It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special...It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.展开更多
Understanding the thermodynamic behavior of complex fluids in confined environments is critical for various industrial and natural processes including but not limited to polymer flooding enhanced oil recovery(EOR).In ...Understanding the thermodynamic behavior of complex fluids in confined environments is critical for various industrial and natural processes including but not limited to polymer flooding enhanced oil recovery(EOR).In this work,we develop Atif-V2.0,an extended classical density functional theory(cDFT)framework that integrates the interfacial statistical associating fluid theory(iSAFT)to model multicomponent associating fluids composed of water-soluble polymers,alkanes,and water.Building on the original theoretical framework of Atif for modeling nanoconfined inhomogeneous fluids,Atif-V2.0 embeds explicit solvent and captures additional physical interactions-hydrogen bonding,which are critical in associating fluid systems.The other key feature of Atif-V2.0 is its ability to account for polymer topology.We demonstrate its capability by predicting the equilibrium structure and thermodynamic behavior of branched hydrolyzed polyacrylamide solutions near hard walls with various branching topologies,which provides a robust theoretical tool for the rational design of EOR polymers.展开更多
It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of exp...It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.展开更多
It is challenging to assess the mechanism responsible for the nucleation of inclusions in metals at high temperatures.The present work therefore systematically investigates the nucleation of cerium oxide inclusions ac...It is challenging to assess the mechanism responsible for the nucleation of inclusions in metals at high temperatures.The present work therefore systematically investigates the nucleation of cerium oxide inclusions according to classical nucleation theory and a two-step nucleation mechanism.The nucleation rates and nucleation radii of these inclusions are obtained,and the results demonstrate a considerable difference between theoretical and experimental values.On the basis of a two-step nucleation mechanism,(CeO_(2))_(n) and(Ce_(2)O_(3))_(n)(n=1-6)clusters were constructed and the thermodynamic properties of both these clusters and of cerium oxide nanoparticles were analyzed.In addition,the entropies and heat capacity changes of cerium oxides were determined using first principles calculations and are found to be consistent with literature data.The present data indicate that the cerium oxide inclusion nucleation pathway can be summarized as[Ce]+[O]→(CeO_(2))n/(Ce_(2)O_(3))_(n)→(Ce_(2)O_(3))_(n)→(Ce_(2)O_(3))_(2)→core(Ce_(2)O_(3)crystal)-shell((Ce_(2)O_(3))_(2) cluster)nanoparticles→(Ce_(2)O_(3))bulk.展开更多
A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge fie...A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.展开更多
Classic Avrami model and its modifications have found diverse applications in describing the thermal and phase behaviors of inorganic metals and organic polymers. The direct introduction of classic Avrami equation to ...Classic Avrami model and its modifications have found diverse applications in describing the thermal and phase behaviors of inorganic metals and organic polymers. The direct introduction of classic Avrami equation to offer quantitative analyses of crystallization kinetic parameters for enantiomeric poly（lactic acid） （PLA） blends may, however, lead to contradictory conclusions. As revealed by this study, during the characterization of isothermal melt and cold crystallization for stereocomplex PLA containing equal-weight poly（L-lactic acid） and poly（D-lactic acid）, the kinetic parameters yielded by Avrami equation are not in line with the classic crystallization hypotheses or the direct morphological observations. The underlying mechanisms, to some extent, lie in the generation of stereocomplex crystals （SCs） during the cooling/heating which affects the subsequent crystallization dynamics. The huge gap between the melting enthalpies of 100% crystalline SCs （142 J/g） and homo-crystals （HCs, 93 J/g） is most likely responsible for the confusing kinetic parameters acquired from the deduction of Avrami equation, which is based on the integration of enthalpies as a function of crystallization time. This prompts for great care that the classic Avrami equation is not applicable to accurately describe the crystallization kinetics of stereocomplex PLA, given the generation of SCs prior to crystallization and the coexistence of HCs and SCs during crystallization.展开更多
The Marxist human rights theory is embodied in several important works by Karl Marx and Friedrich engels. The key point to understand Marxist human rights theory is to read the texts of classic works of Marx. only in ...The Marxist human rights theory is embodied in several important works by Karl Marx and Friedrich engels. The key point to understand Marxist human rights theory is to read the texts of classic works of Marx. only in this way can we grasp the essence of the theory more clearly and internalize it as genuine belief and emotional identity. This theoretical guide should be implemented in concrete actions through concerns and answers to practical questions, in order to highlight the era value of the classic Marxist human rights theory.展开更多
