synthesized.The AS of PPZ can reach 84%without any pre-strain.At last,a PPZ-based all soft artificial heart(ASAH)is built,which works in the similar way with natural myocardium,indicating that this material has great application potential and possibility in the construction of an ASAH for heart failure(HF)patients.
基金the National Science Foundation of China(21161160556)the National Basic Research Program(973program,2013CB834700)the Open Project of State Key Laboratory of Supramolecular Structure and Materials(SKLSSM201302)
文摘In this paper, two AIE-active luminogens (Oxa-pTPE and Oxa-mTPE) constructed from tetraphenylethene and oxadiazole units were successfully synthesized and their thermal, optical and electronic properties were investigated. By linking TPE to the oxadiazole core through meta-or para-position, the intramolecular conjugation is effectively controlled. Thanks to the intelligent molecular design and specific AIE feature, when fabricated as emissive layers in non-doped OLEDs, they exhibit blue or deep-blue emission with CIE coordinates of (0.17, 0.23) and (0.15, 0.12), and good efficiencies with ηC, max and ηP, max up to 1.52 cd A-1 and 0.84 Im W-1 , shedding some light on the construction of deep-blue AIE fluorophores.
基金supported by the National Natural Science Foundation of China (Grant No. 10874220)the Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences (Grant No. KJCX2-YW- W30)the Natinal Basic Research Program of China from the MOST (Grant No. 2011CB932704)
文摘A square graphene single electron transistor (SET) was defined with two side gates, and its transport was studied at low temperature at T = 2 K. At zero magnetic field, Coulomb blockade oscillations were clearly observed near the Dirac point of this device. At high magnetic field, in the quantum Hall regime, we observed ballistic tunneling of the carders through the graphene SET, contrary to the Coulomb blockades observed while approaching the vicinity of the Dirac point.
基金Supported by the Research Council of University of Guilan
文摘In this paper, we have improved the fast ignition scheme in order to have more authority needed for highenergy-gain. Due to the more penetrability and energy deposition of the particle beams in fusion targets, we employ a laser-to-ion converter foil as a scheme for generating energetic ion beams to ignite the fusion fuel. We find the favorable intensity and wavelength of incident laser by evaluating the laser-proton conversion gain. By calculating the source-target distance, proton beam power and energy are estimated. Our analysis is generalized to the plasma degeneracy effects which can increase the fusion gain several orders of magnitude by decreasing the ion-electron collisions in the plasma.It is found that the wavelength of 0.53 μm and the intensity of about 1020W/cm^2, by saving about 10% conversion coefficient, are the suitable measured values for converting a laser into protons. Besides, stopping power and fusion burn calculations have been done in degenerate and non-degenerate plasma mediums. The results indicate that in the presence of degeneracy, the rate of fusion enhances.
基金supported by the Construction Plan for Scientific Research Innovation Teams of Universities in Sichuan Province(Grant No.12TD008)the National Basic Research Program of China(Grant No.2011CB808201)the Scientific Research Fund of Sichuan Provincial Education Department(Grant No.11ZB079)
文摘The structural,electronic and elastic properties of solid nitromethane are investigated under pressure by performing first-principles density functional theory(DFT)calculations within the generalized gradient approximation(GGA)and the local density approximation(LDA).The obtained ground state structure properties are found to be consistent with existing experimental and theoretical results.The pressure-induced variations of structure parameters(a,b,c and V)indicate that the solid nitromethane has an anisotropic compressibility,and the compression along the c direction is more difficult than along a and b directions.From the vibration curves of intermolecular bond length and bond angle,we find that the C—N bond is the most sensitive among these bonds under pressure,suggesting that the C—N bonds may be broken first under external loading.The influence of pressure on the electronic properties of solid NM has been studied,indicating that solid NM is an insulating compound with a large indirect band gap and tends to be a semiconductor with increasing pressure.Finally,we predict the elastic constants and their pressure dependence for the solid NM with the bulk modulus,Young’s modulus,shear modulus and the Poisson’s ratio derived.
基金supported by the National Natural Science Foundation of China(51873110 and 51673120)State Key Laboratory of Polymer Materials Engineering(sklpme2019-2-14)the Fundamental Research Funds for Central Universities。
文摘Dynamically crosslinked materials generally lose their self-healing ability and mechanical robustness in aqueous,acidic,and basic environments due to disruption of their dynamic interactions and bonds.Herein,a micelle-like structure with a hydrophobic outer layer is used to protect ionic interactions.This structure ensures the self-healing and long-term stability of the ionically crosslinked elastomers in aqueous,acidic,and basic environments.The elastomer possesses a tensile strength of 6.7 MPa and a strain at break of 1400%,which is superior to the existing waterproof selfhealing elastomers.The strain sensors and dielectric actuators based on the elastomer are highly stable and self-healable,even in extremely harsh environments.This design strategy of hydrophobic protection for dynamic interactions is quite general,allowing it to be extended to other self-healing materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.12122205 and 11772119)the Six Talent Peaks Project in Jiangsu Province of China(Grant No.2019-KTHY-009).
文摘This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.