Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the...Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle＇s motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.展开更多
A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been d...A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.展开更多
The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the in...The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.展开更多
In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.
Molecular structures of fourteen xanthine tautomers were calculated by using the B3LYP/6-311G**method both in the gas and aqueous phases with full geometry optimization.The Onsager solvation model was employed for aqu...Molecular structures of fourteen xanthine tautomers were calculated by using the B3LYP/6-311G**method both in the gas and aqueous phases with full geometry optimization.The Onsager solvation model was employed for aqueous solution calculations.The structures,total energy,standard enthalpy,standard entropy and standard free energy were obtained.The calculations showed that xanthine existing as the diketo form is the predominant isomer in the gas and aqueous phases.The dioxo-N（7）（H）isomer is more stable than the dioxo-N（9）（H）isomer in the gas and aqueous phases.The results are in good agreement with available experimental results.The entropy effect on the Gibbs free energy of xanthine base is very small and there is little significance for the tautomeric equilibria of the base.The enthalpic term is dominant in the determinatio of tautomeric equilibria.The free energy of solvation is well correlated with the dipole moments of xanthine tautomers.Additionally,origins of the solvent effects were examined by analyzing the changes of the dipole moments due to the change of a solvent polarity.展开更多
According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced a...According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.展开更多
The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model ...The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 10575084)
文摘Based on a general model of Brownian motors, the Onsager coefficients and generalized efficiency of a thermal Brownian motor are calculated analytically. It is found that the Onsager reciprocity relation holds and the Onsager coefficients are not affected by the kinetic energy change due to the particle＇s motion. Only when the heat leak in the system is negligible can the determinant of the Onsager matrix vanish. Moreover, the influence of the main parameters characterizing the model on the generalized efficiency of the Brownian motor is discussed in detail. The characteristic curves of the generalized efficiency varying with these parameters are presented, and the maximum generalized efficiency and the corresponding optimum parameters are determined. The results obtained here are of general significance. They are used to analyze the performance characteristics of the Brownian motors operating in the three interesting cases with zero heat leak, zero average drift velocity or a linear response relation, so that some important conclusions in current references are directly included in some limit cases of the present paper.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91630208,91641107,and 11771437)
文摘A new variational method is proposed to investigate the dynamics of the thin film in a coating flow where a liquid is delivered through a fixed slot gap onto a moving substrate. A simplified ODE system has also been derived for the evolution of the thin film whose thickness hf is asymptotically constant behind the coating front. We calculate the phase diagram as well as the film profiles and approximate the film thickness theoretically, and agreement with the well-known scaling law as Ca2/3 is found.
基金supported by National Science Foundation of USA(Grant No.DMS-1907584)supported by the Fundamental Research Funds for the Central Universities(Grant No.JBK 2202045)+1 种基金supported by National Science Foundation of USA(Grant Nos.DMS-1907519 and DMS-2219384)supported by National Natural Science Foundation of China(Grant No.12271122)。
文摘The viscous dissipation limit of weak solutions is considered for the Navier-Stokes equations of compressible isentropic flows confined in a bounded domain.We establish a Kato-type criterion for the validity of the inviscid limit for the weak solutions of the Navier-Stokes equations in a function space with the regularity index close to Onsager’s critical threshold.In particular,we prove that under such a regularity assumption,if the viscous energy dissipation rate vanishes in a boundary layer of thickness in the order of the viscosity,then the weak solutions of the Navier-Stokes equations converge to a weak admissible solution of the Euler equations.Our approach is based on the commutator estimates and a subtle foliation technique near the boundary of the domain.
基金supported by the National Natural Science Foundation of China No.11731014supported by the Foundation of Guangzhou University:2700050357
文摘In this paper, we introduce the progress of the Euler equation and Onsager conjecture. We also introduce the Euler＇s life, the researches about the incompressible Euler equation, and the Onsager conjecture.
文摘Molecular structures of fourteen xanthine tautomers were calculated by using the B3LYP/6-311G**method both in the gas and aqueous phases with full geometry optimization.The Onsager solvation model was employed for aqueous solution calculations.The structures,total energy,standard enthalpy,standard entropy and standard free energy were obtained.The calculations showed that xanthine existing as the diketo form is the predominant isomer in the gas and aqueous phases.The dioxo-N（7）（H）isomer is more stable than the dioxo-N（9）（H）isomer in the gas and aqueous phases.The results are in good agreement with available experimental results.The entropy effect on the Gibbs free energy of xanthine base is very small and there is little significance for the tautomeric equilibria of the base.The enthalpic term is dominant in the determinatio of tautomeric equilibria.The free energy of solvation is well correlated with the dipole moments of xanthine tautomers.Additionally,origins of the solvent effects were examined by analyzing the changes of the dipole moments due to the change of a solvent polarity.
基金Project supported by the National Key Basic Research Special Foundation of China (Grant No 2006CB921300)the National Natural Science Foundation of China (Grant No 10604063)
文摘According to the general principle of non-equilibrium thermodynamics, we propose a set of macroscopic transport equations for the spin transport and the charge transport, In particular, the spin torque is introduced as a generalized ＇current density＇ to describe the phenomena associated with the spin non-conservation in a unified framework. The Einstein relations and the Onsager relations between different transport phenomena are established. Specifically, the spin transport properties of the isotropic non-magnetic and the isotropic magnetic two-dimensional electron gases are fully described by using this theory, in which only the macroscopic-spin-related transport phenomena allowed by the symmetry of the system are taken into account.
基金Project supported by the National Natural Science Foundation of China(Grant No.21822302)the joint NSFC-ISF Research Program,China(Grant No.21961142020)+1 种基金the Fundamental Research Funds for the Central Universities,Chinathe National College Students'Innovative and Entrepreneurial Training Plan Program,China(Grant No.201910006142).
文摘The drying of liquid droplets is a common phenomenon in daily life,and has long attracted special interest in scientific research.We propose a simple model to quantify the shape evolution of drying droplets.The model takes into account the friction constant between the contact line(CL)and the substrate,the capillary forces,and the evaporation rate.Two typical evaporation processes observed in experiments,i.e.,the constant contact radius(CCR)and the constant contact angle(CCA),are demonstrated by the model.Moreover,the simple model shows complicated evaporation dynamics,for example,the CL first spreads and then recedes during evaporation.Analytical models of no evaporation,CCR,and CCA cases are given,respectively.The scaling law of the CL or the contact angle as a function of time obtained by analytical model is consistent with the full numerical model,and they are all subjected to experimental tests.The general model facilitates a quantitative understanding of the physical mechanism underlying the drying of liquid droplets.