According to the classical mechanics the energy of a celestial body circulating in the solar system is a constant term. This energy is defined by the masses product of the larger and smaller body entering into a mutua...According to the classical mechanics the energy of a celestial body circulating in the solar system is a constant term. This energy is defined by the masses product of the larger and smaller body entering into a mutual attraction as well as the size of the major semiaxis characteristic for the corresponding Kepler orbit. A special situation concerns the planet interaction with the Sun because of a systematic decrease of the Sun mass due to the luminosity effect. The aim of the paper is to point out that even in the case of perfectly constant interacting masses the energy of the moving body should decrease when a quantum treatment of the body motion is considered. The rate of the energy decrease is extremely small, nevertheless it gives a shortening of the distance between the interacting bodies leading to a final effect of a touch of the larger body and a smaller one.展开更多
This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The ...This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The free surface of the half-plane is modeled by the Steigmann-Ogden surface elasticity theory,while the bulk material behavior is described by the classical couple-stress elasticity theory.The adhesion at the contact interface is characterized by the Maugis-Dugdale(MD)adhesive contact model.Building on the fundamental nonclassical Flamant solution,the governing equations and boundary conditions of the nanocontact problem are reformulated into a system of triple integral equations.These equations are solved numerically by the Gauss-Chebyshev quadratures in combination with an iterative algorithm.The validation against the existing literature confirms the accuracy and robustness of the proposed solution methodology.Comprehensive parametric studies are performed to elucidate the critical roles of surface elasticity and couple stresses in adhesive nanocontact.The numerical results provide insights into the complex interactions among surface,couple-stress,and adhesive effects.Specifically,the interplay between the surface and adhesive effects is predominantly competitive,while the interaction between the couple stresses and adhesion exhibits an intricate nature.The findings highlight the necessity of simultaneously considering surface elasticity,couple stresses,and adhesion in nanoindentation analyses to achieve accurate predictions of material responses.展开更多
The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-for...The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches.展开更多
To solve the problems with the existing methods for detecting hollowing defects,such as inconvenient operation,low efficiency and intense subjectivity,and to improve the efficiency of the acoustic-optic fusion method ...To solve the problems with the existing methods for detecting hollowing defects,such as inconvenient operation,low efficiency and intense subjectivity,and to improve the efficiency of the acoustic-optic fusion method for detecting hollowing defects,in this paper the vibration characteristics of hollowing defects are measured and analyzed using a laser self-mixing interferometer.The ceramic tile above the hollowing defect is equivalent to a thin circular plate with peripheral fixed support.According to Kirchhoff's classical circular plate theory and the circular plate displacement function based on the improved Fourier series,a theoretical model of a circular plate is established.By solving the characteristic equation,the theoretical modal parameters of hollowing defects are obtained.Subsequently,an experimental system based on a laser self-mixing interferometer is built,and modal experiments are carried out using the hammering method.The experimental modal parameters are obtained with a professional modal analysis software.Through comparative analysis between the theoretical and experimental modal parameters,the error of the natural frequency results is found to be tiny and the mode shapes are consistent.These results provide theoretical guidance for a practical non-destructive acoustic-optic fusion method for detecting hollowing defects.展开更多
The improvement on the calculation of anti-Stokes energy transfer rate is studied in the present work. The additional proportion coefficient between Stokes and anti-Stokes light intensities of quantum Raman scattering...The improvement on the calculation of anti-Stokes energy transfer rate is studied in the present work. The additional proportion coefficient between Stokes and anti-Stokes light intensities of quantum Raman scattering theory as compared with the classical Raman theory is introduced to successfully describe the anti-Stokes energy transfer. The theoretical formula for the improvement on the calculation of anti-Stokes energy transfer rate is derived for the first time in this study. The correctness of introducing coefficient exp{△E/kT} from well-known Raman scatter theory is demonstrated also. Moreover, the experimental lifetime measurement in Er0.01YbxY1-0.01-xVO4 crystal is performed to justify the validity of our important improvement in the original phonon-assisted energy transfer theory for the first time.展开更多
There are a large number of theories,models or hypotheses in the history of SLA research.A brief introduction is made in this paper on several typical ones which have a great influence on foreign language teaching and...There are a large number of theories,models or hypotheses in the history of SLA research.A brief introduction is made in this paper on several typical ones which have a great influence on foreign language teaching and it is hoped to be useful for the study of SLA research and foreign language teaching.展开更多
Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gra...Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gradients is analyzed thermodynamically based on classical nucleation theory(CNT). Given that the free energy barrier for nucleation is dependent on temperature, different from a uniform temperature usually used in CNT, an assumption of linear temperature distribution in the ice nucleus was made and taken into consideration in analysis. The critical radius of the ice nucleus for nucleation and the corresponding nucleation model in the presence of a temperature gradient were obtained. It is observed that the critical radius is determined not only by the degree of supercooling, the only dependence in CNT, but also by the temperature gradient and even the Young's contact angle. Effects of temperature gradient on the change in free energy, critical radius,nucleation barrier and nucleation rate with different contact angles and degrees of supercooling are illustrated successively.The results show that a temperature gradient will increase the nucleation barrier and decrease the nucleation rate, particularly in the cases of large contact angle and low degree of supercooling. In addition, there is a critical temperature gradient for a given degree of supercooling and contact angle, at the higher of which the nucleation can be suppressed completely.展开更多
We have developed efficient numerical algorithms for solving 3D steadystate Poisson-Nernst-Planck(PNP)equations with excess chemical potentials described by the classical density functional theory(cDFT).The coupled PN...We have developed efficient numerical algorithms for solving 3D steadystate Poisson-Nernst-Planck(PNP)equations with excess chemical potentials described by the classical density functional theory(cDFT).The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation.The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation.Then,the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations.A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed,which reduces computational complexity from O(N2)to O(NlogN),where N is the number of grid points.Integrals involving the Dirac delta function are evaluated directly by coordinate transformation,which yields more accurate results compared to applying numerical quadrature to an approximated delta function.Numerical results for ion and electron transport in solid electrolyte for lithiumion(Li-ion)batteries are shown to be in good agreement with the experimental data and the results from previous studies.展开更多
The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigate...The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.展开更多
Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory（CPT）, the first-order shear deformation plate theory（FPT） and the Reddy＇s third-...Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory（CPT）, the first-order shear deformation plate theory（FPT） and the Reddy＇s third-order shear deformation plate theory（RPT）, analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.展开更多
A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)0321...A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.展开更多
文摘It is shown that Mercury's motion of the perihelion around the Sun, which is believed to be explicable quantitatively only by general relativity, can be fully understood within the frame of the dynamics of special relativity. It is only necessary to take into consideration the relativistic dependence of the planet's inertial and gravitational masses on its velocity (relative to the Sun) in the conservation equations for energy, and linear and angular momenta in the gravitational field. The physical Problem is reduced to a singular, nonlinear differential equation, which is solved numerically for the planet Mercury. The advance of the perihelion of Mercury is shown to be = 42.087' for a period of 100 years, which is in agreement with the as- tronomical observations and the result (by analytical approximations) of general relativity.
基金financially supported by the Key Technologies R&D Program of China National Offshore Oil Corporation(No.KJGG2021-0504)。
文摘Understanding the thermodynamic behavior of complex fluids in confined environments is critical for various industrial and natural processes including but not limited to polymer flooding enhanced oil recovery(EOR).In this work,we develop Atif-V2.0,an extended classical density functional theory(cDFT)framework that integrates the interfacial statistical associating fluid theory(iSAFT)to model multicomponent associating fluids composed of water-soluble polymers,alkanes,and water.Building on the original theoretical framework of Atif for modeling nanoconfined inhomogeneous fluids,Atif-V2.0 embeds explicit solvent and captures additional physical interactions-hydrogen bonding,which are critical in associating fluid systems.The other key feature of Atif-V2.0 is its ability to account for polymer topology.We demonstrate its capability by predicting the equilibrium structure and thermodynamic behavior of branched hydrolyzed polyacrylamide solutions near hard walls with various branching topologies,which provides a robust theoretical tool for the rational design of EOR polymers.
文摘It is currently believed that light quantum or the quantization of light energy is beyond classical physics, and the picture of wave-particle duality, which was criticized by Einstein but has attracted a number of experimental researches, is necessary for the description of light. It is shown in this paper, however, that the quantization of light energy in vacuum, which is the same as that in quantum electrodynamics, can be derived directly from the classical electromagnetic theory through the consideration of statistics based on classical physics. Therefore, the quantization of energy is an intrinsic property of light as a classical electromagnetic wave and has no need of being related to particles.
基金Project supported by the National Natural Science Foundation of China(52064011,52274331)Science and Technology Planning Project of Guizhou(Qian Ke He Ji Chu ZK[2021]258,Qian Ke He Chengguo[2022]089,Qian Ke He Chengguo[2021]086)。
文摘It is challenging to assess the mechanism responsible for the nucleation of inclusions in metals at high temperatures.The present work therefore systematically investigates the nucleation of cerium oxide inclusions according to classical nucleation theory and a two-step nucleation mechanism.The nucleation rates and nucleation radii of these inclusions are obtained,and the results demonstrate a considerable difference between theoretical and experimental values.On the basis of a two-step nucleation mechanism,(CeO_(2))_(n) and(Ce_(2)O_(3))_(n)(n=1-6)clusters were constructed and the thermodynamic properties of both these clusters and of cerium oxide nanoparticles were analyzed.In addition,the entropies and heat capacity changes of cerium oxides were determined using first principles calculations and are found to be consistent with literature data.The present data indicate that the cerium oxide inclusion nucleation pathway can be summarized as[Ce]+[O]→(CeO_(2))n/(Ce_(2)O_(3))_(n)→(Ce_(2)O_(3))_(n)→(Ce_(2)O_(3))_(2)→core(Ce_(2)O_(3)crystal)-shell((Ce_(2)O_(3))_(2) cluster)nanoparticles→(Ce_(2)O_(3))bulk.
文摘A systematic method is developed to studY the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton＇s second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.
基金financially supported by the National Natural Science Foundation of China(No.21604016)National Undergraduate Innovation Training Program(No.201610657004)
文摘Classic Avrami model and its modifications have found diverse applications in describing the thermal and phase behaviors of inorganic metals and organic polymers. The direct introduction of classic Avrami equation to offer quantitative analyses of crystallization kinetic parameters for enantiomeric poly（lactic acid） （PLA） blends may, however, lead to contradictory conclusions. As revealed by this study, during the characterization of isothermal melt and cold crystallization for stereocomplex PLA containing equal-weight poly（L-lactic acid） and poly（D-lactic acid）, the kinetic parameters yielded by Avrami equation are not in line with the classic crystallization hypotheses or the direct morphological observations. The underlying mechanisms, to some extent, lie in the generation of stereocomplex crystals （SCs） during the cooling/heating which affects the subsequent crystallization dynamics. The huge gap between the melting enthalpies of 100% crystalline SCs （142 J/g） and homo-crystals （HCs, 93 J/g） is most likely responsible for the confusing kinetic parameters acquired from the deduction of Avrami equation, which is based on the integration of enthalpies as a function of crystallization time. This prompts for great care that the classic Avrami equation is not applicable to accurately describe the crystallization kinetics of stereocomplex PLA, given the generation of SCs prior to crystallization and the coexistence of HCs and SCs during crystallization.
基金a periodical achievement of “Research on Sinicization of Marxist Human Rights Theory” as a branch project of “Research on Several Major basic Theories of Human Rights Issues”(project No.:2016MZd009)which is a major project of social science of the country and a major research project for 2016 of the project on Marxism theory research and construction of the CpC Central Committee
文摘The Marxist human rights theory is embodied in several important works by Karl Marx and Friedrich engels. The key point to understand Marxist human rights theory is to read the texts of classic works of Marx. only in this way can we grasp the essence of the theory more clearly and internalize it as genuine belief and emotional identity. This theoretical guide should be implemented in concrete actions through concerns and answers to practical questions, in order to highlight the era value of the classic Marxist human rights theory.
文摘According to the classical mechanics the energy of a celestial body circulating in the solar system is a constant term. This energy is defined by the masses product of the larger and smaller body entering into a mutual attraction as well as the size of the major semiaxis characteristic for the corresponding Kepler orbit. A special situation concerns the planet interaction with the Sun because of a systematic decrease of the Sun mass due to the luminosity effect. The aim of the paper is to point out that even in the case of perfectly constant interacting masses the energy of the moving body should decrease when a quantum treatment of the body motion is considered. The rate of the energy decrease is extremely small, nevertheless it gives a shortening of the distance between the interacting bodies leading to a final effect of a touch of the larger body and a smaller one.
基金Project supported by the National Natural Science Foundation of China(No.12072072)。
文摘This paper investigates the adhesive nanocontact behavior of an elastic halfplane indented by a rigid cylindrical indenter,incorporating the simultaneous effects of surface elasticity,couple stresses,and adhesion.The free surface of the half-plane is modeled by the Steigmann-Ogden surface elasticity theory,while the bulk material behavior is described by the classical couple-stress elasticity theory.The adhesion at the contact interface is characterized by the Maugis-Dugdale(MD)adhesive contact model.Building on the fundamental nonclassical Flamant solution,the governing equations and boundary conditions of the nanocontact problem are reformulated into a system of triple integral equations.These equations are solved numerically by the Gauss-Chebyshev quadratures in combination with an iterative algorithm.The validation against the existing literature confirms the accuracy and robustness of the proposed solution methodology.Comprehensive parametric studies are performed to elucidate the critical roles of surface elasticity and couple stresses in adhesive nanocontact.The numerical results provide insights into the complex interactions among surface,couple-stress,and adhesive effects.Specifically,the interplay between the surface and adhesive effects is predominantly competitive,while the interaction between the couple stresses and adhesion exhibits an intricate nature.The findings highlight the necessity of simultaneously considering surface elasticity,couple stresses,and adhesion in nanoindentation analyses to achieve accurate predictions of material responses.
基金supported by the National Natural Science Foundation of China(10772014)
文摘The separation of variables is employed to solve Hamiltonian dual form of eigenvalue problem for transverse free vibrations of thin plates,and formulation of the natural mode in closed form is performed.The closed-form natural mode satisfies the governing equation of the eigenvalue problem of thin plate exactly and is applicable for any types of boundary conditions.With all combinations of simplysupported(S)and clamped(C)boundary conditions applied to the natural mode,the mode shapes are obtained uniquely and two eigenvalue equations are derived with respect to two spatial coordinates,with the aid of which the normal modes and frequencies are solved exactly.It was believed that the exact eigensolutions for cases SSCC,SCCC and CCCC were unable to be obtained,however,they are successfully found in this paper.Comparisons between the present results and the FEM results validate the present exact solutions,which can thus be taken as the benchmark for verifying different approximate approaches.
基金Project supported by the National Key Research and Development Program of China(Grant No.2023YFF0722900)the Beijing Engineering Research Center of Aerial Intelligent Remote Sensing Equipments Fund(Grant No.AIRSE20233)the National Natural Science Foundation of China(Grant No.62175144)。
文摘To solve the problems with the existing methods for detecting hollowing defects,such as inconvenient operation,low efficiency and intense subjectivity,and to improve the efficiency of the acoustic-optic fusion method for detecting hollowing defects,in this paper the vibration characteristics of hollowing defects are measured and analyzed using a laser self-mixing interferometer.The ceramic tile above the hollowing defect is equivalent to a thin circular plate with peripheral fixed support.According to Kirchhoff's classical circular plate theory and the circular plate displacement function based on the improved Fourier series,a theoretical model of a circular plate is established.By solving the characteristic equation,the theoretical modal parameters of hollowing defects are obtained.Subsequently,an experimental system based on a laser self-mixing interferometer is built,and modal experiments are carried out using the hammering method.The experimental modal parameters are obtained with a professional modal analysis software.Through comparative analysis between the theoretical and experimental modal parameters,the error of the natural frequency results is found to be tiny and the mode shapes are consistent.These results provide theoretical guidance for a practical non-destructive acoustic-optic fusion method for detecting hollowing defects.
基金supported by the National Natural Science Foundation of China (Grant No.10674019)
文摘The improvement on the calculation of anti-Stokes energy transfer rate is studied in the present work. The additional proportion coefficient between Stokes and anti-Stokes light intensities of quantum Raman scattering theory as compared with the classical Raman theory is introduced to successfully describe the anti-Stokes energy transfer. The theoretical formula for the improvement on the calculation of anti-Stokes energy transfer rate is derived for the first time in this study. The correctness of introducing coefficient exp{△E/kT} from well-known Raman scatter theory is demonstrated also. Moreover, the experimental lifetime measurement in Er0.01YbxY1-0.01-xVO4 crystal is performed to justify the validity of our important improvement in the original phonon-assisted energy transfer theory for the first time.
文摘There are a large number of theories,models or hypotheses in the history of SLA research.A brief introduction is made in this paper on several typical ones which have a great influence on foreign language teaching and it is hoped to be useful for the study of SLA research and foreign language teaching.
文摘Understanding the behaviours of ice nucleation in non-isothermal conditions is of great importance for the preparation and retention of supercooled water. Here ice nucleation in supercooled water under temperature gradients is analyzed thermodynamically based on classical nucleation theory(CNT). Given that the free energy barrier for nucleation is dependent on temperature, different from a uniform temperature usually used in CNT, an assumption of linear temperature distribution in the ice nucleus was made and taken into consideration in analysis. The critical radius of the ice nucleus for nucleation and the corresponding nucleation model in the presence of a temperature gradient were obtained. It is observed that the critical radius is determined not only by the degree of supercooling, the only dependence in CNT, but also by the temperature gradient and even the Young's contact angle. Effects of temperature gradient on the change in free energy, critical radius,nucleation barrier and nucleation rate with different contact angles and degrees of supercooling are illustrated successively.The results show that a temperature gradient will increase the nucleation barrier and decrease the nucleation rate, particularly in the cases of large contact angle and low degree of supercooling. In addition, there is a critical temperature gradient for a given degree of supercooling and contact angle, at the higher of which the nucleation can be suppressed completely.
基金the Materials Synthesis and Simulation across Scales(MS3)Initiative(Laboratory Directed Research and Development(LDRD)Program)at Pacific Northwest National Laboratory(PNNL).Work by GL was supported by the U.S.Department of Energy(DOE)Office of Science’s Advanced Scientific Computing Research Applied Mathematics program and work by BZ by Early Career Award Initiative(LDRD Program)at PNNL.PNNL is operated by Battelle for the DOE under Contract DE-AC05-76RL01830.
文摘We have developed efficient numerical algorithms for solving 3D steadystate Poisson-Nernst-Planck(PNP)equations with excess chemical potentials described by the classical density functional theory(cDFT).The coupled PNP equations are discretized by a finite difference scheme and solved iteratively using the Gummel method with relaxation.The Nernst-Planck equations are transformed into Laplace equations through the Slotboom transformation.Then,the algebraic multigrid method is applied to efficiently solve the Poisson equation and the transformed Nernst-Planck equations.A novel strategy for calculating excess chemical potentials through fast Fourier transforms is proposed,which reduces computational complexity from O(N2)to O(NlogN),where N is the number of grid points.Integrals involving the Dirac delta function are evaluated directly by coordinate transformation,which yields more accurate results compared to applying numerical quadrature to an approximated delta function.Numerical results for ion and electron transport in solid electrolyte for lithiumion(Li-ion)batteries are shown to be in good agreement with the experimental data and the results from previous studies.
文摘The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.
基金Project supported by the National Natural Science Foundation of China (No. 10125212)
文摘Based on the mathematical similarity of the axisymmetric eigenvalue problems of a circular plate between the classical plate theory（CPT）, the first-order shear deformation plate theory（FPT） and the Reddy＇s third-order shear deformation plate theory（RPT）, analytical relations between the eigenvalues of circular plate based on various plate theories are investigated. In the present paper, the eigenvalue problem is transformed to solve an algebra equation. Analytical relationships that are expressed explicitly between various theories are presented. Therefore, from these relationships one can easily obtain the exact RPT and FPT solutions of critical buckling load and natural frequency for a circular plate with CPT solutions. The relationships are useful for engineering application, and can be used to check the validity, convergence and accuracy of numerical results for the eigenvalue problem of plates.
文摘A classical field theory for a Schrodinger equation with a non-Hermitian Hamiltonian describing a particle with position-dependent mass has been recently advanced by Nobre and Rego-Monteiro(NR)[Phys.Rev.A 88(2013)032105].This field theory is based on a variational principle involving the wavefunction Ψ(x,t) and an auxiliary fieldΦ{x,t).It is here shown that the relation between the dynamics of the auxiliary field Φ(x,t) and that of the original wavefunction Ψ(x,t) is deeper than suggested by the NR approach.Indeed,we formulate a variational principle for the aforementioned Schrodinger equation which is based solely on the wavefunction Ψ(x,t).A continuity equation for an appropriately defined probability density,and the concomitant preservation of the norm,follows from this variational principle via Noether's theorem.Moreover,the norm-conservation law obtained by NR is reinterpreted as tie preservation of the inner product between pairs of solutions of the variable mass Schrodinger equation.
